![Process Modeling 11
• Model validation and testing; comparison of the model predictions with
experimental data or comparison of the prediction from high-level
models against detailed models
• Documentation of the modeling assumptions and their justification and
of the derivation of the model equations
This chapter focuses on modeling issues involved in the process design,
analysis, and control of multiphase systems. The next section briefly highlights
the differences in modeling objectives that lead to process simulation and process
optimization problems, before a number of relevant modeling techniques are
reviewed in the context of process imaging and analysis. The final section of this
chapter addresses practical issues in simulation and optimization for process
design, diagnostics, and control on the basis of fluid separation processes.
For details on the model development procedure, the reader is referred to the
textbooks by Rice and Do [1]; Luyben [2]; Biegler, Grossmann, and Westerberg
[3]; Abbott and Basco [4]; and Haykin [5]. When developing a mathematical
model, the engineer should always be aware that all model predictions are wrong
to some extent. The engineer should always ensure that the model accuracy is
sufficient to make the model useful for the given purpose while keeping the model
complexity as low as possible.
2.2 SIMULATION VS. OPTIMIZATION
As mentioned above, process models are developed to support a particular aspect
of process design or operation. Simulation models are developed to enable the
prediction of the behavior of a particular system. Different models are developed
depending upon the level of abstraction that is of interest for a particular system.
For predictions at a molecular level, quantum mechanistic models, molecular
dynamic models, and Monte Carlo models are frequently used. Predictions at the
equipment and process level range from detailed CFD models that can predict
fluid flow behavior for defined equipment geometries, via dynamic lumped
parameter process models for the simulation of process control systems and
process start-up behavior, to modular unit operation models as employed in
commercial steady-state simulators, as well as abstract business models that
enable the simulation of entire product supply chains. Simulation models are
completely specified systems of equations, i.e., the models have no degrees of
freedom. In other words, the modeler has made all design and operational deci-
sions about these systems.
In contrast to the above, it is possible to make use of process models to
automatically and systematically determine optimal choices for design and oper-
ational decisions. Process optimization models generally consist of a number of
equality and inequality constraints (the process models and specifications) that
are functions of continuous and binary variables, and of an objective function
that is to be optimized by exploiting the system’s degrees of freedom. Objective
functions are measures of the process performance of the particular system.
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![12 Process Imaging for Automatic Control
Examples include cost functions, yields, and environmental impact. Conservation
equations are typical examples of equality constraints, whereas product purity or
equipment sizes are typical examples of inequality constraints. There are different
classes of optimization problems (linear programs, nonlinear programs, mixed
integer linear or nonlinear programs) and different methods for their solution,
depending on the mathematical form of the objective function, the equality and
inequality constraints, and the existence of continuous or discrete variables.
Details of optimization techniques can be found in Diwekar [6].
Process optimization offers the advantage of decision support to the design
engineer. With increasing complexity of engineering systems, it is virtually impos-
sible for the designer to explore manually all the promising operational and design
scenarios in a finite time. As a result, good choices can be easily missed, which
often results in low system performance. It is therefore important to provide the
engineer with optimization-based support tools that guide the selection of good
candidates. The differences between simulation and optimization-based
approaches to design decision-making have recently been highlighted by
Rigopoulos and Linke [7], who apply optimization techniques to systematically
explore design and operational candidates for a bioreaction system in waste
water treatment.
Imaging information is generally used in conjunction with simulation efforts,
as, for instance, in fluid flow and mixing simulations validated through process
tomography. However, the application of optimization-based techniques has
yielded powerful tools that speed up and improve the quality of operational and
design decision-making using process models derived from first principles. Its
combination with the process imaging techniques that are discussed in other
chapters of this book could yield a new generation of tools to guide process
design and operations and should be the focus of future research efforts.
2.3 PROCESS MODELS FOR IMAGING
AND ANALYSIS
Whether a model is used for simulation or optimization, it must describe accu-
rately the behavior of the system under investigation. In this section, we review
a number of modeling approaches for process analysis that are regularly employed
in conjunction with process imaging techniques. Process imaging techniques are
frequently used to validate fluid flow and mixing models derived from first
principles. In many cases it is not possible to derive process models from first
principles. For such systems, artificial neural networks (ANNs) are often devel-
oped to model relationships between sets of process data and images.
2.3.1 FLUID FLOW AND MIXING MODELS
Chemical processing equipment design and operation require systematic tools
that enable the visualization of physicochemical phenomena. The most important
incentive to use computational simulation tools in equipment design is economic
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![Process Modeling 13
pressure. Such tools are more and more replacing lengthy scale-up studies and
can be used to analyze and coordinate experimental efforts and support the
determination of design parameters that are difficult to measure in “real life”
systems [8]. CFD and cell models are frequently used to simulate fluid flow and
mixing phenomena in processing equipment. Due to the fundamental difficulties
in accurate modeling of turbulence phenomena in multiphase systems, it is vital
to validate and assess these models by comparing the simulated flow images with
those obtained from real-life experiments [9], e.g., by using tomographic sensors
[8, 10–12].
Due to increased availability of computing power and advances in model
accuracy, CFD models are now routinely employed in single-phase fluid flow
simulations. A number of commercial CFD software packages are available (e.g.,
FLUENT, CFX, FEMLAB). Such packages generate and solve the partial differ-
ential equations given by the space- and time-dependent heat, mass, and momen-
tum balances (Navier–Stokes equations). Although these model equations can
generally predict accurately the behavior of single-phase systems, a number of
problems in the description of multiphase phenomena have been reported [10].
These arise because the fundamentals of phase interactions are not yet properly
understood, and CFD packages impose their own simplifications in the description
of these phenomena. These limitations may lead to significant discrepancies
between the model predictions and observations in real-life phenomena. More-
over, the complexity of the partial differential equations and the fine subdivision
needed to solve them may lead to incomplete numerical convergence, and the
computations are highly demanding. However, extensive research efforts in the
area of computational fluid dynamics have made progress toward overcoming
these problems. The CFD packages allow the inclusion of user-defined subrou-
tines so that additional modeling detail can be added to describe multiphase
phenomena more accurately. An example of such an advance is the development
of a CFD model for two-phase flow in packings and monoliths and its experi-
mental validation using capacitance tomography [11], which is described in
Chapter 4.
Due to the problems associated with CFD models for multiphase systems,
alternative modeling approaches have been developed. One such simplified empir-
ical fluid mechanics modeling technique for the description of mixing phenomena
is based on the “network of zones” concept [13]. In this technique, the equipment
volume is divided into a large number of interacting well-mixed cells (zones).
Each cell is described by a simple first-order ordinary differential equation.
Network-of-zones models are therefore smaller and simpler to solve than CFD
models, but even so, good accuracy has been observed in the description of mixing
phenomena in single as well as multiphase (gas–liquid, liquid–solid) systems
measured using electrical resistance tomography [10]. Another approach to mod-
eling multiphase systems has recently been presented by Gupta et al. [14] for the
description of gas and liquid/slurry phase mixing in churn turbulent bubble
columns. Such systems cannot be accurately addressed using CFD models at
present. Gupta et al. [14] decompose the overall simulation problem, i.e., they
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![14 Process Imaging for Automatic Control
estimate the gas and liquid phase recirculation rates in the reactor with a submodel
that uses a two-fluid approach in solving the Navier–Stokes equations that are the
input to the mechanistic reactor model. By effectively decomposing the problem,
they keep the model size at moderate levels.
2.3.2 DATA- AND IMAGE-DRIVEN MODELS
It is often difficult or very time consuming to establish mathematical models
derived from first principles for a number of chemical processing systems. This
is the case where fundamental knowledge is incomplete and cannot fully describe
the system’s behavior or where models become too large to be solved numerically.
Examples include multiphase modeling such as describing relations between heat
transfer and bubble dynamics [15], modeling of bioreaction systems [16], and
the derivation of mathematical models from industrial process data for use in
process control [17]. To derive models for such systems, data-driven modeling
tools such as ANNs are often employed. The advantage of such supervised
learning methods is the possibility of training the models with data sets.
A typical ANN is shown in Figure 2.1 (right side). It consists of a set of
highly interconnected processing units that mimic the function of neurons. Each
“neuron” has a number of inputs and outputs, all of which are weighted by
individual multiplicative factors (as depicted on the left side of the figure). The
individual neurons sum all the products of their inputs and the associated con-
nection weights together with a set of bias values. This sum is then transformed
using a sigmoidal transfer function, and the resulting signal is sent to the outputs.
The biases and the connection weights are adjustable. Neural networks are
trained by adjusting the weights and biases to obtain the desired mapping of
FIGURE 2.1 Artificial neural network model structure (right side). A single neuron is
depicted on the left.
m
imwim,n + Bm
Transfer function
won,1 won,2
i1 i2 i3 i4
wi1,n wi2,n wi3,n wi4,n
o1 o2
o2
o1
i4
i3
i2
i1
Output layer
Hidden layer
Input layer
∑
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![Process Modeling 15
input data (stimuli) to output data (response), using sets of multivariate data of
known system inputs and outputs. The trained ANNs are then used to predict
output data from new input data (i.e., data not included in the training set). Kell
and Sonnleitner [16] describe common pitfalls in applying and training ANNs
and give recommendations for good modeling practice. Recommendations
include ensuring the network is trained with a consistent set of data to guarantee
the applicability of the model and not using the model on data outside the range
of the training data. Extrapolation using ANNs is dangerous, as these models
have not been derived from first principles. This lack of physical insight also
makes these models difficult to interpret. ANNs and other supervised learning
(heuristic) methods are often employed for reconstructing electrical tomography
images, as discussed in Chapter 4. The heuristic models have the advantage that
they can be implemented quickly and can relate measurements directly to the
variables of interest.
Supervised learning models are useful for making process imaging informa-
tion gathered using multidimensional sensors available for decision support in
process operations and control. Apart from model validation using tomographic
sensors for process analysis and design, such multidimensional sensors have been
widely applied in process monitoring through visualization in a variety of systems
including combustion systems [18] and food production [19]. Process images
generally provide a more comprehensive assessment of the current state of the
process than can be gained through measurement of single process variables.
Recent research has focused on the development of strategies for using process
images to estimate the process state variables (see Chapter 6) used in control
systems. The integration of image information into control systems requires
real-time processing of the image information from the sensors for data compres-
sion and pattern recognition. This is a major challenge in view of the amount of
information provided by process imaging applications.
Self-learning methods such as self-organizing maps can be applied to detect
intrinsic features in the images and provide compact representations of the mul-
tidimensional signals that can be integrated into control loops. Such image pro-
cessing is crucial for feedback control applications, to enable the comparison of
the measured signal (image) with the reference (set point) signal. Recently,
Sbarbaro et al. [20] presented two strategies for the implementation of image
processing in feedback process control systems. The first, a classical feedback
control strategy, involves the reduction of the multidimensional information
obtained from the sensors to a one-dimensional signal representing a specific
characteristic of the original signal. Such a strategy involves the application of
signal processing algorithms that can be difficult to apply in real time. The second
strategy does not use signal processing algorithms; it avoids introducing errors
into the interpretation of the multidimensional signals through the application of
pattern recognition techniques. Following this strategy, the control system is
designed using ANNs and finite state machines [21]. Both strategies have been
successfully demonstrated for the control of fluidized bed systems. Additional
control strategies are discussed in Chapter 7.
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![16 Process Imaging for Automatic Control
2.4 PROCESS MODELING FOR DESIGN, CONTROL,
AND DIAGNOSTICS
Process design, automation, and diagnostics are based on quantitative methods
and concepts of process simulation. The simulations employ process models
and the balance equations for mass, components, energy, and momentum. Due
to the model complexities, they are solved iteratively. Numerous types of
models are published in the literature; as mentioned previously, these vary in
their degree of detail or accuracy and in their application. For process design
and optimization, very detailed models are required; these are termed rigorous
models, e.g., equilibrium or nonequilibrium models [22, 23] and CFD models
[24, 25]. In contrast to the rigorous models, so-called short-cut models
(reduced models) are also frequently used; these include linear models, qual-
itative models [26], and trend models [27, 28]. The rigorous models are based
on the balance equations for mass, energy, and momentum. In process mod-
eling, it is always necessary to abstract from the real-world process an ideal-
ized description (in the form of equations, relations, or logic circuits) that is
more amenable to analysis [29]. Hangos and Cameron [30] describe a formal
representation of the assumptions in process modeling. Linninger et al. [31]
and Bogusch [32] describe a modeling tool for efficient model development.
Weiten and Wozny [33] describe an advanced information management system
for knowledge-based documentation. Zerry et al. [34] published a method of
modeling integrated documentation in MathML and automated transfer to
Java-based models.
2.4.1 DEFINING THE MODEL
For the formulation of the balance equations for a chemical engineering or energy
process, additional information on the properties of the deployed fluids is
required. In addition to pure component properties, accurate description of the
mixture properties is of vital importance to the model accuracy. The importance
of the properties data and the calculation of properties are discussed by
Kister [35], Carlson [36], Shacham et al. [37], and Gani et al. [38].
In Figure 2.2 a typical flow sheet of a chemical engineering process is
depicted. The figure displays the various process units, such as compressors,
reactors, and de-misters. The performance of a number of these units depends on
the effectiveness of fluid flow, fluid contacting, and mixing. The effectiveness of
the processes is linked to the internal spatial distributions of fluid inside the
equipment, and it is important to model these accurately. Since the fundamental
knowledge required for the accurate modeling of turbulence phenomena is still
incomplete, the models need to be assessed and validated with experimental
information in the form of process images. Internal spatial distributions are
particularly important in reaction, mixing, heat exchange, and thermal separation
equipment.
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![Process Modeling 19
default values are selected in view of market conditions, previous processes, expe-
rience, and sensitivity analysis. For the above example (Figure 2.3), the following
information needs to be specified:
• Tray number 1, 2, 3, …, j – 1, j, j + 1, …, NST
• Feed tray j
• Feed flow Fj
• Feed temperature, concentration, pressure
• Geometry of the tray, area, weir height, weir length
• Condenser and reboiler area
• Design of condenser and reboiler (e.g., total, falling film, thin film;
cooling water and heating medium conditions)
With this data the mathematical model is developed as shown in Figure 2.4.
For the reboiler and the condenser, the heat transfer equations are integrated
into the process model. For closed-loop dynamic simulation as shown in
Figure 2.5, the control structure (connection of controlled and manipulated vari-
ables) and the controller type have to be predefined. The set points are normally
given as the steady-state design values, and the controller parameters have to be
optimized. In some cases, the sensor dynamics and actor dynamics have to be
considered. Muske and Georgakis [39] describe an optimal measurement system
design procedure for chemical processes.
In the commonly used flow-driven simulation procedure, the direction of the
flow is specified a priori. The more realistic “pressure driven” simulation proce-
dure is more complex, and thus more physical and process data need to be
considered. A detailed description of pressure drops, the valve characteristics,
and the pump diagram have to be introduced in the simulation model. The basic
set of equations required to simulate a column, as shown in Figure 2.3 and
Figure 2.4 for the flow-driven calculation procedure, includes overall material
balances, component material balances, energy balances, summation equations
(mole fractions), phase equilibrium relations, control algorithms, and other func-
tions such as hold-up correlations and pressure drop correlations.
The nonlinear differential-algebraic equation (DAE) system can be solved using
a simultaneous solution procedure. The time dependency can be linearized by Euler
FIGURE 2.5 Layout of a closed-loop process control system (w(t): set point, e(t): set
point error).
Process
− u(t) y(t)
e(t)
w(t)
manipulated
variable
set point
state
variable
PID
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![Process Modeling 21
The equilibrium model in Figure 2.6a uses the relations for vapor–liquid (VL)
and liquid–liquid (LL) equilibrium. The models in Figure 2.6b and Figure 2.6c
take only one or two of the existing three mass (or heat) transfer rates into
consideration. The model shown in Figure 2.6d is the generalized description of
all transfer streams. The degree of accuracy desired for the description of transfer
rates depends on the application and focus of the model. To calculate the mass
transfer, an accurate description of the product of mass transfer coefficient (k)
and mass transfer area (a) is needed. For VL mass transfer, a large number of
correlations to predict this product are available from the literature. For VLL (i.e.,
both liquids exchanging mass with the vapor phase), the transfer coefficients and
the transfer area are generally unknown. Figure 2.7 illustrates the excellent results
that are possible by incorporating greater levels of detail in the model [22].
A more detailed description of the film area is possible using CFD simulation.
CFD models are needed to describe wave films [40]. Figure 2.8 and Figure 2.9
show comparisons of the calculated and measured mass transfer characteristics
in a packed column. These comparisons are encouraging, in a qualitative sense.
