Abstract A new simple method of establishing Inflow Performance Relationship for gas condensate wells is proposed. The proposed method uses transient pressure test data to estimate effective permeability as function of pressure and then uses it to convert production BHFP data into pseudopressure to establish well performance. Requirement of relative permeability as function of saturation thus has been completely eliminated. Effective permeability of either phase can be used to predict the production of second phase. A scheme has also been devised to estimate the effective permeability using well testing mathematical models available in literature. Also mathematical models of well deliverability loss due to condensate deposition when dew point pressure is reached, and deliverability gain due to condensate mobility when P is reached have been developed. Pseudopressure curves for both oil and gas phase have been developed for quick conversion of pressure data into pseudopressure. Relative permeability curves if available can also be used, however, the knowledge of saturation has to be known at all the stages of the depletion to be able to use them.
Trang 1Copyright 2002, Society of Petroleum Engineers Inc
This paper was prepared for presentation at the SPE Gas Technology Symposium held in
Calgary, Alberta, Canada, 30 April—2 May 2002
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Abstract
A new simple method of establishing Inflow Performance
Relationship for gas condensate wells is proposed The
proposed method uses transient pressure test data to estimate
effective permeability as function of pressure and then uses it
to convert production BHFP data into pseudopressure to
establish well performance Requirement of relative
permeability as function of saturation thus has been
completely eliminated Effective permeability of either phase
can be used to predict the production of second phase A
scheme has also been devised to estimate the effective
permeability using well testing mathematical models available
in literature
Also mathematical models of well deliverability loss due
to condensate deposition when dew point pressure is reached,
and deliverability gain due to condensate mobility when P* is
reached have been developed Pseudopressure curves for both
oil and gas phase have been developed for quick conversion of
pressure data into pseudopressure Relative permeability
curves if available can also be used, however, the knowledge
of saturation has to be known at all the stages of the depletion
to be able to use them
Gas condensate reservoirs are primarily gas reservoirs As
the pressure declines with depletion, reservoir conditions of
pressure may go below dew point and liquid begins to buildup
Such reservoirs may go under liquid buildup without showing
any trace of liquid production Sudden well deliverability loss
and very high skin factor estimates from pressure tests are
strong indicators of liquid buildup PVT characteristics like
phase diagram help identify the problem too As the critical
conditions are reached such reservoirs become two phase
in nature
