Technical Notes - Simplified Form of the Material Balance Equation

The material balance equation has been used for many years by engineers to determine reservoir performance. The use of this equation in general has been twofold: first, to determine the oil-in-place in a reservoir; and second, to predict the future performance. The Schilthuis form of the material balance equation, or one equivalent to it, has been used by many of the engineers. The use of the Schilthuis form in predicting future performance has proved to be laborious in that one generally must make several estimates at each step of the trial and error calculation before arriving at a check of the oil-in-place. A method is presented for expediting the calculations. The Schilthuis form of the material balance has been rearranged into a more useable form. In using the material balance to predict the future performance of a reservoir, it has become common practice to estimate the incremental oil production for each step of the calculation which corresponds to a given pressure reduction. Instead of estimating the incremental oil production, the method outlined in this paper better lends itself to estimating the instantaneous gas-oil ratio. A check of oil-in-place is more easily accomplished by estimating gas-oil ratio since it is less sensitive to small inaccuracies. This method incorporates the same self-checking feature inherent in the Schilthius form. DEVELOPMENT OF SIMPLIFlED EQUATION In the development of the simplified equation, the Schilthuis form of the material balance equation will he used. Substituting in Equation 1 for and rearranging terms In Equation 2, the cumulative oil production (n) is multiplied by a factor which is uniquely a function of pressure. Also, the cumulative gas production (G) and net water influx are also multiplied by factors which are a function of pressure alone. These factors are called and are defined as follows: Using these factors, Equation 2 becomes The equation in this form is easier to manipulate mathematically than any of the previous forms which, have been used. Sources of data for the pressure factors are a bottom-hole fluid analysis and the ratio of initial gas cap volume to oil volume in the reservoir. AID IN DETERMlNING THE ORIGINAL OIL-IN-PLACE Each of the curves and +, have a similar shape. Each is infinite at the bubble point pressure. As lhe pressure is reduced below the bubble point, the