Analysis and Interpretation of Pressure-Decay Tests for Gas/Bitumen and Oil/Bitumen Systems: Methodology Development and Application of New Linearized and Robust Parameter-Estimation Technique Using Laboratory Data

Summary Diffusion mixing is a dominant process in the absence of convective mixing in various reservoir processes, such as carbon dioxide (CO2) flooding of fractured reservoirs, heavy-oil and bitumen recovery, solution-gas-drive processes, and the gas-redissolution process in a depleted reservoir. In these processes, the diffusivity governs the rate and extent of mixing of light hydrocarbons/nonhydrocarbons with the oil that enhances the oil recovery through in-situ viscosity reduction. It is one of the key parameters for the design and understanding of displacement processes. Because of its significance in various aspects of oil-recovery processes, several experimental and theoretical studies were recently performed on the measurement of gas diffusivity in oils. Experimental work most commonly uses the pressure-decay (PD) concept because of its simplicity and the potential extraction of other necessary parameters, such as Henry's constant. However, the parameter estimation from these tests is dependent on nonlinear regression, which might have several issues such as nonconvergence, nonuniqueness or multiplicity in solution, and high sensitivity toward noise and the time span of the data. Therefore, in this paper, Ratnakar and Dindoruk (2015) is extended and New experimental data are provided from a PD test for CO2 diffusion into bitumen at 80°C and approximately 700 psi. A robust inversion technique for parameter estimation is presented for exponentially decaying late-transient data, which can be used with any PD model used in the literature. The validity and applicability of the inversion technique is demonstrated against numerical data that are generated for a PD system by solving a diffusion model with continuity in the state variable (using Henry's constant) and molar flux at the gas/oil interface. Most importantly, the issues with the nonlinear-regression technique are resolved using the linearized technique. The inversion technique presented in the work is dependent on a combination of linear regression and numerical integration using a modified, more-convenient form of the fundamental equations rather than a nonlinear regression on the fundamental equations as derived. This integral-based linear representation avoids the multiple solutions and can be used with limited data sets and/or when noise in the experimental data is significant, especially in industrial-grade experiments.