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

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Appendix F

Case for Variable Bottom-Hole Rate (Chapter 8)

Using the dimensionless expressions from Eqs. (8.11) to (8.15), the problem described by Eqs. (8.4)–(8.10) can be written as

ω1pD1tDw1rDrDrDpD1rD+2k˜DpD1pD3=0ω3pD3tD+2k˜D2pD3pD1pD2=0ω2pD2tDw2rDrDrDpD2rD+2k˜DpD2pD3=0

si1_e  (F.1)

pDj0whentD0,j=1,2,3

si2_e  (F.2)

pDj0whenrD,j=1,2

si3_e  (F.3)

wjrDpDjrDrD=1=qDj,j=1,2

  (F.4)

pwDj=pDjsjrDpDjrDrD=1,j=1,2

  (F.5)

qD2=fpwD1

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