Reservoir Engineering–General - Study of Gas Reservoirs Subject to Water Drive on Electronic Differential Analyzer

The behavior of gas-storage reservoirs subject to water drive is investigated through analog simulation on an electronic differential analyzer. The simulation technique developed on an LM-10 computer permits the prediction of reservoir volume or pressure resulting from the movement of water in the surrounding aquifer. The method developed on the analog computer consists of setting up an appropriate transfer-function circuit and feeding the arbitrary time-varying boundary conditions as an input signal. The input may be specified as gas reservoir pressure, pore volume or the water flux. Several cases studied include an isolated gas reservoir on a limited aquifer, interference among three reservoirs adjacent to a common aquifer and the growth of gas-storage volume on an aquifer. It is concluded that the method developed on an electronic differential analyzer provides an excellent technique to simulate and investigate the behavior of gas reservoirs subject to water drive. The agreement between the reservoir performance as predicted from the simulation technique and as measured from actual field data is found to be better than the range usually encountered in predicting water-drive behavior. INTRODUCTION It is generally known that some gas-storage reservoirs are located on top of blanket sands of large extent, saturated with brine called aquifers. Because the volume of the body of water associated with aquifers is usually very large and water is compressible, the cyclic pressure variations encountered in normal storage service inevitably cause unsteady, compressible flow conditions in the adjacent aquifers. The solution to radial diffusivity equation for a limited aquifer for constant terminal conditions has been know111 since the early 1930's. The solution for the constant terminal conditions for an infinite aquifer was puhlished in 1949.2 The proldem of handling the unsteady flow of water through a porous medium with time-varying boundary conditions has been studied by many investigators through the use of graphical,3 digital4 computing techniques or on an R-C type of electrical analog called a reservoir analyzer.5 The digital computer performs a series of arithmetic calculations to superimpose the solutions of constant terminal conditions, while the R-C type of analyzer permits the simulation of the continuous medium by means of "lumped-cell" electrical resistance and capacitance elements based on finite-difference approximations. The graphical method is based on the convolution integral solution of the partial differential equalion. The purpose of the present study was to simulate the behavior of an aquifer on a general-purpose, electronic differential analyzer to obtain the influx of water or the change in pressure at the reservoir continuous1r and quickly. The use of the electronic differential analyzer was based on well known solutions for the constant terminal conditions already available in the literature.2,6-8 THEORETICAL DEVELOPMENT MODEL. The gas reservoir (R) is described in relation to an aquifer in Fig. 1. The permeability and porosity of an aquifer sand, the viscosity of the brine, and the compressibility of the brine and the formation are assumed to be constant. It further is assumed that the blanket sand is not thick enough to give appreciable vertical pressure distribution. The model in consideration is circular with radial geometry. The aquifer radius can be of limited or infinite extent. The gas-water interface is assumed to be fully segregated, and the displacement of the gas by