Study On Relative Permeability Prediction Model Based On Fractal Theory

Relative permeability is one of the important parameters in reservoir engineering and numerical simulation.It is used to characterize the interaction between fluid and rock,and its accuracy is directly related to the distribution of underground fluid and the rationality of development program.However,due to the small number of core samples in field practice,the test results of relative permeability are not enough to represent the difference of reservoir,and the deviation of the results is large.Therefore,it is urgent to establish a new method for calculating relative permeability based on reservoir difference.In this paper,Es₃¹ reservoir of an oilfield is taken as the research object.Firstly,in view of the experimental results of rock cast thin section and SEM,the mineral petrological characteristics,pore types and pore throat distribution characteristics are described,which lays the foundation of physical parameters for fractal description.Secondly,according to the characteristics of mercury injection curve and fractal theory,the fractal model characterizing pore structure is established,and it was analyzed that the pore throat had multistage fractal characteristics.The fractal dimension of pore is calculated to be 1.3829～1.5553,and the fractal dimension of tortuosity is calculated to be 1.1063～1.3869,and then the correlation between fractal dimension and porosity and permeability is clarified.Then,according to the bundle of capillary theory and Poiseuille’s law,a fractal prediction model of oil-water relative permeability is established,which considering pore structure and water film thickness.Comparing the experimental results,it is concluded the error is small,which verifies the accuracy of the model.And the influence of four parameters including pore fractal dimension,tortuosity fractal dimension,minimum pore radius/maximum pore radius,and water film thickness on relative permeability are clarified.Finally,Finally,the established model is used to predict the relative permeability of different types of blocks,and it is used in the phase permeability partition of the reservoir numerical simulation.The results show that in the historical fitting after relative permeability zoning,the stage of rapid and rapid change of water content obviously has higher fitting accuracy,the distribution law of remaining oil is more clear,and the later adjustment is more targeted.The relative permeability model established in this paper,based on fractal theory,which fully considers the difference characteristics of reservoir,realizes fine simulation,and better guides the quantitative description and benefit development of remaining oil.