Formation Evaluation By The Reservoir Limit Test
Authors: Jones Park J. 
Published: December 2007

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This paper is to be presented at the Rocky Mountain Joint Regional Meeting on May 24–25, 1962, in Billings, Montana, and is considered the property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Technology or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in Journal of Petroleum Technology or Society of Petroleum Engineers Journal is granted on request, providing proper credit is given that publication and the original presentation or the paper.

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and considered for publication in one of the two SPE magazines with the paper.

Applications or the reservoir limit test are made in this paper to the following; one producing well, the possible productive and proved acreage, the Y functions for transient and steady flow, the drawdown for a shut-in well, the permeability and radius of a skin and of a stimulated well, two producing wells, the distance from a producing well to a sealing fault, the pore volume and geometric shape or a fault block, the radius or an equivalent fictitious reservoir, the two principal equations for testing gas wells, and to the evaluation or the back-pressure equation [for gas wells completed in low-permeability reservoirs] from transient-flow field data.

Introduction

Consider a producing well completed in a homogeneous isotropic reservoir. A constant producing rate of BQ reservoir 3/D causes the pressure drawdown j= P - P at r ft from the well after t days of production. Darcy's law gives the resistivity to fluid flow in psi per unit flow rate as

M 0.1412 u D = = ..........(1) 1.127 (2 pi) hk hk

where h is the net pay thickness in feet and K, the effective Permeability in Darcy units. The resistivity D is one formation constant. Another is the diffusivity. In square feet per day, is

N = 6.328 K U E 0............................[2]

where h is the porosity. The effective coefficient of expansion E is the reservoir barrels of fluid available per psi drop on one barrel of pore space, cv E = EOSO + EgSg + EWSW + ..............[3] 0 in which + Sg + Sw - l

and Cv denotes the vertical component of rock compressibility. The coefficient of expansion for a reservoir oil EO may be estimated by Trube's method. For a reservoir gas, Eg is defined by

which can be evaluated with the aid of the paper by Rice. The formation constants D, E and can be evaluated from field data by methods considered below.

Kelvins line sink solution gives the drawdown j in terms of the dimensionless parameter u r2/4nt as*

BDQ j = W (u) ....................(4) 2

*For a variable producing rate, BQ = F [theta], the drawdown is given by

where theta is the time variable with limits zero and t.