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W. G. Pritchard Lab Seminar: 4:00-5:00 PM, 320 Whitmore Laboratory

	            **Tuesday September 14, 2004**
	
Mathematical model for the productivity index of an oil well

Dinara Khalmanova

Department of Engineering Science & Mechanics
Penn State University
 

Abstract:

Motivated by the reservoir engineering concept of the productivity index of 
a producing oil well in an isolated reservoir, we analyze a time dependent 
functional, diffusive capacity, on the solutions to initial boundary value 
problems for a parabolic equation. Sufficient conditions providing for time 
independent diffusive capacity are given for different boundary conditions. 
The dependence of the constant diffusive capacity on the type of the 
boundary condition (Dirichlet, Neumann or third-type boundary condition) is
investigated using a known variational principle and confirmed numerically 
for various geometrical settings. An important comparison between two 
principal constant values of the diffusive capacity is made, leading to the 
establishment of criteria when the so-called pseudo-steady-state and 
boundary-dominated productivity indices of a well significantly differ from 
each other. The third type of boundary condition is shown to model the thin 
skin effect for the constant wellbore pressure production regime for a 
damaged well. The questions of stabilization and uniqueness of the time 
independent values  of the diffusive capacity are addressed. The derived 
formulas are used to numerically evaluate the productivity index of a well 
in a general three-dimensional reservoir for a variety of well 
configurations.

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