However, further model development for better performance would require the
use of process imaging techniques for model validation. For on-line optimization,
process images could also be used to update mass transfer and interfacial area
information used in the process model automatically. More research in this direc-
tion is necessary in the future.
The derived model can also be used for safety column analysis [41]. Can
et al. [42] give the application of the described model equations for safety analysis
FIGURE 2.7 Temperature profile of a packed three-phase distillation column separat-
ing an acetone–toluene–water mixture at finite reflux. (From Repke, J.U., Villain, O.,
and Wozny, G., Computer-Aided Chemical Engineering 14:881–886, 2003. With per-
mission.)
0
0.5
1
1.5
2
2.5
50 55 60 65 70 75 80 85 90 95 100 105
Temperature (°C)
Packed
Height
(m)
Experimental
Equilibrium model
Nonequilibrium model
(vapor)
Nonequilibrium model
(average liquid)
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![26 Process Imaging for Automatic Control
liquid leaves the stage to the stage below (phase II). In phase III, vapor from the
stage below is entering the stage and heating it up until, in phase IV, the mixture’s
bubble pressure (pbub) reaches pset, the set pressure (here 1 bar). In phase V the
stage pressure is higher than the pressure from the stage above, so vapor is leaving
the stage. In phase VI the stage is operating at steady state. In phases I to IV the
first set of equations is active. The switching point is reached when pbub = pset.
Then the phase equilibrium equation is applied. Comparison of the model and
experimental values shows good agreement, as shown in Figure 2.13. Reepmeyer
et al. [43] give details of the study.
The amount of information needed for the development of a dynamic model
and for rigorous simulation of the complete start-up process is tremendous. All
component and kinetic data have to be known, as well as the column, operation,
and control specifications. The computational time required to complete one
simulation run is long. Therefore, it is desirable to find a simple method of
predicting the influence of changes in manipulated or input variables such as
heating duty, reflux ratio, feed compositions, and flow. The impact of the manip-
ulated variable on the start-up time is easier to understand on the basis of a
reduced and simplified model. As an example, a reactive column can be reduced
to a two-stage model consisting of a reboiler and a condenser, as depicted in
Figure 2.15.
The model assumes that the condenser hold-up is negligible, the phases are
in equilibrium, and the reaction takes place only in the liquid phase. From the
component balance for the species XA around the reboiler (the hold-up should
be constant), the following equation results:
(2.1)
where HUB is the reaction volume (hold-up); F, L, and B are the molar flow rates
of feed, reflux, and bottom streams, respectively; YB, XD, and XB are the corre-
sponding vapor and liquid component mole fractions in the bottom and distillate
streams; and rA is the reaction rate. Introducing the phase equilibrium equation
FIGURE 2.14 Different simulation phases of a sample plate during the start-up process.
Pin: pressure at the stage above the feed stage.
T = Tfeed
L L L L L
V V V V
V V
T > Tfeed
L
p = 1 bar
T = 298°K
p = pbub p > pin Steady
state
II III IV V
I VI
Feed
L L L L L
L
HU
dX
dt
F X V Y L X B X r HU
B
A
FA B D B A B
⋅ = ⋅ − ⋅ + ⋅ − ⋅ − ⋅
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![28 Process Imaging for Automatic Control
The variables where interaction during control of the start-up process is
possible are the vapor stream V (influenced using the heating power), the feed
flow rate F, and the reflux stream L. Utilizing this formulated equation for all
components yields a system with four components described by a 4 ×4 matrix
where the eigenvalues of the matrix give an idea of the time constants underlying
this system. The steady-state values are known in advance. Setting the manipulating
variables V and L, to, for example, V = L or L = 0 provides to the start-up strategy
a total reflux condition or total distillate removal, respectively. In Reepmeyer et al.
[43], the ethyl acetate process is analyzed as a reactive distillation using the
reduced model. A comparison of the rigorous and the reduced model is given
in Table 2.1. As can be seen, the time constant is capable of predicting the
effects of variable changes on the start-up time. Here the total reflux strategy
(V = L) shows the largest start-up time and has the highest time constant. The
total distillate removal strategy (L = 0) shows the smallest time constant; there-
fore, it should deliver the fastest start-up time.
The simplifications introduced by the reduced model limit the discussion to
the effect of the manipulated variables (here, heating power in the form of vapor
stream V and the reflux L). Furthermore, due to the linearization (which is valid
around the operating point), complex and highly non-ideal characteristics of the
process are incompletely described. Nevertheless, using the reduced model, the
start-up of a nonreactive [44] and heat-integrated distillation column [45] and of
a reactive distillation column with “simple” reaction can be estimated in terms
of the time constant to represent the trend of the start-up time. For more complex
reactive distillation processes, rigorous dynamic modeling from an initially cold
and empty state is necessary.
2.4.4 CONTROL AND OPTIMIZATION
In process control, linearized Laplace-transformed models are often used. The
advantages and disadvantages of such models are discussed elsewhere [46, 47].
Alici and Edgar [48] extend existing strategies for the solution of the nonlinear
dynamic data reconciliation problem by using the process model as a constraint,
TABLE 2.1
Comparison of Time Constant (Reduced Model)
and Start-Up Time (Detailed Simulation) for the
Ethyl Acetate Process
Strategy Simulation (min) Time Constant (min)
Conventional 175 118.9
Total reflux 225 122.4
Total distillate removal 183 93.2
Time optimal 191 118.1
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![Process Modeling 29
expressed above as the differential-algebraic Equation 2.4. Qualitative models
are also often used in process control. Figure 2.16 shows the fundamental
model behavior to depict the qualitative dynamic performance of a system.
This model class describes the system’s behavior for a certain time constant
or oscillating behavior. Vianna and McGreavy [26] use another solution, using
graph theory.
For optimization, the model equation system given above has to be expanded.
The degrees of freedom will be reduced so that selected design variables such as
unit number, tray number, pressure, and additional variables for operation (e.g.,
controller parameters, control structure) can be optimized. The expanded process
model is described in the following form:
Min J(x,t,y,u,d,p,r,c,ζ)
f(x,t,y,u,d,p,ζ) = 0 equilibrium constraints (mass, equilibrium,
summation, and heat)
g(x,t,y,u,d,p,ζ) ≥ 0 nonequilibrium constraints
h(x,t,y,u,d,p,r,ζ) = 0 controller equations
where x0, y0, u0 are initialization variables, c is the cost parameter, p is the model
parameter, ζ is uncertainties, d is disturbances, u is manipulated variables, r is
controlled variables, and t is time.
Optimization under uncertainty is often necessary for robust process design
and operation. Wendt et al. [49] propose a new approach to solve nonlinear
FIGURE 2.16 Trend models: different models classes to characterize the response of
process variables. (From Vedam, H., and Venkatasubramanian, V.A., Proc. American
Control Conference, Albuquerque, 1997; MC Kindsmüller, L Urbas, Situation Awareness
in der Fahrzeug- und Prozessführung. Bonn: DGLR Bericht; 2002–04, 131–152.)
A H
K
D
C
B
E F G J
I
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![30 Process Imaging for Automatic Control
optimization problems under uncertainty, in which some dependent variables are
to be constrained with a predefined probability. Such problems are called “opti-
mization under chance constraints.” The proposed approach is applied to the
optimization of reactor networks and a methanol–water distillation column.
Wendt et al. [50] describe the application of the column model. A two-pressure
column system modeled by the mass, equilibrium, summation, and heat (MESH)
equations and solved by the algorithm described above is optimized with the
sequential quadratic programming (SQP) method. In the optimization approach,
the entire computation is divided into one layer for optimization and one layer
for simulation. The model equations are integrated in the simulation layer, so that
the state variables and their sensitivities can be calculated for given controls. The
control variables, defined as piecewise constant, are calculated in the optimization
layer by SQP as the decision variables. A reduction in start-up time of up to 80%
was identified using this approach.
The application of the optimization method for a probabilistically constrained
model-predictive controller is described by Li et al. [51]. The optimal design and
control of a high-purity industrial distillation system is described by Ross et al.
[52]. They developed a software implementation for the solution of the mixed
integer dynamic optimization (MIDO) problem and optimized a two-pressure
column system to improve operability and to identify a new process design with
improved economics.
The problem of inconsistent initial values of the dependent variables is
described by Wu and White [53]. Borchardt [54] describes a promising parallel
approach for large-scale real-world dynamic simulation applications, such as
plant-wide dynamic simulation in the chemical process industry. This approach
partitions the system of differential and algebraic model equations into smaller
blocks which can be solved independently. Considerable speed-up factors were
obtained for the dynamic simulation of large-scale distillation plants, covering
systems with up to 60,000 model equations.
Holl and Schuler [55] give an overview of process simulation in industrial
application and operation. The nonlinear DAE-system mentioned in Section 2.4.1
is used for steady-state on-line optimization by Basak et al. [56], for plant-wide
process automation [57], and for operator training systems [58] where the oper-
ators are able to assess the process performance.
REFERENCES
1. RG Rice, DD Do. Applied Mathematics and Modeling for Chemical Engineers.
New York: John Wiley & Sons, 1995.
2. WL Luyben. Process Modeling, Simulation and Control for Chemical Engineers,
2nd ed. New York: McGraw Hill, 1990.
3. LT Biegler, IE Grossmann, AW Westerberg. Systematic Methods of Chemical
Process Design. Upper Saddle River, NJ: Prentice Hall, 1997.
4. MB Abbott, DR Basco. Computational Fluid Dynamics. Singapore: Longman
Scientific & Technical, 1989.
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- 6. Process Imaging for Automatic Control DK3008_half-series-title 4/28/05 10:47 AM Page A
- 7. ELECTRICAL AND COMPUTER ENGINEERING A Series of Reference Books and Textbooks FOUNDING EDITOR Marlin O. Thurston Department of Electrical Engineering The Ohio State University Columbus, Ohio 1. Rational Fault Analysis, edited by Richard Saeks and S. R. Liberty 2. Nonparametric Methods in Communications, edited by P. Papantoni-Kazakos and Dimitri Kazakos 3. Interactive Pattern Recognition, Yi-tzuu Chien 4. Solid-State Electronics, Lawrence E. Murr 5. Electronic, Magnetic, and Thermal Properties of Solid Materials, Klaus Schröder 6. Magnetic-Bubble Memory Technology, Hsu Chang 7. Transformer and Inductor Design Handbook, Colonel Wm. T. McLyman 8. Electromagnetics: Classical and Modern Theory and Applications, Samuel Seely and Alexander D. Poularikas 9. One-Dimensional Digital Signal Processing, Chi-Tsong Chen 10. Interconnected Dynamical Systems, Raymond A. DeCarlo and Richard Saeks 11. Modern Digital Control Systems, Raymond G. Jacquot 12. Hybrid Circuit Design and Manufacture, Roydn D. Jones 13. Magnetic Core Selection for Transformers and Inductors: A User’s Guide to Practice and Specification, Colonel Wm. T. McLyman 14. Static and Rotating Electromagnetic Devices, Richard H. Engelmann 15. Energy-Efficient Electric Motors: Selection and Application, John C. Andreas 16. Electromagnetic Compossibility, Heinz M. Schlicke 17. Electronics: Models, Analysis, and Systems, James G. Gottling 18. Digital Filter Design Handbook, Fred J. Taylor 19. Multivariable Control: An Introduction, P. K. Sinha 20. Flexible Circuits: Design and Applications, Steve Gurley, with contributions by Carl A. Edstrom, Jr., Ray D. Greenway, and William P. Kelly DK3008_half-series-title 4/28/05 10:47 AM Page B
- 8. 21. Circuit Interruption: Theory and Techniques, Thomas E. Browne, Jr. 22. Switch Mode Power Conversion: Basic Theory and Design, K. Kit Sum 23. Pattern Recognition: Applications to Large Data-Set Problems, Sing-Tze Bow 24. Custom-Specific Integrated Circuits: Design and Fabrication, Stanley L. Hurst 25. Digital Circuits: Logic and Design, Ronald C. Emery 26. Large-Scale Control Systems: Theories and Techniques, Magdi S. Mahmoud, Mohamed F. Hassan, and Mohamed G. Darwish 27. Microprocessor Software Project Management, Eli T. Fathi and Cedric V. W. Armstrong (Sponsored by Ontario Centre for Microelectronics) 28. Low Frequency Electromagnetic Design, Michael P. Perry 29. Multidimensional Systems: Techniques and Applications, edited by Spyros G. Tzafestas 30. AC Motors for High-Performance Applications: Analysis and Control, Sakae Yamamura 31. Ceramic Motors for Electronics: Processing, Properties, and Applications, edited by Relva C. Buchanan 32. Microcomputer Bus Structures and Bus Interface Design, Arthur L. Dexter 33. End User’s Guide to Innovative Flexible Circuit Packaging, Jay J. Miniet 34. Reliability Engineering for Electronic Design, Norman B. Fuqua 35. Design Fundamentals for Low-Voltage Distribution and Control, Frank W. Kussy and Jack L. Warren 36. Encapsulation of Electronic Devices and Components, Edward R. Salmon 37. Protective Relaying: Principles and Applications, J. Lewis Blackburn 38. Testing Active and Passive Electronic Components, Richard F. Powell 39. Adaptive Control Systems: Techniques and Applications, V. V. Chalam 40. Computer-Aided Analysis of Power Electronic Systems, Venkatachari Rajagopalan 41. Integrated Circuit Quality and Reliability, Eugene R. Hnatek 42. Systolic Signal Processing Systems, edited by Earl E. Swartzlander, Jr. 43. Adaptive Digital Filters and Signal Analysis, Maurice G. Bellanger 44. Electronic Ceramics: Properties, Configuration, and Applications, edited by Lionel M. Levinson DK3008_half-series-title 4/28/05 10:47 AM Page C
- 9. 45. Computer Systems Engineering Management, Robert S. Alford 46. Systems Modeling and Computer Simulation, edited by Naim A. Kheir 47. Rigid-Flex Printed Wiring Design for Production Readiness, Walter S. Rigling 48. Analog Methods for Computer-Aided Circuit Analysis and Diagnosis, edited by Takao Ozawa 49. Transformer and Inductor Design Handbook: Second Edition, Revised and Expanded, Colonel Wm. T. McLyman 50. Power System Grounding and Transients: An Introduction, A. P. Sakis Meliopoulos 51. Signal Processing Handbook, edited by C. H. Chen 52. Electronic Product Design for Automated Manufacturing, H. Richard Stillwell 53. Dynamic Models and Discrete Event Simulation, William Delaney and Erminia Vaccari 54. FET Technology and Application: An Introduction, Edwin S. Oxner 55. Digital Speech Processing, Synthesis, and Recognition, Sadaoki Furui 56. VLSI RISC Architecture and Organization, Stephen B. Furber 57. Surface Mount and Related Technologies, Gerald Ginsberg 58. Uninterruptible Power Supplies: Power Conditioners for Critical Equipment, David C. Griffith 59. Polyphase Induction Motors: Analysis, Design, and Application, Paul L. Cochran 60. Battery Technology Handbook, edited by H. A. Kiehne 61. Network Modeling, Simulation, and Analysis, edited by Ricardo F. Garzia and Mario R. Garzia 62. Linear Circuits, Systems, and Signal Processing: Advanced Theory and Applications, edited by Nobuo Nagai 63. High-Voltage Engineering: Theory and Practice, edited by M. Khalifa 64. Large-Scale Systems Control and Decision Making, edited by Hiroyuki Tamura and Tsuneo Yoshikawa 65. Industrial Power Distribution and Illuminating Systems, Kao Chen 66. Distributed Computer Control for Industrial Automation, Dobrivoje Popovic and Vijay P. Bhatkar 67. Computer-Aided Analysis of Active Circuits, Adrian Ioinovici 68. Designing with Analog Switches, Steve Moore 69. Contamination Effects on Electronic Products, Carl J. Tautscher 70. Computer-Operated Systems Control, Magdi S. Mahmoud 71. Integrated Microwave Circuits, edited by Yoshihiro Konishi DK3008_half-series-title 4/28/05 10:47 AM Page D
- 10. 72. Ceramic Materials for Electronics: Processing, Properties, and Applications, Second Edition, Revised and Expanded, edited by Relva C. Buchanan 73. Electromagnetic Compatibility: Principles and Applications, David A. Weston 74. Intelligent Robotic Systems, edited by Spyros G. Tzafestas 75. Switching Phenomena in High-Voltage Circuit Breakers, edited by Kunio Nakanishi 76. Advances in Speech Signal Processing, edited by Sadaoki Furui and M. Mohan Sondhi 77. Pattern Recognition and Image Preprocessing, Sing-Tze Bow 78. Energy-Efficient Electric Motors: Selection and Application, Second Edition, John C. Andreas 79. Stochastic Large-Scale Engineering Systems, edited by Spyros G. Tzafestas and Keigo Watanabe 80. Two-Dimensional Digital Filters, Wu-Sheng Lu and Andreas Antoniou 81. Computer-Aided Analysis and Design of Switch-Mode Power Supplies, Yim-Shu Lee 82. Placement and Routing of Electronic Modules, edited by Michael Pecht 83. Applied Control: Current Trends and Modern Methodologies, edited by Spyros G. Tzafestas 84. Algorithms for Computer-Aided Design of Multivariable Control Systems, Stanoje Bingulac and Hugh F. VanLandingham 85. Symmetrical Components for Power Systems Engineering, J. Lewis Blackburn 86. Advanced Digital Signal Processing: Theory and Applications, Glenn Zelniker and Fred J. Taylor 87. Neural Networks and Simulation Methods, Jian-Kang Wu 88. Power Distribution Engineering: Fundamentals and Applications, James J. Burke 89. Modern Digital Control Systems: Second Edition, Raymond G. Jacquot 90. Adaptive IIR Filtering in Signal Processing and Control, Phillip A. Regalia 91. Integrated Circuit Quality and Reliability: Second Edition, Revised and Expanded, Eugene R. Hnatek 92. Handbook of Electric Motors, edited by Richard H. Engelmann and William H. Middendorf 93. Power-Switching Converters, Simon S. Ang 94. Systems Modeling and Computer Simulation: Second Edition, Naim A. Kheir 95. EMI Filter Design, Richard Lee Ozenbaugh 96. Power Hybrid Circuit Design and Manufacture, Haim Taraseiskey DK3008_half-series-title 4/28/05 10:47 AM Page E
