Title: ?????? Advanced Reservoir Engineering
1?????? Advanced Reservoir Engineering
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3Textbooks and references
 (A) Dake , L.P., Fundamentals of Reservoir
 Engineering, revised edition, Elsevier
Scientific  B.V., Amsterdam, the Netherlands, 2001.
 (B) Ahmed, T., and McKinney, P., Advanced
 Reservoir Engineering, Gulf Publishing
 Company, Houston, Texas, 2004
 (B) Craft, B.C., and Hawkins, M.F. , Revised
 by Terry, R.E. , Applied Petroleum
Reservoir  Engineering, Second edition., Prentice
Hall ,  Englewood Cliffs, New Jersey, 1991.
4Textbooks and references
 (C) Lee, J., Well Testing, SPE Textbook
 series, Society of Petroleum Engineers
of  AIME, Dallas, Texas, 2002.
 (D) ?????,???? (??? ????, Chapter 24 )
,????????????????,?????,???, 2004.  (E) Journal papers
5Advanced Reservoir Engineering by Ahmed, T., and
McKinney, P
 Well testing analysis
 Water influx
 Unconventional gas reservoir
 Performance of oil reservoir
 Predicting oil reservoir
 Introduction to oil fieldeconomics
6? ?
 Introduction to reservoir engineering
  Gas reservoir
  PVT analysis for oil
  Material balance applied to oil
 The flow equations of singlephase and twophase
flow of hydrocarbon in porous media   Darcys law and applications
  The basic differential equation in a
porous medium  Solutions to the flow equations of hydrocarbon in
porous media   Steady and semisteady states
  Unsteady state
 Pressure drawdown and buildup analysis for oil
and gas wells  Decline curve analysis
 Case study
7Part 1 Introduction to Reservoir Engineering
 The primary functions of a reservoir
 engineer
 the estimation of hydrocarbon in place
 the calculation of a recovery factor , and
 the attachment of a time scale to the recovery
 Note
 pressure/flow rate information ?
 parameters/future flow rate/future
pressure
8Outlines of Reservoir Engineering
 (1) Introduction
 Petrophysical properties ( Rock properties)
 Fluid properties (gas, water, crude properties)
 Calculations of hydrocarbon volumes
 Fluid pressure regimes
 (2) Gas reservoirs
 Calculating gas in place by the volumetric method
 Calculating gas recovery factor
 Material balance calculation (Depletion Water
drive)  Hydrocarbon phase behavior (gas condensate phase
behavior)  The gas equivalent of produced condensate and
water  (3) PVT analysis for oil
 Definition of the basic PVT parameters
 Determination of the basic PVT parameters in the
lab. And conversion for field operating
conditions.
9Outlines of Reservoir Engineering cont.
 (4) Material balance applied to oil
 reservoirs
 General form of the material balance equation for
a hydrocarbon reservoir (Undersaturated and
Saturated reservoir)  Reservoir drive mechanisms
 Solution gas drive
 Gas cap drive
 Natural water drive
 (5) Darcys law and applications
10Outlines of Reservoir Engineering cont.
 (6) The basic differential equation for radial
flow  in a porous medium
 Derivation of the basic radial flow equation
 Conditions of solution
 Linearization of radial flow equation
 (7) Well inflow equations for stabilized flow
 conditions
 Semi steady state solution
 Steady state solution
 Generalized form of inflow equation (for semi
steady state)
11Outlines of Reservoir Engineering cont.
 (8) The constant terminal rate solution of the
radial  diffusivity equation and its
application to oil well  testing
 Constant terminal rate solution
 General Transient flow
 Semi steady state flow
 Superposition theorem general theory of well
testing  The Matthews, Brons, Hazebroek pressure buildup
theory  Pressure buildup analysis techniques
 Multirate drawdown testing
 The effects of partial well completion
 Afterflow analysis
12Outlines of Reservoir Engineering cont.
 (9) Gas well testing
  Linearization and solution of the basic
differential equation  for the radial flow of a real gas
  The Russell, Goodrich, et al. Solution
technique   The AlHussainy, Ramey, Crawford solution
technique   Pressure squared and pseudo pressure solution
technique   NonDarcy flow determination of the
nondarcy  coefficient
  The constant terminal rate solution for the
flow of a real gas   General theory of gas well testing
  Multirate testing of gas well
  Pressure building testing of gas wells
  Pressure building analysis in solution gas
drive reservoirs
13Outlines of Reservoir Engineering cont.
 (10) Natural water influx
  Steady state model
  Unsteady state model
  The van Everdingen and Hurst edgewater
drive  model
  Bottom water drive model
  Pseudo steady state model (Fetkovich
model)   Predicting the amount of water influx
14Fluid Pressure Regimes
 The total pressure at any depth
 weight of the formation rock
 weight of fluids (oil, gas or water)