Finally, a field example is analyzed to show the use of new method developed and a step-by-step procedure is used
to establish the well performance Small operators, Independents, will benefit from this method at the most, since data acquisition like relative permeability curves require the
laboratory experiments on cores, an expensive procedure
Introduction
Retrograde Gas-condensate systems have not been treated
so intensively as solution gas reservoirs have been Main reason is the phase behavior of light (C1-C10) hydrocarbons
in the reservoirs Retrograde gas-condensate reservoirs are primarily gas reservoirs A zone of liquid begins to form as the dew point pressure is reached The liquid keeps accumulating and does not flow until the critical liquid saturation is reached Pressure at this point in the reservoir is termed P* Interestingly, this liquid may re-vaporize as the pressure further crosses the lower line on two-phase envelope of phase diagram This behavior of re-vaporization of the oil phase is called the “Retrograde behavior.” Fig.2 through Fig.4 show the schematics of such phenomenon in vertical and horizontal well Deliverability loss in such conditions is mainly due to two reasons: a) Gas undergoing liquid phase and b) permeability impairment by the liquid Thus both have to be handled mathematically to predict the well performance with reasonable accuracy
Fig 1 Phase behavior of the condensate fluids
SPE 75503
Establishing Inflow Performance Relationship (IPR) for Gas Condensate Wells
Sarfraz A Jokhio and Djebbar Tiab/University of Oklahoma, SPE MEMBERS
Trang 2P e
P d
P *
P w f
S w c
Fig.2 Three regions in a gas condensate reservoir with
vertical well
P i
P d
P *
P wf
Fig.3 Three regions indicating two-phase flow around the
horizontal well, single-phase flow but with liquid buildup, and
the free gas flow in the farther region
P *
P wf
Fig.4 Fluid and pressure distribution around the fully
penetrating horizontal well
Literature Review
The quantitative two-phase flow in the reservoirs was first
researchers who indicated that the curvature in IPR curve of
solution gas drive reservoirs is due to the decreasing relative
permeability of the oil phase with depletion Based on
constant GOR at a given instant (not for whole life of the
psuedo-steady state two phase flow equation based on relative
permeabilities of each phase, and provided the industry an
equation that would revolutionize the performance prediction
Predicting production behavior of a well in gas-condensate reservoirs has been a topic of continuous research lately Simple correlation for productivity index estimations for oil wells (J = q/∆P) was being used until 1968 for solution
solution-gas reservoirs, which handles the two-phase flow of oil and gas Vogel using Weller’s concepts was able to generate family of IPR curve in terms of only two parameters
issues in predicting production performance of condensate
Gas-Condensate well deliverability using simulator and by keeping the track of saturation with pressure and relative permeability The most recent work on the gas condensate
Predicting well performance of gas-condensate wells
