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Well Test Analysis for Multilayered Reservoirs with Formation Crossflow by Chengtai Gao, Hedong Sun

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Appendix E

Approximate Solution and Its Extension When Each Layer of a Two-Layer Reservoir Produces Independently (Chapter 7)

Suppose a homogeneous two-layer reservoir is penetrated by a well. Layer 1 and Layer 2 produce independently with constant dimensionless rates qD1 and qD2, respectively. The problem is expressed as follows:

1ηD1pD1tD1rDrDrDpD1rD+k˜D1w1pD1pD2=0

si1_e

and

1ηD2pD2tD1rDrDrDpD2rD+k˜D1w2pD2pD1=0

si2_e  (E.1)

wirDpDirDrD=1=qDi,i=1,2

  (E.2)

pDi0,i=1,2,whenrD

  (E.3)

and

pDi0,i=1,2,whentD0

  (E.4)

Using

pD=

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