Material Balance for a Bottom-Water-Drive Gas Reservoir

A material balance is developed for a gas reservoir in which the rising gas/water contact remains horizontal. The time-integrated cumulative water influx is introduced, which for numerical computations is sometimes more advantageous than the van Everdingen and Hurst integral. On the basis of the equations developed, material balance calculations of the history of an actual gas field are carried out to calculate the water influx. The strength of the estimated radial, limited aquifer, which must supply the water for the influx, is determined. It appears that the strength decreases with time and asymptotically approaches a limiting value. (Some possible reasons for this decrease are mentioned.) If we take the strength as constant and equal to the limiting value, however, very small deviations from the past pressures occur. With the same value for the strength of the aquifer, the future behavior of the gas reservoir is computed, assuming constant gas production rate and no water production. Introduction For a depletion-type gas reservoir - i.e., when there is no water encroachment - the average gas pressure is a function of the cumulative production pressure is a function of the cumulative production and can easily be calculated from a material balance. For a gas reservoir bounded by an aquifer, the average gas pressure also depends on the water influx, which in turn depends on the rate of pressure decline and thus on the production rate. In this case the material balance is much more complicated. In the following we have developed the material balance of a bottom-water-drive gas reservoir, in which the rising gas/water contact remains horizontal. In a numerical example, the equations are applied to an actual gas field in Northwest Germany. THE GAS RESERVOIR Let us consider a gas reservoir bounded by a horizontal gas/water contact. The bulk area of a horizontal cross-section through the reservoir at a height b above the original gas/water contact is denoted by A(h), and the part of this area taken up by free gas is denoted by F(h). in which and Swc are the average values of porosity and connate water saturation at level h. porosity and connate water saturation at level h. Function F(h) can also be considered as the free gas volume in the reservoir at level h per unit height. Consequently, the free gas volume in the reservoir between the original gas/water contact h = 0 and a certain level h = h' is 0 The total original free gas volume in the reservoir is in which H is the height of the top of the gas-bearing formation above the original gas/water contact; i.e., the closure of the reservoir. The original volume of free gas in place, measured at standard conditions, is where the reciprocal gas formation volume factor is defined by Since in general we may take the average reservoir temperature for Tres, 1/Bg is a function of pressure only. A fair approximation of Eq. 4 is obtained by taking (1/Bg)i independently of h and equal to the value corresponding to the average initial reservoir pressure. Then pressure. Then SPEJ P. 328