 1 psi/ft depth(ft)
15Fluid Pressure Regimes
16Pressure gradient for sandstone
 Pressure gradient for sandstone
17Overburden pressure
 Overburden pressure (OP)
 Fluid pressure (FP) Grain or matrix
pressure (GP)  OPFP GP
 In nonisolated reservoir
 PW (wellbore pressure) FP
 In isolated reservoir
 PW (wellbore pressure) FP GP
 where GPltGP
18Normal hydrostatic pressure
 In a perfectly normal case , the water pressure
at any depth  Assume (1) Continuity of water pressure to the
surface  (2) Salinity of water does not
vary with depth. 

psia 
psi/ft for pure water 


psi/ft for saline water
19Abnormal hydrostatic pressure ( No continuity of
water to the surface)
 psia
 Normal hydrostatic pressure
 c 0
 Abnormal (hydrostatic) pressure
 c gt 0 ? Overpressure (Abnormal high
pressure)  c lt 0 ? Underpressure (Abnormal low
pressure)
20Conditions causing abnormal fluid pressures
 Conditions causing abnormal fluid pressures in
enclosed water bearing sands include  Temperature change ?T 1? ? ?P 125 psi in a
sealed fresh water system  Geological changes uplifting surface erosion
 Osmosis between waters having different salinity,
the sealing shale acting as the semi permeable
membrane in this ionic exchange if the water
within the seal is more saline than the
surrounding water the osmosis will cause the
abnormal high pressure and vice versa.
21Are the water bearing sands abnormally pressured ?

 If so, what effect does this have on the extent
of any hydrocarbon accumulations?
22Hydrocarbon pressure regimes
 In hydrocarbon pressure regimes
 psi/ft
 psi/ft
 psi/ft
23Pressure Kick
 Assumes a normal hydrostatic pressure regime P?
0.45 D 15  In water zone
 at 5000 ft P?(at5000) 5000 0.45 15
2265 psia  at OWC (5500 ft) P?(at OWC) 5500 0.45 15
2490 psia
24Pressure Kick
 In oil zone Po 0.35 x D C
 at D 5500 ft , Po 2490 psi
 ? C 2490 0.35 5500 565 psia
 ? Po 0.35 D 565
 at GOC (5200 ft) Po (at GOC) 0.35 5200
565 2385 psia
25Pressure Kick
 In gas zone Pg 0.08 D 1969 (psia)
 at 5000 ft Pg 0.08 5000 1969 2369
psia
26Pressure Kick
 In gas zone Pg 0.08 D C
 At D 5500 ft, Pg P? 2490 psia
 2490 0.08 5500 C
 C 2050 psia
 ? Pg 0.08 D 2050
 At D 5000 ft
 Pg 2450 psia
27GWC error from pressure measurement
 Pressure 2500 psia Pressure
2450 psia  at D 5000 ft at
D 5000 ft  in gaswater reservoir in
gaswater reservoir  GWC ?
GWC ?  Sol. Sol.
 Pg 0.08 D C Pg 0.08 D
C  C 2500 0.08 5000 C 2450
0.08 5000  2100 psia 2050
psia  ? Pg 0.08 D 2100 ? Pg 0.08
D 2050  Water pressure P? 0.45 D 15 Water
pressure P? 0.45 D 15  At GWC Pg P? At GWC Pg
P?  0.08 D 2100 0.45 D 15 0.08 D
2050 0.45 D 15  D 5635 ft (GWC) D 5500 ft
(GWC)
28Results from Errors in GWC or GOC or OWC
 GWC or GOC or OWC location
 affecting
 volume of hydrocarbon OOIP
 affecting
 OOIP or OGIP
 affecting
 development plans
29Volumetric Gas Reservoir Engineering
 Gas is one of a few substances whose state, as
defined by pressure, volume and temperature (PVT)  One other such substance is saturated steam.

