Post on 01-Jan-2016
description
Analysis of Layered Gas Reservoir Performance Using a Quasi-Analytical Solution for
Rate and Pressure Behavior
I Nengah Suabdi
Department of Petroleum EngineeringTexas A & M University
9 May 2001
OutlineOutline
Introduction Objectives Assumptions Semi-analytical solutions New Type Curves for Layered Gas Reservoirs Field Application Conclusions
IntroductionIntroduction
Depletion Performance Analysis:
Can single-layer model performance detect layering..? , layer volume..?, or effect of drawdown..?
Is a single layer model satisfactory..?
Fetkovich, M.J. et.al (1990)– Using numerical simulations
Layered-gas reservoir depletion study:
k2
k1 Layer-1
Layer-2
No-Crossflow
Single layer model..?where : k1>k2 ..?
3000
2500
2000
1500
1000
500
p/z
, ps
ia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
k1/k2 = 1
pi/zi
Single Layer or Equivalent Single
Layer Model
1.To provide a quasi-analitycal solution for the depletion performance of a well produced at a common production pressure in a layered gas reservoir.
2. To utilize this quasi-analytical gas flow solution as a mechanism for charac-terizing the performance of layered gas reservoirs.
ObjectivesObjectives
The proposed analysis techniques will be used to estimate the following properties for a layered gas reservoir system:
The permeability ratio (2-layer case).Layer productivity index (Jg)The total original gas-in-place (G).The total flow capacity (kh product).The moveable reserves in each layer.
ObjectivesObjectives
Schematic diagram of layered reservoir
Layer-1
Layer- 2
Layer- 3
Layer- n
Assumptions:
h1
Physical ModelPhysical Model
h2k2
k1
No-CrossflowProduction is commingled
Two-layer (dry) gas reservoir No crossflow in the reservoir Homogeneous (except klayer)
Bounded radial system (pseudosteady-state flow)
Production is commingled at a constant BHP
Layer-1
Layer-2
Gas Diffusivity Equation in terms of :pressure (Gas Diffusivity Equation in terms of :pressure (pp), ), pseudopressure (pseudopressure (pppp), and time :), and time :
is not constant because µ and ct are functions of pressure
tp
z
pk
rp
zp
r r
r1 ct
0.0002637
t
p
k
r
p r
r
r1 ptp c
0.0002637
surepseudopres p
:
dp z(p) )p(
p
: .al et Hussainy,-Al
p
b
p
pp
p
where
2
Plot of the Viscosity-Compressibility FunctionPlot of the Viscosity-Compressibility Function(Ansah (Ansah et.alet.al))
Dt
tii p CC
Semi-Analytical SolutionsSemi-Analytical Solutions
We can then develop the dimensionless decline rate (qDd), pressure (pD), and cumulative production (GpD).
We consider the "first-order polynomial model" for correlating the curves. This result is given by Ansah, et al. as:
The fundamental form of stabilized flow equation is given by
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :
pwfp p - p J q gg
D
Dp
wDpt
tii
ti
gg dp
c c
c
J q
Scf/D/psiindex, typroductivi well Jg
c Sc Sc c fwcwggt
Gas MBE for moderate to low pressure reservoirs:
Semi-Analytical SolutionsSemi-Analytical Solutions
Where the dimensionless pressures are defined by:
or G
Gp -
zp
zp
i
i
1
GGp -
zp
zp
ii
1
z
p
p
zp
ii
D
Dimensionless Pressure (pD)
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :
0 p ; t
p wDDd
D
0.5 1
1
0
wD
Dd wDwDwD
Dd wDwDwDwDD p;
tp - exp p - - p tp - exp p - p
pp1111
zp
zp
ii
wfwf
wD p
z
p
zp i
ijD
j
ii
D p zp or
zp
p
Dimensionless Decline Rate (qDd)
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :
p ; t
q wD
n
1 j Ddj Dd 0
2 0.5 1
1
0exp
4
12
2
p;tp - p-p