is challenging and a necessity at the same time Its use in optimizing production equipment including tubing, artificial lift systems, pumps, and surface facilities is of paramount importance
Mathematical Basis
Flow of real gases in porous media in the presence of more than one phase can be expressed using Darcy's law Under pseudo-steady state conditions and in field units total gas flow rate is expressed as follows:
gt
For vertical wells
+
−
=
a w
r r
h C
75 0 ln
00708 0
(3)
And for horizontal wells
+
− +
=
a H
w
S C
r A
b C
75 0 ln ln
00708 0 2 /
+
=
∆
r
wf
P
rg s
o o
ro
B
k k R B
k k mP
µ
permeability inside the integral Eq.5 can further be divided into three equations representing Region-1, Region-2 and the Region-3 as discussed by Fevang and
Region-1 (Inner wellbore region)
+
=
∆
*
g1
P
rg s
o o ro wf
dp B
k k R B
k k mP
µ
Region-2 (Region where liquid develops)
Trang 3∫
=
∆
d
P
rg dp B
k k
mP
Region-3 (Only gas region)
=
∆
R
d
P
wi
B S
k
k
mP
µ
1 )
(
It is not likely that three regions occur altogether at the same
time But it is most likely that any of the two exist at a given
moment in time
Producing Gas Oil Ratio
As the pressure drops below the dew point, producing
relationship exists between the producing gas oil ratio and the
pressure as shown in Fig.5 It dives as the P* approaches and
liquid becomes mobile However, it stabilizes as effective
liquid permeability stabilizes
o free g free o
S free o free g
oT
gT
P
R q q
R q q
q
q
R
, ,
, ,
+
+
=
+
+
=
=
o g g rg o
o ro
S o o ro g
g rg
OT
gT
P
R B
k B
k C
R B
k B
k C
q
q
R
µ µ
µ µ
On simplification
g g
o o ro
rg
s
B
B k
k
R
+
µ
µ
1 1
−
+
+
=
g g
o o ro
rg o g
g
o o ro
rg
s
P
B
B k
k R B
B k
k
R
R
µ
µ µ
µ
(12)
−
−
=
o o
g g P o
s P
ro
rg
B
B R R
R
R
k
k
µ
µ
−
−
=
=
o o
ro g g P o
s P
rg
g
B
kk B R
R
R R
kk
k
µ
µ
−
−
=
=
g g
rg o o s P
P o ro
o
B
kk B R
R
R R
kk
k
µ
µ 1
(15)
Modeling Pseudopressure Function
Substituting Eq.15 and 14 in Eq.6 and simplifying
results the gas phase pseudopressure function in terms of gas
and oil effective permeability, respectively
Gas Phase
( ) ( )
−
−
=
*
rg g
g1,
) 1 ( ) ( k.k
P
S o P g g wf
dp P R R
R R R B mP
−
− +
=
∆
P
s p s o o
ro o
g wf
dp R R
R R R B
k k mP
1
, 1
Oil Phase
9.0E +3 10.0E+3 11.0E+3 12.0E+3 13.0E+3 14.0E+3 15.0E+3 16.0E+3 17.0E+3
3800 4000
4200 4400
4600 4800
5000
Pressure [psia]
P*
Fig 5 Producing gas oil ratio as a function of pressure
(Eq.12)
1 10 100 1000 10000
Pressure [psi]
P* = 4300 psi
Fig.6 Ratio of gas relative permeability to oil relative permeability as a function of pressure (Eq.13)
8000 10000 12000 14000 16000 18000 20000
3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000
Pressure[psia]
Pd = 5000 psi
P*
Rp 1/Ro
Fig 7 Determination of P*, pressure at which liquid is mobile
in a multiphase system
Trang 4In order to model oil phase Eq.1 can be written as
qot = qofree + qg.Ro
ot
Since oil phase is mobile in only Region-1 therefore the oil
phase pseudopressure can be written as
+
=
∆
*
o1
P
P
o g g rg o
o
ro wf
dp R B
k k B
k
k
mP
µ
Substituting Eq 14 and Eq 15 in Eq 19 respectively result the
oil phase pseudopressure function in terms of oil and gas
effective permeability, respectively
−
−
=
∆
*
1
1
o
o1,
P
s o o o ro wf
dp R R
R R B
k k
mP
+
