A Mathematical Model of the Steam Drive Process Applications

Abstract

This paper was prepared for the 45th Annual California Regional Meeting of the Society of Petroleum Engineers of AIME, to be held in Ventura, Calif., April 2–4, 1975. 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 OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, 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 discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Introduction Previously reported calculations of Previously reported calculations of oil displacement by continuous steam injection either ignore the effects of gravity override or simulate them numerically. This paper describes a theoretical analysis of the problem that leads to a relatively simple solution. A steam zone is assumed near the overburden. Calculations include (1) the rates of steam zone thickness increase vs time since steam first arrived, (2) the steam zone areal increase rate, and (3) total oil displaced (from the steam and underlying hot water zones). The mathematical derivation is to be submitted to the SPE Journal. Equations describing the steam drive process are presented, applied in an process are presented, applied in an example, and discussed as to limits of validity. Predicted and observed steam drive behaviors are compared for Chevron's Ten Pattern Steam Flood in the Kern River Field, California. Also discussed are methods of application for economic and engineering analysis. OUTLINE OF GRAVITY OVERRIDE MODEL Steam injected during steam flooding rises to the top of the injection interval, causing the steam zone to grow downward as well as areally. The vertical rate is determined by the rate of steam condensation from heat diffusion into the overburden and the liquid-filled underlying reservoir. The rate of areal growth is determined by the balance between the net energy injected as steam and that required from steam condensation to sustain vertical growth. The amount of oil displaced from below the lower steam interface can be predicted from the temperature profile there and a critical temperature. The latter depends on the flow properties of the reservoir and fluids. The model presented here is like that of Marx and Langenheim in that neither assumes a particular areal geometry.