- 11. 97. Robust Control System Design: Advanced State Space Techniques, Chia-Chi Tsui 98. Spatial Electric Load Forecasting, H. Lee Willis 99. Permanent Magnet Motor Technology: Design and Applications, Jacek F. Gieras and Mitchell Wing 100. High Voltage Circuit Breakers: Design and Applications, Ruben D. Garzon 101. Integrating Electrical Heating Elements in Appliance Design, Thor Hegbom 102. Magnetic Core Selection for Transformers and Inductors: A User’s Guide to Practice and Specification, Second Edition, Colonel Wm. T. McLyman 103. Statistical Methods in Control and Signal Processing, edited by Tohru Katayama and Sueo Sugimoto 104. Radio Receiver Design, Robert C. Dixon 105. Electrical Contacts: Principles and Applications, edited by Paul G. Slade 106. Handbook of Electrical Engineering Calculations, edited by Arun G. Phadke 107. Reliability Control for Electronic Systems, Donald J. LaCombe 108. Embedded Systems Design with 8051 Microcontrollers: Hardware and Software, Zdravko Karakehayov, Knud Smed Christensen, and Ole Winther 109. Pilot Protective Relaying, edited by Walter A. Elmore 110. High-Voltage Engineering: Theory and Practice, Second Edition, Revised and Expanded, Mazen Abdel-Salam, Hussein Anis, Ahdab El-Morshedy, and Roshdy Radwan 111. EMI Filter Design: Second Edition, Revised and Expanded, Richard Lee Ozenbaugh 112. Electromagnetic Compatibility: Principles and Applications, Second Edition, Revised and Expanded, David Weston 113. Permanent Magnet Motor Technology: Design and Applications, Second Edition, Revised and Expanded, Jacek F. Gieras and Mitchell Wing 114. High Voltage Circuit Breakers: Design and Applications, Second Edition, Revised and Expanded, Ruben D. Garzon 115. High Reliability Magnetic Devices: Design and Fabrication, Colonel Wm. T. McLyman 116. Practical Reliability of Electronic Equipment and Products, Eugene R. Hnatek 117. Electromagnetic Modeling by Finite Element Methods, João Pedro A. Bastos and Nelson Sadowski 118. Battery Technology Handbook, Second Edition, edited by H. A. Kiehne 119. Power Converter Circuits, William Shepherd and Li Zhang DK3008_half-series-title 4/28/05 10:47 AM Page F
- 12. 120. Handbook of Electric Motors: Second Edition, Revised and Expanded, edited by Hamid A. Toliyat and Gerald B. Kliman 121. Transformer and Inductor Design Handbook, Colonel Wm T. McLyman 122. Energy Efficient Electric Motors: Selection and Application, Third Edition, Revised and Expanded, Ali Emadi 123. Power-Switching Converters, Second Edition, Simon Ang and Alejandro Oliva 124. Process Imaging For Automatic Control, edited by David M. Scott and Hugh McCann 125. Handbook of Automotive Power Electronics and Motor Drives, Ali Emadi DK3008_half-series-title 4/28/05 10:47 AM Page G
- 14. Process Imaging for Automatic Control David M. Scott DuPont Company Wilmington, Delaware, U.S.A. Hugh McCann University of Manchester Manchester, UK Boca Raton London New York Singapore A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc. DK3008_half-series-title 4/28/05 10:47 AM Page i
- 15. Published in 2005 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2005 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8247-5920-6 (Hardcover) International Standard Book Number-13: 978-0-8247-5920-9 (Hardcover) Library of Congress Card Number 2004061911 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Process imaging for automatic control / edited by David M. Scott and Hugh McCann. p. cm. Includes bibliographical references and index. ISBN 0-8247-5920-6 (alk. paper) 1. Tomography--Industrial applications. 2. Image processing--Industrial applications. I. McCann, Hugh. II. Scott, David M. III. Title. TA417.25.P7497 2005 670.42'7--dc22 2004061911 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Taylor & Francis Group is the Academic Division of T&F Informa plc. DK3008_Discl.fm Page 1 Wednesday, April 13, 2005 3:16 PM
- 16. Preface Industry has traditionally relied on point sensors such as thermocouples and pressure gauges, allied to relatively superficial process models, to control its operations. However, as manufacturing processes and associated numerical mod- els become increasingly complex, additional types of information are required. For example, typical process measurement needs now include contamination detection, particulate size and shape, concentration and density profile (in pipes and tanks), and thermal profile. In research and development of processes and products, detailed numerical models need to be validated by experimental deter- mination of parameters such as the distributions of different flow phases and chemical concentration. In many cases, imaging systems are the only sensors that can provide the required information. Process imaging is used to visualize events inside industrial processes. These events could be the mixing between two component materials, for example, or the completion of a chemical reaction. The image capture process can be conventional (e.g., directly acquired with a CCD camera), recon- structed (e.g., tomographic imaging), or abstract (sensor data represented as an image). New cameras, versatile tomographic technology, and increasingly powerful computer technology have made it feasible to apply imaging and image processing techniques to a wide range of process measurements. Pro- cess images contain a wealth of information about the structure and state of the process stream. For control applications, data can be extracted from such images and fed back to the process control system to optimize and maintain production. This book, written by a collaboration of international experts in their respec- tive fields, offers a broad perspective on the interdisciplinary topic of process imaging and its use in controlling industrial processes. Its aim is to provide an overview of recent progress in this rapidly developing area. Both academic and industrial points of view are included, and particular emphasis has been placed on the practical applications of this technology. This book will be of interest to process engineers, electrical engineers, and instrumentation developers, as well as plant designers and operators from the chemical, mineral, food, and nuclear industries. The discussion of tomographic technology will also be of particular interest to workers in the clinical sector. We hope that, through reading this book, researchers in both academia and industry with an interest in this area will be encouraged and facilitated to pursue it further. They will be joining a large band of devotees who have already come a long way in this endeavor. By disseminating the state of the art of process DK3008_C000.fm Page v Wednesday, April 27, 2005 10:17 AM
- 17. imaging for automatic control, it is our deepest wish that the process engineering community will find many more useful applications for this exciting new technology. David M. Scott DuPont Central Research & Development Wilmington, Delaware, U.S.A. Hugh McCann University of Manchester Manchester, U.K. DK3008_C000.fm Page vi Wednesday, April 27, 2005 10:17 AM
- 18. Editors David Scott is a physicist at the DuPont Company’s main research facility in Wilmington, Delaware, where he has been developing industrial imaging appli- cations for two decades. He joined DuPont in 1986 after completing his PhD in atomic and molecular physics at the College of William & Mary; he also holds the BA (Earlham College, 1981) and MS (William & Mary, 1984) degrees in physics. He initially worked on nondestructive evaluation of advanced composite materials through radioscopy (real-time x-ray imaging), x-ray computed tomogra- phy, and ultrasonic imaging. He also developed several new optical and ultrasonic sensors for gauging multilayer films and other industrial process applications. He started working on process applications of tomography in the early 1990s and was the sole non-EU participant at the early ECAPT process tomography con- ferences in Europe. He co-chaired the first two worldwide conferences on this topic in San Luis Obispo, California (1995) and Delft (1997). In 1996 Dr. Scott was invited to establish a research group in the area of particle characterization and was appointed its group leader. His primary research interest is on-line characterization of particulate systems, and his research activ- ities have included process tomography and in-line ultrasonic measurement of particle size. He collaborates internationally with several academic groups, and these collaborations have demonstrated the application of tomography in poly- merization reactions and paste extrusion processes. The scope of his group at DuPont has expanded to include interfacial engineering and characterization of nanoparticle systems. Dr. Scott has published over 30 technical papers in peer- reviewed journals, presented keynote and plenary lectures at many international conferences, authored more than 15 company research reports, and edited several journal special issues. He holds several patents. Hugh McCann has been deeply involved in measurement technique develop- ment, with heavy emphasis on multidimensional techniques, throughout a research career spanning more than 25 years. As professor of industrial tomog- raphy at the University of Manchester (formerly UMIST) since 1996, he now leads one of the world’s foremost imaging research groups. He graduated from the University of Glasgow (BSc Physics, 1976, and PhD 1980) and was awarded the university’s Michael Faraday Medal in 1976. For ten years, he worked in high energy particle physics at Glasgow, Manchester, CERN (Geneva) and DESY (Hamburg), to test and establish the so-called Standard Model of physics. During this time, he developed techniques to image particle interactions, based on bubble chambers and drift chambers. The JADE collaboration in which he worked at DESY was awarded a special prize of the European Physical Society in 1995 for DK3008_C000.fm Page vii Wednesday, April 27, 2005 10:17 AM
- 19. discovery of the gluon in the early 1980s, and elucidation of its properties. In 1986, Dr. McCann embarked on ten years of research and development at the Royal Dutch/Shell group’s Thornton Research Centre, and was the founding group leader of Shell’s specialist engine measurements group. His research on in-situ engine measurement technology was recognized by the SAE Arch T. Colwell Merit Award in 1996. At the University of Manchester, Dr. McCann has extended industrial tomog- raphy into the domain of specific chemical contrast, incorporating infrared absorp- tion, and optical fluorescence. He has explored microwave tomography and has investigated electrical impedance tomography for medical applications. His current research is dominated by IR chemical species tomography and brain function imaging by electrical impedance tomography, and he collaborates intensively with a wide range of scientists and engineers in both academia and industry. Dr. McCann teaches undergraduate and postgraduate classes in measurement theory and instrumentation electronics. He was head of the department of elec- trical engineering and electronics (1999–2002), and chairman of U.K. professors and heads of electrical engineering (2003–2005). He has published more than 80 papers in peer-reviewed journals and many conference papers. DK3008_C000.fm Page viii Wednesday, April 27, 2005 10:17 AM
- 20. Contributors James A. Coveney G.K. Williams Research Centre for Extractive Metallurgy Department of Chemical and Biomolecular Engineering The University of Melbourne Melbourne, Australia Stephen Duncan Department of Engineering Science University of Oxford Oxford, U.K. Tomasz Dyakowski School of Chemical Engineering and Analytical Science University of Manchester Manchester, U.K. Neil B. Gray G.K. Williams Research Centre for Extractive Metallurgy Department of Chemical and Biomolecular Engineering The University of Melbourne Melbourne, Australia Brian S. Hoyle School of Electronic and Electrical Engineering University of Leeds Leeds, U.K. Artur J. Jaworski School of Mechanical, Aerospace, and Civil Engineering University of Manchester Oxford Road Manchester, U.K. Jari P. Kaipio Department of Applied Physics University of Kuopio Kuopio, Finland Antonis Kokossis Centre for Process and Information Systems Engineering University of Surrey Guildford, Surrey, U.K. Andrew K. Kyllo G.K. Williams Research Centre for Extractive Metallurgy Department of Chemical and Biomolecular Engineering The University of Melbourne Melbourne, Australia Patrick Linke Centre for Process and Information Systems Engineering University of Surrey Guildford, Surrey, U.K. Matti Malinen Department of Applied Physics University of Kuopio Kuopio, Finland DK3008_C000.fm Page ix Wednesday, April 27, 2005 10:17 AM
- 21. Hugh McCann Department of Electrical Engineering and Electronics University of Manchester Manchester, U.K. Jens-Uwe Repke Institute of Process Dynamics and Operation Technical University Berlin Berlin, Germany Anna R. Ruuskanen Department of Applied Physics University of Kuopio Kuopio, Finland David M. Scott Central Research and Development DuPont Company Experimental Station Wilmington, Delaware, U.S.A. Aku Seppänen Department of Applied Physics University of Kuopio Kuopio, Finland Volker Sick Department of Mechanical Engineering University of Michigan–Ann Arbor Ann Arbor, Michigan, U.S.A. Erkki Somersalo Institute of Mathematics Helsinki University of Technology Helsinki, Finland Satoshi Someya National Institute of Advanced Industrial Science and Technology (AIST) Tsukuba, Ibaraki, Japan Masahiro Takei Department of Mechanical Engineering Nihon University Tokyo, Japan Arto Voutilainen Department of Applied Physics University of Kuopio Kuopio, Finland Richard A. Williams Institute of Particle Science & Engineering School of Process, Environmental and Materials Engineering University of Leeds Leeds, West Yorkshire, U.K. Günter Wozny Institute of Process Dynamics and Operation Technical University Berlin Berlin, Germany Dongming Zhao Electrical and Computer Engineering University of Michigan–Dearborn Dearborn, Michigan, U.S.A. DK3008_C000.fm Page x Wednesday, April 27, 2005 10:17 AM
- 22. Contents Chapter 1 The Challenge .......................................................................................................1 David M. Scott and Hugh McCann Chapter 2 Process Modeling..................................................................................................9 Patrick Linke, Antonis Kokossis, Jens-Uwe Repke, and Günter Wozny Chapter 3 Direct Imaging Technology ................................................................................35 Satoshi Someya and Masahiro Takei Chapter 4 Process Tomography ...........................................................................................85 Brian S. Hoyle, Hugh McCann, and David M. Scott Chapter 5 Image Processing and Feature Extraction ........................................................127 Dongming Zhao Chapter 6 State Estimation ................................................................................................207 Jari P. Kaipio, Stephen Duncan, Aku Seppänen, Erkki Somersalo, and Arto Voutilainen Chapter 7 Control Systems................................................................................................237 Stephen Duncan, Jari P. Kaipio, Anna R. Ruuskanen, Matti Malinen, and Aku Seppänen Chapter 8 Imaging Diagnostics for Combustion Control .................................................263 Volker Sick and Hugh McCann DK3008_C000.fm Page xi Wednesday, April 27, 2005 10:17 AM
- 23. Chapter 9 Multiphase Flow Measurements.......................................................................299 Tomasz Dyakowski and Artur J. Jaworski Chapter 10 Applications in the Chemical Process Industry ...............................................333 David M. Scott Chapter 11 Mineral and Material Processing......................................................................359 Richard A. Williams Chapter 12 Applications in the Metals Production Industry ..............................................401 James A. Coveney, Neil B. Gray, and Andrew K. Kyllo Index .................................................................................................................435 DK3008_C000.fm Page xii Wednesday, April 27, 2005 10:17 AM
- 24. 1 1 The Challenge David M. Scott and Hugh McCann CONTENTS 1.1 Motivation....................................................................................................1 1.2 Road Map ....................................................................................................3 1.3 Vista.............................................................................................................8 1.1 MOTIVATION The technology behind manufacturing and energy extraction processes is one of the principal keys to the prosperity of humankind. This technology provides an enormous range of products and facilities to enable us to live in a manner that could not have been imagined only a century ago. Besides the indisputable benefits that many of us enjoy, many challenges arise as well. Some are inherently political, such as the fair distribution of the benefits that accrue, and access to fossil fuel sources in countries that are themselves less able than others to enjoy the benefits. Others are fundamentally technological in nature, such as improving the efficiency of usage of fossil fuels, reducing the environmental impact of processes, improving the economic performance of manufacturing operations, and developing new processes that enable the manufacture of new products. This book is devoted to the technological challenges and to one aspect in particular. Despite the sophistication of modern process technology, there are still huge benefits to be realized in many processes by more fully exploiting their funda- mental physics and chemistry. The key to this puzzle is the underlying techno- logical challenge addressed in this book: how can we combine the ability to “see inside” industrial processes with models of the fundamental phenomena, in order to improve process control? Industrial processes tend to be highly complex and capital-intensive opera- tions.A generic industrial process is depicted in Figure 1.1. The feedstock material, whose composition, mass flow rate, and phase distribution often vary with time, is introduced to the core process (e.g., a catalytic reactor or a flotation tank). The chemistry or physics driving the core process will generally depend upon the conditions in the process vessel. Therefore, quantities such as the distribution and flow of various phases, temperature, mixing conditions, and even the condition of the vessel itself all affect the outcome of the process. At the completion of the core process, the product must be separated from the waste stream. Clearly, the DK3008_C001.fm Page 1 Tuesday, April 12, 2005 11:32 AM
- 25. 2 Process Imaging for Automatic Control separation step is affected by the composition and other characteristics of the material. The product stream must generally be assessed for quality control, and even the waste stream must often be controlled so that allowable (legally enforced) emissions levels are not exceeded. Measurement and control technology can simplify the operation of process equipment, improve product quality and asset productivity, and minimize waste by increasing first-pass yield. Thus there are real economic incentives for improv- ing the control of these processes. Traditionally, the feedback used for industrial control systems was based on scalar quantities such as temperature and pressure measured at single points in the process. Due to the increasingly stringent demands on the quality of products produced by increasingly complex systems, scalar sensors can no longer provide all of the necessary information. Two-dimensional and sometimes three- or four-dimensional (including the dimension of time) infor- mation is needed to determine the state of the process. Process imaging technology provides this higher dimensionality. The term process imaging refers to the use of image-based sensors, data processing concepts, and display methods for obtaining information about the internal state of industrial processes. These data are used for research and devel- opment of new processes and products, process monitoring, and process control. The process generally includes equipment such as pipes, chemical reactors, or robotic systems, but it could also be a procedure, such as management of inven- tory. In any case, process imaging extracts information about the process based on spatio-temporal patterns in planar or volume images. These images can be obtained directly (as with a camera) or indirectly (via tomographic reconstruction from a data set of lower dimensionality). FIGURE 1.1 Generic industrial process. Product Stream Waste Stream Feedstock Stream(s) Separation Phase distribution Mass flow rate Composition Phase distribution flow Reactant mixing Composition (x, t) Temperature (x, t) Vessel condition Particulate content Composition —Organic —Inorganic —Biological agents Phase distribution Flow regime Humidity Composition Quality Composition Properties Core Process DK3008_C001.fm Page 2 Tuesday, April 12, 2005 11:32 AM
