Analytical Modeling of Oil Recovery by Steam Injection: Part I – Upper Bounds

Abstract

Abstract This paper deals with the derivation of upper bounds for the growth of the steam zone in steam injection processes for one- or multidimensional reservoirs at constant or variable injection rates. The bounds are derived from the integral balances describing a reservoir of arbitrary geometry by introducing lower bounds for the heat losses to the surrounding area and the hot liquid zone. In this way, the effect of preheating in the hot liquid zone is estimated to determine the recovery efficiency of a steam drive. The growth rate of a one-dimensional steam zone at variable injection rates is subject to two upper bounds resulting from the total thermal energy and the latent heat balances, respectively. Each of the bounds controls the rate of growth of the steam zone in a certain time interval, depending on the dominant mode of heat transfer in the hot liquid zone. At constant injection rates, the steam zone growth at large times is controlled by the bound based on the latent heat balance. This balance depends on a dimensionless parameter, F, defined as the ratio of the latent heat to the total heat injected. Based on the relative magnitude of F with respect to the critical value F = 2/π, the region of validity of the Marx-Langenheim solution is delineated on a Ts vs. fs diagram. The Marx-Langenheim solution is satisfactory at large times when F>2/π and becomes less satisfactory as F assumes smaller values. Similar upper bounds are obtained for a two-dimensional steam drive (thin reservoirs). In three-dimensional reservoirs, on the other hand, bounds are derived only for a special form of displacement (separable front). These bounds depend on the geometric parameter κ that measures the extent of gravity override. By means of simple analytical models for the steam front shape, κ can be determined in terms of the physical variables of the process.