Modeling Of Deformed Porous Materials Induced By Gas Adsorption And Its Applications

It is generally accepted that gas adsorption can induce the deformation of porous materials, in which the knowledge of the deformed solid matrix is very important for economic developments and many other applications. Particularly, it is crucially concerned to recovery of coal bed methane(CBM) and carbon dioxide sequestration in coal reservoirs in the viewpoint of constitutive model, which is usually employed to describe the swelling of porous materials. On the one hand, much work in the past has been mostly focused on the phenomena of gas adsorption in chemistry science, which is usually concerned only with the inert adsorbent and does not deal with the deformation of solid matrix. On the other hand, the constitutive models used to compute the deformation of porous materials have significantly been developped by means of continuum thermodynamics, which cannot be used to describe the interaction between pore liquid and solid matrix. Thus, combining with the two subjects, further studies of constitutive models of porous materials with adsorption effect should be required. This PhD thesis was dedicated to the study for constitutive model of porous materials with adsorption effect based on the knowledge of porous thermodynamics, finite deformation theory and surface physical chemistry. In particular, the study of swelling coal induced by gas(CH4 and CO2) adsorption was carried out completely. Four conclusions are summarized as follows:(1) from mechanics of porous elastoplasticity and the principle of maximum plastic dissipation, the expressions of volumetric stress and pore pressure as function of volumetric strain, porosity and shear strain were obtained without adsorption effect. It was shown that both the volumetric stress and the pore pressure are depended upon not only volumetric strain and porosity but also shear strain when appearred plastic deformation. However, they were depended on only the volumetric strain and the porosity when occurred elastic deformation. With the help of Helmholtz free energy and Drucker-Prager yield criteria, the explicit formulation of elastoplastic tangent modulus was given under the assumptions of infinitesimal deformation and associated flow rule.(2) On the basis of constitutive model of porous materials without adsorption effect under infinitesimal deformations, the corresponding constitutive model at finite deformation was obtained according to the local multiplicative decomposition of deformation and the nonlinear evolution of porosity. In the principal stress space, consistent tangent modulus was discussed completely at finite deformation. By means of the logarithmic strain at finite deformation, we showed that the computing implementation of constitutive model for both the small deformation and the finite deformation is identical, according to the return mapping algorithm. In the numerical examples, we concluded that the compressive stress increased slightly when the solid was in plastic state due to finite deformation effect, although the no hardening yield surface was chosen.(3) Considering two boundary conditions, two different differential equations used to calculate the swelling and permeability change of coals induced by gas(CH4 and CO2) adsorption were obtained, respectively. Analogous to the atmospheric pressure in the gravity field, the pore pressure in adsorption field was assumed to change along the normal direction of the solid surface. Using virial expansion for some physical quantities in thermodynamics, the pore pressure imposed on the solid surface is assumed as a function of bulk pressure for a porous material under isothermal conditions. The advantages of the developed model under these assumptions in the thesis are that it can be used to not only describe the physical and mechanical properties of porous materials in the viewpoint of macroscopic scale, but also explain the causes of the swelling coals induced by gas(CH4 and CO2) adsorption from the micro point of view. A general formulation between surface strain and volumetric strain was derived under infinitesimal deformation conditions. The surface stress induced by gas adsorption can be modified by some kind of isothermal adsorption such as Langmuir isothermal adsorption and van der Waals equation of state. By providing that the ratio of current permeability to initial one was equal to the cubic ratio of current porosity to initial porosity, the differential equations for permeability change was consequently obtained. The present simulations showed that the predictions from the model are not only in good agreement with the experimental results of permeability change of coal induced by gas(CO2 and CH4) adsorption under confined pressure conditions in the literature but also much better than that simulated by the Shi-Durucan model and the Palmer-Mansoori model. The same results were obtained in the numerical examples of swelling coals induced by gas adsorption. It was shown that the numerical results of adsorption-induced permeability change and swelling of coal are strongly sensitive to the coefficients of pore pressure which are closely associated with the interactions between adsorbed gas and solid matrix. We concluded that the bulk modulus and the Biot coefficient separately play key roles in the characterization of permeability change and swelling of the coals under coupled actions.(4) On the basis of the elastic constitutive model of porous materials with adsorption effect under infinitesimal deformations, the corresponding elastoplastic constitutive model could be obtained by using plastic theory and additive decompositions of small strain and linear porosity. The elastoplastic constitutive model with adsorption effect at finite deformation was then derived with the help of the local multiplicative decomposition and the nonlinear evolution of porosity. The functional relation between finite volumetric strain of porous materials and nonlinear Lagrangian porosity was developed under the infinitesimal deformations of solid matrix. The first-order derivatives of specific surface area with respect to finite volumetric strain and nonlinear porosity change were accordingly derived. Finally, the implementation of elastoplastic constitutive model with adsorption effect could be derived in terms of the closest point project method.