−
−
=
∆
*
,
1
1
P
rg o s p
p o g
o
wf
dp B
k k R R R
R R mP
Modeling Effective Permeability as a Function of Pressure:
Vertical Wells (Pressure Drawdown Test)
The effective oil and gas permeability during pressure
( )
∂
∂
−
=
=
t
P h
B q
kk
k
wf
o o free o ro
o
ln
6
( )wf SP
free g rg
g
t
mP h
q kk
k
∂
∂
−
=
ln
6
70 ,
Above equations are valid for a fully developed semi-log
straight line Both the equation can also be written as
Pressure Buildup
∆
∆ +
∂
∂
−
=
=
t
t t
P h
B q kk
k
ws
o o o ro
o
ln
6
70 µ
(24)
Similarly
SP ws
free g rg
g
t
t t
mP h
q kk
k
∆
∆ +
∂
∂
−
=
=
ln
6
To be more accurate following equation can be used
SP ti gi
t g ws
free g rg
g
c t
c t t d
dmP h
q kk
k
∆
∆ +
−
=
=
µ
µ ln
6
(26)
Several gas well tests were simulated in order to establish relationship between pressure and effective permeability for gas wells
0 0.02 0.04 0.06 0.08 0.1
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Pressure [psi]
Ko Kg
Fig 8 Effective permeability from pressure test data in a
multiphase system (Vertical Well)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
P ressure [psi]
Fig.9 Oil effective permeability as a function of pressure
(Vertical Well)
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
P ressure [psia]
Fig 10 Gas effective permeability as a function of pressure
during a pressure test
Trang 50.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
3010 3260 3510 3760 4010 4260 4510 4760
5010
Pressure [psia]
From Left To Right
qo [STB/D]
10 40 100 200
Fig 11 Effect of oil flow rate on effective oil permeability
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
3000 3500
4000 4500
5000
5500
Pressure [psi]
From Left
To Right
q g [Mscf/D]
50 100 300 750 1000
Fig 12 Effect of gas flow rate on effective gas permeability
Horizontal Wells
Earlty Time Radial Flow Regime
Equation of this flow regime during a pressure drawdown test is
+
−
=
−
m
w t
z y
z y w wf
i
s
r c
t k k k
k L
B q P
P
866 0 227 3
log 6
According to Darcy law the flow rate of any phase towards the wellbore is the function of the preesure But pressure is function of the distance from the wellore
w m
m
rm m
r
P B
rLkk x
∂
∂
µ
π 2 10 127
the permeabilty in horizontal and vertical direction
) ln(
2 2
2
t
P t
P t dz
dP z r
P r
∂
∂
−
∂
∂
−
=
=
∂
∂
(29) Substituting above equation in a Darcy law, one gets
∂
∂
−
) ln(
2
2 10 127
t
P B
Lkk x
m m
rm
π
Solving for Effective permeability, results
∂
∂
−
=
) ln(
6 70
t
P L
B q kk
wf
m m m rm
µ
For Oil phase
∂
∂
−
=
) ln(
6
t
P L
B q
kk
wf
o o free o ro
µ
And for gas phase
SP wf
free g rg
t
mP L
q kk
∂
∂
−
=
) ln(
6
70 ,
(33)
Similarly for pressure buildup
∂
∂
−
=
) ln(
6 70
H ws
o o o ro
t
P L
B q
(34)
SP H ws
free g rg
t
mP L
q kk
∂
∂
−
=
) ln(
6
possible from a transient well pressure data to develop the relative permeability curves provided absolute formation permeability is known Such curves like the absolute permeability (in single phase systems) obtained from the
Trang 6pressure transient data are the averaged values that capture
the effects of fluid and formation properties If the radial line
is masked by the wellbore effects or the linear flow regime, it
