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Transcript of SPE-59760-MS
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Copyright 2000, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the 2000 SPE/CERI Gas Technology Symposiumheld in Calgary, Alberta Canada, 35 April 2000.
This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300
words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
AbstractA simple spreadsheet model has been developed to estimate
Original Gas In Place (OGIP), layer productivity and
recoverable reserves for wells with commingled production,
completed in multi-layered tight gas reservoirs.
Differentiating the productivity between multiple layers of
contrasting permeability is old technology. This model,
however, replicates the observed material balance trend while
also honouring total well production data by varying layer
properties. The P/Z trend of the higher permeability layersand lower permeability layers is mapped to envelope the
productivity index (PI) weighted P/Z curve that is used to
match historical data.
This technique has been made applicable to the multi-layered
reservoir environment by grouping the various kh terms, from
all high permeability layers, into one model layer and all
low permeability kh values into the tighter model layer.
Published literature1has already shown that the generation of
the layer P/Z curves is applicable for reservoirs with
permeability in the range of 0.1 to 10 md. The model has been
successfully applied to match and predict the productivity for
various wells in Cooper Basin fields, with permeability in thisrange, and P/Z plots that exhibit curvature. Case studies show
that any change in bottom hole pressure conditions (eg.
compression) or skin (eg. stimulation) can also be accounted
for in the model. Various simulation models have been
generated to confirm this techniques applicability to wells in
Australias Cooper Basin, and to establish the PI weighting
method.
IntroductionA common feature of wells completed in a multi-layered, tigh
gas field is that material balance calculations can vary
substantially from volumetric estimations of the OGIP
volume. The material balance (P/Z) plots are inherently
flawed in tight gas reservoirs, as build-up tests require
abnormally long shut-in times before pressure stabilization is
achieved. Without lengthy shut-in periods, required beforepressure equalization will occur between all layers, the
material balance calculations will under-estimate OGIP if
extrapolating a straight line from the initial pressure of the P/Z
plot. This problem becomes more prevalent in multi-layered
reservoirs with increasing permeability contrasts.
The spreadsheet used to determine OGIP in both the
relatively lower (tighter) layers and relatively higher
permeability layers is based on technology that has been
around for a long time. We have consolidated this technology
and added an additional feature, that of a PI weighted P/Z
curve
MethodologyCurvature in a material balance plot for a typical Cooper Basin
reservoir is attributed to water influx, differential depletion or
both. The PI weighted material balance technique is
applicable where differential depletion occurs. Other pre
requisites to this technique include:
Reservoir layers must be isolated, ensuring no crossflowwithin the reservoir (e.g. coal or shale barriers).
The well must not have been shut-in for extensiveperiods, allowing pressure equalization through the
wellbore.
The kh contrast between layers must not be significantlymore than one order of magnitude.
The first two points ensure conditions of differentia
depletion are met, however the third point is less intuitive and
will be explained with application of the PI weighting
function. Essentially, the match is difficult to achieve as the
permeability contrast approaches two orders of magnitude.
SPE 59760
Material Balance for Multi-layered, Commingled, Tight Gas ReservoirsFrank Kuppe and Shelin Chugh, SPE, Epic Consulting Services Ltd., and Paul Connell, SPE, Fekete Australia Pty. Ltd.
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2 FRANK KUPPE, SHELIN CHUGH, PAUL CONNELL SPE 59760
If differential depletion in the multi-layered reservoir is not
recognized, the classical P/Z curve may be applied in ways
that lead to erroneous OGIP volumes. Early time data will use
a straight-line extrapolation, under-estimating OGIP.
Alternatively, a line of best fit may be attempted to yield an
OGIP value that does not honor early or late data. Finally,
extrapolation of the last few data points usually over-estimates
OGIP.
Figure 1: Curved P/Z Plot
This phenomenon will occur where permeability usually
varies by at least an order of magnitude between layers. The
layers are separated by a flow barrier (i.e. shale or coal) and
therefore deplete independently in proportion to their
respective productivity indices.
