Vertical segregation of water is defined as the tendency of water to slump downwards in a vertical sense while undergoing a lateral/areal displacement. In reality, this phenomenon is driven by the density difference between reservoir fluids (oil, water) as well as the reservoir’s vertical permeability heterogeneity. If water is injected at one end of a hypothetical thick and homogeneous sand, the injected water would advance laterally and slump vertically as described by the 1-D Buckley-Leverette (BL) mathematical model. Aspect ratio is defined as the ratio of a grid’s lateral size to its thickness (Dx/Dz). There is the usual constraint to keep Dz as small as possible to allow the description of fine vertical heterogeneities that may be important for flow modeling, there is also the constraint to make Dx large enough to ensure a manageable total number of grids that available computational resources can handle. These constraints lead towards an increasing simulation grid aspect ratio. The purpose of this paper is to demonstrate the impact of increasing aspect ratio on the simulation of vertical segregation of water and present an improved methodology based on BTKr_cor (Kayode 2017) for modelling of vertical oil- water segregation in numerical reservoir simulation. Simulation results from synthetic reservoir model cases are used.

The base-case scenario contains a hypothetical 5-spot injection pattern with 1200 feet injector-producer distance. The wells are placed in a fine-scale grid with block dimensions of 5ft x 5ft x 1ft. After one year of water injection, the simulated saturation-depth profile around the water injector was found to compare favorably with the analytical BL profile. The study included sensitivities varying (i) vertical (kv) / horizontal (kh) permeability ratio, (ii) grid-size (iii) introduction of permeability heterogeneities and (iv) the application of BTKr_cor relative permeability scaling (Kayode 2017). The impact these parameters have on the simulated vertical water segregation are presented.

Simulation results demonstrate that with increasing aspect ratio, the vertical water segregation becomes more pronounced than shown by the fine-scale base case results. The use of low kv/kh values to reduce vertical segregation in large simulation grids resulted in a mismatch of up to 10 units of remaining oil saturation around the injectors. It was however found that regardless of grid size and permeability heterogeneity, the use of the BTkr_cor approach shows the best match with fine grid simulation results.

The methodology described in this publication allows improved numerical simulation of vertical segregation while respecting observed kv/kh ratio from sources like pressure transient analysis (PTA), core data, and vertical interference tests (VIT).

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