should be extrapolated Several algorithms are available in the
literature to calculate the log derivative of the pressure
Early Time Linear Flow Regime
This flow period is represented by
( z m)
z y w t y z w
wf
k k L
B q c
k
t h
L
qB P
φ
128
8
(36)
Taking the derivative of pressure with respect to square root
of time gives
t y z
L
qB
t
d
P
d
φ
µ
128
8
=
∆
(37)
y, results
1 128
8
)
(
−
=
t d
P d h L c B q P
t
o o o ey
φ
µ
(38) For Gas phase
( )
t SP z
g ey
c t d
mP d h L P
q P
k
φ µ
1 )
(
128 8
∆
Late Radial Flow Regime
This flow regime is represented by
(z m)
o
w t x x
y z
wf
i
s s
k z
k y
Lw
B
q
L c
t k k
k h
Bo q P
P
+
+
−
=
−
µ
φµ µ
2
141
023 2 log
6
162
2
Taking the time log derivative of this equation, and then
solving for effectve permeability, results
Oil Phase
( )
) ln(
6 70
t d
dP h
Bo q k
k
P
k
wf z
O x
y
exy
µ
=
Gas Phase
( )
SP
wf z
free g x
y rg
exy
t d
dmP h
q k
k
k
P
k
=
=
) ln(
6
70 ,
(42)
Late Time Linear Flow
This flow period during a drawdown pressure test is
represented by
(x z m)
z y w t y z
x
s s s k k L
B q c
k
t h
h
qB
φ
128
8
(43)
Thus effective permeability in y-direction from this period is
estimated as follows
Oil Phase
t O z
X
O O ey
c t d
P d h h
B q P
k
φ
µ
∆
)
t SP X
Z g
g ey
c t d
mP d h h P
q P
k
φ µ
1 )
(
128 8
∆
10 100 1000
Tim e[ hrs]
Fig.14 Simulated horizontal wellbore pressure response without wellbore storage and skin indicating early and late radial flow regimes
0 1 5
0 1 7
0 1 9
0 2 1
0 2 3
0 2 5
0 2 7
0 2 9
0 3 1
4 4 0 0
4 4 5 0
4 5 0 0
4 5 5 0
4 6 0 0
4 6 5 0
4 7 0 0
4 7 5 0
4 8 0 0
4 8 5 0
4 9 0 0
P re s s u re [p s i]
N o F lo w U p p e r a n d L o w e r
B o u n d a ry E ffe c ts
Fig.15 Profile of oil effective permability from horizontal well pressure data with upper and lower noflow boundary effects
0 1 5
0 1 7
0 1 9
0 2 1
0 2 3
0 2 5
0 2 7
0 2 9
0 3 1
4 3 0 0
4 4 0 0
4 5 0 0
4 6 0 0
4 7 0 0
4 8 0 0
4 9 0 0
P re s s u re [p s i]
Fig 16 Profile of oil effective permability from horizontal well pressure data without upper and lower noflow boundary effects
Trang 70.1
1
10
100
Tim e[ h rs]
Fig 17 An infinite acting (lateral direction) horizontal well
pressure response without wellbore storage and skin
factor.(Fully developed late radial flow regime)
0
0 5
1
1 5
2
2 5
3
3 5
4
4 5
5
4 9 8 0
4 9 8 2
4 9 8 4
4 9 8 6
4 9 8 8
4 9 9 0
4 9 9 2
4 9 9 4
4 9 9 6
4 9 9 8
5 0 0 0
P r e s s u r e [ p s i ]
Fig 18 Profile of oil effective permability from horizontal
well pressure data with upper and lower noflow
boundary effects
0 5
0 5 5
0 6
0 6 5
0 7
0 7 5
0 8
0 8 5
0 9
0 9 5
1
4 9 8 2
4 9 8 4
4 9 8 6
4 9 8 8
4 9 9 0
4 9 9 2
4 9 9 4
4 9 9 6
4 9 9 8
5 0 0 0
P r e s s u r e [ p s i ]
Fig.19 Gas effective permeability profile from pressure test in
horizontal wells
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
4300 4400 4500 4600 4700 4800 4900 5000
Pressure [psi]
From Left to Right
qo [STB/D]
10 40 100 200
Fig.20 Effect of condensate flow rate on effective permeability to oil (Horizontal Well Pd = 5000 psi)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
4300 4400 4500 4600 4700 4800 4900 5000 5100
P ressure [psi]
From Left to
R ight
qg [M scf/D ] 50 100 300 750 1000
