Wave Equation Based On Non-Newtonian Fluid Of Fractional Derivative Constitutive Model In Double-Porosity Medium

Tight oil as a kind of unconventional resources has become a central issue of petroleum exploration industry. Researching on seismic wave propagation problem in porous media which saturated with fluid is the key to tight reservoirs to improve the exploration accuracy of oil and gas. The reasons for the difficulties of wave velocity prediction in tight reservoirs as follows: First, many prediction results obtained from the classical Biot theory often deviates from the actual situation according to a number of practical experiences, and wave dispersion and attenuation often occurs in the ultrasonic frequency band; numerical examples show that the Biot theory is more unsuitable for the calculation under conditions of low permeability. Second, the effect of non-Newtonian fluid characteristics to the wave propagation is not clear because the porosity and permeability of tight reservoirs is very low. In addition, the porous structure of this medium is very complex, and the heterogeneous characteristic is strong, characterization of complex pore inner space is necessary. I explored these questions preliminary in this thesis. Thus the main content of my thesis is to develop the wave equations which could obtain the seismic wave velocity dispersion and attenuation relationship to describe the wave propagation characteristics well, and then realize velocity prediction in tight oil reservoirs. Details are as follows:(1) Analysis and verify the non-Newtonian characteristics of porous fluid in tight reservoir. On the basis of researched literatures and combined with the results of molecular dynamics simulations, I analysis the characteristics of fluid in micro/nano channels and flow behavior, then put forward the point that non-Newtonian constitutive model is more appropriate to describe the fluid’s relationship of shear stress and shear rate in micro and nano pipe.(2) Introducing the dissipation mechanism caused by fluid internal viscous. In view of the porous fluid exhibits solid-like characteristics, I assume that the fluid can withstand shear stress in the flowing process. The fluid’s flow under wave’s exciting will cause additional dissipation of itself due to viscous forces. Assuming that there is a linear function between this part of dissipative and viscous force.(3) Establish the wave equations for the tight dual-porosity porous medium based on non-Newtonian fluids with fractional constitutive model. Starting from the analytical mechanics Hamiltonian principle, establish the potential function, the kinetic energy and dissipation function of tight reservoirs dual-porosity structure medium with fluid-solid two-phase. Then, derive the wave equation based on the Lagrange equation, solve the equations in frequency-wavenumber domain and we will obtain the theoretical velocity dispersion and attenuation curves under the parameter conditions of low porosity and permeability. At last, compare the calculated results with the classical theory’s results.A number of numerical examples illustrate the effect of the non-Newtonian fluid to seismic wave dispersion and attenuation. Then I will analysis the effects of permeability to the calculation results. Finally, apply the theoretical predictions to the experimental data and log data to verify the validity and applicability of the method in this thesis.