The productivity index (PI), measured in units of flow per
unit of pressure drop (i.e. MMcfd/psi), is represented by
various forms of Darcys equation, two of which are presentedas in Eq. 1 and Eq. 2.
For Gas Flow
Considering rock properties and skin change relativelylittle over time, the pressure depletion in each layer becomes
the primary parameter controlling layer productivity.
During theearly-transient period,the fractional production
rate from each layer is approximately equal to the ratio of the
flow capacity of each layer to the total reservoir flow capacity.
That is, for two layers
and
As the reservoir behavior passes into the late-transien
period, the fractional production rate from each layer changes
At pseudo-steady state, the fractional production rate from
each layer is proportional to the ratio of the pore volume x
compressibility product of each layer to the total reservoir
pore volume.
Figure 2: High Permeability and Low Permeability Layers
To describe how the productivity of each layer varies over
time, we can use the two layer system depicted above to
represent the consolidated high permeability and low
permeability layers of a multi-layered tight gas reservoir
Assuming an initial reservoir pressure of 3500 psi in both
layers, the high kh layer will deplete more rapidly over time
to, say 2000 psi, while the lower kh layer has only depleted to
3000 psi. Although the kh is constant for each layer the
relative productivity of the lower kh layer is increasing as the
pressure (i.e. energy) in the high kh layer diminishes more
rapidly.
Fetkovich2 showed how the pressure drop (compared to
total production) varies with respect to permeability and
volume contrasts between layers. Pressures measured from
buildup tests track the pressure of the most permeable layer
Measured buildup pressures from a simulated two-layer mode
have been superimposed on Fetkovichs plot (Figure 3). To
generate typical measured buildup pressures the well in the
simulation model was shut-in for a period of 5 days, the
maximum observed shut-in period in the analyzed wells. Over
( )( )
( )1...............................................................ln SrrB
PPkhq
we
wf
+
=
( )3.......................................................12211
22
2
12
hkhk
hk
q
q
q
q
+==
( )4....................................................................2211
111
hkhk
hk
q
q
+=
( ) ( )[ ] ( )2...........................................................wfgg PmPmJq =
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SPE 59760 MATERIAL BALANCE FOR MULTI-LAYERED, COMMINGLED, TIGHT GAS RESERVOIRS 3
time, the measured pressure diverges from the already curved,
pressure trend of the high permeability layer.
Figure 3: Pressure Response in each Layer
To obtain a more accurate prediction of OGIP, the
challenge was to develop a Layered Material Balance
spreadsheet that matches actual data by averaging P/Z curves,
for representative high kh and low kh layers, with an
appropriate weighting factor. The weighting factor is
applied to respective layer productivity indices.
Buildup Response in Layered ReservoirsPressures measured from buildup analyses are inherently false
as the time required to reach equalization between
differentially depleted layers is much longer than the typical
shut-in period of a buildup test.
Pseudo-steady state flow generally begins much later in acommingled system than in the equivalent single-layer system
because of the complex variation in flow contribution of each
layer and the different times required for boundary effects to
be felt. Cobb, Ramey, and Miller1indicate that pseudo-steady
state flow begins at approximately
where k1/k2 2
for a single well in the center of a closed, circular, two-layer
reservoir with equal porosity, compressibility, viscosity, andthickness. Note that (tDA)pss 0.1 for a single-layer, closed,circular system. The time required to achieve pseudo-steady
state would therefore be some 200 times longer for a two layer
system, having a 10-fold permeability contrast, than for a
single layer system.
Figure 4 shows a typical dimensionless Horner plot for a
two-layer system and displays the well established
characteristics discussed by Lefkovits et al.4 Section EF is
initial semi-log straight line from which (kh)t can be
determined. Section FG reflects the leveling-off of the
buildup trace analogous to a single-layer system attaining
static pressure. This period is followed by a final rise in the
pressure buildup trace that reflects the pressurization of the
more depleted layer. Point H represents the average pressure
of the system. Note that the average pressure is based on the
pore volume-compressibility product of the two layers and isrealized only after crossflow (through the wellbore
diminishes between the tighter, less depleted layers, to the
more permeable, more depleted layers.
