HW8 Key (323K)

# HW8 Key (323K) - Homework #8 Key PGE323K 20 points 1....

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Homework #8 Key PGE323K 20 points 1. Inflow into a fractured well more closely approximates linear flow rather than radial. The objective of this exercise is to gain further understanding about stabilized flow into a hydraulically fractured well through development of the appropriate solutions in Cartesian coordinates. a. Solve the diffusivity equation for stabilized flow in Cartesian coordinates. The constant terminal rate condition for this coordinate system is P x x = 0 = q μ o k o A where x = 0 is the location of the fracture face; the external boundary in this case is at x = L. The drainage area is A = LW. Derive additionally the following Start with the diffusivity equation in Cartesian coordinates and its corresponding boundary conditions for stabilized flow. 1 α P t = 2 P x 2 (1) P x x = 0 = q μ o Ak o o (2a) P x x = L = f q μ o Ak o o (2b)q where f  0 is semi-steady state and f  1 is steady state flow. Start by writing Eq. (1) as two ordinary differential equations

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## This note was uploaded on 02/13/2012 for the course PGE 323K taught by Professor Lake during the Spring '08 term at University of Texas at Austin.

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HW8 Key (323K) - Homework #8 Key PGE323K 20 points 1....

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