- 26. The Challenge 3 Process imaging can be implemented by a wide variety of techniques. For this reason, the field is inherently interdisciplinary and draws from the contribu- tions of process engineers (such as chemical engineers, mechanical engineers, and metallurgists), electronic engineers, physicists, mathematicians, chemists, computer programmers, and many others. The field has grown tremendously over the past decade due to the development of high-performance imaging systems and advances in computational power. The technologies involved include: • Video camera systems • Fiber optics • Computers • Display systems • Optical systems • Lasers • Electronics • Instrumentation development • Image intensification • Tomography • Inverse problem mathematics • Image analysis After the desired information is extracted from the images, it is used to estimate the state of the process as part of an overall control scheme. This area has also witnessed very significant recent advances. There are several considerations in determining how the measured data should be best processed. These include the quality of data, information required con- cerning the process, what the information is to be used for, and the time that can be tolerated to process the data. A more simplistic processing option that mini- mizes on-line computation time is often chosen to satisfy these requirements. A single-number output rather than a fully reconstructed image may be sufficient in many cases to provide the required information regarding the process. Such output is easier to feed into a control loop and reduces ambiguity for operator interpretation. In other cases a more detailed image of the system is required, or a complex model may be used to relate the state of the process to the image or to the measurements that underlie the image in the case of tomographic systems. 1.2 ROAD MAP The first half of this book introduces the concepts and tools used to control industrial processes through process imaging, and the second half presents several applications of the technology in various industries. The intention of this “road map” section is to help the reader choose an optimal route through the book by presenting the theme of each chapter and its relation to the others. However, we believe that ultimately the content of each chapter will be of interest to a wide variety of scientists and engineers. DK3008_C001.fm Page 3 Tuesday, April 12, 2005 11:32 AM
- 27. 4 Process Imaging for Automatic Control A complete control application can be described by the five steps shown in Figure 1.2. The actual implementation may not be as linear as suggested by the figure, but conceptually the output from each step does tend to flow into the successive step. The ultimate goal of process imaging is improved control or operation of industrial processes.A starting point for this effort is the development of a suitable model for the process under consideration, including a description of the process, the control issues involved, and the data to be provided by the system. The model identifies the process variables and the expected outputs. Process models can be implemented in various ways, e.g., using computational fluid dynamics (CFD), neural networks, or wavelets. Chapter 2 provides an overview of process modeling techniques used to address these issues; although the emphasis is on the chemical engineering industry, the principles are widely applicable. As an example, CFD and other techniques are used to simulate fluid flow and mixing in process equipment, to help predict the impact of changes in flow rate. Due to the difficulty of correctly simulating turbulence in a multiphase system, such models must be validated with empirical data. Once validated, they provide insight into the loca- tion and type of measurements that will provide feedback about the current state of the industrial process. In practice, the model must evolve concurrently with the acquisition of empirical data, and the interpretation of the data depends to some extent on the process model. A wide variety of technologies are used to obtain images of industrial processes. They can be classified as either direct or indirect (reconstructed) imaging. Direct imaging (such as an in-process video camera) refers to the recording of visual scenes (which may be invisible to the human eye, such as infrared or x-ray imaging). FIGURE 1.2 Steps involved in process imaging for a control application. Process Control Process Modeling Direct Imaging Indirect Imaging Image Processing Feature Extraction State Estimation DK3008_C001.fm Page 4 Tuesday, April 12, 2005 11:32 AM
- 28. The Challenge 5 Traditionally, this type of image was recorded directly on photographic film (some- times with an intensifier screen). Modern applications use electronic sensors that have largely supplanted the use of film. Relevant issues involve the selection of the appropriate light source (lasers or white light sources) and sensor (CCD, intensified CCD, thermal sensor, etc.). Chapter 3 describes these aspects together with optical components such as lenses and laser scanning systems. Innovative examples of direct imaging include particle imaging velocimetry (PIV), measurement of pres- sure across a surface by observing color change of pressure-sensitive paint, mea- surement of pH and temperature profiles by fluorescence imaging, and micro-scale imaging of shear stress in fluids. The other broad class of imaging technology is indirect imaging, in which cross-sectional two- or three-dimensional images are calculated through tomo- graphic methods: measurements are made around the boundary of the measure- ment subject, and these data are inverted by a mathematical algorithm. Tomog- raphy itself has become familiar through various applications in the field of diagnostic medical imaging, which use x-ray CT or MRI “scanners.” Chapter 4 introduces process tomography, which has been successfully applied to a large number of industrial processes. These techniques provide unique information about the internal state of the industrial process, extending even to the imaging of one chemical species as it mixes with several others, even when they are all in the same thermodynamic phase. Many physical sensing mechanisms may be used to obtain information about the internal details of the process necessary for reconstructing a cross-sectional image. Each modality, or sensing mechanism, has its own set of strengths or weaknesses in relation to a given application. The most prominent modalities include measurement of electrical properties (by measuring capacitance, imped- ance, or just resistance), x-ray or gamma-ray absorption, positron emission, and optical emission or absorption. The actual reconstruction of the image can be quite difficult due to the ill-posed nature of the inverse problem. Nevertheless, a variety of reconstruction approaches have been devised, including back-projection, trans- form methods, iterative methods, model-based reconstruction, and heuristic approaches (which include neural networks). Until recently, the technical complexity of process tomography has prevented most industrial users from exploring potential applications of this technology. Several companies now sell commercial turnkey process tomography systems. The increased availability of such devices at affordable prices is expected to increase the number of industrial applications and thus to augment the impressive efforts of companies that have been in the vanguard of this development. Regardless of the source, once a digital image has been obtained, the relevant information must be extracted. It is generally necessary to perform some postpro- cessing on the digital images (e.g., to enhance the contrast or flatten the background intensity levels) in order to maximize the amount of information that can be extracted. Chapter 5 describes a set of image processing (as opposed to process imaging) tools commonly used to enhance digital images. The primary tasks involved in digital image processing include image enhancement (or restoration) DK3008_C001.fm Page 5 Tuesday, April 12, 2005 11:32 AM
- 29. 6 Process Imaging for Automatic Control and feature extraction. These operations are performed on digital images, which are essentially two- or three-dimensional arrays of numbers stored in computer memory. Image enhancement includes gray level transformations, histogram equal- ization, spatial filtering, and image enhancement by frequency-domain filtering. Image restoration is accomplished by filtering fluctuations (i.e., noise) from images, based on an understanding of the applicable noise model. Typical approaches use mean filters, adaptive filters, or frequency-domain filtering. Feature extraction is based on segmentation and feature representation con- cepts. Segmentation refers to the operation of splitting an image into a set of regions of interest, where each region contains a particular feature of interest. Segmentation methods include edge detection, exclusion of pixels whose gray levels do not meet a predefined threshold value, and morphological methods. Feature representation (such as Freeman chain codes or descriptions in terms of moments) is used to describe the principal features that have been extracted from the image. Morphological operations such as dilation, erosion, opening, and closing are also used to identify the salient features in an image. These methods are used to produce a well-defined set of data from which the process state may be estimated. Control systems are based on state-space representations of the systems that are to be controlled. The controlled variables are functions of the state variables; in several cases the controlled variables are identical to some of the state variables. Extracted features of the process images are used to estimate the state variables for the process under consideration. Chapter 6 reviews the most important state esti- mation methods used to optimize processes. In most cases the state variables refer to continuous time processes while the measurements occur only at certain time instants. The state-space representation of a dynamical system can be approximated by a discrete-time continuous state-space model, and the time evolution of the state can be represented as a first-order difference system. The most commonly used method for state estimation is the Kalman filter, which yields a recursive and computationally effective solution. However, other approaches such as fixed-lag and fixed-interval smoothers can in some cases give estimates that are superior to Kalman filtering or other real-time estimates. In a typical process, the state is inherently of infinite dimension and thus cannot be estimated with any computational methods. Chapter 6 discusses the example of imaging Navier–Stokes flow with electrical impedance tomography. The state is described as a stochastic partial differential equation with partially unknown boundary values. Spatial discretization methods are used to approximate this model as a finite-dimensional first-order Markov system, and numerical results are shown. Process control systems use the estimated state variables to determine the corrective action necessary to keep a process operating within defined specifi- cations. In control applications, process imaging technology is unique in that it provides detailed information about distributed systems, where physical prop- erties vary spatially as well as temporally. Chapter 7 considers several system models (mass transport, convection systems, convection-diffusion equations) DK3008_C001.fm Page 6 Tuesday, April 12, 2005 11:32 AM
- 30. The Challenge 7 from a control viewpoint. Typical control strategies are discussed, including linear quadratic regulation, model predictive control (MPC), effects of input and output constraints, and nonlinear systems. The conversion of the partial differential equation models into state-space form generally entails an approximation to create a finite-dimensional state-space model. Control performance criteria (i.e., how “control” of a process profile is defined) are based on the concepts of controllability and observability. These two factors directly impact the number and locations of actuators and sensors needed for a particular application. Implementation issues such as limitations of actuators and speed of response are also considered in Chapter 7. To begin the consideration of actual applications of process imaging, Chapter 8 discusses its use in the development and control of combustion systems, with a strong emphasis on internal combustion engines. There are very large economic and ecological benefits to be derived from improved control of combustion processes, and pressures both from the market and from environmental legis- lation have resulted in large efforts in academia and industry alike to exploit image-based process measurements. Crucial features of combustion include fuel preparation, combustion, and pollutant formation. Active imaging techniques are used to look at fuel sprays (optical imaging based on Mie scattering), the hydro- carbon content of vapors (direct and indirect imaging based on fluorescence, absorption, and Raman spectroscopy), and the flame front itself (photographic and tomographic techniques). Flow fields are studied using PIV, in which the motion of tracer particles is tracked with a high-speed camera in order to deter- mine the velocity field. Dopant techniques (using fluorescent tracers) are often used to study fuel/air mixtures. Postcombustion imaging, based on detection of hydroxyl radicals or tracer material, provides information about the removal of waste gases, their subsequent treatment, and their eventual release into the envi- ronment. For incineration or power generation operations, the ability to image plumes of exhaust gases is critical for a scientific assessment of the impact on the surrounding community. Transient three-dimensional multiphase flows are characteristic of many industrial processes. The experimental observation and measurement of such flows are extremely difficult, and over the past decade many tomographic methods have been developed into reliable tools for investigating these complex phenom- ena. Chapter 9 describes how information about flow behavior can be extracted from tomographic images, to provide valuable insight into the internal structure of flow instabilities such as plugs and slugs. The solids mass flow rate in freight pipeline systems (hydraulic or conveying systems) can also be measured. Chapter 10 examines real-world applications of process imaging technology in the chemical process industry. A wide variety of process measurement needs have been met through either direct or indirect imaging, and this chapter includes several examples of process control schemes that rely on the technology described in this book. Additional uses include research and development of new products or manufacturing processes and process monitoring to improve fundamental understanding of the process itself. The cited examples include contamination DK3008_C001.fm Page 7 Tuesday, April 12, 2005 11:32 AM
- 31. 8 Process Imaging for Automatic Control detection and measurement of particulate size and shape, mixture uniformity, amount of fluidization, process efficiency, and various factors related to product quality. Chapter 11 highlights the imaging methods that have been developed for industrial application in the mineral and materials processing industries. These industries deal with particulate suspensions of solids, gases, and liquids in liquids or gases or in the form of complex multiphase mixtures. Examples include measuring multiphase flow rate and auditing the operation of hydrocyclones used in mineral separation. Tomographic measurements also pertain to the design and monitoring of de-oiling cyclones and particle separation in flotation cells and columns. The metals production industry presents a significant challenge to process control due to the severe operating conditions found in metallurgical furnaces and molten material handling processes, which include refining and casting of the final product. In many of these operations, the sensing technology will be subjected to particularly harsh environments involving high temperatures and aggressive materials. Sensing systems must be designed to withstand such chal- lenging environments. Chapter 12 introduces applications of process imaging technology to the metals production industry. The suitability of techniques for these applications and the impact of their use are discussed, with regard to the measurement technique as well as the manner in which the measured data are processed to provide information regarding the state of the process. This state estimation, as noted above, is a prerequisite for process control. Applications of process imaging to the metals production industry include sensors for detection of entrained slag in steel, thermal imaging for monitoring flow profiles of molten materials, and hearth monitoring in blast furnaces to monitor refractory wear. 1.3 VISTA Process imaging is already in use in a number of industries, as described in detail in this volume. The wealth of demonstrated applications of process imaging attests to the versatility of the technology and to the impact that it has already had, particularly on process and product development. The availability of commercial systems that implement the concepts described in this book will surely soon result in additional applications and extensions to other industries. Does this book describe the pinnacle of achievement of the marriage of process engineering with imaging and control technology? Or does it establish a “base camp” from which new groups of travelers can embark on the road to establishing new and more profound applications of imaging technology and control in the process industries? Or, to return to the key question posed at the beginning: can we indeed further exploit our capability to model fundamental physical and chemical phenomena and to “see inside” industrial processes, in order to control them better and achieve much more desirable outcomes? We are sure that after reading the remainder of this book, you will agree with us that the potential is huge. DK3008_C001.fm Page 8 Tuesday, April 12, 2005 11:32 AM
