part 14 deliverability testing
TRANSCRIPT
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Deliverability Testing - WTA
Chapter 14
Deliverability Testing
It has long been used to predict the
capability of a gas well to deliver against
a specific flow bottomhole pressure.
,
originated from Rawlins and Schellhardt
(1936).
In my view, it is an application of
multirate superposition to infer reservoir
properti es and AOFP.
Rawlins-Schellhardt Equation
n
C 22 =
It is an emprical equation, not derivedfrom diffisuvit y equation.
wrsc ,,
To determine C and n, we conduc t flow after
flow (FAF) tests, isochronal, or modified
isoch ronal (MIC) tests.
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FAF Tests
t1 t2 t3t4
4321 tttt 1t
2t 3t 4t
FAF Test Analysis
( )n
jwfrjsc ppCq 2
,
2
, =
2
1
2
2log1 p
p 22p
( ) ( ) )log(1log1log ,2 ,2 Cn
qn
pp jscjwfr +=
=
1,
2,logsc
sc
q
qn
qsc,1
2
1p
qsc,2
( )n
x
xsc
p
qC
2
,
=
xp
qsc,x
Isochronal Tests
TT T T1
t 2t 3t
321 ttt
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Isochronal Test Analysis
( )
( )
n
jwfrjsc
pptCq 2
,
2
,
=
q1q2q3 q4
Iscohronal Test Analysis
( )( )n
jwfrjsc pptCq 2
,
2
, =
Isochronal Test Analysis
Then make a plot of C (C1/n or C1/(1-2n) ) vs. logt
To determine k, s ve D (see Tureyen et al., SPE 63095)
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MIC Tests
T T T T T TT
MIC Analysis
In terms of the real gas pseudo-pressure,
m(p), we have:
During transient radial flow:
Theoretical Deliverability Equations
( ) ( ) scscjwfi BqqtApmpmpm 2, )()( +==
During PSS Flow:
( ) ( ) scscjwf BqAqpmpmpm 2,)( +==
( ) ( )sc
sc
jwfBqA
q
pmpm+=
,or
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Deliverability Testing - WTA
Theoretical Deliverability Equations
In previous equatons, the coefficients A(t), B
ve A are given by:
( )
+
= s
rc
kt
kh
TtA
wit
2/1
21688ln
1422)(
+
= s
rC
A
kh
TA
wA
2/1
278.1
4ln
1422
Dkh
TB
1422=
Analysis of Iscohronal and MICWith Theoretical Equations
( ) ( )[ ]B
mpmBAAAOF
2
7.1442 ++=
In terms of the real gas pseudo-pressure, p2,
we have:
During transient radial flow:
Theoretical Deliverability Equations
During PSS Flow:
or
scscjwfi qBqtApp , ) +=
scscjwf qBqAppp 22 ,
22 +==
sc
sc
jwfqBA
q
pp
2
,
2
+=
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Theoretical Deliverability Equations
In previous equatons, the coefficients are
given by:
+
= sktTz
tA
2/1
2ln
1422)(
wit
+
= s
rC
A
kh
TzA
wA
2/1
278.1
4ln
1422
Dkh
TzB
=
1422
Reservoir Parameters From
Deliverability Testing
The flow and buildup portions, if the
pressure data are recorded, of the
deliverability are good sourc es to
estimate reservoir parameter and
boundaries using the pressure transient
methods discussed previously.
A MIC Test Example
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Analysis of Indiv idual Buildups Log-log diagnostic plots for four buildup portions of
the MIC test in terms of m(p) and its derivative
Why do we
separation in
m(p)
No separation
in derivative?
derivative