part 14 deliverability testing

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  • 8/13/2019 Part 14 Deliverability Testing

    1/7

    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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    Deliverability Testing - WTA

    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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    Deliverability Testing - WTA

    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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    Deliverability Testing - WTA

    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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    Deliverability Testing - WTA

    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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    Deliverability Testing - WTA

    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