Figure 4: Generic Buildup Profile for a Layered Reservoir
This buildup response was readily replicated with a three-
layer simulation model (with Cartesian coordinates) with
typical parameters observed in a Cooper Basin well.
Model size = 4000 x 4000 x 50 kh1= 50 md-ft kh2= 5 md-ft An impermeable layer separates the two permeable
layers.
Porosity = 10%, Sw= 25% OGIP = 10.2 Bcf per layer Gas rate = 2 MMcfd
In this example some 8.5 Bcf was produced before the
final shut-in. The corresponding buildup curve replicates the
generic buildup profile for a layered reservoir. Note tha
approximately 100 years is required before the pressures
equalize between layers.
( ) ( ) ( )5.......................................................13.2 87.021 kkt pssDA
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4 FRANK KUPPE, SHELIN CHUGH, PAUL CONNELL SPE 59760
Figure 5: Modeled Cooper Basin Type Well
Note also that P*, the false pressure is usually a low
approximation of the equalized reservoir pressure. Prior to thefinal shut-in, the well was shut-in five times for nine 1 week
buildup periods, usually every two years, in the simulation
model. The pressure profiles of the two average layer
pressures form the pressure envelope. Buildup points
represent the extrapolated shut-in pressure, determined from
pressure transient analysis and confirm the close correlation to
the high permeability layer. The final buildup was for a
duration of 100 years to obtain an equalized P/Z point for the
material balance plot.
Figure 6: Layer Pressures and Equalized Pressure
The line drawn between "P/Z equalized" and the initial P/Z
point is the straight line material balance plot that extrapolates
to the true, total system, OGIP.
The difficulties in predicting OGIP in multi-layered
reservoirs are prevalent in both material balance and decline
analysis techniques. As already discussed, the buildup
pressures do not yield a straight line on the material balance
plot. The plot would under-estimate OGIP at early times and
over-estimate OGIP during the latter portion of the wellsproductive life. Similarly, with decline analysis, semi-log
extrapolation of early rate vs. cumulative production data will
under-estimate recoverable reserves. Extrapolation of late rate
vs. cumulative production data, with and empirically derived
hyperbolic "b" (decline) factor, may over-estimate recoverable
reserves.
A more powerful method of determining OGIP is attained
if we combine the two techniques. A unique, simultaneou
match of the P/Z and cumulative production history is
achieved by modifying the OGIP and productivity index for
each layer. The material balance and productivity for all, or
any single, layer(s) is included in the spreadsheet with the
following.
1. Material Balance:
2. Gas Flow:
for multiple layers
where
m(P), the gas pseudo-pressure, is used in place ofpressure to account for variations ofand Z with pressure.
In addition to these two relationships the cumulative gas
production is tracked with
( ) ( ) [ ]( ){ } (................./)()(1 2121 GGtGptGpZPZP initial ++=
( =
= n
j
giT tqtq1
8............................................................).........()(
( )11.......................................................................)(0
=t
gp dttqG
( ) ( ) ( 7.......................................................
= iwfiggi PmPmJq
( 9..........................458.2
ln2
11424
2
++= g
wA
g DqSrC
ATkhJ
( ) (1...................................................................20
dpZ
PPm
P
P
=
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SPE 59760 MATERIAL BALANCE FOR MULTI-LAYERED, COMMINGLED, TIGHT GAS RESERVOIRS 5
The "Weighted" P/Z CurveAs mentioned often in the literature, the recorded buildup
pressure of a well completed in a multi-layered reservoir
closely approximates the pressure in the high permeability
intervals. We attempted to duplicate measured pressure by
proportioning the pressure in each of the two representative
layers to generate a productivity index weighted P/Z curve.
The following plot shows four curves. The upper and lowercurves represent the "pressure envelope" or low permeability
and higher permeability layer pressures, respectively. The two
middle curves, used to attempt a match of recorded buildup
pressures, are the productivity index weighted P/Z curves.
