The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and production measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available.
A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows.
A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.
A reliable value for the reserves can be obtained only if reservoir data are very accurate or if past production performance has been subjected to abrupt variations in the production rate.
No unique value for the reserves can be obtained from reservoir past production performance.
This conclusion has been based upon theoretical considerations and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented.
As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gpj, Wpj) and n output variables (pj), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multivariable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production Gp(t) and Wp(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "blackbox". It has been demonstrated that for a black box the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance.
JPT
P. 237ˆ