tpexpp q wD
n
j
Ddj wDwDwD
)Ddj wD -wDDd
-11
(
layer of number total n index layer j
Dimensionless Cumulative Production (GpD)
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :
0
exp11
exp1 1
1
2
p; tp - p - -p
tp - - p - wD
DdjwDwDwD
DdjwDwDpD
n
j
G
p ; t
wDDdj
DdjpD
n
j0
0.5 1
0.5
1
tG
ppD Recovery Fractional
G G
G
In field units, the dimensionless "decline" time is defined as:
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :t = Time, dayskj = Permeability ( layer j), mdj = Porosity ( layer j), fractioncti = Total system compressibility, psia-1
re = Radius of the external boundary, ft
21
ln1 -21
1
- rr
rrrc
t t
wa
e2
wa
e2
wa tiiDdj
j
jk
0.00634
21
ln1 -21
1
- rr
rrr c
t k t
wa
e2
wa
e2
tiiDd
wa0.00634
Semi-Analytical SolutionsSemi-Analytical Solutions
Where :Cj = Stabilized flow coefficient layer-j, Mscf/D/psi2
kj = Permeability ( layer j ), mdj = Porosity ( layer j ), fractioncti = Total system compressibility, psi-1
pref = (pi + pwf)/2, psi
Gas rate production for each layer (qgj) in-term of (p/z)2 is defined as
zp
zp
C q2
wf
wf2
jg j
j
cp
z
rr
h k C
refpt
wa
e
jj
43
lnT1.4232
j
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Av
era
ge
Re
se
rvo
ir P
res
su
re/z
-fa
cto
r (p
bar
,j /
z j )
, ps
ia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
pwf/z = 271 psia (constant)
pi/zi = 2732 psia
k1/k2 = 1 k2
k1
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Avera
ge R
eserv
oir
Pre
ssu
re/z
-facto
r (
pb
ar,
j / z
j ),
psia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1
3
1/3
pwf/z = 271 psia (constant)
pi/zi = 2732 psia
k2
k1
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Avera
ge R
eserv
oir
Pre
ssu
re/z
-facto
r (
pb
ar,
j / z
j ),
psia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1
3
1x101
1/3
1x10-1
pwf/z = 271 psia (constant)
pi/zi = 2732 psia
k2
k1
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Avera
ge R
eserv
oir
Pre
ssu
re/z
-facto
r (
pb
ar,
j / z
j ),
psia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1
3
1x101
1x102
1/3
1x10-1
1x10-2
pwf/z = 271 psia (constant)
pi/zi = 2732 psia
k2
k1
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Ave
rag
e R
eser
voir
Pre
ssu
re/z
-fac
tor
(pb
ar,j
/ z j
),
psi
a
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
pwf/z = 271 psia (constant)
pi/zi = 2732 psia
k2
k1
Vol Layer-1
Vol Layer-2
pwD = 0.1 G
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Ave
rag
e R
eser
voir
Pre
ssu
re/z
-fac
tor
(p
bar
,j /
z j )
, p
sia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1 to 0.5)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf =(0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265-1253) psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
pwf/zwf = 271 psia (constant)
pi/zi = 2732 psia
pwf/zwf = 528 psia (constant)
k2
k1
G
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Ave
rag
e R
eser
voir
Pre
ssu
re/z
-fac
tor
(p
bar
,j /
z j )
, p
sia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1 to 0.5)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf =(0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265-1253) psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
pwf/zwf = 271 psia (constant)
pi/zi = 2732 psia
pwf/zwf = 528 psia (constant)
pwf/zwf = 811 psia (constant)
k2
k1
G
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Ave
rag
e R
eser
voir
Pre
ssu
re/z
-fac
tor
(pb
ar,j
/ z j
),
psi
a
