Interference Between Constant-Rate and Constant-Pressure Reservoirs Sharing a Common Aquifer

A practical pressure transient analysis method is presented for interpreting interference between two oil fields or an oil field and a gas field sharing a common aquifer. One oil field is approximated as a constant-rate line source. The other interfering field is represented by a finite-radius circular source producing at constant rate or constant pressure. pressure. A rigorous application of the superposition principle is discussed, making use of a new model where a constant rate line source produces exterior to a circular boundary. Both constant pressure and impermeable internal boundaries are considered. Dimensionless pressure drop curves for both boundary conditions are presented. For the case of a line source producing near a constant-pressure internal boundary, producing near a constant-pressure internal boundary, dimensionless curves for the instantaneous rate and the cumulative injection from this internal boundary are given. These curves may be used to forecast the actual injection/production rate and the cumulative injection/ production at the interfering reservoir as a function of time. production at the interfering reservoir as a function of time. Introduction Pressure interference between hydrocarbon reservoirs Pressure interference between hydrocarbon reservoirs situated in a common aquifer is important in understanding and forecasting the behavior of these reservoirs under exploitation. The fluid driving energy stored in a reservoir is a function of its average pressure. Production in one reservoir causes a pressure drawdown at another reservoir and, hence, changes its deliverability and economic value over a long period of time. Bell and Shepherd I considered the pressure behavior of the Woodbine sand in east Texas, which contains several reservoirs. They presented a pressure loss map that shows that production from the east Texas field affected an extensive area of the Woodbine aquifer. Moore and Truby, using an electric analyzer, described the pressure behavior of five producing fields sharing a pressure behavior of five producing fields sharing a common aquifer. They presented pressure histories for each of the five reservoirs. Every pressure history consisted of five pressure drops. The first pressure drop at a reservoir was caused by its own production, to which four interfering pressure drops caused by the neighboring reservoirs were added. The interfering effect of the TXL field on the average pressure at Wheeler field was larger than the drawdown at Wheeler field caused by its own production. production. In describing interference between two reservoirs sharing a common infinite aquifer, some assumptions as to the shape of these reservoirs must be made. Theis presented the solution for a constant-rate line source in presented the solution for a constant-rate line source in an infinite system. Staliman modified this solution for a semi-infinite system bounded by a linear boundary. If the two reservoirs may be approximated by two line sources, their pressure effects may be superposed in space to yield the pressure interference between them. super-position in space is used to assemble the effects of several producing/injecting reservoirs in the same aquifer. producing/injecting reservoirs in the same aquifer. Carslaw and Jaeger presented solutions for a single finite-radius source in an infinite medium producing at either constant rate or constant pressure. Van Everdingen and Hurst applied those solutions to flow in reservoirs. Mortada used those solutions to describe interference between oil fields and, using superposition in space, calculated the pressure response of a reservoir to its own production and to production from an interfering production and to production from an interfering reservoir. If the reservoirs are of finite radii and are not approximated by line sources, the method of superposition in space must be used with care so that the inner boundary conditions are not violated. By superposing a finite-radius source in an infinite system onto another finite-radius source in an infinite system, the inner boundary conditions at both sources are violated. Mortada's results, therefore, are only approximate. Hursts presented a method for calculating pressure interference between finite-radius reservoirs that includes the material-balance equations. Hursts and Mortada also considered interference between oil fields connected to an aquifer with two permeability regions. Mueller and Witherspoon used the finite-radius constant-rate solution and normalized the time scale to describe interference pressure changes. They concluded that, for practical pressure changes. They concluded that, for practical purposes, interference points at a distance larger than 20 times purposes, interference points at a distance larger than 20 times the radius of the source have a line-source response. Uraiet and Raghavan presented interference log-log type curves for a finite-radius source producing at a constant pressure. In this study, two circular reservoirs in an infinite system are considered. One reservoir is approximated as a constant-rate line source. The other reservoir is considered to be a finite-radius source producing at either a constant rate or a constant pressure. Only single-step changes in rate or pressure are discussed, since they are the basis for superposition in time. SPEJ P. 419