SUMMARYInterface elements are a powerful tool for modelling discontinuities. Herein, we develop an interface element that is based on the isogeometric analysis concept. Through Bézier extraction the novel interface element can be cast in the same format as conventional interface elements. Consequently, the isogeometric interface element can be implemented in a straightforward manner in existing finite element software by a mere redefinition of the shape functions. The interface elements share the advantages of isogeometric continuum elements in that they can exactly model the geometry. On the other hand, they inherit the simplicity of conventional interface elements, but also some deficiencies, like the occurrence of traction oscillations when a high interface stiffness is used. The extension towards poroelasticity is rather straightforward, and in this situation the smoother flow profiles and the ensuing preservation of local mass balance are additional advantages. These are demonstrated at the hand of some example problems.
We present an alternative numerical approach for predicting the behaviour of a deformable fluid-saturated porous medium. The conventional finite element technology is replaced by isogeometric analysis that uses non-uniform rational B-splines. The ability of these functions to provide higher-order continuity and to exactly represent complex geometries makes isogeometric analysis a suitable candidate for accurately modeling a poroelastic medium. After some preliminaries regarding the formulation of isogeometric finite elements using Bézier extraction and a concise outline of poroelasticity theory, we describe how isogeometric finite elements can be used for a mixed formulation that results in case of a porous medium. The manuscript concludes by one-dimensional and two-dimensional examples, which demonstrate the superiority of the results of isogeometric finite element analysis in terms of the smoothness of the results compared with conventional finite element analysis and suggest that the requirement on the minimum time step for consolidation problems can be mitigated using interpolation functions that possess a higher-order continuity.
ReuseThis article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can't change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.A large deformation formulation for fluid flow in a progressively fracturing porous material AbstractA general numerical model has been developed for fluid flow in a progressively fracturing porous medium subject to large deformations. The fluid flow away from the crack is modelled in a standard manner using Darcy's relation, while in the discontinuity Stokes' flow is assumed, taking into account the change of permeability due to progressive damage evolution inside the crack. The crack is described in a discrete manner by exploiting the partition-of-unity property of finite element shape functions. The nucleation and the opening of micro-cracks are modelled by a tractionseparation relation. A heuristic approach is adopted to model the orientation of the cracks at the interfaces in the deformed configuration. A two-field formulation is derived, with the solid and the fluid velocities as unknowns. The weak formulation is derived next, assuming a Total Lagrangian formulation. This naturally leads to a set of coupled equations for the continuous and for the discontinuous parts of the mixture. The resulting discrete equations are nonlinear due to the cohesive-crack model, the large-deformation kinematic relations, and the coupling terms between the fine scale and the coarse scale. The capabilities of the model are shown at the hand of some example problems.
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Abstract. We present here a gas deliverability computational model for single reservoir with multi wells. The questions of how long the gas delivery can be sustained and how to estimate the plateau time are discussed here. In order to answer such a question, in this case, a coupling method which consists of material balance method and gas flow equation method is developed by assuming no water influx in the reservoir. Given the rate and the minimum pressure of gas at the processing plant, the gas pressure at the wellhead and at the bottom hole can be obtained. From here, the estimation of the gas deliverability can be done. In this paper we obtain a computational method which gives direct computation for pressure drop from the processing plant to the wells, taking into account different well behavior. Here AOF technique is used for obtaining gas rate in each well. Further Tian & Adewumi correlation is applied for pressure drop model along vertical and horizontal pipes and Runge-Kutta method is chosen to compute the well head and bottom hole pressures in each well which then being used to estimate the plateau times. We obtain here direct computational scheme of gas deliverability from reservoir to processing plant for single reservoir with multi-wells properties. Computational results give different profiles (i.e. gas rate, plateau and production time, etc) for each well. Further by selecting proper flow rate reduction, the flow distribution after plateau time to sustain the delivery is computed for each well.
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