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1 to 0.5)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf =(0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265-1253) psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
pwf/zwf = 271 psia (constant)
pi/zi = 2732 psia
pwf/zwf = 528 psia (constant)
pwf/zwf = 811 psia (constant)
pwf/zwf = 1073 psia (constant)
k2
k1
G
Pressure Depletion Decline Type Curve Pressure Depletion Decline Type Curve
3000
2500
2000
1500
1000
500
0
Ave
rag
e R
eser
voir
Pre
ssu
re/z
-fac
tor
(p
bar
,j /
z j )
, p
sia
25x106 20151050
Total Cumulative Gas Production (Gpt),MSCF
Legend: (Case: pwD = 0.1 to 0.5)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf =(0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265-1253) psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
pwf/zwf = 271 psia (constant)
pi/zi = 2732 psia
pwf/zwf = 528 psia (constant)
pwf/zwf = 811 psia (constant)
pwf/zwf = 1073 psia (constant)
pwf/zwf = 1346 psia (constant)
k2
k1
G
Depletion Decline Rate Type Curve Depletion Decline Rate Type Curve
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1)
pwD = 0.1 (pwf = 265 psia)
1x103
1x102
1x101
k1/k21
Layer-1 (m ore perm eable layer)
Layer-2 (less perm eable layer)
k2
k1
Rate Depletion Decline Type Curve Rate Depletion Decline Type Curve
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.2)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
1x103
1x102
1x101
k1/k21
Layer-1 (m ore perm eable layer)
Layer-2 (less perm eable layer)
k2
k1
Rate Depletion Decline Type Curve Rate Depletion Decline Type Curve
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.3)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
pwD = 0.3 (pwf = 775 psia)
1x103
1x102
1x101
k1/k21
Layer-1 (m ore perm eable layer)
Layer-2 (less perm eable layer)
k2
k1
Rate Depletion Decline Type Curve Rate Depletion Decline Type Curve
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2
zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.4)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
pwD = 0.3 (pwf = 775 psia)
pwD = 0.4 (pwf = 1010 psia)
1x103
1x102
1x101
k1/k21
Layer-1 (m ore perm eable layer)
Layer-2 (less perm eable layer)
k2
k1
Rate Depletion Decline Type Curve Rate Depletion Decline Type Curve
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.5)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
pwD = 0.3 (pwf = 775 psia)
pwD = 0.4 (pwf = 1010 psia)
pwD = 0.5 (pwf = 1253 psia)
1x103
1x102
1x101
k1/k21
Layer-1 (m ore perm eable layer)
Layer-2 (less perm eable layer)
k2
k1
GGpDpD vs. Dimensionless Decline Time ( vs. Dimensionless Decline Time (ttDdDd) )
10-3
10-2
10-1
100
101
102
Dim
ensi
on
less
Cu
mu
lati
ve G
as P
rod
uct
ion
(G
pD )
10-2
10-1
100
101
102
103
104
105
Dimensionless Decline Time (t Dd,t )
Legend: (Case: pwD = 0.1)
p/z (k1/k2) = 1
p/z (k1/k2) = 1x101
p/z (k1/k2) = 3x101
p/z (k1/k2) = 1x102
p/z (k1/k2) = 3x102
p/z (k1/k2) = 1x103
Properties: (Case: pwD = 0.1)
k1/k2 = varying from 1 to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2
zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1 1x10
1
3x101
1x102 3x10
2 1x10
3
Layer-1 (more permeable layer)
Layer-2 (less permeable layer)
k2
k1
Stabilized Gas Flow Coefficient (cStabilized Gas Flow Coefficient (cjj))
102
103
104
105
106
107
108
(p
bar,
j / z
j )2
- (
pw
f / z
wf )
2,
psia
2
101
102
103
104
105
106
107
108
109
qg,j , Mscf/D
Legend: (Case: pwD = 0.1)
( p/z )2 - ( pwf/zwf )
2 (k1/k2) = 1
( p/z )2 - ( pwf/zwf )
2 (k1/k2) = 3
