2. The Production System
is the system that transports reservoir fluids from
the subsurface reservoir to the surface, processes
and treats the fluids, and prepares the fluids for
storage and transfer to a purchaser..
A complete oil or gas production system consists
Reservoir;
Wellbore/well;
tubular goods and associated equipment;
surface wellhead
flowlines and processing equipment i.e.
separators;
artificial lift equipment i.e. pumps;
transportation pipelines
of:
5. The layout is
significantly more
complicated when
more wells,
separators, and
other process
equipment are
required to
produce the field
subsea production system
7. The Production System
Principal elements of a simple production
system of a naturally flowing oil as
the production casing or liner.
the
the
the
the
tubing string.
production packer.
wellhead and tubing hanger,
and
christmas tree.
8. The Production System
flow characteristics of the system from the reservoir up
to the wellbore, through sub surface, surface
equipment, and finally to a storage vessel or pipeline,
is accompanied by a series of pressure drops.
The dependence of rate on pressure drop is the
essence of most production engineering problems is
usually considered in two ways.
The rate-pressure relationship is considered at
a specific point along the flow path, that is, at
the wellbore or at the wellhead.
The pressure traverse along the flow path is
considered at a constant flow rate, that is, pressure
distribution around the wellbore or along the
tubing.
9. Nodal analysis
Production system and
associated pressure losses
Pressure at the outer boundary of the reservoir is the
starting point for the pressure traverse, which ends at
transfer line pressure or at atmospheric pressure in the
12. The Production System
Engineering analysis of well performance is
essentially an investigation of
relationship in three cases:
steady state production
gradual long-term changes
depletion
the pressure-rate
due to reservoir
short-term transient behavior following a sudden
change in flow conditions
13. Overview of Reservoir
All production of oil/gas starts from the essence of
hydrocarbons within the porous media or reserviour
A reservoir can be defined as a porous and
permeable underground formation containing an
individual bank of hydrocarbons confined by
impermeable rock or water barriers and is
characterized by a single natural pressure system.
Others terminologies are:
• field which is an area that consists of one or
more reservoirs all related to the same
structural feature and
• A pool an area consisting of one or more
reservoirs in isolated structures
14. Hydrocarbon accumulations
Are classified as oil, gas condensate, and
gas reservoirs depending on the initial
reservoir condition in the phase diagram
An oil that is at a pressure above its
bubble-point pressure is called an
‘undersaturated oil ’ because can dissolve
more gas at the given temperature.
it
An oil that is at its bubble-point pressure is called a
‘‘saturated oil’’ because it can dissolve no more gas
at the given temperature.
Single (liquid)-phase flow prevails in an
undersaturated oil reservoir, whereas two-phase
(liquid oil and free gas) flow exists in a saturated oil
reservoir.
16. Hydrocarbon accumulations
On the basis of boundary type which determines
driving mechanism, oil reservoirs can be
classified
Water-drive reservoir,
Gas-cap drive reservoir,
Dissolved-gas drive reservoir
18. Recall the Darrcy’s
q kAdp
equation
dr
Where, A is a radial area
at a distance
r, and is given by
Based on this equation the
established considering
• steady,
• transient and
• pseudo-steady-state
flow behavior can be
flow
19. Transient Flow
Flow in this case is governed by the diffusivity
equation described by the pressure profile in
an infinite-acting, radial reservoir, with a slightly
compressible and constant viscosity fluid
The pressure drawdown equation describing the declining flowing bottomhole
pressure, Pwf, while the well is flowing at a constant rate q. is given as
20. Steady-State Well Performance
Parameters including flow rate and all pressures are in
variant with time
> For a verical well Pe and Pwf are cinstant with time
Reservoir schematic for steady-state flow into a well
(6.1)
21. Steady-State Well Performance
Considering the effect of near well bore
Eq. 6.1
becomes
damage (skin effect)
For P=pe and r =re
for oil fields it becomes
22. Steady-State Well Performance
The two important concepts to be noted hera are
Effective
From
wellbore radius
Productivity
difference.
index (PI) i.e. the production rate divided by the pressure
25. Pseudo-Steady-state flow
Pressure at the outer boundary of a reservoir is
no longer constant, instead declines at a
constant
rate with time
the pressure drop from the diffusivity equation is
given as
since Pe is not known at any given time. As case, the average reservoir
pressure, , can be obtained from periodic pressure buildup tests.