- 32. 9 2 Process Modeling Patrick Linke, Antonis Kokossis, Jens-Uwe Repke, and Günter Wozny CONTENTS 2.1 Introduction..................................................................................................9 2.2 Simulation vs. Optimization......................................................................11 2.3 Process Models for Imaging and Analysis ...............................................12 2.3.1 Fluid Flow and Mixing Models ....................................................12 2.3.2 Data- and Image-Driven Models...................................................14 2.4 Process Modeling for Design, Control, and Diagnostics .........................16 2.4.1 Defining the Model .......................................................................16 2.4.2 Detailed Models.............................................................................20 2.4.3 Start-Up and Shut-Down...............................................................22 2.4.4 Control and Optimization..............................................................28 References ...........................................................................................................30 2.1 INTRODUCTION Process models are used extensively in the design and analysis of chemical processes and process equipment. Such models are either sets of differential or algebraic equations that theoretically describe the features of a process system of interest to the designer, or heuristic or self-learning models that have been developed from process data. Process models enable the prediction of the system’s performance and thus enhance the understanding of the system while reducing the need for extensive experimental efforts. Models are derived to predict perfor- mance of a chemical process at steady state, dynamic behavior of a process, flow patterns inside process equipment, or even physical properties at a molecular level. The mathematical complexity of a model depends greatly upon its purpose, which determines the level of detail that is required to be captured by the model, the size of the system that is to be modeled, and the length scales to be considered. Process models can be developed with the aim of simulating the performance of a given system or of exploiting degrees of freedom to determine optimal choices for process design and operation. Optimization models offer the advantage that they incorporate decision-making capabilities, whereas simulation models enable the testing of systems for which there are no degrees of freedom, i.e., systems for which all design and operational decisions have been made by the engineer. DK3008_C002.fm Page 9 Tuesday, April 26, 2005 2:11 PM
- 33. 10 Process Imaging for Automatic Control It is important to derive any model such that its complexity is low enough for it to be efficiently solved numerically, but at the same time detailed enough to capture realistically the system’s behavior. With the rapid advances in solution algorithms and computing power, the past two decades have seen significant increases in model sizes and complexities. For instance, three-dimensional com- putational fluid dynamics (CFD) models are now routinely applied for reactor simulations, replacing the two-dimensional reactor models frequently used a decade ago. The mathematical representation of systems from a molecular level through to a process or business level requires modeling across the length scales. Even with advances in computing power, it is a major challenge to solve integrated models that combine models from various levels of abstraction. This is due to the mathematical nature of the models at the individual levels of detail. Higher-level models, such as those used for simulations of entire process flow sheets, are designed as “lumped parameter” models to keep the model complexity at moderate levels. Such models assume properties to be uniform within the physical component modeled and typically consist of a set of algebraic or ordinary differential equations. On the other hand, lower-level models such as CFD models describe systems at smaller length scales. Such models give a detailed account of local effects that are neglected in the higher-level models. Lower-level models typically contain partial differential equations to describe local and dynamic effects. Multilevel modeling, the meaningful integration of models across differ- ent levels of detail, is a major research challenge. Regardless of the level of abstraction and the type of process model to be developed, the modeling process is a systematic, well-documented activity. The derivation of a mathematical model involves the following steps: • Problem definition, including identification of the modeling goals and the relevant chemical, physical and geometric quantities and selection of the dependent and independent variables • Identification of the detail required to describe the phenomena of interest and availability of systems knowledge: definition of required length scale; selection of the problem boundaries; selection of physical property and reaction models; selection of conservation laws for mass, energy, or momentum that need to be considered in the model; degrees of freedom for optimization; possible approximations for problem complexities • Derivation of the model from first principles (conservation laws and prob- lem specifics defined in the previous steps) or by training self-learning models on process data • Identification and checking of consistency of process data sources required for self-learning model development, if derivation of the model from first principles is not feasible (e.g., fundamental knowledge is lacking) • Selection of an appropriate solution strategy to solve the model DK3008_C002.fm Page 10 Tuesday, April 26, 2005 2:11 PM
- 34. Process Modeling 11 • Model validation and testing; comparison of the model predictions with experimental data or comparison of the prediction from high-level models against detailed models • Documentation of the modeling assumptions and their justification and of the derivation of the model equations This chapter focuses on modeling issues involved in the process design, analysis, and control of multiphase systems. The next section briefly highlights the differences in modeling objectives that lead to process simulation and process optimization problems, before a number of relevant modeling techniques are reviewed in the context of process imaging and analysis. The final section of this chapter addresses practical issues in simulation and optimization for process design, diagnostics, and control on the basis of fluid separation processes. For details on the model development procedure, the reader is referred to the textbooks by Rice and Do [1]; Luyben [2]; Biegler, Grossmann, and Westerberg [3]; Abbott and Basco [4]; and Haykin [5]. When developing a mathematical model, the engineer should always be aware that all model predictions are wrong to some extent. The engineer should always ensure that the model accuracy is sufficient to make the model useful for the given purpose while keeping the model complexity as low as possible. 2.2 SIMULATION VS. OPTIMIZATION As mentioned above, process models are developed to support a particular aspect of process design or operation. Simulation models are developed to enable the prediction of the behavior of a particular system. Different models are developed depending upon the level of abstraction that is of interest for a particular system. For predictions at a molecular level, quantum mechanistic models, molecular dynamic models, and Monte Carlo models are frequently used. Predictions at the equipment and process level range from detailed CFD models that can predict fluid flow behavior for defined equipment geometries, via dynamic lumped parameter process models for the simulation of process control systems and process start-up behavior, to modular unit operation models as employed in commercial steady-state simulators, as well as abstract business models that enable the simulation of entire product supply chains. Simulation models are completely specified systems of equations, i.e., the models have no degrees of freedom. In other words, the modeler has made all design and operational deci- sions about these systems. In contrast to the above, it is possible to make use of process models to automatically and systematically determine optimal choices for design and oper- ational decisions. Process optimization models generally consist of a number of equality and inequality constraints (the process models and specifications) that are functions of continuous and binary variables, and of an objective function that is to be optimized by exploiting the system’s degrees of freedom. Objective functions are measures of the process performance of the particular system. DK3008_C002.fm Page 11 Tuesday, April 26, 2005 2:11 PM
- 35. 12 Process Imaging for Automatic Control Examples include cost functions, yields, and environmental impact. Conservation equations are typical examples of equality constraints, whereas product purity or equipment sizes are typical examples of inequality constraints. There are different classes of optimization problems (linear programs, nonlinear programs, mixed integer linear or nonlinear programs) and different methods for their solution, depending on the mathematical form of the objective function, the equality and inequality constraints, and the existence of continuous or discrete variables. Details of optimization techniques can be found in Diwekar [6]. Process optimization offers the advantage of decision support to the design engineer. With increasing complexity of engineering systems, it is virtually impos- sible for the designer to explore manually all the promising operational and design scenarios in a finite time. As a result, good choices can be easily missed, which often results in low system performance. It is therefore important to provide the engineer with optimization-based support tools that guide the selection of good candidates. The differences between simulation and optimization-based approaches to design decision-making have recently been highlighted by Rigopoulos and Linke [7], who apply optimization techniques to systematically explore design and operational candidates for a bioreaction system in waste water treatment. Imaging information is generally used in conjunction with simulation efforts, as, for instance, in fluid flow and mixing simulations validated through process tomography. However, the application of optimization-based techniques has yielded powerful tools that speed up and improve the quality of operational and design decision-making using process models derived from first principles. Its combination with the process imaging techniques that are discussed in other chapters of this book could yield a new generation of tools to guide process design and operations and should be the focus of future research efforts. 2.3 PROCESS MODELS FOR IMAGING AND ANALYSIS Whether a model is used for simulation or optimization, it must describe accu- rately the behavior of the system under investigation. In this section, we review a number of modeling approaches for process analysis that are regularly employed in conjunction with process imaging techniques. Process imaging techniques are frequently used to validate fluid flow and mixing models derived from first principles. In many cases it is not possible to derive process models from first principles. For such systems, artificial neural networks (ANNs) are often devel- oped to model relationships between sets of process data and images. 2.3.1 FLUID FLOW AND MIXING MODELS Chemical processing equipment design and operation require systematic tools that enable the visualization of physicochemical phenomena. The most important incentive to use computational simulation tools in equipment design is economic DK3008_C002.fm Page 12 Tuesday, April 26, 2005 2:11 PM
- 36. Process Modeling 13 pressure. Such tools are more and more replacing lengthy scale-up studies and can be used to analyze and coordinate experimental efforts and support the determination of design parameters that are difficult to measure in “real life” systems [8]. CFD and cell models are frequently used to simulate fluid flow and mixing phenomena in processing equipment. Due to the fundamental difficulties in accurate modeling of turbulence phenomena in multiphase systems, it is vital to validate and assess these models by comparing the simulated flow images with those obtained from real-life experiments [9], e.g., by using tomographic sensors [8, 10–12]. Due to increased availability of computing power and advances in model accuracy, CFD models are now routinely employed in single-phase fluid flow simulations. A number of commercial CFD software packages are available (e.g., FLUENT, CFX, FEMLAB). Such packages generate and solve the partial differ- ential equations given by the space- and time-dependent heat, mass, and momen- tum balances (Navier–Stokes equations). Although these model equations can generally predict accurately the behavior of single-phase systems, a number of problems in the description of multiphase phenomena have been reported [10]. These arise because the fundamentals of phase interactions are not yet properly understood, and CFD packages impose their own simplifications in the description of these phenomena. These limitations may lead to significant discrepancies between the model predictions and observations in real-life phenomena. More- over, the complexity of the partial differential equations and the fine subdivision needed to solve them may lead to incomplete numerical convergence, and the computations are highly demanding. However, extensive research efforts in the area of computational fluid dynamics have made progress toward overcoming these problems. The CFD packages allow the inclusion of user-defined subrou- tines so that additional modeling detail can be added to describe multiphase phenomena more accurately. An example of such an advance is the development of a CFD model for two-phase flow in packings and monoliths and its experi- mental validation using capacitance tomography [11], which is described in Chapter 4. Due to the problems associated with CFD models for multiphase systems, alternative modeling approaches have been developed. One such simplified empir- ical fluid mechanics modeling technique for the description of mixing phenomena is based on the “network of zones” concept [13]. In this technique, the equipment volume is divided into a large number of interacting well-mixed cells (zones). Each cell is described by a simple first-order ordinary differential equation. Network-of-zones models are therefore smaller and simpler to solve than CFD models, but even so, good accuracy has been observed in the description of mixing phenomena in single as well as multiphase (gas–liquid, liquid–solid) systems measured using electrical resistance tomography [10]. Another approach to mod- eling multiphase systems has recently been presented by Gupta et al. [14] for the description of gas and liquid/slurry phase mixing in churn turbulent bubble columns. Such systems cannot be accurately addressed using CFD models at present. Gupta et al. [14] decompose the overall simulation problem, i.e., they DK3008_C002.fm Page 13 Tuesday, April 26, 2005 2:11 PM
- 37. 14 Process Imaging for Automatic Control estimate the gas and liquid phase recirculation rates in the reactor with a submodel that uses a two-fluid approach in solving the Navier–Stokes equations that are the input to the mechanistic reactor model. By effectively decomposing the problem, they keep the model size at moderate levels. 2.3.2 DATA- AND IMAGE-DRIVEN MODELS It is often difficult or very time consuming to establish mathematical models derived from first principles for a number of chemical processing systems. This is the case where fundamental knowledge is incomplete and cannot fully describe the system’s behavior or where models become too large to be solved numerically. Examples include multiphase modeling such as describing relations between heat transfer and bubble dynamics [15], modeling of bioreaction systems [16], and the derivation of mathematical models from industrial process data for use in process control [17]. To derive models for such systems, data-driven modeling tools such as ANNs are often employed. The advantage of such supervised learning methods is the possibility of training the models with data sets. A typical ANN is shown in Figure 2.1 (right side). It consists of a set of highly interconnected processing units that mimic the function of neurons. Each “neuron” has a number of inputs and outputs, all of which are weighted by individual multiplicative factors (as depicted on the left side of the figure). The individual neurons sum all the products of their inputs and the associated con- nection weights together with a set of bias values. This sum is then transformed using a sigmoidal transfer function, and the resulting signal is sent to the outputs. The biases and the connection weights are adjustable. Neural networks are trained by adjusting the weights and biases to obtain the desired mapping of FIGURE 2.1 Artificial neural network model structure (right side). A single neuron is depicted on the left. m imwim,n + Bm Transfer function won,1 won,2 i1 i2 i3 i4 wi1,n wi2,n wi3,n wi4,n o1 o2 o2 o1 i4 i3 i2 i1 Output layer Hidden layer Input layer ∑ DK3008_C002.fm Page 14 Tuesday, April 26, 2005 2:11 PM
- 38. Process Modeling 15 input data (stimuli) to output data (response), using sets of multivariate data of known system inputs and outputs. The trained ANNs are then used to predict output data from new input data (i.e., data not included in the training set). Kell and Sonnleitner [16] describe common pitfalls in applying and training ANNs and give recommendations for good modeling practice. Recommendations include ensuring the network is trained with a consistent set of data to guarantee the applicability of the model and not using the model on data outside the range of the training data. Extrapolation using ANNs is dangerous, as these models have not been derived from first principles. This lack of physical insight also makes these models difficult to interpret. ANNs and other supervised learning (heuristic) methods are often employed for reconstructing electrical tomography images, as discussed in Chapter 4. The heuristic models have the advantage that they can be implemented quickly and can relate measurements directly to the variables of interest. Supervised learning models are useful for making process imaging informa- tion gathered using multidimensional sensors available for decision support in process operations and control. Apart from model validation using tomographic sensors for process analysis and design, such multidimensional sensors have been widely applied in process monitoring through visualization in a variety of systems including combustion systems [18] and food production [19]. Process images generally provide a more comprehensive assessment of the current state of the process than can be gained through measurement of single process variables. Recent research has focused on the development of strategies for using process images to estimate the process state variables (see Chapter 6) used in control systems. The integration of image information into control systems requires real-time processing of the image information from the sensors for data compres- sion and pattern recognition. This is a major challenge in view of the amount of information provided by process imaging applications. Self-learning methods such as self-organizing maps can be applied to detect intrinsic features in the images and provide compact representations of the mul- tidimensional signals that can be integrated into control loops. Such image pro- cessing is crucial for feedback control applications, to enable the comparison of the measured signal (image) with the reference (set point) signal. Recently, Sbarbaro et al. [20] presented two strategies for the implementation of image processing in feedback process control systems. The first, a classical feedback control strategy, involves the reduction of the multidimensional information obtained from the sensors to a one-dimensional signal representing a specific characteristic of the original signal. Such a strategy involves the application of signal processing algorithms that can be difficult to apply in real time. The second strategy does not use signal processing algorithms; it avoids introducing errors into the interpretation of the multidimensional signals through the application of pattern recognition techniques. Following this strategy, the control system is designed using ANNs and finite state machines [21]. Both strategies have been successfully demonstrated for the control of fluidized bed systems. Additional control strategies are discussed in Chapter 7. DK3008_C002.fm Page 15 Tuesday, April 26, 2005 2:11 PM
