The one-dimensional steam injection simulator, developed in part I of thiswork to track the movement of the steam front as it progresses through aone-dimensional core, is extended to two dimensions. Tha technique forhandling a dynamic grid, and the block-balance method used to develop thefinite-difference approximation to the governing equations, boundary conditions, and matching conditions (at tha steam front) are described inconsidera are presented forthe two-dimensional simulation. An extensive survey of ehe open literaturedescribing the physical properties of the Cold lake heavy oil dgposit,required for the numerical simulation of the oil recovery process, was alsocarried out. Tables of reported propeties are provided in the report, andvalues considered representative are summarized.