Recall that productivity, in the gas equation, is based on the
difference in pseudo-pressures and not pressures. Pseudo-
pressure has units of P2/uZ. We found that the P
2 term was
too sensitive as a weighting function and therefore utilized a P
term.
When using the pressure difference, rather than pseudo-
pressure difference in the weighting function, we achieve the
match shown by the lower of the two middle curves. The gas
flow equation justifies the use of a P (pressure) term when
pressure gradients are low, as is the case when proportioning
with respect to pressure gradients in a tight gas reservoir.
Pressure gradients become even smaller ( P2!0) during
the latter portion of the wells productive life. The pressure
gradient for a highly compressible fluid, represented by
can therefore be reduced to
when pressure gradients are small.
For our purposes, use of the P term in the productivity
index facilitates the history match in the latter period of the
P/Z curve and does not compromise the history match during
the earlier portion of the P/Z curve (i.e. replicates match with
P2term).
Figure 7: Establishing the Weighting Function
Having developed a means of matching historical pressure
data, the matching procedure utilized in the spreadsheet isbriefly summarized as follows (note that the IDC technique
referred to below, is the Inverted Decline Curve method for
determining kh within the wells drainage area).
Matching Procedure:
Allocate stratified khs, from log analyses, into high kh& low kh layer.
Layers with kinsitu 1.0 md were considered lowpermeability layers.
Layers with kinsitu 1.0 md were considered highpermeability layers.
Normalize kh from logs to IDC derived kh.
Enter skin from IDC analysis. Enter bottom hole pressure history. Enter wells production history and recorded buildup
pressures.
Two plots used to achieve match in spreadsheet1) P/Z curves for each layer and total production
2) Cumulative production vs. time (for each layer and
total production).
Enter low initial approximation for OGIP2(low kh layervolume).
Progressively increase OGIP1, (high perm OGIP) untiweighted P/Z curve matches early P/Z data.
Tune kh1 and OGIP1 by matching slope on cumulative
production plot. Increase OGIP2 volume and iterate with kh2 until besmatch achieved on both P/Z and cumulative production
curve.
( )13.....................................................................2t
P
k
cP
=
( ) ( )12........................................ln 22 PP
Z
t
P
k
cP
+
=
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6 FRANK KUPPE, SHELIN CHUGH, PAUL CONNELL SPE 59760
Case Study #1Well #1 is a good candidate for this application. Production is
relatively isolated and therefore has not been drained by offset
wells. The well has not been shut-in for extended periods,
allowing pressure equalization between layers. The well also
exhibits at least a one-order magnitude contrast in
permeability between the higher permeability and lower
permeability layers. Finally, the various layers are alsoseparated by impermeable coal or shale intervals, ensuring
zero crossflow between layers. These conditions comprise the
primary pre-requisites to applying this technique
Table 1: Well #1 Parameters
Log derived kh intervals are arithmetically averaged for
the well and used as a guide for maintaining the relative
difference between layer productivity. Considering the
stratified nature of the wells in the Cooper Basin, an arithmetic
average is a good representation of the aggregate kh
contribution of multiple layers. However, the effective
permeability is usually lower to capture the heterogeneities
and complexities of the geology (ie. channels and crevassesplays) in the drainage area. The log derived permeability is
therefore used to maintain the ratio of high kh to low kh,
however is equated to a total kh value derived from other
means such as pressure transient analyses or advanced decline
analyses. For this study, the Inverted Decline Curve5method
was used to determine the effective permeability.
Using the aforementioned matching procedure, the
following match is achieved for the P/Z trend:
Figure 8: Matching the P/Z Curve for Well #1
The corresponding match on the cumulative production
trend is as follows:
Figure 9: Cumulative Production Match for Well #1
The match was achieved with an overall OGIP volume of
34 Bcf, equally distributed between the lower permeability (k
~ 0.2 md effective) and higher permeability (k ~ 5.0 md
effective) layers. If we assume that the low permeability
layer, the inherently less sensitive layer (due to the low gas
influx), could accommodate the additional 16 Bcf required to
match booked reserves, we achieve the match shown in Figure
10.