- 39. 16 Process Imaging for Automatic Control 2.4 PROCESS MODELING FOR DESIGN, CONTROL, AND DIAGNOSTICS Process design, automation, and diagnostics are based on quantitative methods and concepts of process simulation. The simulations employ process models and the balance equations for mass, components, energy, and momentum. Due to the model complexities, they are solved iteratively. Numerous types of models are published in the literature; as mentioned previously, these vary in their degree of detail or accuracy and in their application. For process design and optimization, very detailed models are required; these are termed rigorous models, e.g., equilibrium or nonequilibrium models [22, 23] and CFD models [24, 25]. In contrast to the rigorous models, so-called short-cut models (reduced models) are also frequently used; these include linear models, qual- itative models [26], and trend models [27, 28]. The rigorous models are based on the balance equations for mass, energy, and momentum. In process mod- eling, it is always necessary to abstract from the real-world process an ideal- ized description (in the form of equations, relations, or logic circuits) that is more amenable to analysis [29]. Hangos and Cameron [30] describe a formal representation of the assumptions in process modeling. Linninger et al. [31] and Bogusch [32] describe a modeling tool for efficient model development. Weiten and Wozny [33] describe an advanced information management system for knowledge-based documentation. Zerry et al. [34] published a method of modeling integrated documentation in MathML and automated transfer to Java-based models. 2.4.1 DEFINING THE MODEL For the formulation of the balance equations for a chemical engineering or energy process, additional information on the properties of the deployed fluids is required. In addition to pure component properties, accurate description of the mixture properties is of vital importance to the model accuracy. The importance of the properties data and the calculation of properties are discussed by Kister [35], Carlson [36], Shacham et al. [37], and Gani et al. [38]. In Figure 2.2 a typical flow sheet of a chemical engineering process is depicted. The figure displays the various process units, such as compressors, reactors, and de-misters. The performance of a number of these units depends on the effectiveness of fluid flow, fluid contacting, and mixing. The effectiveness of the processes is linked to the internal spatial distributions of fluid inside the equipment, and it is important to model these accurately. Since the fundamental knowledge required for the accurate modeling of turbulence phenomena is still incomplete, the models need to be assessed and validated with experimental information in the form of process images. Internal spatial distributions are particularly important in reaction, mixing, heat exchange, and thermal separation equipment. DK3008_C002.fm Page 16 Tuesday, April 26, 2005 2:11 PM
- 40. Process Modeling 17 Reactors and separation columns assume particular importance for process sim- ulation. The internal streams within the columns are in counter-current flow, causing numerical problems and requiring greater effort for the sequential-oriented solving of the model equations. The differential equations used to model reaction equipment in many cases result in boundary value problems that are difficult to solve simulta- neously or sequentially with the models of the other process units. When types of pumps and valves are taken into account in the process model, the solution effort is increased further. Often these elements have to be considered in pressure-driven or closed-loop dynamic simulations. It is common to develop simulation models for single-unit operations that are solved sequentially and subsequently linked to a complete process flow sheet. Modern equation-oriented simulation software solves the models simultaneously, which offers significant advantages for dynamic simu- lations. As mentioned above, an important aspect in the dynamic process analysis and simulation is the estimation of thermodynamic state and transfer values. On the other hand, the dimensioning and geometry of the equipment and plant have a significant impact on the process dynamics. Consequently, the geometry has to be taken into consideration for dynamic process analysis. For illustration purposes, Figure 2.3 and Figure 2.4 show a simulation model for a single distillation column. The design engineer has to answer a number of questions by using the model. For instance, how many trays are required to perform the separation? What is the best feed location and column pressure? How many controllers are necessary? What are the best controlled variables? What is the best pairing of the controlled variables with the manipulated variables? What is the best location of the sensors? What is the optimal set point? What are the best controller parameters? To solve the model, it is necessary to determine its degree of freedom, i.e., the number of variables minus the number of equations. To simulate the model, the problem has to be fully specified. A number of variables equivalent to the degrees of freedom are generally specified as design parameters. The basis or FIGURE 2.2 Flow sheet of a typical chemical engineering industrial process. reactor condenser cooler distillation reboiler decanter flash 1 tank compressor 2 3 4 6 7 8 11 12 13 14 15 5 10 9 pipe transport I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVIII XVII XIV XIX XX XXI XXII XXIII XXIV XXV XXVI DK3008_C002.fm Page 17 Tuesday, April 26, 2005 2:11 PM
- 41. 18 Process Imaging for Automatic Control FIGURE 2.3 Flow sheet of a distillation column (F, z: feed flow rate and composition; B, xB: bottom flow rate and composition; D, xD: distillate flow rate and composition). FIGURE 2.4 Schematic of a stage model for a distillation column. Indices denote j: stage number, i: component, kw: cooling water, and hd: steam. V is the vapor flow rate, z is the mole fraction, Q is the heating duty, m is the utility mass flow rate, k is the heat transfer coefficient, and A is the heat exchanger area. PC S V B, xB D, xD QC FC TC TC LC F, z TC FC TC LC condenser reboiler Qj feed splitter splitter distillate bottom Fj D B 1 NST j j + 1 j − 1 Lj Vj zF j,i Qj = mHD·䉭 hLV Qj = mKW·CPKW·䉭 TKW Qj = kj·Aj·䉭θj DK3008_C002.fm Page 18 Tuesday, April 26, 2005 2:11 PM
- 42. Process Modeling 19 default values are selected in view of market conditions, previous processes, expe- rience, and sensitivity analysis. For the above example (Figure 2.3), the following information needs to be specified: • Tray number 1, 2, 3, …, j – 1, j, j + 1, …, NST • Feed tray j • Feed flow Fj • Feed temperature, concentration, pressure • Geometry of the tray, area, weir height, weir length • Condenser and reboiler area • Design of condenser and reboiler (e.g., total, falling film, thin film; cooling water and heating medium conditions) With this data the mathematical model is developed as shown in Figure 2.4. For the reboiler and the condenser, the heat transfer equations are integrated into the process model. For closed-loop dynamic simulation as shown in Figure 2.5, the control structure (connection of controlled and manipulated vari- ables) and the controller type have to be predefined. The set points are normally given as the steady-state design values, and the controller parameters have to be optimized. In some cases, the sensor dynamics and actor dynamics have to be considered. Muske and Georgakis [39] describe an optimal measurement system design procedure for chemical processes. In the commonly used flow-driven simulation procedure, the direction of the flow is specified a priori. The more realistic “pressure driven” simulation proce- dure is more complex, and thus more physical and process data need to be considered. A detailed description of pressure drops, the valve characteristics, and the pump diagram have to be introduced in the simulation model. The basic set of equations required to simulate a column, as shown in Figure 2.3 and Figure 2.4 for the flow-driven calculation procedure, includes overall material balances, component material balances, energy balances, summation equations (mole fractions), phase equilibrium relations, control algorithms, and other func- tions such as hold-up correlations and pressure drop correlations. The nonlinear differential-algebraic equation (DAE) system can be solved using a simultaneous solution procedure. The time dependency can be linearized by Euler FIGURE 2.5 Layout of a closed-loop process control system (w(t): set point, e(t): set point error). Process − u(t) y(t) e(t) w(t) manipulated variable set point state variable PID DK3008_C002.fm Page 19 Tuesday, April 26, 2005 2:11 PM
- 43. 20 Process Imaging for Automatic Control approximation, resulting in an equation system that can be solved by a Newton– Raphson procedure for each time step. For this, the equation system will be refor- mulated in a vector description where all equations are given as a vector G(X) = 0. A modified Gauss algorithm can be used to solve the linearized balance equation system. The method also enables the simulation of different process units such as membranes, reactors, columns and connected units, and complex flow sheets. 2.4.2 DETAILED MODELS To eliminate the assumption of phase equilibrium, the coupled mass and heat transfer across each boundary have to be considered in a nonequilibrium or rate-based model. For the case of three-phase distillation, the tray models shown in Figure 2.6 describe the separation process at several levels of detail. FIGURE 2.6 Possible balance regions for three-phase vapor–liquid–liquid (VLL) con- tacting on a distillation column stage. (a) Equilibrium model. (b) Nonequilibrium model considering V–L mass transfer. (c) Nonequilibrium model considering L–L mass transfer. (d) Full nonequilibrium model considering V–L–L mass transfer. Indices are defined in Figure 2.4; flow rates are given by F (feed), V (vapor), L (liquid 1), L (liquid 2); mole fractions are denoted as y (vapor), x (liquid 1), x (liquid 2); K is the equilibrium constant; a is interfacial area, N is specific mass transfer rate. Vj Vj+1 L′j−1 L′′j−1 K′i,j ∗ x′i,j = yi,j Ki,j ∗ x′i,j = x′′i,j Ki,j ∗ x′i,j = x′′i,j L′ L′′ V L′j L′′j F v j Vj+1 L′j L′′j F v j F′j F′′j (a) L′′ L′ V dz (b) (Nij V′aj V′) L′ L′′ Vj+1 L′j L′′j F v j Vj L′j−1 L′′j−1 V dz F′j F′′j Vj L′j−1 L′′j−1 F′j F′′j (Nij V′aj V′) (Nij ′−′′aj ′−′′) (c) L′ Vj+1 Vj L′′j L′′j−1 L′j−1 L′j F′′j F′j Fv j (Nij V′aj V′) (Nij V′′aj V′′) V (Nij ′−′′ aj ′−′′ ) dz (d) L′′ DK3008_C002.fm Page 20 Tuesday, April 26, 2005 2:11 PM
- 44. Process Modeling 21 The equilibrium model in Figure 2.6a uses the relations for vapor–liquid (VL) and liquid–liquid (LL) equilibrium. The models in Figure 2.6b and Figure 2.6c take only one or two of the existing three mass (or heat) transfer rates into consideration. The model shown in Figure 2.6d is the generalized description of all transfer streams. The degree of accuracy desired for the description of transfer rates depends on the application and focus of the model. To calculate the mass transfer, an accurate description of the product of mass transfer coefficient (k) and mass transfer area (a) is needed. For VL mass transfer, a large number of correlations to predict this product are available from the literature. For VLL (i.e., both liquids exchanging mass with the vapor phase), the transfer coefficients and the transfer area are generally unknown. Figure 2.7 illustrates the excellent results that are possible by incorporating greater levels of detail in the model [22]. A more detailed description of the film area is possible using CFD simulation. CFD models are needed to describe wave films [40]. Figure 2.8 and Figure 2.9 show comparisons of the calculated and measured mass transfer characteristics in a packed column. These comparisons are encouraging, in a qualitative sense. However, further model development for better performance would require the use of process imaging techniques for model validation. For on-line optimization, process images could also be used to update mass transfer and interfacial area information used in the process model automatically. More research in this direc- tion is necessary in the future. The derived model can also be used for safety column analysis [41]. Can et al. [42] give the application of the described model equations for safety analysis FIGURE 2.7 Temperature profile of a packed three-phase distillation column separat- ing an acetone–toluene–water mixture at finite reflux. (From Repke, J.U., Villain, O., and Wozny, G., Computer-Aided Chemical Engineering 14:881–886, 2003. With per- mission.) 0 0.5 1 1.5 2 2.5 50 55 60 65 70 75 80 85 90 95 100 105 Temperature (°C) Packed Height (m) Experimental Equilibrium model Nonequilibrium model (vapor) Nonequilibrium model (average liquid) DK3008_C002.fm Page 21 Tuesday, April 26, 2005 2:11 PM
- 45. 22 Process Imaging for Automatic Control of a distillation column, including the relief system. The model describes the operational failures in a distillation column. At the top of the column, a safety valve is introduced in both the process model and the pilot plant for experimental validation (see Figure 2.10). In addition to the basic model equations described above, equations to describe the relief flow are introduced, and the model is formulated in gPROMS (Process Systems Enterprise Limited, London, U.K.). For experimental purposes a second condenser and an additional tank with a two-phase split are introduced so that the vapor relief flow and the liquid relief flow can be analyzed separately. To simulate the system, a relief stream has to be integrated in the tray model for the first tray (Figure 2.11). Figure 2.12 shows a typical scenario of a cooling water failure for a methanol–water separation with the relief procedure. After 5 min the cooling water flow was reduced from 160 l/h to 20 l/h, to increase pressure in the system. Comparison of the theoretical results and the pilot plant experiments shows good agreement between the experimental and theoretical pressure–time dependency. 2.4.3 START-UP AND SHUT-DOWN Another application of the described models is the simulation of start-up and shut-down processes of distillation columns. Figure 2.13 compares the simulated and measured temperature profiles for a transesterification reactive distillation column. The selected equilibrium model accounts for chemical reaction and is FIGURE 2.8 Comparison of experimental data and two predictions from two CFD models for the analysis of the shadow surface of a thin film in a packed distillation column. The finer MESH 2 achieves more accurate predictions of the experimental data. As: shadow surface area, Ap: packing surface area. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 Liquid Flow Rate (cm2/s) Specific Shadow Area A S /A p (m 2 /m 2 ) Experiments Simulation (Mesh 1) Simulation (Mesh 2) DK3008_C002.fm Page 22 Tuesday, April 26, 2005 2:11 PM
- 46. Process Modeling 23 FIGURE 2.9 Comparison of CFD simulation (left) with images of flow experiments through distillation pack- ings (right). The CFD simulation is capable of predicting the observed array of rivulets and dry arches. Superficial Velocity 0.300 0.225 0.150 0.075 0.000 CFX DK3008_C002.fm Page 23 Tuesday, April 26, 2005 2:11 PM
- 47. 24 Process Imaging for Automatic Control used to describe the start-up and shut-down of a reactive distillation column, assuming: • Reaction only takes place in the liquid phase (homogeneously catalyzed) • Vapor and liquid phase are in equilibrium at steady state • Vapor phase shows ideal behavior (for operation at ambient pressure) A single set of equations is not sufficient to simulate a start-up from the cold and empty state to steady-state operation. For example, during fill-up and heating of the column, the plates are not at physical or chemical equilibrium. Therefore, FIGURE 2.10 Structure diagram for a column relief simulation (left) and schematic plot of the pilot plant (right) with relief system including an additional condenser to analyze failure of cooling water supply. FIGURE 2.11 Tray with a relief stream. Relief Tray Cond 2 Tank Feeder Tray 22 Tray 13 Tray1 FC Feed D B FC FC LC PC B1 LC Qelec. Reboiler Splitter Drum Cond 2 Frelief Relief Tray Vj+1 Lj−1 Lj Vj DK3008_C002.fm Page 24 Tuesday, April 26, 2005 2:11 PM
- 48. Process Modeling 25 additional sets of equations that are active at different times during the dynamic simulation are needed. The first set of equations is active during the fill-up and heating process of the column. Once the boiling conditions of a plate are reached, the second set is activated. The start-up process for a single plate is depicted in Figure 2.14. In phase I, the plate is empty, cold, and at ambient pressure. The feed fills the plate until FIGURE 2.12 Comparison of simulation and experiment for a typical scenario of a cooling water failure for a methanol–water separation with the relief procedure. FIGURE 2.13 Dynamic validation of a reactive distillation column start-up: experiments vs. simulation for a transesterification process. (From Reepmeyer, F., Repke, J.U., and Wozny, G., Chemical Engineering & Technology, 26:81–86, 2003. With permission.) 1400 1350 1300 1250 1200 1150 1100 1050 1000 00:00:00 00:30:00 01:00:00 Pressure (mbar) Experiment Time (hours:minutes:seconds) Simulation 290 340 390 440 0 120 240 360 480 Time (min) T (K) Tray 1 experiment Tray 1 simulation Reboiler experiment Reboiler simulation DK3008_C002.fm Page 25 Tuesday, April 26, 2005 2:11 PM
- 49. 26 Process Imaging for Automatic Control liquid leaves the stage to the stage below (phase II). In phase III, vapor from the stage below is entering the stage and heating it up until, in phase IV, the mixture’s bubble pressure (pbub) reaches pset, the set pressure (here 1 bar). In phase V the stage pressure is higher than the pressure from the stage above, so vapor is leaving the stage. In phase VI the stage is operating at steady state. In phases I to IV the first set of equations is active. The switching point is reached when pbub = pset. Then the phase equilibrium equation is applied. Comparison of the model and experimental values shows good agreement, as shown in Figure 2.13. Reepmeyer et al. [43] give details of the study. The amount of information needed for the development of a dynamic model and for rigorous simulation of the complete start-up process is tremendous. All component and kinetic data have to be known, as well as the column, operation, and control specifications. The computational time required to complete one simulation run is long. Therefore, it is desirable to find a simple method of predicting the influence of changes in manipulated or input variables such as heating duty, reflux ratio, feed compositions, and flow. The impact of the manip- ulated variable on the start-up time is easier to understand on the basis of a reduced and simplified model. As an example, a reactive column can be reduced to a two-stage model consisting of a reboiler and a condenser, as depicted in Figure 2.15. The model assumes that the condenser hold-up is negligible, the phases are in equilibrium, and the reaction takes place only in the liquid phase. From the component balance for the species XA around the reboiler (the hold-up should be constant), the following equation results: (2.1) where HUB is the reaction volume (hold-up); F, L, and B are the molar flow rates of feed, reflux, and bottom streams, respectively; YB, XD, and XB are the corre- sponding vapor and liquid component mole fractions in the bottom and distillate streams; and rA is the reaction rate. Introducing the phase equilibrium equation FIGURE 2.14 Different simulation phases of a sample plate during the start-up process. Pin: pressure at the stage above the feed stage. T = Tfeed L L L L L V V V V V V T > Tfeed L p = 1 bar T = 298°K p = pbub p > pin Steady state II III IV V I VI Feed L L L L L L HU dX dt F X V Y L X B X r HU B A FA B D B A B ⋅ = ⋅ − ⋅ + ⋅ − ⋅ − ⋅ DK3008_C002.fm Page 26 Tuesday, April 26, 2005 2:11 PM