( p/z )2 - ( pwf/zwf )
2 (k1/k2) = 1x10
1
( p/z )2 - ( pwf/ zwf )
2 (k1/k2) = 1x10
2
( p/z )2 - ( pwf/ zwf )
2 (k1/k2) (k1/k2) = 1x10
3
Case: (pwD = 0.1)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2
zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
Layer-2 Layer-1
k1/k2 = 1 3 1x101 1x10
2 1x10
3
k2
k1
p/z vs G vs GpD,t pD,t Function
1.0
0.8
0.6
0.4
0.2
0.0
p/z
fu
nc
= (
p/z
- p
wf/z
wf)
/ (p
i/zi -
pw
f /z w
f )
1.00.80.60.40.20.0 GpD ,t func = Gp,t /G
Case: (pwD = 0.1-0.5)
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978-0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3
Legend: (Case: pwD = 0.1-0.5)
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
Layer-1( more permeable layer )
Layer-2( less permeable layer )
Field Application (Field Application (p/zp/z vs. vs. GGptpt Curve Example)Curve Example)
Well Beavers 1-11 (Hugoton Field, Kansas, USA)400
350
300
250
200
150
100
50
0
p/z
, p
sia
30,00025,00020,00015,00010,0005,0000
Total Cumulative Gas Production (Gpt), MMSCF
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Field Application (Field Application (p/zp/z vs. vs. GGptpt Curve Example)Curve Example)
Well Beavers 1-11 (Hugoton Field, Kansas, USA)400
350
300
250
200
150
100
50
0
p/z
, p
sia
30,00025,00020,00015,00010,0005,0000
Total Cumulative Gas Production (Gpt), MMSCF
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Field Application (Field Application (p/zp/z vs. vs. GGptpt Curve Example)Curve Example)
Well Beavers 1-11 (Hugoton Field, Kansas, USA)400
350
300
250
200
150
100
50
0
p/z
, p
sia
30,00025,00020,00015,00010,0005,0000
Total Cumulative Gas Production (Gpt), MMSCF
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Field Application (Field Application (p/zp/z vs. vs. GGptpt Curve Example)Curve Example)
Well Beavers 1-11 (Hugoton Field, Kansas, USA)400
350
300
250
200
150
100
50
0
p/z
, p
sia
30,00025,00020,00015,00010,0005,0000
Total Cumulative Gas Production (Gpt), MMSCF
Well Beavers 1-11("parent well")
Kansas Hugoton Field
p/zp/z versus Gpt —Cartesian format. versus Gpt —Cartesian format.
Well Beavers 1-11 (Hugoton Field, Kansas, USA)400
350
300
250
200
150
100
50
0
p/z
, p
sia
30,00025,00020,00015,00010,0005,0000
Total Cumulative Gas Production (Gpt), MMSCF
Well Beavers 1-11("parent well")
Kansas Hugoton Field
k1/k2 = 68
k2/k1 = 1 x 68-1
pw f/zw f = 20
More Permeable Layer
Less Permeable Layer
G = 24.11 BSCF
qqgg versus prod time —semilog format. versus prod time —semilog format.
Well Beavers 1-11 (Hugoton Field, Kansas, USA)
10-1
100
101
102
103
104
Ga
s P
rod
uc
tio
n R
ate
, q
g, M
SC
F/D
70x103 605550454035302520151050
Total Production Time , Days
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Legend: Data Model
qqgg versus prod time —log-log format. versus prod time —log-log format.
Well Beavers 1-11 (Hugoton Field, Kansas, USA)
10-1
100
101
102
103
104
Ga
s P
rod
uc
tio
n R
ate
, q
g, M
SC
F/D
10-1
100
101
102
103
104
105
Total Production Time , Days
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Legend: Data Model
GGptpt versus prod time —semilog format.versus prod time —semilog format.
Well Beavers 1-11 (Hugoton Field, Kansas, USA)
10-1
100
101
102
103
104
105
To
tal C
um
ula
tiv
e G
as
Pro
du
cti
on
, G
p,t, M
MS
CF
20x103 1614121086420
Total Production Time , Days
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Legend: Data Model
GGptpt versus prod time —log-log format.versus prod time —log-log format.