30The equation of state for an ideal gas

 (Field units used in the industry)
 p psia V ft3 T OR absolute
temperature  n lbm moles nthe number of lb moles,
one lb mole is  the molecular
weight of the gas expressed in pounds.  R the universal gas constant
 10.732 psia ft3 / (lbmmole0R)
 Eq (1.13) results form the combined efforts
of Boyle, Charles,  Avogadro and Gay Lussac.

31The equation of state for real gas
 The equation of Van der Waals (for one lb mole of
gas  where a and b are dependent on the nature of the
gas.  The principal drawback in attempting to use eq.
(1.14) to describe the behavior of real gases
encountered in reservoirs is that the maximum
pressure for which the equation is applicable is
still far below the normal range of reservoir
pressures
32The equation of state for real gas
 the BeattieBridgeman equation
 the BenedictWebbRubin equation
 the nonideal gas law
33Nonideal gas law
 Where z zfactor gas deviation factor
 supercompressibility factor

34Determination of zfactor
 There are three ways to determination zfactor
 (a)Experimental determination
 (b)The zfactor correlation of standing and
 katz
 (c)Direct calculation of zfactor
35(a) Experimental determination
 n mole s of gas
 p1atm Treservoir temperature gt VV0
 pVnzRT
 z1 for p1 atm
 gt14.7 V0nRT

 n mole of gas
 pgt1atm Treservoir temperature gt VV
 pVnzRT
 pVz(14.7 V0)
 By varying p and measuring V, the isothermal
z(p) function can be  readily by obtained.
36(b)The zfactor correlation of standing and katz
 Requirement
 Knowledge of gas composition or gas gravity
 Naturally occurring hydrocarbons primarily
 paraffin series CnH2n2
 Nonhydrocarbon impurities CO2, N2 and H2
 Gas reservoir lighter members of the paraffin
series, C1  and C2 gt 90 of the volume.
37The StandingKatz Correlation
 knowing Gas composition (ni)
 ? Critical pressure (Pci)
 Critical temperature (Tci) of each
component  ? ( Table (1.1) and P.16 ) ?
 ? Pseudo critical pressure (Ppc)
 Pseudo critical temperature (Tpc) for
the mixture 

 ? Pseudo reduced pressure (Ppr)
 Pseudo reduced temperature (Tpr)

 ? Fig.1.6 p.17 ? zfactor
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39(b)The zfactor correlation of standing and katz
 For the gas composition is not available and the
gas gravity (air1) is available.  The gas gravity (air1)
 ( )
 ? fig.1.7 , p18
 Pseudo critical pressure (Ppc)
 Pseudo critical temperature (Tpc)
40(b)The zfactor correlation of standing and katz
 ? Pseudo reduced pressure (Ppr)
 Pseudo reduced temperature (Tpr)
 ? Fig1.6 p.17
 ? zfactor
 The above procedure is valided only if impunity
(CO2,N2 and H2S) is less then 5 volume.
41(c) Direct calculation of zfactor
 The HallYarborough equations, developed using
the StarlingCarnahan equation of state, are  where Ppr the pseudo reduced pressure
 t1/Tpr Tprthe pseudo reduced
temperature  ythe reduced density which can be
obtained as the  solution of the equation as
followed  This nonlinear equation can be conveniently
solved for y using the simple NewtonRaphson
iterative technique.
42(c) Direct calculation of zfactor
 The steps involved in applying thus are
 make an initial estimate of yk, where k is an
iteration counter (which in this case is unity,
e.q. y10.001  substitute this value in Eq. (1.21)unless the
correct value of y has been initially selected,
Eq. (1.21) will have some small, nonzero value
Fk.  (3) using the first order Taylor series
expansion, a better  estimate of y can be determined as

