# Transient pressure behavior for a reservoir with continuous permeability distribution in the invaded zone

El-Khatib, Noaman A.F. (2009) Transient pressure behavior for a reservoir with continuous permeability distribution in the invaded zone. In: 16th Middle East Oil and Gas Show and Conference 2009, MEOS 2009, 15 March 2009 through 18 March 2009, Manama.

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## Abstract

A mathematical model is presented for a reservoir with a continuous permeability distribution in the invaded zone. An analytical solution of the system was obtained in Laplace space. Solutions in real time space for the pressure and pressure derivative are obtained by numerical inversion of the Laplace transform using Stehfest algorithm. Solutions were obtained for infinite reservoirs and for finite reservoirs with closed and constant pressure outer boundaries. The permeability in the invaded zone varies from a skin permeability K<sub>s</sub> at the wellbore to the original permeability K<sub>e</sub> at the end of the invaded zone R<sub>s</sub>. The effects of the permeability ratio, the depth of invasion, the reservoir size, and the wellbore storage were investigated. Results of this study show that for this permeability distribution, the permeability ratio has a profound effect on the pressure behavior while the depth of invasion plays an insignificant role. It also showed that the use of the average permeability of the invaded zone in the steady state skin equation gives almost identical results of the additional pressure drop due to formation damage at large times as those obtained from the exact solution. An approximate solution can be used for relatively high invasion depths (R<sub>SD</sub> &gt; 20) which shows that the additional pressure drop is independent of the invasion depth Copyright 2009. Society of Petroleum Engineers.

Item Type: Conference or Workshop Item (Paper) Analytical solutions; Approximate solution; Average permeability; Constant pressures; Exact solution; Formation damage; Infinite reservoirs; Laplace space; Numerical inversion; Permeability distribution; Permeability ratio; Pressure derivatives; Real time; Skin permeability; Steady state; Stehfest algorithm; Transient pressures; Well bore storage; Wellbore; Boring; Capillarity; Equations of state; Laplace transforms; Mathematical models; Oil field equipment; Oil well drilling; Oil wells; Pressure drop; Pressure effects; Skin; Petroleum reservoir engineering T Technology > TN Mining engineering. Metallurgy Departments > Geoscience & Petroleum Engineering 245 Prof Dr Noaman Abd El Fttah Mohamed El Khatib 01 Mar 2010 03:55 19 Jan 2017 08:25

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