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

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Appendix H

Solution of the Problem (Chapter 9)

Using the dimensionless expressions in Eqs. (9.28)(9.38) and the following approximate expressions at interfaces z=0 and z=h3,

p1zz=h3=p1p1z=h3h1/2andp2zz=0=p21z=0p2h2/2

si1_e  (H.1)

Eqs. (9.8)(9.21) becomes

ω1pD1tDw1ΔDpD1+2kvD1pD1pD1zD=1=0

si2_e  (H.2)

ω2pD2tDw2ΔDpD2+2kvD2pD2pD2zD=0=0

si3_e  (H.3)

pDj0whentD0,j=1,2

  (H.4)

pDj0whenrD,j=1,2

  (H.5)

wjrDpDjrDrD=1=qDj,j=1,2

  (H.6) ...

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