Appendix B

Approximate Solution of the Diffusivity Crossflow Problem in n-Layer Reservoirs (Chapter 3)

Suppose a well produces from all layers in an n-layer reservoir at a common wellbore pressure and a constant total rate, q, for t>0si1_e. Under the assumptions we made, the problem can be described as follows. The equations are

1ηipit1rrrpir+k˜i1kihipipi1+k˜ikihipipi+1=0,i=1,2,,n;k˜0=k˜n=0

si2_e  (B.1)

where ηi=kiϕiμctsi3_e and k˜ is the semipermeability ...

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