HW8 Solution

# HW8 Solution - Homework 8 PGE 323k Reservoir Engineering...

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Homework 8 PGE 323k: Reservoir Engineering: Primary Recovery 20 points Productivity of a Fractured Well Inflow into a fractured well more closely approximates linear rather than radial flow. 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. See figure below. 1. 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 hW 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 2. Give the following end-members: P(x) for steady state flow, and P(x,t) for semi- steady state flow. 3. Expressions for the average pressure, P , for steady state flow and, P (t) , for semi- steady state flow. 4. Definitions of productivity index (in terms of P ) for both steady state and semi-steady state flow. The PI definition should include a skin factor.

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