TY - JOUR
T1 - A new method for evaluating the productivity index of nonlinear flows
AU - Aulisa, Eugenio
AU - Ibragimov, Akif
AU - Walton, Jay R.
N1 - Funding Information:
We thank Mary Wheeler from UT Austin for her support of this project. We are indebted to Joanne Fredrich of Sandia National Labs and Zee Wang of ChevronTexaco, who contributed the rock physics data for diatomite. The authors gratefully acknowledge support for this work from the U.S. Department of Energy’s Natural Gas and Oil Technology Partnership Program (NGOTP). Oil industry partners for this project include BP, ChevronTexaco, ExxonMobil, Halliburton, and Schlum-berger. The second author is employed at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-ACO4-94AL85000.
PY - 2009/12
Y1 - 2009/12
N2 - This paper addresses the effects of nonlinearity of flows on the value of the productivity index (PI) of the well. Experimental data show that, during the dynamic process of hydrocarbon recovery, the PI stabilizes to some constant value, which, in general, is a nonlinear function of both the pressure drawdown and the production rate. Linear Darcy flow is well understood, and excellent approximate formulas are available for the PI in various well/reservoir geometries. To handle the more realistic nonlinear situation, the current practice is to solve the nonlinear problem multiple times for different values of production rate and then add ad-hoc corrective parameters in the linear formulas to reproduce the nonlinear nature of the flow. In this paper, we propose a rigorous framework to measure the PI of a well for nonlinear Forchheimer flows. Our approach, based on recent progress in the modeling of transient Forchheimer flows, uses both analytical and numerical techniques. It provides, for a wide class of reservoir geometries, an accurate relation between the PI for nonlinear Forchheimer flows and the PI for linear Darcy flows. The proposed method of building look-up tables and analytical formulas serves as an effective tool for fast PI evaluation in nonlinear cases.
AB - This paper addresses the effects of nonlinearity of flows on the value of the productivity index (PI) of the well. Experimental data show that, during the dynamic process of hydrocarbon recovery, the PI stabilizes to some constant value, which, in general, is a nonlinear function of both the pressure drawdown and the production rate. Linear Darcy flow is well understood, and excellent approximate formulas are available for the PI in various well/reservoir geometries. To handle the more realistic nonlinear situation, the current practice is to solve the nonlinear problem multiple times for different values of production rate and then add ad-hoc corrective parameters in the linear formulas to reproduce the nonlinear nature of the flow. In this paper, we propose a rigorous framework to measure the PI of a well for nonlinear Forchheimer flows. Our approach, based on recent progress in the modeling of transient Forchheimer flows, uses both analytical and numerical techniques. It provides, for a wide class of reservoir geometries, an accurate relation between the PI for nonlinear Forchheimer flows and the PI for linear Darcy flows. The proposed method of building look-up tables and analytical formulas serves as an effective tool for fast PI evaluation in nonlinear cases.
UR - http://www.scopus.com/inward/record.url?scp=70350702153&partnerID=8YFLogxK
U2 - 10.2118/108984-PA
DO - 10.2118/108984-PA
M3 - Article
AN - SCOPUS:70350702153
VL - 14
SP - 693
EP - 706
JO - SPE Journal
JF - SPE Journal
SN - 1086-055X
IS - 4
ER -