An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non-linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non-linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable. and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.

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An implicit coupled double‐porosity model has been presented for simulating the behavior of deformable fissured porous media. The finite element technique was used to develop the numerical approximation of the governing equations. Using the proposed model, the effect of matrix deformation on the behavior of fissured porous media was studied. It was found that (1) the response of a deformable fissured porous medium is identical to that of rigid formations with regard to three distinct periods of early, intermediate, and late time responses; (2) while matrix deformation can significantly contribute to the late time productivity of fissured porous media, it has very limited effect on the early time productivity; (3) during the early time response period, fluid pressure tends to rise in porous blocks before starting to fall; this is believed to be consistent with the coupling behavior of deformable fissured porous media; and (4) the fissure response of a deformable fissured porous medium may be practically simulated using the model proposed by Barenblatt et al. (1960) and Warren and Root (1963).

SUMMARYThe problem of ill-conditioning in anisotropic and heterogeneous flow regions using plane and axisymmetric conditions is studied. A new concept, conditioning ratio, which covers all the possible factors significantly affecting the problem of ill-conditioning (e.g. aspect ratio, heterogeneity and anisotropy) is proposed. It has been shown that there is an upper limit for this conditioning ratio, beyond which the stiffness matrix of the modelled region will be ill-conditioned. Using this limiting value and considering the fact that flow behaviour in a single fracture is, basically, independent of the value of permeability normal to the plane of the fracture, k,, a criterion is established to calculate the value of k , for thin elements. By adopting this criterion the problem of ill-conditioning could be avoided, regardless of the value of the aspect ratio. The reliability of the proposed criterion is examined by using thin elements with very large aspect ratio (up to lo6) in modelling the pumping problem from a well fully intersecting a vertical fracture. The comparison of the numerical results with the available analytical solutions is found to be very satisfactory.