There are many influence factors of displacement efficiency. In this paper, by literature research [3] - [8] and reservoir method, the influence factors are permeability, porosity, oil viscosity and the pore volume multiple of injected water.

Reservoir permeability and porosity characterize the influence of rock microscopic pore structure on percolation capacity. The large number of experimental results shows that there is a positive correlation between displacement efficiency and reservoir permeability and porosity. If the reservoir porosity and permeability is higher, displacement efficiency is higher.

The oil viscosity in place has great influence on oil displacement efficiency. If the oil viscosity in place is low, then the pistons drive is formed easily during water displacement.

The pore volume ratio of injected water is defined as the ratio of the volume of injected water to reservoir pore volume. Experiments show that with the increase of injection multiple, displacement efficiency increases. But the increase rate is different at different stages of development and different pore volume multiple of injected water. Especially, the increase rate is smaller when the development of oil reservoir is at high water cut period. Because this article takes displacement efficiency at limited water cut of Bohai oilfield as object, the pore volume multiple of injected water is very high, the pore volume multiple of injected water has little influence on oil displacement efficiency.

In this paper, the displacement efficiency experimental data of 118 rocks which come from 65 development wells of 34 oilfields have been collected. On this basis, the data which has unreasonable experimental condition and inaccurate result is rejected. Finally, the displacement efficiency experimental data of 99 cores which come from 65 development wells of 34 oilfields has been collected as sample data. The sample data covers the typical oil fields in Bohai oilfield, which is highly representative.

In order to further verify the data reliability, the correlation between three influence factors and displacement efficiency is analyzed. Figure 1 shows that permeability, porosity and oil viscosity in place of sample data has good relation with displacement efficiency. The sample data are reliable.

The process of empirical formula establishment the formula is the process of obtaining the relationship between three influence factors and displacement efficiency. There are two methods in regression formula, one method is multivariate linear regression (Equation (2)); the other method is multivariate nonlinear regression (Equation (3)).

y ^ = a 1 x 1 + a 2 x 2 + ⋯ + a n x n + b , (2)

y ^ = f ( x 1 ) + f ( x 2 ) + ⋯ + f ( x n ) + b , (3)

The method of multivariate nonlinear regression has high accuracy, but the calculation is complicated and difficult to operate. In the conditions of guaranteeing the accuracy, the method of multivariate linear regression is easy to operate and simple to calculate. By comparison, the method of multivariate linear regression is used to establish empirical formula. Considering that the range of permeability and oil viscosity in place is very large, the two parameters are expressed in logarithmic form. The sample data is substituted into the Equation (2), there are 99 equations (Equation (4)):

{ E D 1 = a 1 ϕ 1 + a 2 log k 1 − a 3 log μ 1 + b E D 2 = a 1 ϕ 1 + a 2 log k 1 − a 3 log μ 1 + b                                               ⋮ E D 99 = a 1 ϕ 99 + a 2 log k 99 − a 3 log μ 99 + b , (4)

Use least square method and Gaussian elimination method to solve equations.

The solution process is as follows: Use Gaussian elimination method to solve Equation (4). The values of a 1 , a 2 , ⋯ , a 6 and b are obtained.

Through a series of operations, finally, a new empirical formula (Equation (5)) of displacement efficiency is established.

E D = 0.002 ϕ + 0.053 lg k − 0.034 lg μ o + 0.443 , (5)

where E D is displacement efficiency, f; ϕ is porosity, %; k is permeability, mD; μ o is oil viscosity in place, mPa・s.