 where
 (4) iterate, using eq. (1.21) and eq. (1.22),
until satisfactory  convergence is obtained(5) substitution
of the correct value of y in  eq.(1.20)will give the zfactor.
 (5) substitution of the correct value of y in
eq.(1.20)will give the zfactor.
43Application of the real gas equation of state
 Equation of state of a real gas
 This is a PVT relationship to relate surface to
reservoir volumes of hydrocarbon.  the gas expansion factor E,
 Real gas equation for n moles of gas at standard
conditions  ?
 Real gas equation for n moles of gas at reservoir
conditions  ?
 ?gt
 ?gt surface
volume/reservoir volume 
SCF/ft3 or STB/bbl
44Example
 Reservoir condition
 P2000psia T1800F(180459.6)639.60R
z0.865  ?gt

surface volume/reservoir  or
SCF/ft3 or STB/bbl 
45(2) Real gas density
 where nmoles Mmolecular weight)
 at any p and T
 For gas
 For air

46(2) Real gas density

 At standard conditions zair zgas 1
 in general
 (a) If is known, then
or ,  (b) If the gas composition is known, then
 where

47(3)Isothermal compressibility of a real gas
since
p.24, fig.1.9
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49Exercise 1.1  Problem
 Exercise1.1 Gas pressure gradient in the
 reservoir
 (1) Calculate the density of the gas, at
 standard conditions, whose
 composition is listed in the table 11.
 (2) what is the gas pressure gradient in
 the reservoir at 2000psia and
 1800F(z0.865)
50Exercise 1.1  solution 1
 (1) Molecular weight of the gas
 since
 or from
 At standard condition
51Exercise 1.1  solution 2
 (2) gas in the reservoir conditions



52Exercise 1.1  solution 3
53Gas Material Balance Recovery Factor
 Material balance

 Production OGIP (GIIP)  Unproduced gas
 (SC) (SC) (SC)
 Case 1no water influx (volumetric
 depletion reservoirs)
 Case 2water influx (water drive reservoirs)
54Volumetric depletion reservoirs  1
 No water influx into the reservoir from the
adjoining aquifer.  Gas initially in place (GIIP) or Initial gas in
place(IGIP)  G Original gas in place (OGIP)
 Standard
Condition Volume  Material Balance (at standard conditions)
 Production GIIP  Unproduced gas
 (SC) (SC) (SC)
 Where G/Ei GIIP in reservoir volume or
reservoir volume filled with gas HCPV
55Volumetric depletion reservoirs  2
56 In Eq.(1.33)
 HCPV?const. because
 1. the connate water in reservoir will expand
 2. the grain pressure increases as gas
 (or fluid) pressure declines
57 58GP
GP
pore vol.
GP
GP
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62p/z plot
 From Eq. (1.35) such as
 A straight line in
p/z v.s Gp plot means that the reservoir is  a depletion type
p/z
Abandon pressure pab
0
Gp
G
In
p/z
Yamx
Gp/GRF 1.0
0
63Water drive reservoirs
 If the reduction in reservoir pressure leads to
an expansion of adjacent aquifer water, and
consequent influx into the reservoir, the
material balance equation must then be modified
as  Production GIIP  Unproduced gas
 (SC) (SC) (SC)
 Gp G  (HCPVWe)E
 Or
 Gp G (G/EiWe)E
 where We the cumulative amount of water influx
resulting  from the pressure drop.
 Assumptions
 No difference between surface and reservoir
volumes of  water influx
 Neglect the effects of connate water expansion
and pore  volume reduction.
 No water production
64Water drive reservoirs
 With water production
 where WeEi /G represents the fraction of the
initial hydrocarbon pore volume flooded by water
and is,  therefore, always less then unity.
65Water drive reservoirs
in water flux reservoirs
Comparing
in depletion type reservoir
66Water drive reservoirs