26. Pseudo-Steady-state flow
The a volumetrically weighted pressure/ average
reservoir pressure is used
Introducing the skin effect and incorporating the term 3/4 into the logarithmic
expression leads to the inflow relationship for a no-flow boundary oil
reservoir
27. • Tanking into consideration the drainage shape and well
position
• a generalized equation for any shape is
Where, γ is Euler's constant, usually equal to 1.78 and
is a shape factor as given in table below
Pseudo-Steady-state flow
29. Examples
The Lamar No. 1 was tested for eight hours at a rate of about
38 STB/D. Wellbore flowing pressure was calculated to be 585
psia, based on acoustic liquid level measurements. After shutting
the well in for 24 hours. the bottomhole pressure reached a
static value of 1125 psia. also based on acoustic level readings.
The rod pump used on this well is considered undersized. and
a larger pump can be expected to reduce wellbore flowing
pressure to a level near 350 psia (just above the bubble-point
pressure). Calculate the following:
1. productivity index J
2. absolute open flow based on a constant productivity index
3. oil rate for a wellbore flowing pressure of 350 psia
4. wellbore flowing pressure required to produce 60STB/D
30. Inflow Performance
All well deliverability equations relate the well
production rate and the driving force in the
reservoir, that is, the pressure difference
between the initial, outer boundary or average
reservoir pressure and the flowing bottomhole
pressure.
The relationship of the bottomhole pressure, 𝑃𝑤f ,
and the production rate, q is called inflow
performance relationship" (IPR) curve
For under saturated reservoirs steady, transient
and pseudo state equations are useful in
establishing IPR curve
34. Effects of Water Production; Relative
Permeability
in petroleum reservoirs, water is always present
at least as connate water (
s𝑤c
).
Therefore, permeability should be considered as
effective, and it would be invariably less than
the one obtained from core flooding or other
laboratory techniques using a single fluid.
Relative permeabilities are determined in the
laboratory and are characteristic of a given
reservoir rock and its saturating fluids. It is not a
good practice to use relative permeabilities
obtained for one reservoir to predict the
performance of another.
and water permeability respectively, md, m2, kro,
Where, ko , k𝑤
oil
oil and
kr𝑤
m2
water permeability respectively (no dimension), k is permeability md,
35. Thus, in an undersaturated oil
reservoir, inflow equations must
be
written for both oil and water
The ratio qw/ qo is referred to as the
water-oil ratio. In an almost depleted
reservoir it would not be unusual to
obtain water-oil ratios of 10 or
larger.
Such a well is often referred to as a
"stripper" with production rates of
less than 10 STB/d of oil
Usually, relative permeability curves are
presented as functions of the water
saturation, Sw, as shown. When the
water
saturation, Sw, is the connate water
saturation, Swc. no free water would flow
and therefore its effective permeability,
37. Production from Two-Phase Reservoirs
In most cases oil will be produced along with free
gas in the reservoir, either because
the reservoir pressure is naturally below
the bubble point pressure (saturated
reservoirs) or
because the flowing bottomhole pressure
is set below bubble point pressure point i.e. to
provide adequate driving force
Depending on the properties of the oil and the
pressure and temperature at the drainage
boundary, the point where oil reaches its saturated
state may
lie anywhere along the flow path toward the stock
38. As oil flows from the
reservoir drainage
boundary to a
wellbore, up the
production tubing
and through the
surface and process
equipment eventually
reaches a saturated
state
Thereafter, gas comes out of solution as pressure drops
along the flow path, forming a two-phase gas/oil system
40. Production from Two-Phase Reservoirs
Note that
the amount of gas dissolved in oil at reservoir
conditions is dependent on the overall composition
of the fluid.
