Abstract
The heavy-oil flow in porous media is characterized by non-Darcy law with variable threshold pressure gradient (TPG) due to the large fluid viscosity. However, available analytical and numerical models hardly consider this effect, which can lead to erroneous results. This paper is aimed at presenting an innovative approach and establishing a numerical simulator to analyze the heavy-oil flow behavior with waterflooding. The apparent viscosity of the oil phase and flow correction coefficient characterized by the TPG were applied to describe the viscosity anomaly of heavy oil. Considering the formation heterogeneity, the TPG was processed into a variable related to mobility and the directionality. The discretization and linearization of the mathematical model were conducted to establish a fully implicit numerical model; the TPG value on each grid node was obtained through oil phase mobility interpolation, and then, the Jacobi matrix was reassembled and calculated to solve pressure and saturation equations. The corresponding simulator was thus developed. The pre-/postprocessing module of the simulator is connected to ECLIPSE; then, an efficient algorithm is introduced to realize a fast solution. Results show that considering the TPG will not only reduce the waterflooding area but also reduce the oil displacement efficiency because of aggravating the nonpiston phenomenon and interlayer conflict. The numerical simulation study on the TPG of heavy oil provides theoretical and technical support for the rational development and adjustment of water-driven heavy oil.
Highlights
Due to the tremendous growth of oil demand and the depletion of low-viscosity oil reservoir, heavy oil plays an increasingly great role in petroleum supply for the world and more and more attention is turned to heavy-oil development [1,2,3]
Different from the threshold pressure gradient (TPG) in tight oil reservoirs caused by ultralow permeability, the TPG in heavy-oil reservoirs is mainly attributed to the abnormal viscosity [11,12,13]
A large number of mechanism studies have shown that the TPG described in heavy-oil simulation could be summarized into the following three methods: pseudo threshold pressure gradient (PTPG) model, piecewise nonlinear model, and variable permeability model
Summary
Due to the tremendous growth of oil demand and the depletion of low-viscosity oil reservoir, heavy oil plays an increasingly great role in petroleum supply for the world and more and more attention is turned to heavy-oil development [1,2,3]. As the viscosity of heavy oil increases, its non-Newtonian characteristics become more obvious leading to the threshold pressure gradient (TPG) in the low-pressure gradient area [7,8,9]. A large number of mechanism studies have shown that the TPG described in heavy-oil simulation could be summarized into the following three methods: pseudo threshold pressure gradient (PTPG) model, piecewise nonlinear model, and variable permeability model. The PTPG model is the most used model which processes the tangent of the arc segment to treat the curved segment of the flow curve equivalently, while the model reduces the fluid movable range [14,15,16]. To improve the description accuracy of the relationship between the flux and the pressure gradient, the piecewise nonlinear model was presented, such as the exponential function [17] and the power function [18]. The model expressions of these functions are complicated and involve the judgment of the critical point between the linear flow part and the nonlinear flow
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