Implicit Compositional Simulation of Single-Porosity and Dual-Porosity Reservoirs

Abstract

SPE Member Abstract This paper describes an implicit numerical model for compositional simulation of single-porosity and dual-porosity oil or gas condensate reservoirs. A 3-component equation-of-state compositional approach is proposed as a desirable alternative to extended black oil modelling, requiring little more computing time than the latter. The approach is illustrated for an actual near-critical volatile oil reservoir. A simple method for reducing implicit formulation time truncation error is described and illustrated. A new bottomhole constraint function is described for better preservation of production well target rates in compositional models. A new matrix-fracture transfer formulation including matrix-fracture diffusion is presented for the dual-porosity description; its accuracy is presented for the dual-porosity description; its accuracy is examined in connection with several test problems where correct results are available from single-porosity simulation. Results are discussed for a 3D 600-block simulation of a highly fractured near-critical volatile oil reservoir. Introduction This paper describes a fully implicit numerical model for compositional simulation of multidimensional, three-phase flow in single-porosity and naturally fractured reservoirs. A general description of the model is given, followed by a section giving more detail regarding certain features. The model equations are then presented. The major emphasis here relates to the fractured reservoir application. Therefore, the remainder of the paper describes a new matrix-fracture fluid transfer formulation and estimates its accuracy in connection with a number of example or test problems. General Description of the Model The model is fully compositional with a generalized cubic equation-of-state (EOS) for representation of gas-oil phase equilibria and densities. The generalized EOS phase equilibria and densities. The generalized EOS represents the Redlich-Kwong, Soave-Redlich-Kwong, Zudkevitch-Joffe Redlich-Kwong, and Peng-Robinson EOS. A tabular, pressure-dependent K-value option provides an alternative to EOS usage. EOS parameters are obtained using a regression-based PVT program. Different parameter sets are used for reservoir and surface separation parameter sets are used for reservoir and surface separation calculations. This eases the burden of determining parameters and increases EOS accuracy at reservoir and parameters and increases EOS accuracy at reservoir and surface conditions. Viscosities are calculated from the Lohrenz et al correlation and interfacial tension is obtained using the MacLeod-Sugden method. The model simulates 1-, 2- and 3-dimensional flow in Cartesian or cylindrical coordinates Darcy's Law modified by relative permeability and capillary pressure represents the viscous, capillary and gravit forces. Effects of interfacial tension on capillary pressure are included. The model applies to depletion, water injection, cycling (gas injection), and enriched gas/solvent injection operations in reservoir types ranging from black oil to near-critical volatile oil and condensate to lean gas condensate. Applications include simulation of laboratory experiments, cylindrical-coordinate single-well studies and areal, cross-sectional or 3D field-scale studies. Implicit formulations generally have a tendency toward greater numerical dispersion effects than the IMPES formulation. A dispersion-control feature is described which reduces sensitivity of results to time step size in some cases. Production well rate is allocated among layers by pressure and mobility, including an implicit bottomhole pressure and mobility, including an implicit bottomhole constraint treatment to preserve specified target rate. The well rate terms involved are implicit in all variables: compositions, saturations and pressure. A new formulation for the implicit bottomhole target rate constraint gives better preservation of specified rate for the case of compositional simulation. P. 239