Space time and Space velocity, CSTR

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Ideal Reactors for Single
Reaction
Under the Supervision of: Dr. Imran Nazir Unar
Mujeeb UR Rahman 17CH106
Chemical Engineering Department
Chemical Reaction Engineering (CH314)
Mehran University of Engineering &
Technology
Jamshoro, Pakistan

Lecture Objectives
Discussion on:
• Space-time and space-velocity terms
• Performance Equation of Steady-state Mixed Flow Reactor
(CSTR)
• Problem

IDEAL REACTORS FOR A SINGLE REACTION
Space-Time and Space-Velocity
 Just as the reaction time t is the natural performance measure for a batch
reactor, so are the space-time and space-velocity the proper performance
measures of flow reactors.
 These terms are defined as follows:
(6)
(7)

 Thus, a space-velocity of 5 hr-1 means that five reactor volumes of feed at specified
conditions are being fed into the reactor per hour.
 A space-time of 2 min means that every 2 min one reactor volume of feed at specified
conditions is being treated by the reactor.
 Now we may arbitrarily select the temperature, pressure, and state (gas, liquid, or solid)
at which we choose to measure the volume of material being fed to the reactor.
 Certainly, then, the value for space-velocity or space-time depends on the conditions
selected.
 If they are of the stream entering the reactor, the relation between s and τ and the other
pertinent variables is
(8)

 It may be more convenient to measure the volumetric feed rate at some
standard state, especially when the reactor is to operate at a number of
temperatures.
 If, for example, the material is gaseous when fed to the reactor at high
temperature but is liquid at the standard state, care must be taken to specify
precisely what state has been chosen.
 The relation between the space-velocity and space-time for actual feed
conditions (unprimed symbols) and at standard conditions (designated by
primes) is given by
 In most of what follows, we deal with the space-velocity and space-time based
on feed at actual entering conditions; however, the change to any other basis is
easily made.
(9)

INTRODUCTION TO REACTOR DESIGN
Performance Equation for STEADY-STATE MIXED FLOW REACTOR
 The performance equation for the
mixed flow reactor is obtained from
Balance equation (in previous
presentation) which makes an
accounting of a given component
within an element of volume of the
system.
 But since the composition is uniform
throughout, the accounting may be
made about the reactor as a whole.
 By selecting reactant A for
consideration, Eq. becomes
(10)
Fig. 1: Notation for a mixed reactor.

 As shown in Fig. 1, if FA0 = ν0CA0 is the molar feed rate of component A to the
reactor, then considering the reactor as a whole we have
 Introducing these three terms into Eq. 10, we obtain
 which on rearrangement becomes
 OR
(11)

 where XA and rA are measured at exit stream conditions, which are the same
as the conditions within the reactor.
 More generally, if the feed on which conversion is based, subscript 0, enters
the reactor partially converted, subscript i, and leaves at conditions given by
subscript f, we have
 or
 For the special case of constant-density systems XA = 1 – CA/CA0 in, which
case the performance equation for mixed reactors can also be written in terms
of concentrations or
(12)
(13)

 These expressions relate in a simple way the four terms XA, –r A, V, FA0; thus,
knowing any three allows the fourth to be found directly.
 In design, then, the size of reactor needed for a given duty or the extent of
conversion in a reactor of given size is found directly.
 In kinetic studies each steady-state run gives, without integration, the reaction
rate for the conditions within the reactor.
 The ease of interpretation of data from a mixed flow reactor makes its use very
attractive in kinetic studies, in particular with messy reactions (e.g., multiple
reactions and solid catalyzed reactions).

Performance Equation for Ideal Batch Reactor
Fig. 2: Graphical representation of the design equations for mixed flow reactor.

Problem: REACTION RATE IN A MIXED FLOW REACTOR
Fig. 2: Graphical representation of the design equations for mixed flow reactor.
One liter per minute of liquid containing A and B (CA0 = 0.10 mol/liter, CB0 =0.01
mol/liter) flow into a mixed reactor of volume V = 1 liter. The materials react in a
complex manner for which the stoichiometry is unknown. The outlet stream from
the reactor contains A, B, and C (CAf = 0.02 mol/liter, CBf = 0.03 mol/liter, Ccf =
0.04 mol/liter. Find the rate of reaction of A, B, and C for the conditions within the
reactor.

 For a liquid in a mixed flow reactor
εA = 0 and Eq. 13 applies to each of the
reacting components, giving for the
rate of disappearance:
Problem: REACTION RATE IN A MIXED FLOW REACTOR
Fig. 3: Mixed Flow Reactor Conditions
Solution:
 Thus A is disappearing while B and C are being formed.

Space time and Space velocity, CSTR

Space time and Space velocity, CSTR

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