RIASSUNTO
Summary. A computer program based on the continuity and momentum equations for prediction of the flow of gas through low-permeability porous media was developed. This program uses the FORSIM code, which porous media was developed. This program uses the FORSIM code, which is based on the method of lines and several integration algorithms. Transient gas flow rates predicted with the computer program were compared with Inst. of Gas Technology's (IGT's) data for both partially water-saturated and dry tight-sand core samples.
Introduction
During the past decade, there has been an increasing interest in the area of tight-sand technology. The Natl. Petroleum Council estimated that there is about 608 Tcf Petroleum Council estimated that there is about 608 Tcf [17.2 x 10(12) m3] of gas in tight-sand reservoirs in the continental U.S. Historically, it has been uneconomical to produce gas from these reserves because of low natural production rates. Production from some of these formations became economically feasible because of the increase in gas prices and the advent of new stimulation technology, most notably massive hydraulic fracturing (MHF). Accurate reservoir data, however, are necessary to aid in MHF technology and to estimate total production capacity in any given formation. production capacity in any given formation. The literature contains few fundamental studies on flow behavior in tight-sand porous media. Jones and Owens experimentally measured steady-state permeabilities of tight-sand cores to gas and water. They found that for low-permeability cores, gas permeability is greatly reduced under reservoir confining pressure. Sampath conducted a study on western tight sands; his findings confirm those of Jones and Owens. Walls et al. measured gas flow rates through low-permeability cores subjected to reservoir confining pressures using an unsteady-state pulse-decay technique. Freeman and Bush measured pulse-decay technique. Freeman and Bush measured flow rates through low-permeability cores under reservoir confining stress using a nonsteady-state pressure buildup method. Transient and steady-state gas flow rates are measured with IGT's computer-operated rock analysis laboratory (CORAL) under reservoir confining pressure for cores with permeabilities as low as 0.030 x pressure for cores with permeabilities as low as 0.030 x 10(-6) d. The gas flow measurements in CORAL are conducted with both dry and partially saturated samples that have various porosities and permeabilities. porosities and permeabilities. Arastoopour and Adewumi obtained analytical solutions to the linearized gas flow equations and compared them with IGT's data. In this research work, we have developed computer models based on generalized and modified continuity and momentum equations for the flow of gas through low-permeability porous media. Our computer models were comparable with CORAL data. In addition, they allowed accurate prediction of steady-state permeabilities from transient flow data. permeabilities from transient flow data. Governing Equations for Single-Phase Flow
The general governing equations for single-phase, isothermal, transient flow of gas through porous media are for conservation of mass,
....................(1)
and for conservation of momentum,
.........................(2)
The following assumptions are made to describe one-dimensional (1D), horizontal flow through low-permeability porous media. 1. The flow porosity, , and the volume porosity, v, of the porous medium are constant and equal. 2. The density of the gas can be described by p=pM/zRT, where the gas compressibility factor, z, is assumed constant. 3. The frictional force as a result of flow can be described by Fe = 2v/k, where viscosity, , is constant for isothermal flow of gas in a porous medium. 4. The permeability, k, of the system is constant. Note that v is the local volume-averaged velocity of gas in the pores.
Case A-General Flow Equations. By applying these assumptions to Eqs. 1 and 2, we obtained the following expressions:
....................(3)
SPERE
P. 647