The amount of gas remaining in solution at any
other condition depends on the prevailing pressure
and temperature.
The amount and rate of gas liberation depend on
the pressure and temperature profile along the
flow
path.
As gas evolves, the oil shrinks until it stabilizes
in
the stock tank at standard conditions of pressure
41. Overview of Properies of saturated reservoir
Basic properties of saturated
understood incude:
formation volume factor
bubble-point pressure
Fluid Density
Fluid Viscosity
that need to be
Oil and gas gravities
gas/oil ratio (GOR)
and
The ratio of the volume of oil at reservoir conditions
to the volume of oil resulting in the stock tank is
called the formation volume factor (FVF).
42. Overview of Properties of saturated reservoir
the formation volume factor for oil (Bo
) above
the bubble-point pressure includes all of the
solution gas.
At a pressure below the bubble point, Bo
, refers
to the liquid phase and the remaining dissolved
gas at that pressure.
the total formation volume factor, Bt
,, which
accounts for both oil and free gas is
Where,
Rsb
is the solution gas-oil ratio at the bubble-point pressure. If
Bg
is given in res ft3
/SCF, then Bg must be divided by 5. 615 to convert to res bbl/SCF
43. Overview of Propertiesof saturated reservoir
Downhole volumetric flow
Where,
and qo
q𝑙 is the actual liquid flow rate at some location in the well or reservoir
is the stock-tank oil rate. The downhole gas rate depends on the solution
gas-oil ratio
Rs
, according to , Bg is the gas formation volume factor , and
GOR is the gas-oil ratio in SCF/STB.
volumetric fractions occupied by the liquid and gas phases at a given
cross
section
44. Overview of Properties of saturated
reservoir
API relation of gravity to oil gravity, 𝛾o at STP
141.
5
= −
131.5
𝛾𝑜
141.
5
131.5+γAPI
Stock-tank oil density, lbm/ft3 is calculated as
=
62.37𝛾o
45. Overview of Properties of saturated reservoir
The oil-formation volume factor and the solution
gas-oil ratio, Rs, will vary with
pressure.
temperature and
Note, More, property correlations for two-phase
Systems, are available in literature (for
estimating
PVT properties), one of the common
that of
correlation is
Standing, (1981) and
Vasquez and Beggs (1980)
Refer reference book (s)
47. Example
Given
well bore flowing pressure, end of test .
bottomhole temperature .
wellhead flowing pressure. end of
test .
2800psia
160°F
800psia
120°F
96Mscf/D
265bbl/D
1.15 bbl/STB
200psia
90°F
30scf/STB
0.89(air = 1)
0.69 (air= 1)
{0.863(water=
0.07
wellhead flowing temperature. end
of
separator gas flow rate .
separator liquid flow rate .
test .
separator/stock-tank oil volume factor :
separator
separator
separator
separator
pressure .
temperature .
oil gas/oil
ratio
gas gravity .
.
stock-tank
stock-tank
stock-tank
Calculate
vapor (gas) gravity
oil gravity .
water/oil ratio:
:
28°API 1)}
(a)the stock-tank oil rate. (b)
gravity
The total gas/oil ratio and average gas
48. Oil Inflow Performance for a Two-Phase Reservoir
There are numerous empirical relationships
proposed to predict oilwell performance under
two-
phase flow conditions.
