Abstract
In this paper, a robust and pragmatic technique has been proposed to determine the three-phase relative permeability of cold heavy oil production with sand (CHOPS) processes by comprehensively incorporating dynamic wormhole growth and foamy oil flow with an improved iterative ensemble smoother (IES), which is achieved by normalizing both model parameters and measured production profiles. More specifically, a recently proposed pressure-gradient-based sand failure criterion has been applied to characterize the dynamic wormhole propagations, while the evolution of foamy oil has been achieved through kinetic reactions embedded in a reservoir simulator. Only the three-phase relative permeability of the wormhole network has been parameterized using a power-law model since the multi-phase flow within the wormholes dominates, in particular, production performance of the CHOPS processes. Then, the model parameter matrix consisting of coefficients of the power-law model, the pressure-gradient-based sand failure criterion, and the foamy oil reactions can be inversely and implicitly estimated through the improved IES algorithm, provided that the production profiles of the CHOPS processes are made available. Effects of the wormhole growth and the foamy oil flow on the three-phase relative permeability are implicitly examined through the integrated and improved model parameter matrix. Subsequently, the newly proposed technique was validated by use of a CHOPS experiment in the literature. In addition to the converged three-phase relative permeability, the well matched experimental measurements (i.e., cumulative oil, gas, and sand production) have synergistically proven that the newly proposed method is qualified for accurately determining the three-phase relative permeability in the CHOPS processes. In order to reproduce the transition stage on production profiles, both one set and two sets of three-phase relative permeability were used during the entire production period, though the former fails to do so. It has been substantiated that two sets of the three-phase relative permeability are able to reproduce the transition stage through considering the effects of sand failure and foamy oil of the CHOPS processes. In addition, residual oil saturation of the wormhole network is found to dramatically reduce once the sand production is initialized. Also, it is found that gas relative permeability is more sensitive to the gas saturation for the second set, though it is relatively smaller than that of the first set.
