A treatise on the use of pseudopressure approach for the transient analysis of multiphase production from unconventional reservoirs

Abstract

This thesis presents a formal discussion of the use of the pseudopressure approach to analyze multiphase pressure- and rate-transient data of fractured wells in unconventional reservoirs. Among several options for the treatment of the multiphase flow problem, pseudopressure approach is an attractive semi-analytical choice for pressure- and rate-transient analysis as it reduces the problem to a single-phase flow analogy and enables the use of standard well-test analysis tools and techniques. However, the pseudopressure approach is inherently approximate and its success is strongly dependent on the validity of the assumptions made. Therefore, the appropriate use of the pseudopressure approach requires good documentation and understanding of its underlying assumptions. Most introductions of the pseudopressure approach for multiphase flow in naturally fractured media are based on numerical observations, extensions from known cases, or even by heuristic arguments, which do not permit explicitly delineating the parametric relations and associated assumptions. Therefore, in this thesis, both numerical and analytical approaches are used to document the assumptions and limits of application of the pseudopressure approach for multiphase flow in unconventional reservoirs. For ease of discussion, the problem is reduced to two-phase (oil and gas) linear (1D) flow in a naturally fractured porous medium. The dual-porosity idealization with transient interporosity flow option is used to represent the naturally fractured reservoir. To emulate the properties of unconventional reservoirs, the matrix is assumed to be very tight and the majority of the pore and pore-throat sizes are in the range of tens of nanometers. Due to the extreme pore proximity, the effect of capillary pressure in the matrix system is taken into consideration. The numerical model used in this research is constructed with COZSim, which is a specialty black-oil simulator developed to include the effect of pore proximity on phase behavior. The numerical model is verified under single-phase flow conditions by comparison to the analytical model in the Topaze software of Kappa. In this study, an analytical derivation of the total flow equation in terms of pseudopressure is also presented for two-phase flow in a linear dual-porosity medium. The analytical model provides the basis of the pseudopressure definition and verifies the conditions under which the single-phase flow analogy can be used to analyze multiphase flow responses. An example case is generated by the numerical model and the results in terms of pseudopressure are compared with the corresponding single-phase responses. Comparison of the numerical results with the single-phase analog and the analytical derivations indicate that a single definition of pseudopressure is not possible for all times. The problem is caused by the capillary pressure difference between the matrix and fracture systems. While neglecting the effect of capillary pressure in pseudopressure definition causes deviation from single-phase results at late-times, inclusion of capillary pressure provides a match at late times but causes deviation at early times. The derivation of the analytical model indicates that single-phase definitions of the dual-porosity parameters (storativity and transmissibility) can be extended to multiphase flow as a diffusivity-weighted sum of the individual-phase parameters. The analytical model also provides early-, intermediate-, and late-time asymptotic solutions to be used in the straight-line analysis. The asymptotic solutions reveal the explicit form of the effective properties estimated from straight-line analysis. Finally, a synthetic example is analyzed by using the producing gas-oil ratio (GOR) to generate the saturation profile. Differences are observed between the produced GOR saturation predictions and the simulated saturations. This indicates, for dual-porosity reservoir models, the produced GOR method may not be a suitable option to predict the saturation profile considering the sharp pressure and saturation difference between the matrix and fracture due to the capillary pressure. Therefore, the produced GOR method may need to be enhanced in order to be applied for dual-porosity reservoirs which requires a further research.