Fig.21 effect of condensate flow rate on effective permeability to gas (Horizontal Well Pd = 5000 psi)
Effective Permeability With Measured Surface Rate
In phase changing multiphase environment such as gas condensate systems it is hard to measure the free rate at surface The total rate is the combination of the free oil and gas flow and dissolved gas in oil and vapor phase in the gas phase Thus a scheme is devised to get effective permeability using the surface measured rate from well test analysis instead
of free rate
Pressure transient response in terms of pseudopressure can be represented as
+
−
+
=
−
<
S
r c
P k t
h
q mP
e meas
g P
P
8686 0 2275 3
) ( log ) log(
6
wf
(45a) Gas phase pseudopressure for Region-1 has been define by Eq.16 and 17 With equation 16, Eq 45a can be expressed
as follows
Trang 8( ) ( )
+
−
+
=
−
−
∫
S
r c
P k t
h
q
dp P R R
R R R B
w t
e meas
g
P
S o P g
g
wf
8686 0 2275 3
) ( log ) log(
6
162
) 1
( )
(
k.k
2 ,
*
rg
φµ
µ
Re-arranging, yields
+
−
+
=
−
−
∫
∫
S
r c
P k t
h dp P q
dp P R R
B
R
R
R
w t e P
P
meas
g
P
S o
P
wf
wf
8686 0 2275 3
) ( log ) log(
k.k
6
162
)
(
) 1
(
2
*
rg
,
*
φµ
µ
(47)
Now gas phase effective permeability integral as a function
pressure can be estimated as
( )
∆
=
∫
) ln(
6 162 k.k
, 1 ,
*
rg
t d
mP d h
q dp
P
g g
meas g P
P wf
Gas phase effective permeability now is the derivative of the
above equation Similarly oil phase effective permeability
integral can be estimated as
( )
∆
=
∫
) ln(
6 162 k.k
, 1 ,
*
ro
t d
mP d h
q dp
P
o g
meas g P
P wf
(49)
Oil phase effective permeability then is the derivative of above
equation Using surface oil rate
( )
∆
=
∫
) ln(
6 162 k.k
, 1 ,
*
rg
t d
mP d h
q dp
P
g o
meas o P
P wf
(50)
( )
∆
=
∫
) ln(
6 162 k.k
, 1 ,
*
ro
t d
mP d h
q dp
P
o o
meas o P
P wf
(51)
Establishing IPR
Since pseudopressure has been developed, Rawlins
performance
g
o
Well Deliverability Gain Due to Condensate Production
in Region-1
Single-phase gas pseudopressure for gas reservoirs can be expressed as
=
∆
* sp g,
P
rg
wf
dp B
k k mP
And Eq.16 is the pseudopressure in gas condensate reservoirs
( ) ( )
−
−
=
* rg g
g1,
) 1 ( ) ( k.k
P
S o P g g wf
dp P R R
R R R B mP
Comparing the integral in Eq.16 with single-phase gas pseudopressure in Eq 52, the difference is the gas phase recovery due to liquid production Effective permeability in Eq.16 is lower than that in Eq.52 The recovery term is equal
to
−
−
*
*
) 1
(
P
s p
S o P
wf
p P
P
d P R R
R R R
(53)
Or
P
S O P sp
P P R R
R R R q
wf
2 ,
* ,
*
) 1
(
=
−
−
−
Term in Eq 53 is the production gain factor in the Region-1 due to liquid mobility This can be converted into vapor equivalent as follows
o
o eq
M
133,000
Well Deliverability Loss Due to Condensation
The recovery in the absence of liquid accumulation in Regio-1 would be
=
∆
P
dp B
k mP
µ sp
therefore, well efficiency in this case can be expressed as
100 [%]
,
2 , 2
q
q sP g
P gt p
And the damage factor then is
sP g
P gt sP g p w
q
q q
,
2 , , 2 ,
=
Trang 9( ) ( )
∫
∫
−
−
=
P
rg
P
S O P g
g p
w
wf
wf
dp B
kk C
dp P R R
R R R B C
µ
µ
η
) 1
( ) (
k.k
*
rg
2
−
=
*
) sp
2 rg 2
,
*
) 1
( )
(
k.k
P
S o P rg
p p
w
wf
dp P P P R R
R R R kk
Since effective permeability in single-phase gas reservoirs is
