Vapour extraction (VAPEX) is a nonthermal process using vapourized solvents, with promising potential to reduce steam consumption in heavy-oil recovery. The key recovery mechanisms are convection and molecular diffusion enhanced by various spreading mechanisms [e.g., capillarity and velocity variations at the micro and macroscale (i.e., dispersion and mixing)]. The efficiency of diffusion/dispersion depends significantly on reservoir heterogeneities, which exhibit a wide range of length scales. This paper demonstrates a procedure for quantifying the scaling characteristics of effective mass transfer accounting for heterogeneities based on the volume-averaging approach. Volume averaging is a mathematical technique used to derive continuum equations at coarse scales given representative transport equations at fine scales. Although treatment of transport problems has been published in the past, application to stochastic geological systems is limited. In the proposed procedure, results from a fine-scale numerical flow simulation reflecting the full physics of VAPEX over a small element of the reservoir are integrated by use of the volume-averaging technique to provide effective description of mass transfer at the coarse scale. Scaling characteristics of effective mass transfer are investigated systematically for different heterogeneity distributions. Results show (1) spatial variability of effective-mass-transfer coefficients increases as a solvent chamber advances through the reservoir; (2) mean and variance of effective-mass transfer vary with length scale in a fashion similar to that of recovery statistics; and (3) variability in effective-mass transfer is a strong nonlinear function of heterogeneity. An original contribution is to provide a general framework for developing scaling relationships of effective mass transfer in VAPEX accounting for reservoir heterogeneities. It also presents an important potential in modelling of other solvent-injection applications. Results demonstrate that effective-mass transfer varies with length scale and heterogeneity; hence, it should be represented properly for accurate prediction of recovery performance in simulations using scaled-up reservoir models.

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