Unsteady-State Pressure Response Due to Production With a Slotted Liner Completion

Abstract

Summary The transient behaviour of production from a well with a slotted liner has been solved analytically by the source function method. The unsteady-state pressure response was examined as a function of slot frequency and slot pressure response was examined as a function of slot frequency and slot length, with a penetration ratio of 1:2. The results indicate that limited entry into the well causes skin effects. However, the effects become negligible when three or more slots are distributed around the circumference of the liner. For more than three slots, the well effectively behaves like a continuous-surface cylindrical source (or a line source well, depending on time and location). We conclude that there is likely to be little reduction in flow efficiency in an ideal slotted liner completion, unless some slots are clogged. Introduction A well is completed with a slotted liner when sand problems occur, mainly in unconsolidated formations. The slotted liner is a preperforated tubing. Usually, the slots are milled and machined in vertical rows, parallel to the axis of the pipe. The most common patterns of slot arrangement are staggered vertical, multiple staggered vertical, and horizontal (Fig. 1). Standard spacing of slots is 6 in. between the slots in each vertical row, while their length is usually 1 1/2 to 2 in., depending on their width. The common practice is to specify two rows for each inch of nominal pipe diameter. An analytical solution to the problem of transient pressure response due to production through a liner with staggered vertical rows of slots was found. The technique used was the source function method suggested by Gringarten and Ramey. It applies the use of a line source of finite length that in turn represents one of the systems of slots. The solution technique was verified by comparison with the continuous-surface cylinder solution in the case of a large number of vertical rows of slots. No storage or damaged zone effects were considered. Problem Description Problem Description Consider an infinite, homogeneous, and isotropic porous medium. The transient (unsteady-state) flow of a slightly compressible fluid is governed by the diffusivity equation ............................(1) where = is the diffusivity term. The solution to a particular problem is determined by the initial and boundary conditions. One of the problem is determined by the initial and boundary conditions. One of the most well-known solutions is Kelvin's instantaneous point source function, ............................(2) Eq. 2 represents the pressure drop created at Point M in a reservoir of infinite extent by an instantaneous point source of strength q at Point P, distance d from Point M (Fig. 2). JPT p. 1366