equal to absolute permeability, therefore, above equation can
be rewritten as
−
=
*
2 rg 2
,
*
) 1
( k.k
P
S o P P
p
w
wf
dp P P P R R
R R R k
Eq.61 shows that the delivery loss in Region-1 is only due to
relative permeability loss of the gas phase Partially the loss is
recovered as liquid production
Damage Factor in Region-2
In this region, only gas phase is mobile, therefore;
k.k
2 rg
2
P P
k DF
d
P
P
P d
−
−
(63) Equation 63 indicates that the delivery loss in Region-2 is the
result of permeability loss due to condensation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Qg
P*
Pwf
P
Production Gain in Region-1
Fig.22 Production trend in gas condensate systems
Example-1
This example is taken from reference 12 The 11, 500
ft deep well KAL-5 (Yugoslavia) has following properties
The initial conditions coincide with retrograde conditions In
Table 3 the mP values have been estimated using Eq 16 Once
the derivative of the pseudopressure is estimated, the effective
permeability integral is calculated using Eq.48
Procedure to calculate Table 2
** Calculate the critical temperature and pressure I used correlation for California gases using following equation Tpc = 298.6 SG + 181.89
+ 415.07 Table 1 Well, reservoir and fluid data is given in
following table
Gas SG 0.94 [MW =27.17] API 50 [Assumed]
1305.3(0.94) + 415.07 = 660.57 psi
At 2200 psi
Tr = T/Tpc = 354 + 460 /462.574 = 1.759 Ppr = P/Ppc = 2200/660.57 = 3.33
** Calculate the compressibility factor using Gopal equations given in Appendix A Choose proper equation Following equation fits the above critical conditions of temperature and pressure
Z =(3.33) [-0.0284(1.759) + 0.0625] + 0.4714(1.759) -0.001
= 0.8699
** Calculate the Bg using Eq.P-15
P
zT
B g =0.00504 22
) 460 354 )(
8699 0 ( 00504
=
g
** Calculate gas density using Eq.P-21
RT
P MW x
g
10 601846
=
ρ
Table 2 PVT Properties for example-1
P Ppr Z Bg Vis Rso Ro
200 0.3028 0.9818 0.0201 0.015 42.45 -7.59E-06
600 0.9083 0.9491 0.0065 0.016 150.7 4.83E-06
1000 1.5138 0.9186 0.0038 0.016 271.7 1.26E-05
1400 2.1194 0.8992 0.0026 0.017 400.6 1.90E-05
1800 2.7249 0.8797 0.002 0.018 535.3 2.48E-05
2200 3.3304 0.8701 0.0016 0.019 674.7 3.03E-05
2600 3.936 0.8777 0.0014 0.02 818.1 3.59E-05
3000 4.5415 0.8853 0.0012 0.022 965 4.16E-05
3400 5.147 0.8929 0.0011 0.023 1115 4.78E-05
3800 5.7526 0.8811 0.001 0.025 1267 5.45E-05
4200 6.3581 0.9149 0.0009 0.027 1423 6.20E-05
4600 6.9636 0.9487 0.0008 0.029 1580 7.03E-05
5000 7.5692 0.9825 0.0008 0.031 1739 7.98E-05
5400 8.1747 1.0163 0.0008 0.034 1901 9.05E-05
5800 8.7802 1.0501 0.0007 0.037 2064 1.03E-04
6200 9.3858 1.0839 0.0007 0.04 2229 1.16E-04
6750 10.218 1.1304 0.0007 0.045 2459 1.38E-04
is in psi The gas density is in gm/cc MW is the molecular
weight of the gas
Trang 10) 460 354 )(
73 10 (
00 , 22 ) 17 27 ( 10
601846
+
g
** Calculate the gas viscosity using Eq.P-16,
T M
T M X
+ +
+
=
19
209
) 02
0
4
9
1
) 354 ( ) 17 27 (
19
209
) 354 ))(
17 27 ( 02
0
4
9
1
+ +
+
=
M T
X2 =3.5+986+0.01
) 0.01(27.17 354
986
3.5
2
) 557 6
(
2
0
4
2
) 3 2 ( exp
1
4
) 0886 1 1096) (6.557)(0
exp ) 365
61
(
4
10−
=
g
** Calculate Rso using Eq.P-2
I used following equation for light oils
