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APPENDIX C

Substitution of the dimensionless parameters into eq. (B.1) to eq.(B.8) yield for the main region:

and for the upper region: 

The above equations correspond to the governing equations for a finite conductivity fracture. The solution is well known, Cinco-Ley and Samaniego [5]. By use of the same technique we obtain the following Laplace space solution:

for the wellbore pressure.

For small values of s, which correspond large values of time, the left hand term within the parenthesis may be neglected in comparison with the right hand term. Then 

which may easily be inverted to yield:

For small values of time, which corresponds to large s, eq. (C.9) will simplify to:

Inversion yields:

which corresponds to linear flow. This condition implies that flow from above is negligible.

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