This study is limited to an investigation of the behavior of the flows in and near a fracture. The numerical model simulates multicomponent, multiphase, compressible flow through a horizontal two-dimensional porous medium which is bounded on one side by a one-dimensional fracture. The absolute permeability of the fracture is assumed to be much greater than that of the reservoir matrix, resulting in the simplification that flow in the matrix is predominately perpendicular to the fracture face. Flow in the matrix parallel to the fracture is ignored in this model. The fluid system consists of three components in three phases. Component 1 is the injected fluid, e.g., CO/sub 2/, and can exist in any of the three phases - gas, oil, and water. Component 2 is the hydrocarbon component and is assumed to be heavy enough so that it exists only in the oil phase. Component 3 is the aqueous component and is restricted to the water phase. All fluid properties, except viscosity and relative permeability, are assumed to be linear functions of pressure and composition. The temperature of the system is taken as constant and effects due to capillary pressure and gravity are not included. The mathematical formulation is based on a set of molar continuity equations (one per component), the phase equilibrium condition, and a volume conservation equation. Reduction of this system of equations to a single equation in pressure leads to a sequential (implicit pressure-explicit moles) method of solution. In-step iterations are performed to increase the implicitness of the method. The algorithm includes time step control and a volume balance check. A flow chart of the computer code as well as the source code and input and output formats are included in the Appendix. Three sample problems are examined. 20 references, 6 figures, 2 tables.