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Title: ?????? Advanced Reservoir Engineering


1
?????? Advanced Reservoir Engineering
  • ???? ???? (2007???)
  • ???? ???

2
??
  • ????????????,???????????????????????
  • ????????(??????) ,????????(????????) ?
  • ??????/????????/??????????????????

3
Textbooks 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.

4
Textbooks 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

5
Advanced 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 single-phase and two-phase
    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 semi-steady states
  • - Unsteady state
  • Pressure drawdown and buildup analysis for oil
    and gas wells
  • Decline curve analysis
  • Case study

7
Part 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

8
Outlines 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.

9
Outlines 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

10
Outlines 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)

11
Outlines 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
  • Multi-rate drawdown testing
  • The effects of partial well completion
  • After-flow analysis

12
Outlines 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 Al-Hussainy, Ramey, Crawford solution
    technique
  • - Pressure squared and pseudo pressure solution
    technique
  • - Non-Darcy flow determination of the
    non-darcy
  • coefficient
  • - The constant terminal rate solution for the
    flow of a real gas
  • - General theory of gas well testing
  • - Multi-rate testing of gas well
  • - Pressure building testing of gas wells
  • - Pressure building analysis in solution gas
    drive reservoirs

13
Outlines of Reservoir Engineering cont.
  • (10) Natural water influx
  • - Steady state model
  • - Unsteady state model
  • - The van Everdingen and Hurst edge-water
    drive
  • model
  • - Bottom water drive model
  • - Pseudo steady state model (Fetkovich
    model)
  • - Predicting the amount of water influx

14
Fluid 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)

15
Fluid Pressure Regimes
  • Density of sandstone

16
Pressure gradient for sandstone
  • Pressure gradient for sandstone

17
Overburden pressure
  • Overburden pressure (OP)
  • Fluid pressure (FP) Grain or matrix
    pressure (GP)
  • OPFP GP
  • In non-isolated reservoir
  • PW (wellbore pressure) FP
  • In isolated reservoir
  • PW (wellbore pressure) FP GP
  • where GPltGP

18
Normal 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

19
Abnormal 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)

20
Conditions 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.

21
Are the water bearing sands abnormally pressured ?
  • If so, what effect does this have on the extent
    of any hydrocarbon accumulations?

22
Hydrocarbon pressure regimes
  • In hydrocarbon pressure regimes
  • psi/ft
  • psi/ft
  • psi/ft

23
Pressure 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

24
Pressure 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

25
Pressure Kick
  • In gas zone Pg 0.08 D 1969 (psia)
  • at 5000 ft Pg 0.08 5000 1969 2369
    psia

26
Pressure 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

27
GWC error from pressure measurement
  • Pressure 2500 psia Pressure
    2450 psia
  • at D 5000 ft at
    D 5000 ft
  • in gas-water reservoir in
    gas-water 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)

28
Results 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

29
Volumetric 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.

30
The 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.

31
The 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

32
The equation of state for real gas
  • the Beattie-Bridgeman equation
  • the Benedict-Webb-Rubin equation
  • the non-ideal gas law

33
Non-ideal gas law
  • Where z z-factor gas deviation factor
  • supercompressibility factor

34
Determination of z-factor
  • There are three ways to determination z-factor
  • (a)Experimental determination
  • (b)The z-factor correlation of standing and
  • katz
  • (c)Direct calculation of z-factor

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 z-factor correlation of standing and katz
  • Requirement
  • Knowledge of gas composition or gas gravity
  • Naturally occurring hydrocarbons primarily
  • paraffin series CnH2n2
  • Non-hydrocarbon impurities CO2, N2 and H2
  • Gas reservoir lighter members of the paraffin
    series, C1
  • and C2 gt 90 of the volume.

37
The Standing-Katz 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 ? z-factor

38
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39
(b)The z-factor 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 z-factor correlation of standing and katz
  • ? Pseudo reduced pressure (Ppr)
  • Pseudo reduced temperature (Tpr)
  • ? Fig1.6 p.17
  • ? z-factor
  • The above procedure is valided only if impunity
    (CO2,N2 and H2S) is less then 5 volume.

41
(c) Direct calculation of z-factor
  • The Hall-Yarborough equations, developed using
    the Starling-Carnahan 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 non-linear equation can be conveniently
    solved for y using the simple Newton-Raphson
    iterative technique.

42
(c) Direct calculation of z-factor
  • 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, non-zero 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 z-factor.
  • (5) substitution of the correct value of y in
    eq.(1.20)will give the z-factor.

43
Application 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

44
Example
  • 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
48
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49
Exercise 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 1-1.
  • (2) what is the gas pressure gradient in
  • the reservoir at 2000psia and
  • 1800F(z0.865)

50
Exercise 1.1 -- solution -1
  • (1) Molecular weight of the gas
  • since
  • or from
  • At standard condition

51
Exercise 1.1 -- solution -2
  • (2) gas in the reservoir conditions

52
Exercise 1.1 -- solution -3

53
Gas 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)

54
Volumetric 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

55
Volumetric 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
  • where

58
GP
GP
pore vol.
GP
GP
59
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60
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61
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62
p/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
63
Water 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 - (HCPV-We)E
  • Or
  • Gp G- (G/Ei-We)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

64
Water 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.

65
Water drive reservoirs
  • since

in water flux reservoirs
Comparing
in depletion type reservoir
66
Water 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

67
Water 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

68
Bruns 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
69
Bruns 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
70
Hydrocarbon phase behavior
71
Hydrocarbon phase behavior
72
Hydrocarbon phase behavior
C---------gtD--------------gtE
Residual saturation (flow ceases) ?Liquid H.C
deposited in the reservoir ?Retrograde liquid
Condensate
E---------------gtF
Re-vaporization 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 re-vaporization.
73
Equivalent 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.

74
Equivalent 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)

75
Condensate Reservoir
  • The dry gas material balance equations can also
    be applied to gas condensate reservoir, if the
    single phase z-factor is replaced by the
    ,so-called ,two phase z-factor. 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

76
Condensate 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 z-factor, implicitly assumes that a volume
    of reservoir fluids, below dew point pressure, is
    produced in its entirety to the surface.

77
Condensate 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 z-factor determined
    during the constant volume depletion will be
    lower than the single phase z-factor.
  • 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.

78
????
  • ?????
  • ???
  • ?????
  • ????
  • ????
  • ????(?????,?????),
  • ??, ??????
  • ?????
  • ??????(??)
  • (?k?s?re?xf???????????)
  • Pressure buildup
  • Pressure drawdown
  • ????(water drive)
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