The Some of the described equations are
a) Vogel Equation: the first presented as easy to-
use
method for predicting the performance of oil wells
for pseudo-steady state
49. Oil Inflow Performance for a Two-Phase Reservoir
if the reservoir pressure is above the bubble point and yet the flowing
bottomhole pressure is below, a generalized Vogel inflow
performance
can be written. This can be done for
steady state
transient, steady state, and
pseudo-
At first, qb , the flow rate, where = 𝑃b · can be written as
𝑃𝑤f
50. Oil Inflow Performance for a Two-Phase Reservoir
The productivity index above the bubble point is
simply
51. Oil Inflow Performance for a Two-Phase Reservoir
b) Fetkovich Equation:
based isochronal testing of oil wells to estimate
productivity. It is based on the empirical gas-
well deliverability equation proposed by
Rawlins and Schellhardt.
• A log-log plot of the pressure squared difference vs. flow rate
is expected to plot as a straight line.
• The inverse of the slope yields an estimate of n, the
flow exponent.
• The flow coefficient can be estimated by selecting a flow rate
and pressure on the log-log plot and using the information C
calculated
52. An IPR can be developed by rearranging
Fetkovich’s deliverability equation to obtain
Other relations are
c) Jones, Blount, and Glaze equation:
incorporate non-Darcy flow effects. The basic
equation to describe the flow of oil is
Oil Inflow Performance for a Two-Phase Reservoir
53. Where, a represents the laminar flow coefficient and
b is the turbulence coefficient
The laminar flow coefficient a is the intercept
plot,while the slope of the curve yields the
of the
turbulence coefficient b
d) Neely and Brown equation:
In certain circumstances, both single-phase and
two-phase flow may be occurring in the reservoir.
This results when the average reservoir pressure is
above the bubble point pressure of the reservoir
oil while the flowing bottomhole pressure is less
than the bubble point pressure.
•
•
Oil Inflow Performance for a Two-Phase Reservoir
54. To handle this situation, Neely equation is used
Oil Inflow Performance for a Two-Phase Reservoir
55. e) Wiggins Equation:
for three-phase flow, which is similar in form to
Vogel’s IPR.
The generalized three-phase IPRs for oil and
water, respectively are
Oil Inflow Performance for a Two-Phase Reservoir
56. f) Future Performance Methods
Once the petroleum engineer has estimated
the
current productive capacity of a well, it is often
desired to predict future
purposes.
There are two method
(i) Fetkovich method
performance for planning
exponent n is the deliverability
equal one,
exponent which can be approximated
Assumption: the deliverability exponent does not change between the
present
Oil Inflow Performance for a Two-Phase Reservoir
60. Example
Table below presents data for a multipoint test
on a producing oil well used to demonstrate
the two-phase IPR methods. The average
reservoir pressure for this example is 1,734
psia.
63. Production from Natural Gas Reservoirs
Natural gas reservoirs produce hydrocarbons that exist
primarily in the gas phase at reservoir conditions.
In order to predict the production rate from these
reservoirs, there is a need to review some of the
fundamental properties of hydrocarbon gases
This is particularly important (more so than in the
case of oil reservoirs) because certain physical
properties of gases and gas mixtures vary
significantly with pressure, temperature, and gas
composition.
Following is a brief outline of gas gravity, the real
gas law, gas compressibility factor (and the impact
of nonhydrocarbon gases), gas viscosity, and gas
isothermal compressibility.
64. Overview of the fundamental
properties of hydrocarbon gases
A. Gas Gravity
the
that
The
ratio of the molecular weight of a natural gas
of air, itself a mixture of gases.
molecular weight of air is usually taken as
to
equal to 28.97 (approximately 79% nitrogen
21% oxygen).