- 50. Process Modeling 27 YB = K × XB and the overall mass balance as well as the kinetic balance, (e.g., first-order approach to rA), the above equation yields: (2.2) where XB, XC, and XD are the mole fractions of components B, C, and D in the reaction volume HUB. To derive a time constant from this equation, as a value which indicates a trend of the start-up time, the bilinear terms involving the molar composition of all components must be eliminated. Therefore a linearization around an operating point must be applied: (2.3) where the subscript “0” denotes steady-state values. Inserting the linearization of the bilinear terms in the component balance yields (2.4) FIGURE 2.15 Reduced two-stage model. (From Reepmeyer, F., Repke, J.U., and Wozny, G., Chemical Engineering & Technology, 26:81–86, 2003. With permission.) HUB yB = xD D, xD L, xD V, yB F, xF B, xB HU dX dt F X K L V X F X k X B A FA A A H A ⋅ = ⋅ + − ⋅ − ⋅ − ⋅ − ⋅ ⋅ ( ) ( ) ( 1 X X k X X HU B R C D B − ⋅ ⋅ ⋅ ) X X X X X X X X A B A B A B A B ⋅ ≈ ⋅ + ⋅ − ⋅ 0 0 0 0 dX dt K L V F HU k X X k A B H B A H = − − + − ⋅ ⋅ + − ⋅ ( )( ) ( 1 0 X X X k X X A B R D C 0 0 ) ( ) ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅ − ⋅ ⋅ ( ) k X X F X HU k X X k X X R C D FA B H A B R C D 0 0 0 0 0 DK3008_C002.fm Page 27 Tuesday, April 26, 2005 2:11 PM
- 51. 28 Process Imaging for Automatic Control The variables where interaction during control of the start-up process is possible are the vapor stream V (influenced using the heating power), the feed flow rate F, and the reflux stream L. Utilizing this formulated equation for all components yields a system with four components described by a 4 ×4 matrix where the eigenvalues of the matrix give an idea of the time constants underlying this system. The steady-state values are known in advance. Setting the manipulating variables V and L, to, for example, V = L or L = 0 provides to the start-up strategy a total reflux condition or total distillate removal, respectively. In Reepmeyer et al. [43], the ethyl acetate process is analyzed as a reactive distillation using the reduced model. A comparison of the rigorous and the reduced model is given in Table 2.1. As can be seen, the time constant is capable of predicting the effects of variable changes on the start-up time. Here the total reflux strategy (V = L) shows the largest start-up time and has the highest time constant. The total distillate removal strategy (L = 0) shows the smallest time constant; there- fore, it should deliver the fastest start-up time. The simplifications introduced by the reduced model limit the discussion to the effect of the manipulated variables (here, heating power in the form of vapor stream V and the reflux L). Furthermore, due to the linearization (which is valid around the operating point), complex and highly non-ideal characteristics of the process are incompletely described. Nevertheless, using the reduced model, the start-up of a nonreactive [44] and heat-integrated distillation column [45] and of a reactive distillation column with “simple” reaction can be estimated in terms of the time constant to represent the trend of the start-up time. For more complex reactive distillation processes, rigorous dynamic modeling from an initially cold and empty state is necessary. 2.4.4 CONTROL AND OPTIMIZATION In process control, linearized Laplace-transformed models are often used. The advantages and disadvantages of such models are discussed elsewhere [46, 47]. Alici and Edgar [48] extend existing strategies for the solution of the nonlinear dynamic data reconciliation problem by using the process model as a constraint, TABLE 2.1 Comparison of Time Constant (Reduced Model) and Start-Up Time (Detailed Simulation) for the Ethyl Acetate Process Strategy Simulation (min) Time Constant (min) Conventional 175 118.9 Total reflux 225 122.4 Total distillate removal 183 93.2 Time optimal 191 118.1 DK3008_C002.fm Page 28 Tuesday, April 26, 2005 2:11 PM
- 52. Process Modeling 29 expressed above as the differential-algebraic Equation 2.4. Qualitative models are also often used in process control. Figure 2.16 shows the fundamental model behavior to depict the qualitative dynamic performance of a system. This model class describes the system’s behavior for a certain time constant or oscillating behavior. Vianna and McGreavy [26] use another solution, using graph theory. For optimization, the model equation system given above has to be expanded. The degrees of freedom will be reduced so that selected design variables such as unit number, tray number, pressure, and additional variables for operation (e.g., controller parameters, control structure) can be optimized. The expanded process model is described in the following form: Min J(x,t,y,u,d,p,r,c,ζ) f(x,t,y,u,d,p,ζ) = 0 equilibrium constraints (mass, equilibrium, summation, and heat) g(x,t,y,u,d,p,ζ) ≥ 0 nonequilibrium constraints h(x,t,y,u,d,p,r,ζ) = 0 controller equations where x0, y0, u0 are initialization variables, c is the cost parameter, p is the model parameter, ζ is uncertainties, d is disturbances, u is manipulated variables, r is controlled variables, and t is time. Optimization under uncertainty is often necessary for robust process design and operation. Wendt et al. [49] propose a new approach to solve nonlinear FIGURE 2.16 Trend models: different models classes to characterize the response of process variables. (From Vedam, H., and Venkatasubramanian, V.A., Proc. American Control Conference, Albuquerque, 1997; MC Kindsmüller, L Urbas, Situation Awareness in der Fahrzeug- und Prozessführung. Bonn: DGLR Bericht; 2002–04, 131–152.) A H K D C B E F G J I DK3008_C002.fm Page 29 Tuesday, April 26, 2005 2:11 PM
- 53. 30 Process Imaging for Automatic Control optimization problems under uncertainty, in which some dependent variables are to be constrained with a predefined probability. Such problems are called “opti- mization under chance constraints.” The proposed approach is applied to the optimization of reactor networks and a methanol–water distillation column. Wendt et al. [50] describe the application of the column model. A two-pressure column system modeled by the mass, equilibrium, summation, and heat (MESH) equations and solved by the algorithm described above is optimized with the sequential quadratic programming (SQP) method. In the optimization approach, the entire computation is divided into one layer for optimization and one layer for simulation. The model equations are integrated in the simulation layer, so that the state variables and their sensitivities can be calculated for given controls. The control variables, defined as piecewise constant, are calculated in the optimization layer by SQP as the decision variables. A reduction in start-up time of up to 80% was identified using this approach. The application of the optimization method for a probabilistically constrained model-predictive controller is described by Li et al. [51]. The optimal design and control of a high-purity industrial distillation system is described by Ross et al. [52]. They developed a software implementation for the solution of the mixed integer dynamic optimization (MIDO) problem and optimized a two-pressure column system to improve operability and to identify a new process design with improved economics. The problem of inconsistent initial values of the dependent variables is described by Wu and White [53]. Borchardt [54] describes a promising parallel approach for large-scale real-world dynamic simulation applications, such as plant-wide dynamic simulation in the chemical process industry. This approach partitions the system of differential and algebraic model equations into smaller blocks which can be solved independently. Considerable speed-up factors were obtained for the dynamic simulation of large-scale distillation plants, covering systems with up to 60,000 model equations. Holl and Schuler [55] give an overview of process simulation in industrial application and operation. The nonlinear DAE-system mentioned in Section 2.4.1 is used for steady-state on-line optimization by Basak et al. [56], for plant-wide process automation [57], and for operator training systems [58] where the oper- ators are able to assess the process performance. REFERENCES 1. RG Rice, DD Do. Applied Mathematics and Modeling for Chemical Engineers. New York: John Wiley & Sons, 1995. 2. WL Luyben. Process Modeling, Simulation and Control for Chemical Engineers, 2nd ed. New York: McGraw Hill, 1990. 3. LT Biegler, IE Grossmann, AW Westerberg. Systematic Methods of Chemical Process Design. Upper Saddle River, NJ: Prentice Hall, 1997. 4. MB Abbott, DR Basco. Computational Fluid Dynamics. Singapore: Longman Scientific & Technical, 1989. DK3008_C002.fm Page 30 Tuesday, April 26, 2005 2:11 PM
- 54. Process Modeling 31 5. S Haykin. Neural Networks. Upper Saddle River, NJ: Prentice Hall, 1999. 6. UM Diwekar. Introduction to Applied Optimization and Modeling. Netherlands: Kluwer Academic Publishers, 2003. 7. S Rigopoulos, P Linke. Systematic development of optimal activated sludge pro- cess designs. Comput. Chemical Eng. 26:585–597, 2002. 8. H Lemonnier. Multiphase instrumentation: The keystone of multidimensional multiphase flow modeling. Experimental Thermal Fluid Science 15:154–162, 1997. 9. M Lance, M Lopez de Bertodano. Phase distribution phenomena and wall effects in two-phase flows. Chapter 2 in: Multiphase Science and Technology, Vol. 8. London, Begell House, 1996. 10. R Mann, RA Williams, T Dyakowski, FJ Dickin, RB Edwards. Developments of mixing models using electrical resistance tomography. Chemical Eng. Science 52:2073–2085, 1997. 11. D Mewes, T Loser, M Millies. Modeling of two-phase flow in packings and monoliths. Chemical Eng. Science 54:4729–4747, 1999. 12. HS Tapp, AJ Peyton, EK Kemsley, RH Wilson. Chemical engineering applications of electrical process tomography. Sensors Actuators B 92:17–24, 2003. 13. R Mann, AM El-Hamouz. A product distribution paradox on scaling-up a stirred batch reactor. AIChE J. 41:855–867, 1995. 14. P Gupta, B Ong, MH Al-Dahhan, MP Dudukovic, BA Toseland. Hydrodynamics of churn turbulent bubble columns: gas-liquid recirculation and mechanistic mod- eling. Catalysis Today 64:253–269, 2001. 15. W Chen, T Hasegawa, A Tsutsumi, K Otawara, Y Shigaki. Generalised dynamic modeling of local heat transfer in bubble columns. Chemical Eng. J. 96:37–44, 2003. 16. DB Kell, B Sonnleitner. GMP—Good modeling practice: an essential component of good manufacturing practice. TIBTECH 13:481–492, 1995. 17. MG Allen, CT Butler, SA Johnson, EY Lo, F Russo. An imaging neural network combustion control system for utility boiler applications. Combustion Flames 94:205–214, 1993. 18. G Lu, Y Yan, DD Ward. Advanced monitoring and characterization of combustion flames. Proceedings of IEE Seminar on Advanced Sensors and Instrumentation Systems for Combustion Processes, London, 2000, pp. 3/1–3/40. 19. PE Keller, LJ Kanngas, LH Linden, S Hashem, T Kouzes. Electronic noses and their applications. Proceedings of IEEE Northcon: Technical Applications Con- ference, Portland, 1995, pp. 791–801. 20. D Sbarbaro, P Espinoza, J Araneda. A pattern based strategy for using multidimen- sional sensors in process control. Comput. Chemical Eng. 27:1925–1943, 2003. 21. J Lunze. Stabilization of nonlinear systems by qualitative feedback controllers. Int. J. Control 62:109–128, 1995. 22. JU Repke, OVillain, G Wozny.A nonequilibrium model for three-phase distillation in a packed column: modeling and experiments. Computer-Aided Chemical Eng. 14:881–886, 2003. 23. JH Lee, MP Dudokovic. A comparison of the equilibrium and nonequilibrium models for a multicomponent reactive distillation column. Comput. Chemical Eng. 23:159–172, 1998. 24. FH Yin, CG Sun, A Afacan, K Nandakumar, KT Chuang. CFD modeling of mass-transfer processes in randomly packed distillation columns. Industrial Eng. Chemical Res. 39:1369–1380, 2000. DK3008_C002.fm Page 31 Tuesday, April 26, 2005 2:11 PM
- 55. Exploring the Variety of Random Documents with Different Content
- 59. The Project Gutenberg eBook of John Marvel, Assistant
- 60. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: John Marvel, Assistant Author: Thomas Nelson Page Illustrator: James Montgomery Flagg Release date: January 10, 2013 [eBook #41817] Most recently updated: October 23, 2024 Language: English Credits: Produced by D Alexander, Mary Meehan and the Online Distributed Proofreading Team at http://www.pgdp.net *** START OF THE PROJECT GUTENBERG EBOOK JOHN MARVEL, ASSISTANT ***
- 62. BY THOMAS NELSON PAGE ILLUSTRATED BY JAMES MONTGOMERY FLAGG NEW YORK CHARLES SCRIBNER'S SONS 1909 Copyright, 1909, by CHARLES SCRIBNER'S SONS Published October, 1909 TO THOSE LOVED ONES WHOSE NEVER FAILING SYMPATHY HAS LED ME ALL THESE YEARS
- 63. "To ply your old trade?" I asked.
- 64. CONTENTS CHAPTER PAGE I. My First Failure 1 II. The Jew and the Christian 5 III. The Fight 16 IV. Delilah 26 V. The Hare and the Tortoise 36 VI. The Meteor 44 VII. The Hegira 55 VIII. Padan-Aram 67 IX. I Pitch My Tent 84 X. A New Girl 103 XI. Eleanor Leigh 114 XII. John Marvel 138 XIII. Mr. Leigh 147 XIV. Miss Leigh Seeks Work 154 XV. The Lady of the Violets 172 XVI. The Shadow of Sham 186 XVII. The Gulf 198 XVIII. The Drummer 215 XIX. Re-enter Peck 227 XX. My First Client 245 XXI. The Resurrection of Dix 259 XXII. The Preacher 275 XXIII. Mrs. Argand 286 XXIV. Wolffert's Mission 305 XXV. Fate Leads 319
- 65. XXVI. Coll McSheen's Methods 339 XXVII. The Shadow 354 XXVIII. The Walking Delegate 361 XXIX. My Confession 381 XXX. Seeking One That Was Lost 398 XXXI. John Marvel's Raid 416 XXXII. Doctor Caiaphas 430 XXXIII. The Peace-maker 453 XXXIV. The Flag of Truce 465 XXXV. Mr. Leigh has a Proposal of Marriage Made Him 493 XXXVI. The Riot and Its Victim 507 XXXVII. Wolffert's Neighbors 517 XXXVIII. Wolffert's Philosophy 527 XXXIX. The Conflict 539 XL. The Curtain 563
- 66. ILLUSTRATIONS "To ply your old trade?" I asked Frontispiece Wolffert ... was cursing me with all the eloquence of a rich vocabulary 20 "Hi! What you doin'?" he stammered 60 "But you must not come in" 140 "Perhaps, you are the man yourself?" she added insolently 302 "Speak her soft, Galley" 412 "I suppose it is necessary that we should at least appear to be exchanging the ordinary inanities" 468 I am sure it was on that stream that Halcyone found retreat 556
- 68. I MY FIRST FAILURE I shall feel at liberty to tell my story in my own way; rambling along at my own gait; now going from point to point; now tearing ahead; now stopping to rest or to ruminate, and even straying from the path whenever I think a digression will be for my own enjoyment. I shall begin with my college career, a period to which I look back now with a pleasure wholly incommensurate with what I achieved in it; which I find due to the friends I made and to the memories I garnered there in a time when I possessed the unprized treasures of youth: spirits, hope, and abounding conceit. As these memories, with the courage (to use a mild term) that a college background gives, are about all that I got out of my life there, I shall dwell on them only enough to introduce two or three friends and one enemy, who played later a very considerable part in my life. My family was an old and distinguished one; that is, it could be traced back about two hundred years, and several of my ancestors had accomplished enough to be known in the history of the State—a fact of which I was so proud that I was quite satisfied at college to rest on their achievements, and felt no need to add to its distinction by any labors of my own. We had formerly been well off; we had, indeed, at one time prior to the Revolutionary War, owned large estates—a time to which I was so fond of referring when I first went to college that one of my acquaintances, named Peck, an envious fellow, observed one day that I thought I had inherited all the kingdoms of the earth and the glory of them. My childhood was spent on an old plantation, so far
- 69. removed from anything that I have since known that it might almost have been in another planet. It happened that I was the only child of my parents who survived, the others having been carried off in early childhood by a scourge of scarlet fever, to which circumstance, as I look back, I now know was due my mother's sadness of expression when my father was not present. I was thus subjected to the perils and great misfortune of being an only child, among them that of thinking the sun rises and sets for his especial benefit. I must say that both my father and mother tried faithfully to do their part to counteract this danger, and they not only believed firmly in, but acted consistently on, the Solomonic doctrine that to spare the rod is to spoil the child. My father, I must say, was more lenient, and I think gladly evaded the obligation as interpreted by my mother, declaring that Solomon, like a good many other persons, was much wiser in speech than in practice. He was fond of quoting the custom of the ancient Scythians, who trained their youth to ride, to shoot, and to speak the truth. And in this last particular he was inexorable. Among my chief intimates as a small boy was a little darkey named "Jeams." Jeams was the grandson of one of our old servants—Uncle Ralph Woodson. Jeams, who was a few years my senior, was a sharp-witted boy, as black as a piece of old mahogany, and had a head so hard that he could butt a plank off a fence. Naturally he and I became cronies, and he picked up information on various subjects so readily that I found him equally agreeable and useful. My father was admirably adapted to the conditions that had created such a character, but as unsuited to the new conditions that succeeded the collapse of the old life as a shorn lamb would be to the untempered wind of winter. He was a Whig and an aristocrat of the strongest type, and though in practice he was the kindest and most liberal of men, he always maintained that a gentleman was the choicest fruit of civilization; a standard, I may say, in which the personal element counted with him far more than family connection. "A king can make a nobleman, sir," he used to say; "but it takes
- 70. Jehovah to make a gentleman." When the war came, though he was opposed to "Locofocoism" as he termed it, he enlisted as a private as soon as the State seceded, and fought through the war, rising to be a major and surrendering at Appomattox. When the war closed, he shut himself up on his estate, accepting the situation without moroseness, and consoling himself with a philosophy much more misanthropic in expression than in practice. My father's slender patrimony had been swept away by the war, but, being a scholar himself, and having a high idea of classical learning and a good estimate of my abilities—in which latter view I entirely agreed with him—he managed by much stinting to send me to college out of the fragments of his establishment. I admired greatly certain principles which were stamped in him as firmly as a fossil is embedded in the solid rock; but I fear I had a certain contempt for what appeared to me his inadequacy to the new state of things, and I secretly plumed myself on my superiority to him in all practical affairs. Without the least appreciation of the sacrifices he was making to send me to college, I was an idle dog and plunged into the amusements of the gay set—that set whose powers begin below their foreheads—in which I became a member and aspired to be a leader. My first episode at college brought me some éclat.
