Estimation of Gas in Place Using Optimal Control Theory

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the Improved Oil Recovery Symposium of the Society of Petroleum Engineers of AIME, to be held in Tulsa, Okla., March 22–24, 1976. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper presents a procedure for estimating the gas in place for volumetric gas reservoir using the Material Balance Principle and Optimal Control theory. Principle and Optimal Control theory. The reservoir model includes connate water expansion, rock compaction, shale water influx and limited water influx from a bounded aquifer of limited extent. Hydrocarbon phase behavior includes gas compressibility factors. Validity and predictability of the model have been tested using two published test problems. These problems are:the NS2B Reservoir of the North Ossum Field, Louisiana, andthe Anderson "L" Reservoir in South Texas. The method was then used to determine the reserve of a large gas reservoir in Wyoming. The results obtained from the Wyoming field have been compared with the results obtained using other methods. The results obtained by different methods agree reasonably well. Introduction A reliable estimate of gas in place, recoverable reserve, most probable future life and future production rates, all play very important roles in the Natural Gas Industry. These values are needed for efficient planning of long range contracts and future commitments, scheduling compressor installation, well drilling and other investment decisions. Investment decisions are generally based on profit maximization over the life of the field. Hence, the need for reliable information for management decision can never be over emphasized. Estimation of gas in place or recoverable gas is one of the most important aspects of gas reservoir analysis. Principle methods of predicting gas in place are:Volumetric MethodProduction Decline Method(Rate-Time, Rate-Cum plots)Material Balance Method(P/Z vs Cum. Prod. plot)