水攻法下にある炭酸塩岩質油層の垂直掃効率並びに油層シミュレーション用相対浸透率の推定法

抄録

The vertical sweep efficiency of waterflooding in carbonate reservoirs and the associated relative permeability-saturation relationship were studied with a mathematical reservoir model. The model consisted of 30×25 or 15×10 cells, and the rock properties of each cell were characterized so that the model represented the cross section of carbonate reservoirs. A production well and an injection well were located on each side of the model, and seven cases of waterflooding performance were calculated with various distribution of reservoir rock properties. The performance was then compared with those predicted by three vertical sweep efficiency calculation methods, and it was concluded that the vertical sweep efficiency was best predicted by taking an average of the efficiencies by the two methods: a method based on the Buckley-Leverett displacement principle6) assuming a reservoir consisting of one layer, and the Stiles method5) with the above displacement principle using the smoothed permeability profiles determined by the Fourier series trend analysis. Meanwhile the Stiles method using the unmodified permeability profile of cells penetrated by the injection well gave very low vertical sweep efficiencies in many cases.
Investigation of the absolute permeability revealed that the geometric average of permeabilities of cells penetrated by the wells was almost as large as the absolute permeability of the reservoir determined by the reservoir performance but the arithmetic average was greater, when the horizontal variation of the cell permeability was large, while the arithmetic average was as large as the reservoir permeability but the geometric average was smaller, when the horizontal variation was small.
It was also concluded that the relative permeability, which gives nearly 110% of the predicted vertical sweep efficiency if no truncation error is envisaged, should be employed in a large cell model with only one intermediate cell between the injection well cell and the production well cell, in order to compensate for an effect of truncation errors on the efficiency.