Temperature Distribution Ahead of an Advancing Steam Zone

Abstract

ABSTRACT This paper describes a solution to the diffusivity equation, assuming boundary conditions for a reservoir during steam injection. It should be considerable value for the evaluation of steam drive projects, particularly inview of the growing importance of thermal recovery processes in Canada, INTRODUCTION IN THE THEORETICAL TREATMENT of steam drive processes for the recovery ofheavy oils, one of the problems encountered is the determination of thetemperature distribution ahead of the expanding steam zone. A knowledge of the temperature distribution is of value in predicting the location and rate ofadvance of a steam zone when a temperature build-up is observed at a production or observation well, or to assess the temperature development ahead of a steamzone when its location and rate of advance are known. This paper attempts toassist the resolution of the above problem by extending the theoretical work by Lauwerier which describes the temperature distribution in a line drive model with hot water injection. In this case, the boundary conditions are altered torepresent the situation with steam injection. The Laplace transformation isused to obtain an analytical solution to the equations that ai-e developed. Representative isotherms calculated from this solution are presented ingraphical form. THEORY A plane condensation front is considered to be advancing through permeablestrata bounded by an impermeable cap rock and base rock. The idealized verticalcross section is shown on Figure 1. The problem is formulated as an idealized model by including the following assumptions:The reservoir is homogeneous, isotropic and of constant thickness.The condensation front remains vertical within the sand layer, and thehot condensate flows uniformly through the oil sand ahead of the condensation front.Thermal equilibrium between the fluid and the sand grains is instantaneous.The thermal conductivities of the cap rock, base rock and oil sand are equal.The heat capacities and thermal conductivities are independent of temperatures and pressure.The heat conduction in the horizontal direction is neglected. The above assumptions allow the problem to be formulated by considering only the positive quadrant of Figure 1. because there is symmetry about themid- point of the oil sand. The temperature distribution is therefore described by the set of partial differential equations shown below. (See full paperfor equations)