Well Beavers 1-11 (Hugoton Field, Kansas, USA)
10-1
100
101
102
103
104
105
To
tal C
um
ula
tiv
e G
as
Pro
du
cti
on
, G
p,t, M
MS
CF
101
102
103
104
105
106
Total Production Time , Days
Well Beavers 1-11("parent well")
Kansas Hugoton Field
Legend: Data Model
Estimate properties of Well Beavers 1-11Estimate properties of Well Beavers 1-11
- Total original gas-in-place (G) = 24.11 BSCF
- The permeability ratio (k1/k2) = 68
- Total reservoir thickness, (htot) = 130 ft
- Average reservoir radius, (re) = 3,250 ft
- Average area each layer, (Aavg) = 761.76 Acres
- The total flow capacity, (kh product) = 482 md-ft
- The magnitude of wellbore F. Press (Pwf) = 20 psia
Field Application (Rate typeField Application (Rate type Curve Example)Curve Example)
Nelson well (Hugoton Field, Kansas (USA))
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2
zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.5)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
pwD = 0.3 (pwf = 775 psia)
pwD = 0.4 (pwf = 1010 psia)
pwD = 0.5 (pwf = 1253 psia)1x103
1x102
1x101
k1/k21
101
2
4
6
102
2
4
6
103
2
4
6
104
q, M
SC
F/D
10-2
10-1
100
101
102
103
104
t, Days
Legend: Nelson Well (Hugoton Field)
Matching parameters (Nelson Well)
1.0 q MPDd 1.0 t MPDd
MScf/D500 q MPg Days100 t
MP
10k
k
MP2
1
0.2 p MPwD
2
1
k
k = 10
Jg = 51. 553 Scf/D/psi G = 103.106 x 106 Scf or 0.103 Bscf
Field Application (Rate typeField Application (Rate type Curve Example)Curve Example)
Gas Well- B
10-4
10-3
10-2
10-1
100
101
q D
d
10-2
10-1
100
101
102
103
104
105
t Dd,t
Properties: (pwD = 0.1 - 0.5)
k1/k2 = varying from 1 to 1000
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = (0.978 - 0.931)
pi,1 = pi,2 = 2500 psia
pwf = (265 - 1253) psia (constant)
Legend: (Case : pwD = 0.1 - 0.5)
pwD = 0.1 (pwf = 265 psia)
pwD = 0.2 (pwf = 510 psia)
pwD = 0.3 (pwf = 775 psia)
pwD = 0.4 (pwf = 1010 psia)
pwD = 0.5 (pwf = 1253 psia)1x103
1x102
1x101
k1/k21
102
2
4
6
103
2
4
6
104
2
4
6
105
qg, M
SC
F/D
100
101
102
103
104
105
106
t , Days
Matching parameters:
1.0 qMPDd 1.0 tMPDd
MScf/D500 q MPg Days100 t
MP
10k
k
MP2
1
0.2 pMPwD
2
1
k
k = 10
Jg = 674.327 Scf/D/psi G = 4.495 x 109 Scf or 4.495 Bscf
1. We successfully demonstrated the use of a semi-analytical solution for a single-layer gas system for layered gas reservoir cases presented by Fetkovich, et.al (numerical simulations).
2. A two-layer type curve was developed for the analysis of production performance. The single- layer case can not be used to model the 2-layer case.
3. The sensitivity of individual layer properties was investigated, in particular — permeability ratio, layer volumes, and the effect of drawdown.
Conclusions
Analysis of Layered Gas ReservoirUsing Production Data
I Nengah Suabdi
Department of Petroleum EngineeringTexas A & M University
3 February 2001
Field Application (Example)Field Application (Example)
Curtis well (Hugoton Field, Kansas, USA)
1.0
0.8
0.6
0.4
0.2
0.0
p/z
fu
nct
ion
1.00.80.60.40.20.0
GpD,t function
Case: ( pwD = 0.1-0.5 )
k1/k2 = 1x10-3
to 1x103
h1 = h2, s1 = s2 = 0, 1 = 2
re,1 = re,2, cti,1 = cti,2 , i,1 = i,2zi,1 = zi,2 = 0.915, zwf = 0.978
pi,1 = pi,2 = 2500 psia
pwf = 265 psia (constant)
k1/k2 = 1
3
1x101
1x102
k1/k2 = 1x103
1/3
1x10-1
1x10-2
k1/k2 = 1x10-3 Legend:
p/z (k1/k2) = 1
p/z (k1/k2) = 3 or 1/3
p/z (k1/k2) = 1x101 or 1x10
-1
p/z (k1/k2) = 1x102 or 1x10
-2
p/z (k1/k2) = 1x103 or 1x10
-3
1.0
0.8
0.6
0.4
0.2
0.0
1.00.80.60.40.20.0
Legend: HUGOTON_FIELD Data Well Curtis1_A
Less Permeable Layer