Steam Heating of Fractured Formations Containing Heavy Oil: Basic Premises and a Single-Block Analytical Model

ABSTRACT Interest in modeling thermal processes in naturally fractured reservoirs containing heavy oil has grown considerably because of encouraging results from experimental and theoretical studies as well as pilot tests. However, satisfactory predictive models are still lacking. This paper examines one component of such a model by studying a single block of a naturally fractured reservoir under steam injection, and presenting analytical solutions for heat flow and non-isothermal gravity drainage from the block. The fracture-matrix heat transfer is investigated first by analyzing the governing differential equations. It is found analytically that for a typical matrix block in the steam zone, the transient temperature distribution within a single block is not affected by convection. For physical properties other than those considered in this paper, it is shown that evaluation of the Peclet Number indicates the order of error that will be introduced if convection is neglected. This is found to be in the order of 1% for a typical fractured carbonate reservoir. Next, an integral method is used to obtain the transient temperature distribution within the block, which can be used directly for the heat consumption calculations. The temperature distribution is incorporated into an analytical equation to obtain the thermal drainage rate under gravity flow. The final equation is a relation between the physical properties of a single block and the flow rate in an easy-to-calculate form. The solution of the problem shows that using oil viscosity at average block temperature is adequate for recovery calculations during the heating period. These findings can be used in single block and fieldwide modeling of heat and fluid flow in fractured reservoirs, such as those in the Middle East.