Simplified Water Influx-Pressure Calculations Above the Bubble Point
- F.M. Stewart (Continental Illinois National Bank & Trust Co.)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- September 1959
- Document Type
- Journal Paper
- 89 - 91
- 1959. Original copyright American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Copyright has expired.
- 5.2.1 Phase Behavior and PVT Measurements, 4.3.4 Scale
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A paper by Hurst and van Everdingen in 1949 led to the practical solution of many nonsteady-state flow problems. Subsequently, applications of this material have been discussed by several authors. The purpose of this note is to outline a simplified direct procedure for water-influx pressure predictions for pressures above the bubble point. The proposed procedure is unique in that after the "time-conversion factor" and the "influx constant" are obtained, predictions are made without trial and error. The elimination of trial and error is made possible by expressing certain PVT characteristics as explicit functions of pressure. The procedure is applicable to fields producing at pressures above the bubble point and under radial water drive from an infinite aquifer. In the usual applications it is required to predict (1) withdrawals given future pressure history or (2) reservoir pressure, given future withdrawals or production.
The theory, assumptions and conditions under which the nonsteady-state solutions hold are covered in the references and are not repeated. The simplified direct procedure outlined here has been developed from published solutions for the so-called "pressure case". A similar direct procedure for the same special conditions has been developed for the "rate case"; however, in this instance the procedure is lengthy and offers no advantage over the trial-and-error so1ution. Consequently, this paper covers only the procedure based on the pressure case.
Under the pressure case prediction of withdrawals from a waterdrive field, given the future pressure history, involves the use of a nonsteady-state water-influx term together with the material balance equation. The solution of a particular problem requires the following steps: (1) division of past pressure and production data into equal time intervals; (2) computation of cumulative water influx vs pressure drop for each time interval of past history using the material balance equation; (3) determination of the best values for the "time-conversion factor" and the "influx constant" by equating the nonsteady-state influx term with the influx computed in Step 2 (this requires a trial-and-error procedure); (4) prediction of influx for a given pressure drop using the influx term and the computed factors from Step 3; and (5) calculation of fluids produced using the predicted influx in the material balance equation. A forecast of the water-oil ratio or water production rate is required to complete the calculation.
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