Therefore the gas gravity, symbolized by 𝛾g
and
is
Where, y𝑖 and 𝑀𝑊𝑖 are the mole fraction and molecular weight,
respectively, of an individual component
65. Overview of the fundamental
properties of hydrocarbon gases
Table : Molecular Weights and Critical Properties of Pure Components of Natural Gases
66. Overview of the fundamental
properties of hydrocarbon gases
B. Real Gas Law
general equation of state for gases
Where, Z is the compressibility factor, also called the
gas deviation factor in the petroleum literature. The
universal gas constant, R, is equal to 10.73 psi ft3 /lb-
mol-oR
67. Where, and are the
𝑃p
c
Tpc
pseudo-critical pressure and
temperature of the mixture,
respectively. The
temperature must be
absolute
(R or K), which is simply
°F+ 460°F or °C + 273
The gas deviation factor
for natural gases. (From
Standing and Katz,
1942.)
68. Overview of the fundamental
properties of hydrocarbon gases
C. Gas Viscosity
Many authors have presented gas viscosity
correlations. The Carr, Kobayashi, and
Burrows
(1954) correlation has been the most popular.
71. Gas Formation Volume Factor
For the same mass, nR can be
cancelled out and, after
substitution of Zsc =1, Tse= 60 +
460=520°R, and Psc = 14.7 psi,
Correlations and Useful Calculations for Natural
Refer to the given reading material
Gases
Overview of the fundamental
properties of hydrocarbon gases
72. Approximations of gas well
deliverability
from steady-state relationship developed from Darcy's law
for an incompressible fluid (oil) a
can be established by converting
MSCF/d
using an average value of the gas
natural gas relationship
the flow rate from
STB/d
to
formation volume
between Pe and Pwf it follows
Recall for oil
gas
73. Approximations of gas well
deliverability
for pseudo-steady state, a similar approximation can
be developed as
Steady and pseudo state assume Darcy flow in the reservoir
and are acceptable approximations in terms of properties
for
reasonably small gas flow rates
This equations are commonly presented as
For larger flow rates, where non-Darcy flow is evident in the
reservoir,
Fetkovich Eqn.
74. Approximations of gas well
deliverability
Non-darcy Flow
A more "exact" deliverability relationship for
stabilized gas flow was developed by Aronofsky and
Jenkins (1954) from the solution of the differential
equation for gas flow through porous media using
the Forchheimer (rather than the Darcy) equation for
flow.
This solution is
Darcy
75. Approximations of gas well deliverability
The equation can be written in form of
the constants a and b can be calculated from a "fourpoint test"
is graphed on Cartesian coordinates against
q.
The flowing bottomhole pressure, PwJ, is
calculated for four different stabilized flow rates. The
intercept of the straight line is a, and the slope is b. From b
and its definition, the
77. Approximations of gas well
deliverability
Transient Flow
For flow in a reservoir under transient
conditions can be approximated by the
combination of Darcy's law (rate equation) and
the continuity equation. In general,
Which in radial coordinates
reduces to
From the real gas law
Thus
79. Approximations of gas well
deliverability
Solving equation above in sequential steps (refer
Economides pg 74 ), Leads to analogous expression
for a natural gas deliverability
For real gas pseudo-pressure
as The real gas
pseudo-pressure
function
For low pressure
If pressure squared difference is used
80. Gas Well
Performance
Early estimates of gas well performance were
conducted by opening the well to the atmosphere
and then measuring the flow rate.
Such “open flow” practices were wasteful of gas,
sometimes dangerous to personnel and equipment,
and possibly damaging to the reservoir.
They also provided limited information to estimate
productive capacity under varying flow conditions.
The idea, however, did leave the industry with the
concept of absolute open flow (AOF).
AOF is a common indicator of well productivity and
refers to the maximum rate at which a well could
flow against a theoretical atmospheric backpressure
at
the reservoir.
81. Gas Well
Performance
The productivity of a gas well is determined with
deliverability testing.
Deliverability tests
provide information
that is used to
develop reservoir
rate-pressure
behavior for the well
and generate an
inflow performance
curve or gas-
backpressure curve.
Other are two basic relations useful in analyzing
82. Gas Well
Performance
and Schellhardt equation
Where, C is the flow coefficient
and n is the deliverability
exponent.
