Pressure Analysis for Horizontal Wells

Abstract

This paper presents horizontal well test design and interpretation methods. New analytical solutions are developed, which can be easily handled by a desktop computer, to carry out design as well as interpretation using semi-log and log-log analysis. These analytical solutions point out a distinctive behavior of horizontal wells which is :- At early time, a circular radial flow in avertical plane perpendicular to the well.- At late time, a horizontal pseudo-radial flow. Each type of flow is associated with a semi-log straight line to which semi-log analysis has the adapted. The horizontal pseudo-radial flow takes into account a pseudo-skin depending on system geometry which is a priori defined and estimate Practical time criteria are proposed to determine Practical time criteria are proposed to determine the beginning and the end of each type of flow and provide a guide to semi-log analysis and well test design. We study the behavior of uniform flux or infinite conductivity horizontal wells, with wellbore storage and skin. The homogeneous reservoir is infinite or limited by impermeable or constant pressure boundaries. pressure boundaries. A method is also outlined to transform all our solutions for homogeneous reservoirs into corresponding solutions for double porosity reservoirs. 1 - Introduction The first horizontal producing wells yielded extremely positive results These results made it necessary to study flow around a horizontal well with a view to practical applications : test design and interpretation. The purpose of this study is to provide, with a horizontal well configuration a way :- to decide upon whether a test has to be made ornot : will the test help to obtain the requiredinformation ?- to optimize test time, if necessary : test mustbe long enough to be interpreted.- to interpret the test performed usingapplicable methods. The simplest and most significant analytical approach is first described in this paper. It relates to the transient behavior of a well with no wellbore storage C and no skin S, with a uniform flow (flow per unit length is the same everywhere in the well). Then the wellbore storage, the skin and the effect of the boundaries of the reservoir are taken into account, leading to a practical approach applicable to most real cases. The transposition of these solutions to infinite conductivity wells is described.

Advanced Techniques for Reservoir Simulation and Modeling of Nonconventional Wells

“…Early work along these lines included single horizontal wells (of infinite conductivity) aligned parallel to one side of a box shaped reservoir. Solution methods were successive integral transforms (Goode and Thambynayagam, 1987;Kuchuk et al, 1988) and the use of instantaneous Green's functions (Daviau et al, 1985;Clonts and Ramey, 1986;Ozkan et al, 1989;Babu and Odeh, 1989), resulting in infinite series expressions. More complex well geometries were considered later (Economides et al, 1996;Maizeret, 1996;Ouyang and Aziz, 2001) with the application of numerical integration.…”

Transient pressure behavior of Bingham non-Newtonian fluids for horizontal wells

“…Numerous authors have developed a variety of methods to solve for the pressure response in a reservoir penetrated by a horizontal well (Daviau et al, 1985;Clots and Ramey, 1986;Goode and Thambynayam, 1987;Ozkan et al, 1989;Odeh and Babu, 1990;Kuchuk et al, 1990;Issaka and Ambastha, 1992). Several models have been derived for the design and interpretation of horizontal well pressure tests.…”

“…Daviau et al (1985) used the product of the source functions for isotropic reservoirs with infinite, impermeable or constant pressure outer boundaries. Ozkan et al (1889) and Joshi (1991) present a comprehensive solution for infinite, anisotropic reservoirs with either uniform influx or infinite-conductivity horizontal well.…”

Calculating Pseudo-Steady-State Horizontal Oil Well Productivity in Rectangular Drainage Areas Using a Simple Method

“…Recently, Hagoort (2009) developed an analytical method for the estimation of the productivity of an infinite-conductivity horizontal well in a closed, rectangular box-shaped reservoir. Daviau et al (1985) used the product of the 45 source functions for isotropic reservoirs with infinite, impermeable, or constant pressure outer boundaries. Ozkan et al (1989) and Joshi (1991) presented a comprehensive solution for infinite, anisotropic reservoirs with either uniform influx or an infinite-conductivity horizontal well.…”

“…Ozkan et al (1989) and Joshi (1991) presented a comprehensive solution for infinite, anisotropic reservoirs with either uniform influx or an infinite-conductivity horizontal well. Several authors (Daviau et al, 1985;Odeh and Babu, 1990;Lu and Tiab, 2008;Zeng et al, 2009) have applied the source function 50 method to solve for the pressure in bounded reservoirs. Goode and Thambynayam (1987) considered the horizontal well-bore as a strip source, with a uniform flux distribution along the length.…”