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SPE 59760 MATERIAL BALANCE FOR MULTI-LAYERED, COMMINGLED, TIGHT GAS RESERVOIRS 7
Figure 10: Attempting a Match with Excess OGIP
Note how additional OGIP volumes in the low
permeability layer begins to compromise the history match ofboth the P/Z and Cumulative Production plot during the latter
portion of the history. The tighter layer(s) has more impact
on the latter portion of the curves as this is when its relative PI
is increasing.
Case Study #2A match was achieved for well #2 with 35 Bcf where 15 Bcf
was modeled in the higher kh interval and 20 Bcf was
modeled in the lower kh interval. The log derived kh of 753
mdft, for the higher permeability interval, was reduced to 65
mdft to achieve a match. The corresponding log-derived and
match values in the low permeability layer was 60 mdft and 5
mdft. Total permeability was normalized to match the IDC-derived kh of 70 mdft while honoring the khhigh/khlowratio.
The corresponding match of the P/Z and cumulative
production trends are shown in Figure 11 and Figure 12,
respectively.
Figure 11: Matching the P/Z Curve for Well #2
Figure 12: Cumulative Production Match for Well #2
Recall that the weighted P/Z curve was developed using
simulated buildup periods of one week durations. Whenexamining the shut-in periods for Well #2 we found that four
of the pressure points were measured after a four day shut-in
while three were measured after only only one day. Of the
seven data points, the three in the middle fall slightly below
the matching curve due to the shorter shutin interval
Fortunately, when sufficient data is available, this technique
can be used as a diagnostic tool to help determine why some
points may deviate from a good history match, rather than
compromise the match.
DiscussionThere is some non-uniqueness to the history match
particularly when trying to establish OGIP in the tighterpermeability layer; i.e. 25% in the tight layer, for wells inexamined in this study. The resolution will of course depend
upon the absolute value of permeability in the tighter layer
As the permeability decreases, the maximum possible error
increases. Our approach, when matching OGIP, is to
gradually increase OGIP2(the gas volume in the tighter layer)
until an acceptable match is achieved. The match wil
therefore trend to the more conservative side of the "tight gas
OGIP" component.
The various strengths of the developed "Layered Materia
Balance" technique can be summarized as follows:
Good diagnostic tool to determine OGIP in multi-layeredreservoirs. Accounts for operational effects (i.e. compression
stimulation or reperforation) on production decline and
material balance curves.
Enables user to QC pressure data. Can be used to allocate production between commingled
layers (over time).
Can be used to forecast total or individual layerproduction.
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8 FRANK KUPPE, SHELIN CHUGH, PAUL CONNELL SPE 59760
The weaknesses include:
Layer skin factors affect the buildup response, whichaffects the Horner false pressure. The applied skin factor
represents average skin across all layers and does not
capture variations between each layer.
Not considering effects of water influx or hydrocarboncondensation below the dew point.
Cannot capture pressure equalization effects when wellis shut-in for extended time.
Productivity index weighting works well when kh ratiosdiffer by one order of magnitude. If the kh contrast is
higher, two layers may under-estimate the total OGIP of
the commingled system4.
Sensitive to quality of pressure data.
Although many of the wells in the Cooper Basin wells
exhibit differential depletion from multiple horizons (as
established from RFT testing), they may be exempt from
having this technique applied. Many of the wells have been
shut-in for extended periods (allowing inter-layer pressure
equalization) or have minimal data points. It is also difficultto discern curvature on a P/Z plot with only 2 or 3 data points.
However, considering that gas influx from tighter horizons
becomes more prevalent during the latter portion of the wells
history, additional testing is recommended and could increase
the number of qualifying wells by an order of magnitude.
In addition, to improve the quality of OGIP and reservoir
characterization, in any applicable field, the following
procedures are recommended.
Apply a consistent method for determining P* frombuildup tests.