- 71. II THE JEW AND THE CHRISTIAN I arrived rather late and the term had already begun, so that all the desirable rooms had been taken. I was told that I would either have to room out of college or take quarters with a young man by the name of Wolffert—like myself, a freshman. I naturally chose the latter. On reaching my quarters, I found my new comrade to be an affable, gentlemanly fellow, and very nice looking. Indeed, his broad brow, with curling brown hair above it; his dark eyes, deep and luminous; a nose the least bit too large and inclining to be aquiline; a well-cut mouth with mobile, sensitive lips, and a finely chiselled jaw, gave him an unusual face, if not one of distinction. He was evidently bent on making himself agreeable to me, and as he had read an extraordinary amount for a lad of his age and I, who had also read some, was lonely, we had passed a pleasant evening when he mentioned casually a fact which sent my heart down into my boots. He was a Jew. This, then, accounted for the ridge of his well- carved nose, and the curl of his soft brown hair. I tried to be as frank and easy as I had been before, but it was a failure. He saw my surprise as I saw his disappointment—a coolness took the place of the warmth that had been growing up between us for several hours, and we passed a stiff evening. He had already had one room-mate. Next day, I found a former acquaintance who offered to take me into his apartment, and that afternoon, having watched for my opportunity, I took advantage of my room-mate's absence and moved out, leaving a short note saying that I had discovered an old friend who was very desirous that I should share his quarters. When I next met Wolffert, he was so stiff, that although I felt sorry for him and was ready to be as civil as I might, our acquaintance thereafter
- 72. became merely nominal. I saw in fact, little of him during the next months, for he soon forged far ahead of me. There was, indeed, no one in his class who possessed his acquirements or his ability. I used to see him for a while standing in his doorway looking wistfully out at the groups of students gathered under the trees, or walking alone, like Isaac in the fields, and until I formed my own set, I would have gone and joined him or have asked him to join us but for his rebuff. I knew that he was lonely; for I soon discovered that the cold shoulder was being given to him by most of the students. I could not, however, but feel that it served him right for the "airs" he put on with me. That he made a brilliant exhibition in his classes and was easily the cleverest man in the class did not affect our attitude toward him; perhaps, it only aggravated the case. Why should he be able to make easily a demonstration at the blackboard that the cleverest of us only bungled through? One day, however, we learned that the Jew had a room-mate. Bets were freely taken that he would not stick, but he stuck—for it was John Marvel. Not that any of us knew what John Marvel was; for even I, who, except Wolffert, came to know him best, did not divine until many years later what a nugget of unwrought gold that homely, shy, awkward John Marvel was! It appeared that Wolffert had a harder time than any of us dreamed of. He had come to the institution against the advice of his father, and for a singular reason: he thought it the most liberal institution of learning in the country! Little he knew of the narrowness of youth! His mind was so receptive that all that passed through it was instantly appropriated. Like a plant, he drew sustenance from the atmosphere about him and transmuted what was impalpable to us to forms of beauty. He was even then a man of independent thought; a dreamer who peopled the earth with ideals, and saw beneath the stony surface of the commonplace the ideals and principles that were to reconstruct and resurrect the world. An admirer of the Law in its ideal conception, he reprobated, with the fury of the Baptist,
- 73. the generation that had belittled and cramped it to an instrument of torture of the human mind, and looked to the millenial coming of universal brotherhood and freedom. His father was a leading man in his city; one who, by his native ability and the dynamic force that seems to be a characteristic of the race, had risen from poverty to the position of chief merchant and capitalist of the town in which he lived. He had been elected mayor in a time of stress; but his popularity among the citizens generally had cost him, as I learned later, something among his own people. The breadth of his views had not been approved by them. The abilities that in the father had taken this direction of the mingling of the practical and the theoretical had, in the son, taken the form I have stated. He was an idealist: a poet and a dreamer. The boy from the first had discovered powers that had given his father the keenest delight, not unmingled with a little misgiving. As he grew up among the best class of boys in his town, and became conscious that he was not one of them, his inquiring and aspiring mind began early to seek the reasons for the difference. Why should he be held a little apart from them? He was a Jew. Yes, but why should a Jew be held apart? They talked about their families. Why, his family could trace back for two thousand and more years to princes and kings. They had a different religion. But he saw other boys with different religions going and playing together. They were Christians, and believed in Christ, while the Jew, etc. This puzzled him till he found that some of them—a few—did not hold the same views of Christ with the others. Then he began to study for himself, boy as he was, the history of Christ, and out of it came questions that his father could not answer and was angry that he should put to him. He went to a young Rabbi who told him that Christ was a good man, but mistaken in His claims. So, the boy drifted a little apart from his own people, and more and more he studied the questions that arose in his mind, and more and more he suffered; but more and more he grew strong.
- 74. The father, too proud of his son's independence to coerce him by an order which might have been a law to him, had, nevertheless, thrown him on his own resources and cut him down to the lowest figure on which he could live, confident that his own opinions would be justified and his son return home. Wolffert's first experience very nearly justified this conviction. The fact that a Jew had come and taken one of the old apartments spread through the college with amazing rapidity and created a sensation. Not that there had not been Jews there before, for there had been a number there at one time or another. But they were members of families of distinction, who had been known for generations as bearing their part in all the appointments of life, and had consorted with other folk on an absolute equality; so that there was little or nothing to distinguish them as Israelites except their name. If they were Israelites, it was an accident and played no larger part in their views than if they had been Scotch or French. But here was a man who proclaimed himself a Jew; who proposed that it should be known, and evidently meant to assert his rights and peculiarities on all occasions. The result was that he was subjected to a species of persecution which only the young Anglo-Saxon, the most brutal of all animals, could have devised. As college filled rapidly, it soon became necessary to double up, that is, put two men in one apartment. The first student assigned to live with Wolffert was Peck, a sedate and cool young man—like myself, from the country, and like myself, very short of funds. Peck would not have minded rooming with a Jew, or, for that matter, with the Devil, if he had thought he could get anything out of him; for he had few prejudices, and when it came to calculation, he was the multiplication-table. But Peck had his way to make, and he coolly decided that a Jew was likely to make him bear his full part of the expenses—which he never had any mind to do. So he looked around, and within forty-eight hours moved to a place out of college where he got reduced board on the ground of belonging to some
- 75. peculiar set of religionists, of which I am convinced he had never heard till he learned of the landlady's idiosyncrasy. I had incurred Peck's lasting enmity—though I did not know it at the time—by a witticism at his expense. We had never taken to each other from the first, and one evening, when someone was talking about Wolffert, Peck joined in and said that that institution was no place for any Jew. I said, "Listen to Peck sniff. Peck, how did you get in?" This raised a laugh. Peck, I am sure, had never read "Martin Chuzzlewit"; but I am equally sure he read it afterward, for he never forgave me. Then came my turn and desertion which I have described. And then, after that interval of loneliness, appeared John Marvel. Wolffert, who was one of the most social men I ever knew, was sitting in his room meditating on the strange fate that had made him an outcast among the men whom he had come there to study and know. This was my interpretation of his thoughts: he would probably have said he was thinking of the strange prejudices of the human race—prejudices to which he had been in some sort a victim all his life, as his race had been all through the ages. He was steeped in loneliness, and as, in the mellow October afternoon, the sound of good-fellowship floated in at his window from the lawn outside, he grew more and more dejected. One evening it culminated. He even thought of writing to his father that he would come home and go into his office and accept the position that meant wealth and luxury and power. Just then there was a step outside, and someone stopped and after a moment, knocked at the door. Wolffert rose and opened it and stood facing a new student—a florid, round-faced, round-bodied, bow-legged, blue-eyed, awkward lad of about his own age. "Is this number ——?" demanded the newcomer, peering curiously at the dingy door and half shyly looking up at the occupant. "It is. Why?" Wolffert spoke abruptly.
- 76. "Well, I have been assigned to this apartment by the Proctor. I am a new student and have just come. My name is Marvel—John Marvel." Wolffert put his arms across the doorway and stood in the middle of it. "Well, I want to tell you before you come in that I am a Jew. You are welcome not to come, but if you come I want you to stay." Perhaps the other's astonishment contained a query, for he went on hotly: "I have had two men come here already and both of them left after one day. The first said he got cheaper board, which was a legitimate excuse—if true—the other said he had found an old friend who wanted him. I am convinced that he lied and that the only reason he left was that I am a Jew. And now you can come in or not, as you please, but if you come you must stay." He was looking down in John Marvel's eyes with a gaze that had the concentrated bitterness of generations in it, and the latter met it with a gravity that deepened into pity. "I will come in and I will stay; Jesus was a Jew," said the man on the lower step. "I do not know him," said the other bitterly. "But you will. I know Him." Wolffert's arms fell and John Marvel entered and stayed. That evening the two men went to the supper hall together. Their table was near mine and they were the observed of all observers. The one curious thing was that John Marvel was studying for the ministry. It lent zest to the jokes that were made on this incongruous pairing, and jests, more or less insipid, were made on the Law and the Prophets; the lying down together of the lion and the lamb, etc. It was a curious mating—the light-haired, moon-faced, slow-witted Saxon, and the dark, keen Jew with his intellectual face and his deep-burning eyes in which glowed the misery and mystery of the ages.
- 77. John Marvel soon became well known; for he was one of the slowest men in the college. With his amusing awkwardness, he would have become a butt except for his imperturbable good-humor. As it was, he was for a time a sort of object of ridicule to many of us—myself among the number—and we had many laughs at him. He would disappear on Saturday night and not turn up again till Monday morning, dusty and disheveled. And many jests were made at his expense. One said that Marvel was practising preaching in the mountains with a view to becoming a second Demosthenes; another suggested that, if so, the mountains would probably get up and run into the sea. When, however, it was discovered later that he had a Sunday-school in the mountains, and walked twelve miles out and twelve miles back, most of the gibers, except the inveterate humorists like myself, were silent. This fact came out by chance. Marvel disappeared from college one day and remained away for two or three weeks. Wolffert either could not or would not give any account of him. When Marvel returned, he looked worn and ill, as if he had been starving, and almost immediately he was taken ill and went to the infirmary with a case of fever. Here he was so ill that the doctors quarantined him and no one saw him except the nurse—old Mrs. Denny, a wrinkled and bald- headed, old, fat woman, something between a lightwood knot and an angel—and Wolffert. Wolffert moved down and took up his quarters in the infirmary—it was suggested, with a view to converting Marvel to Judaism—and here he stayed. The nursing never appeared to make any difference in Wolffert's preparation for his classes; for when he came back he still stood easily first. But poor Marvel never caught up again, and was even more hopelessly lost in the befogged region at the bottom of the class than ever before. When called on to recite, his brow would pucker and he would perspire and stammer until the class would be in ill-suppressed convulsions, all the more enjoyable because of Leo Wolffert's agonizing over his wretchedness. Then
- 78. Marvel, excused by the professor, would sit down and mop his brow and beam quite as if he had made a wonderful performance (which indeed, he had), while Wolffert's thin face would grow whiter, his nostrils quiver, and his deep eyes burn like coals. One day a spare, rusty man with a frowzy beard, and a lank, stooping woman strolled into the college grounds, and after wandering around aimlessly for a time, asked for Mr. Marvel. Each of them carried a basket. They were directed to his room and remained with him some time, and when they left, he walked some distance with them. It was at first rumored and then generally reported that they were Marvel's father and mother. It became known later that they were a couple of poor mountaineers named Shiflett, whose child John Marvel had nursed when it had the fever. They had just learned of his illness and had come down to bring him some chickens and other things which they thought he might need. This incident, with the knowledge of Marvel's devotion, made some impression on us, and gained for Marvel, and incidentally for Wolffert, some sort of respect.
- 79. III THE FIGHT All this time I was about as far aloof from Marvel and Wolffert as I was from any one in the college. I rather liked Marvel, partly because he appeared to like me and I helped him in his Latin, and partly because Peck sniffed at him, and Peck I cordially disliked for his cold-blooded selfishness and his plodding way. I was strong and active and fairly good-looking, though by no means so handsome as I fancied myself when I passed the large plate-glass windows in the stores; I was conceited, but not arrogant except to my family and those I esteemed my inferiors; was a good poker- player; was open-handed enough, for it cost me nothing; and was inclined to be kind by nature. I had, moreover, several accomplishments which led to a certain measure of popularity. I had a retentive memory, and could get up a recitation with little trouble; though I forgot about as quickly as I learned. I could pick a little on a banjo; could spout fluently what sounded like a good speech if one did not listen to me; could write, what someone has said, looked at a distance like poetry and, thanks to my father, could both fence and read Latin. These accomplishments served to bring me into the best set in college and, in time, to undo me. For there is nothing more dangerous to a young man than an exceptional social accomplishment. A tenor voice is almost as perilous as a taste for drink; and to play the guitar, about as seductive as to play poker.
- 80. I was soon to know Wolffert better. He and Marvel, after their work became known, had been admitted rather more within the circle, though they were still kept near the perimeter. And thus, as the spring came on, when we all assembled on pleasant afternoons under the big trees that shaded the green slopes above the athletic field, even Wolffert and Marvel were apt to join us. I would long ago have made friends with Wolffert, as some others had done since he distinguished himself; for I had been ashamed of my poltroonery in leaving him; but, though he was affable enough with others, he always treated me with such marked reserve that I had finally abandoned my charitable effort to be on easy terms with him. One spring afternoon we were all loafing under the trees, many of us stretched out on the grass. I had just saved a game of baseball by driving a ball that brought in three men from the bases, and I was surrounded by quite a group. Marvel, who was as strong as an ox, was second-baseman on the other nine and had missed the ball as the center-fielder threw it wildly. Something was said—I do not recall what—and I raised a laugh at Marvel's expense, in which he joined heartily. Then a discussion began on the merits in which Wolffert joined. I started it, but as Wolffert appeared excited, I drew out and left it to my friends. Presently, at something Wolffert said, I turned to a friend, Sam Pleasants, and said in a half-aside, with a sneer: "He did not see it; Sam, you—" I nodded my head, meaning, "You explain it." Suddenly, Wolffert rose to his feet and, without a word of warning, poured out on me such a torrent of abuse as I never heard before or since. His least epithet was a deadly insult. It was out of a clear sky, and for a moment my breath was quite taken away. I sprang to my feet and, with a roar of rage, made a rush for him. But he was ready, and with a step to one side, planted a straight blow on my jaw that, catching me unprepared, sent me full length on my back. I was up in a second and made another rush for him, only to be caught in the same way and sent down again.
- 81. When I rose the second time, I was cooler. I knew then that I was in for it. Those blows were a boxer's. They came straight from the shoulder and were as quick as lightning, with every ounce of the giver's weight behind them. By this time, however, the crowd had interfered. This was no place for a fight, they said. The professors would come on us. Several were holding me and as many more had Wolffert; among them, John Marvel, who could have lifted him in his strong arms and held him as a baby. Marvel was pleading with him with tears in his eyes. Wolffert was cool enough now, but he took no heed of his friend's entreaties. Standing quite still, with the blaze in his eyes all the more vivid because of the pallor of his face, he was looking over his friend's head and was cursing me with all the eloquence of a rich vocabulary. So far as he was concerned, there might not have been another man but myself within a mile.
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