Note: solutions for gas well performance in terms
pressure-squared are appropriate only at low
reservoir pressures.
of
As a result, Rawlins and Schellhardt’s deliverability
equation can be rewritten in terms of pseudo
pressure
as
83. Gas Well
Performance
Where, C and n are determined in the same manner as for.
The values of n range from 0.5 to 1.0, depending on flow
characteristics. Flow characterized by Darcy’s equation will
have a flow exponent of 1.0, while flow that exhibits non-
Darcy flow behavior will have a flow exponent ranging from
0.5 to
1.0.
The Rawlins and Schellhardt deliverability equation is not
rigorous, but it is still widely used in deliverability
analysis and has provided reasonable results for high-
permeability gas wells over the years.
can rewritten to facilitate the development of the
inflow performance curve. In terms of pressure-
squared, the relationship is
84. Gas Well
Performance
Houpeurt Equation
developed a theoretical deliverability relationship
for stabilized flow with a Forchheimer velocity
term to account for non-Darcy flow effects in high-
velocity gas production.
The resulting relationship can be written in terms of
pressure-squared or pseudopressure as;
These Eqns are quadratic in terms of the flow rate, and the
solutions can be written for convenience as shown as
85. Gas Well
Performance
Jones, Blount, and Glaze suggested Houpeurt’s relationship
be rewritten as shown in equations below to allow the
analysis of well-test data to predict deliverability
A plot of the difference in pressures squared divided by the
flow rate or the difference in pseudopressure divided by the
flow rate vs. the flow rate yields a straight line on a coordinate
graph. The intercept of the plot is the laminar flow coefficient
a, while turbulence coefficient b is obtained from the slope of
the curve.
86. Gas Well
Performance
Once these two coefficients have been determined,
deliverability can be estimated from the following
relationships in terms
pseudopressure.
of pressure-squared or
After the coefficients of the deliverability equations have
been determined, the relationships can be used to estimate
production rates for various bottomhole flowing pressures
88. Examples
Data below
Given the reservoir
(i) For steady state condition, draw the bottomhole pressure vs
flow rate. Assume that s = 0 and re= 1490 ft (A 160 acres).
91. Solution
(ii) First calculate the time required for stabilized
flow from
Therefore, the stabilized
will be in effect after this
relationship implied by non Dacy Eqn.
time.
97. Solution (Cont…)
Thus
Following the same
procedure
for the other times the
transient IPR curves for 10 days, 3 months, and 1 year is
98. Discusion 1
The well produced gas from the Red Fork formation
at rates varying from 1.0 to 5.5 MMscf/D during a
four-point
below
multirate isochronal test as shown in Table
Tasks
1.
2.
3.
Calculate the backpressure slope 𝑛
Determine the IPR constant C and
calculate the absolute open flow (i.e., calculated
maximum rate)
99. Discussion
test
2
Given multirate
data for a well
producing as shown in
Table below
(i) Calculate the productivity
index J. based on the
lowest four rates. What is
the extrapolated maximum
oil rate. based on the
straight- line IPR
assumption?
Tubing Perfonnance Relation
100. Discussion 2
Plot the data on Cartesian coordinate paper. Use only
(ii)
point 10 (1260STB/O, 1267psia) to determine q0m•• with
the Vogel equation. Plot and tabulate the calculated
rates
give
n
corresponding to the bottomhole flowing pressure
in table below
using the
Repeat step 2 normalized backpressure
(iii)
equation with n = 1 instead of the Vogel equation.
Plot the data on log-log paper to establish if
(iv)
normalized Fetkovich equation is valid. What are the
constants C and n for this well?
Repeat step 2 using Fetkovich equation. with n = 0.7
(v)
instead of the Vogel equation. The value n = 0. 7 is taken
from the log-log plot in step 4. What is
AOF?
the calculated
Hint: All Cartesian coordinate plots should be on same graph
