Experimental Study on the Influence of Fracturing Fluid Retention on Shale Gas Diffusion Law

Shale gas reservoirs have poor physical properties and a large number of micro-nano pores have been developed.Shale gas wells have no natural productivity and need fracturing reconstruction measures to put into production.However,the fracturing fluid will enter the reservoir space of shale matrix after fracturing and affect the production of shale gas.At present,there is no consensus on the influence of fracturing fluid retention on gas well production.Based on this,the paper adopts gas molecular transport analyzer to carry out experimental research on the influence of fracturing fluid on shale gas diffusion law after entering matrix pores.The results show that:(1)Compared with the diffusion capacity of single-phase shale gas,the diffusion capacity of shale gas decreases significantly when fracturing fluid is present in the reservoir;(2)In the process of fracturing fluid flowback,when the water saturation in the reservoir decreases from 50%to 0,the gas well productivity increases by about 60%.(3)When fracturing fluid exists in the reservoir,the pore diameter has an exponential relationship with the shale gas diffusion coefficient,and the diffusion coefficient increases exponentially with the increase of pore diameter.The research of this paper provides theoretical basis for guiding the efficient development of shale gas wells.

Notes on Stefan-Maxwell Equation versus Graham's Diffusion Law

Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.

Chloride Diffusivity Analysis of Existing Concrete Based on Fick's Second Law

According to the existing concrete core samples obtained in site, chloride concentration and porosity of existing normal hydraulic concrete were measured, and chloride diffusivity in existing hydraulic concrete was studied. By Fick’s second law, the chloride diffusion coefficients in the steady diffusion area were calculated. The chloride diffusion of different mix proportion concrete was tested, and chloride diffusion coefficients and porosities of freshly concrete were measured, moreover, the relationship between diffusion coefficient and porosity was analyzed. The results show that the varying law of chloride diffusion coefficient with exposure time of existing concrete can be predicted in a better way by Fick’s second law and water-cement ratios or porosity of concrete and chloride concentration in existing concrete.

Simplification and Application of Boyd Membrane-diffusion Equation

The having-been-used-for-50-year Boyd membrane diffusion Equation-In(1 - F) = R t can be deduced into F = kt through using Maclanrin expansion equation and the Lagerange remainders. The latter is a simple membrane diffusion equation, which is available to judge if the exchanging course of the resin obeys the rules of membrane-diffusion mechanism more conveniently.

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

A class of one-way isothermal mass transfer processes with Fick’s diffusive mass transfer law[g ∝Δ(c)]is investigated in this paper.Based on the definition of the mass entransy,the entransy dissipation function which reflects the irreversibility of mass transfer ability loss is derived.The optimal concentration allocations of the key components corresponding to the highand low-concentration sides for the minimum entransy dissipation of the mass transfer process are obtained by applying opti- mal control theory and compared with the strategies of the minimum entropy generation,constant mass transfer flux(constant concentration difference),and constant concentration ratio(constant chemical potential difference).The results are as follows. For the optimal mass transfer strategy of the minimum entransy dissipation,the product of the square of the key component concentration difference between the high-and the low-concentration sides and the inert component concentration at the low-concentration side is a constant,while for that of the minimum entropy generation,the ratio of the square of the key com-ponent concentration difference between the high-and the low-concentration sides to the key component concentration at the low-concentration side is a constant;when the mass transfer process is not involved in energy conversion process,the optimi-zation principle should be the minimum entransy dissipation;the mass transfer strategy of constant concentration difference is superior to that of constant concentration ratio.The results obtained in this paper can provide some theoretical guidelines for optimal designs and operations of practical mass transfer processes.