 In eq.(1.41) the following two parameters to be
determined  G We
 History matching or aquifer fitting to find We
 Aquifer modelfor an aquifer whose dimensions are
of the same order of magnitude as the reservoir
itself.  Where Wthe total volume of water and depends
primary on the  geometry of the aquifer.
 ?Pthe pressure drop at the original
reservoir aquifer boundary
67Water drive reservoirs

 The material balance in such a case would be as
shown by plot A in fig1.11, which is not
significantly different from the depletion line  For case B C in fig 1.11(p.30) gtChapter 9
68Bruns et. al method
 This method is to estimate GIIP in a water drive
reservoir  From Eq. (1.40) such as
is plot as function of
69Bruns et. al method
 The result should be a straight line, provided
the correct aquifer model has been selected.  The ultimate gas recovery depends both on
 (1) the nature of the aquifer ,and
 (2) the abandonment pressure.
 The principal parameters in gas reservoir
engineering  (1) the GIIP
 (2) the aquifer model
 (3) abandonment pressure
 (4) the number of producing wells and their
mechanical define
is plot as function of
70Hydrocarbon phase behavior
71Hydrocarbon phase behavior
72Hydrocarbon phase behavior
CgtDgtE
Residual saturation (flow ceases) ?Liquid H.C
deposited in the reservoir ?Retrograde liquid
Condensate
EgtF
Revaporization of the liquid condensate
? NO! Because H.C remaining in the reservoir
increase ?Composition of gas reservoir changed
?Phase envelope shift SE direction Thus,
inhibiting revaporization.
73Equivalent gas volume
 The material balance equation of eq(1.35) such as
 Assume that a volume of gas in the reservoir was
produced as gas at the surface.  If, due to surface separation, small amounts of
liquid hydrocarbon are produced, the cumulative
liquid volume must be converted into an
equivalent gas volume and added to the cumulative
gas production to give the correct value of Gp
for use in the material balance equation.
74Equivalent gas volume
 If n lbm mole of liquid have been produced, of
molecular weight M, then the total mass of liquid
is  where ?0 oil gravity (water 1)
 ?w density of water (62.43 lbm/ft3)
75Condensate Reservoir
 The dry gas material balance equations can also
be applied to gas condensate reservoir, if the
single phase zfactor is replaced by the
,socalled ,two phase zfactor. This must be
experimentally determined in the laboratory by
performing a constant volume depletion
experiment.  Volume of gas G scf , as charge to a PVT cell
 PPiinitial pressure (above dew point)
 TTrreservoir temperature
76Condensate Reservoir
 p decrease ? by withdraw gas from the cell, and
measure gas Gp  Until the pressure has dropped to the dew point
 The latter experiment, for determining the single
phase zfactor, implicitly assumes that a volume
of reservoir fluids, below dew point pressure, is
produced in its entirety to the surface.
77Condensate Reservoir
 In the constant volume depletion experiment,
however, allowance is made for the fact that some
of the fluid remains behind in the reservoir as
liquid condensate, this volume being also
recorded as a function of pressure during the
experiment. As a result, if a gas condensate
sample is analyzed using both experimental
techniques, the two phase zfactor determined
during the constant volume depletion will be
lower than the single phase zfactor.  This is because the retrograde liquid condensate
is not included in the cumulative gas production
Gp in equation(1.46), which is therefore lower
than it would be assuming that all fluids are
produced to the surface, as in the single phase
experiment.
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 Pressure buildup
 Pressure drawdown
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