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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.

    References1. Ahmed H. el-Banbi, and Robert A. Wattenbarger:

    Analysis of Commingled Tight Gas Reservoirs, paper

    SPE 36736 (October 1996).

    2. Fetkovich, M.J., Bradley, M.D., Works, A.M. andThrasher, T.S.: Depletion Performance of Layered

    Reservoirs Without Crossflow; SPEFE, September 1990)

    310-18.

    3. Cobb, W.M., Ramey, H.J. and Miller, F.G.: WelltestAnalysis for Wells Producing Commingled Zones, SPE

    3014 (January 1972).

    4. Lefkovits, H.C., Hazebroek, P. and Matthews, C.S.: AStudy of the Behavior of Bounded Reservoirs Composed

    of Stratified Layers, SPE 1329 (March 1961).

    5. Reitman, N.D.: An Integrated Method for OptimizingHydraulic Fracture Design for Tight Gas Wells, SPE

    39930.

    6. Mattar, L.: Theory and Practice of the Testing of GasWells, ERCB, Third Edition (1975).

    7. Kuchuk, F.J. and Wilkinson, D.J.: Transient Pressure

    Behavior of Commingled Reservoirs, SPEFE (March1991) 111.

    8. Doherty, H.L. and Earlougher, R.C.: Advances inWelltest Analysis, Monograph Volume 5.

    9. Lee, W.J. and Hopkins C.W.: Characterization of TightReservoirs, SPE 29091.

    10. Gao C., Raghavan R. and Lee W.J.: Responses ofCommingled Systems with Mixed Inner and Outer

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