Intersperse short buildup tests with longer ones toconfirm if and/or when the semi-log straight line isreached.
Conduct multi-rate tests to verify layering; i.e. varyinginflow will confirm varying layer PIs which, with
known khs, establishes levels of depletion.
Improve resolution on advanced decline analysestechniques (such as Inverted Decline Curves) by
applying daily telemetry data.
Record test conditions such as shut-in time precedingstatic gradient measurements.
Change production allocation ratios, between the variouscompleted formations, more frequently. This can be
done readily with the layer productivity determined fromapplication of this technique.
Centralize data storage (i.e. production data, pressurehistory, well activities, log analyses, etc.).
ConclusionsCurved P/Z plots, resulting from differential depletion in
multiple, isolated reservoir layers in the Australian Cooper
Basin, has been replicated with a unique matching technique.
Higher permeability and lower permeability layers, of a
multi-layered single phase (gas) reservoir, are consolidated
into a two layer model so that the depletion from these
representative layers could be matched with a productivity
index weighted P/Z curve. The technique can be successfully
applied where the permeability contrast between the higher
and tighter layers does not exceed an order of magnitude, there
is no crossflow occurring in the reservoir and the well has notbeen shut-in for extended periods (allowing crossflow in the
wellbore).
Simultaneous matches of the material balance and
production trend (rate or cumulative production vs. time) are
obtained to ensure a representative value of OGIP and kh is
generated for each of the two layers.
This technique substantiates the phenomenon o
productivity index weighted shut-in pressures and applies a
method to quantify this phenomenon. Any operationa
changes (i.e. stimulation, additional compression, re
perforations) will affect the productivity index of each layer
and can therefore also be captured by this material balance
technique. After achieving a history match, the developed
spreadsheet can be used to generate a total well forecast
Alternatively, forecasts can be obtained for each layer
simultaneously generating the varying production allocation
factors.
NomenclatureA= reservoir drainage area, ft
2
B= formation volume factor, RB/STB
c= compressibility, psia1
CA= shape factor
D= non-darcy flow coefficient, (Mscf/D)-1
G= original gas in place, MMscf
Gp= cumulative gas produced, MMscf
h= formation thickness, ft
Jg= real gas flow coeffieient, Mscf.cp/D/psi2
k= permeability, md
m(P)= real gas pseudo-pressure, psi2/cp
m(!)= real gas pseudo-pressure at average reservoirpressure, psi
2/cp
m(Pwf) = pseudo pressure at bottom hole flowing pressure,
psi2/cp
P= pressure, psia
Pwf= bottom hole flowing pressure, psia
P*= extrapolated pressure, psia!= material-balance average reservoir pressure, psia
PI= productivity index, Mscf/d/psi
q= production rate, STB/D
qg= gas production rate, Mscf/D
qt= total flow rate in a commingled system, Mscf/D
re= external boundary radius, ft
rw= wellbore radius, ft
S= skin factor
Sw= Water saturation
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SPE 59760 MATERIAL BALANCE FOR MULTI-LAYERED, COMMINGLED, TIGHT GAS RESERVOIRS 9
t= time, days
tDA= dimensionless time based on drainage area
T= reservoir temperature,oR
Z= gas deviation factor
= porosity
= viscosity, cp
P= pressure gradient
Subscriptsg= gas
i= initial
pss= pseudo-steady state
1= layer 1, high kh layer
2= layer 2, low kh layer
AcknowledgmentsWe thank Joost Herweijer for valuable discussions on
upscaling techniques and reservoir heterogeneities. We also
thank the South Australian Cooper Basin Joint Venture forgiving us permission to publish this paper. This work was
done during the Integrated Reservoir Study of ten of their
Cooper Basin tight gas reservoirs.
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Reservoirs Without Crossflow; SPEFE, September 1990)
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Boundary Conditions Using Derivaties, SPE 22681.
11. Russell D.G., Prats M.: Performance of LayeredReservoirs with Crossflow-Single Compressible Fluid
Case, SPE Journal (March 1962) 53.
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