Appendix E
where index s denotes side region, see fig. 1.
For the side region, the governing equations are:
By use of the solution procedure of Cinco-Ley and Samaniego [5] the following Laplace space solution was obtained:
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 be inverted to yield:
For small values of time which corresponds to large value of the Laplace variable s, the right hand term in eq. (E.9) may be neglected. Then
which may be inverted to yield:
The above equation corresponds to linear flow in the main region which is perpendicular to the well. This condition, which corresponds to the conventional linear flow period [1], implies that the flow in the side regions is negligible.
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