674.73 scf/STB
** Calculate vapor phase in gas phase, Ro [STB/MMscf],
using following equation
s s
s o
R R
R x
73 674
3815 42 ) 73 674 623 1 ) 73 674 ( 10 706
4
66
−
R o
** Producing gas oil ratio, Rp, is measured at surface during
the well test, 9,470 SCF/STB
Table 3 Pressure and pseudopressure data, with Eq.16
Time P mP1g,g ∆mP t.d∆mP/d(ln(t) Integral[Keg]
Pr = 6750 248.3555
0.167 1174.5 11.4 1.709663
0.333 1226.7 12.4369 2.746561
0.5 1303.6 14.04406 4.353722 3.84810177
1 1490.6 18.34433 8.653984 6.18010128
2 1751.6 25.25937 15.56903 16.4412385
4 2279.4 42.35781 32.66747 33.7942807
6 2759.4 60.66817 50.97782 49.9686048
8 3246.5 81.41431 71.72397 79.5896594
12 4210 127.6456 117.9553 117.600946
16 5162 174.5628 164.8725 133.490764
22 6161 221.9433 212.2529 92.4258768
28 6336.5 229.9477 220.2574 66.411804 Start of SLL
34 6406.1 233.0914 223.4011 20.7617509 0.002727533
42 6452.5 235.1772 225.4869 12.3720492 0.004577121
50 6487.3 236.7363 227.046 7.66378648 0.007389084
58 6507.6 237.6437 227.9533 7.0386556 0.008045338
68 6526.5 238.4871 228.7967 6.60753927 0.008570265
82 6556.9 239.8407 230.1504 4.96192743 0.011412573
97 6574.3 240.614 230.9236 5.41043564 0.010466507
112 6587.3 241.1909 231.5005 3.83858505 0.014752405
Procedure to calculate Table 3
** Having calculated table 2 convert the pressure data into pseudopressure using Eq.16 without the k.krg term
−
−
= ∫
* g1
) 1
( ) ( 1
P
S O P g
g wf
dp P R R
R R R B
mP
The integral can be evaluated numerically as follows
−
−
= ∫
* g1
) 1
( ) ( 1
P
S O P g
g wf
dp P R R
R R R B
mP
µ
( )
∫
=
* g1
P
P B
dp P X mP
) 0 200 ( 2 )
200 ( = X0+X200 −
mP
) 0 200 ( 2
079 3242 0 ) 200
) 200 600 ( 2
76 9882 079 3242 ) 200 ( ) 600
) 200 600 ( 2
76 9882 079 3242 9 324207 )
600
2949175.7 an so on
Procedure to calculate pseudopressure derivative group,
Using following equation
1 1
1 1
1 1
) ln(
) ln(
) ln(
) ln(
) ln(
) ln(
)
− +
+ +
−
−
∆ +
∆
∆
∆
∆ +
∆
∆
∆
=
∆
i i
i i
i i
i i
t t
mP d t
t
mP d
t d
mP d
Table 4 Integral evaluation data
P Bg Gas Vis Rso Ro X = R p (1R o R s )/
psi [bbl/scf] [Cp] [scf/bbl] [B/scf] Rp = 9,470
200 0.020138962 0.01538971 42.4507256 -7.58E-06 3242.079135
600 0.00648931 0.01583345 150.745544 4.83E-06 9882.761598
1000 0.003768687 0.0164451 271.735901 1.26E-05 16554.87436
1400 0.002634882 0.0171969 400.595154 1.90E-05 22868.63006
1800 0.00200499 0.0180827 535.308167 2.48E-05 28846.64708
2200 0.00162264 0.01910453 674.732422 3.03E-05 34022.62432
2600 0.00138497 0.0202691 818.123291 3.59E-05 37847.212
3000 0.001210678 0.02158655 964.953491 4.16E-05 40893.98613
3400 0.001077396 0.02306997 1114.82825 4.78E-05 43171.70082
3800 0.000951253 0.02473525 1267.43994 5.45E-05 45676.80014
4200 0.000893679 0.02660116 1422.54187 6.20E-05 45136.22568
4600 0.000846117 0.02868952 1579.93115 7.03E-05 43948.96444
5000 0.000806166 0.03102551 1739.43787 7.98E-05 42180.59821
5400 0.000772133 0.03363803 1900.91724 9.05E-05 39887.95688
5800 0.000742794 0.03656014 2064.24487 1.03E-04 37120.43519
6200 0.000717241 0.03982965 2229.31177 1.16E-04 33921.35589
6750 0.000687051 0.04497274 2458.94556 1.38E-04 28887.92587
At t = 68 hours and P = 6526.5 psi