Introduction

Many reservoirs are bounded on a portion or all of their peripheries by water-bearing rocks called aquifers (from Latin, aqua [water], ferre [to bear]). The aquifers may be so large (compared with the reservoirs they adjoin) that they appear infinite for all practical purposes; they may also be so small as to be negligible in their effect on reservoir performance. The aquifer itself may be entirely bounded by impermeable rock so that the reservoir and aquifer together form a closed, or volumetric, unit (Fig. 9.1). On the other hand, the reservoir may outcrop at one or more places where it may be replenished by surface waters (Fig. 9.2). Finally, an aquifer may be essentially horizontal with the reservoir it adjoins, or it may rise, as at the edge of structural basins, considerably above the reservoir to provide some artesian kind of flow of water to the reservoir.

Figure 9.1 A reservoir analyzer study of five fields, completed in a closed aquifer in the Ellenburger formation in West Texas (after Moore and Truby¹).

Figure 9.2 Geologic cross section through the Torchlight Tensleep Reservoir, Wyoming (after Stewart, Callaway, and Gladfelter²).

In response to a pressure drop in the reservoir, the aquifer reacts to offset, or retard, pressure decline by providing a source of water influx or encroachment by (1) expansion of the water, (2) expansion of other known or unknown hydrocarbon accumulations in the aquifer rock, (3) compressibility of the aquifer rock, and/or (4) artesian flow, which occurs when the aquifer rises to a level above the reservoir, whether it outcrops or not, and whether or not the outcrop is replenished by surface water.

To determine the effect that an aquifer has on the production from a hydrocarbon reservoir, it is necessary to be able to calculate the amount of water that has influxed into the reservoir from the aquifer. This calculation can be made using the material balance equation when the initial hydrocarbon amount and the production are known. The Havlena-Odeh approach to material balance calculations, presented can sometimes be used to obtain an estimate for both water influx and initial hydrocarbon amount.^3,4 For the case of a water-drive reservoir, no original gas cap, and negligible compressibilities, Eq. (3.13) reduces to the following:

F = NE_o+W_e

or

If correct values of W_e are placed in this equation as a function of reservoir pressure, then the equation should plot as a straight line with intercept, N, and slope equal to unity. The procedure to solve for both W_e and N in this case involves assuming a model for W_e as a function of pressure, calculating W_e, making the plot of F/E_o versus W_e/E_o, and observing if a straight line is obtained. If a straight line is not obtained, then a new model for W_e is assumed and the procedure repeated.

Choosing an appropriate model for water influx involves many uncertainties. Some of these include the size and shape of the aquifer, and aquifer properties, such as porosity and permeability. Normally, little is known about these parameters, largely because the cost to drill into the aquifer to obtain the necessary data is not often justified.

Several models that have been used in reservoir studies to calculate water influx amounts are considered. These models can be generally categorized by a time dependence (i.e., steady state or unsteady state) and whether the aquifer is an edgewater or bottomwater drive.