Mathematical Models And Numerical Algorithms For Calculating Physical Parameters Of Oil And Gas Formations

The physical parameters of oil and gas reservoirs mainly include porosity and permeability.The former describes the reservoir properties of rocks,the latter characterizes the properties of fluid passing through,which directly affects the production of oil and gas wells exploitation.Therefore,it is of great significance to accurately calculate porosity and permeability for oil and gas wells.However,there are still some limitations in the existing models and methods for calculating porosity and permeability,and the accuracy and reliability of the calculation results are relatively low.For example,the dual laterolog response model for calculating porosity does not take non-fractured factors into account,and some parameters(fracture angle and resistivity)are difficult to obtain,resulting in a large error in the calculated porosity.Again,the post pressure drop model for the calculation of permeability is only to consider in the case of a Newtonian liquid,while the post pressure fluid is usually a power law type,as a result the calculation model and method are not in accordance with the actual situation.In view of the above engineering background and existing problems,a new mathematical model for calculating porosity and permeability is established,and the research work of mathematical theories and numerical methods is carried out.During the master's research period,the following achievements have been achieved.(1)Through the analysis of the influence factors of porosity,a new mathematical model for porosity calculation is established by selecting the density,neutron,natural gamma and acoustic wave as the factors of porosity in the logging parameters.(2)The theoretical study of the new mathematical model is carried out,the existence theorem and the stability condition of the model solution are given.At the same time,a numerical algorithm for the new mathematical model is proposed for the case with a large number of conditions.(3)Aiming at the actual situation of post pressure fluid,we have considered the power law fluid and the corresponding Cater filtration model,and a new mathematical model for calculating permeability is established.(4)For the partial differential equation and its initial and boundary conditions,the analytic solution of the Laplace image function is derived by using the Laplace transformation,and the expression of the implied permeability is derived by using the Laplace inversion.(5)According to the pressure drop data,an automatic fitting model for the inversion of permeability and power law index is proposed,and a variety of optimization algorithms are studied and tested for the characteristics of the model,and the relaxation search algorithm which is suitable for the model characteristics is selected as the final numerical solution.