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An UnCoupled Radial Flow Poroelastic Model with Local Thermal (Non) Equilibrium

机译:具有局部热(非)平衡的解耦径向流动络弹簧模型

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This paper introduces a new thermo-poroelastic model in terms of analytic equations, to describe the rock deformation produced by fluid injection/extraction in geothermal reservoirs, using radial coordinates. The model is fully coupled in isothermal poroelastic conditions, but is thermally uncoupled if local thermal non-equilibrium (LTNE) is considered. The uncoupled model describes the flow of fluid and conductive-convective heat in linearly deformable porous rocks according to linear Biot's theory. The fluid flow can be of Darcy's type or non-Darcian. There are thirteen unknowns in this model: fluid pressure, variation of the fluid content in the pores, radial displacement of the solid skeleton, radial and tangential strains and stresses, porosity, deformation velocity of the solid, fluid velocity and rock and fluid temperatures, respectively. Except the temperatures, all the unknowns are explicit functions of radius and time f(r, t). Considering LTNE, there is an effective volumetric heat transfer q_(sf) [W/m~3 ] between the solid skeleton and the liquid. The porosity is estimated as a function of fluid pressure and temperature. The radial deformation of the solid rock u_r is an irrotational vector field, as a consequence, the variation of the fluid content ζ_f, becomes proportional to the pore pressure p_f, which is calculated using the classical Theis model. In these conditions, the diffusion equation of ζ_f is integrated to obtain the solid radial displacement u_r (r, t) in analytical form. The system of simultaneous equations with all its unknowns is immediately solved in cylindrical coordinates. Once the fluid velocity is obtained, the fluid temperature can be computed using a new analytical solution of the diffusion-convection equation. This radial thermoporoelastic model is didactic, useful and simple to use. It allows to explore different conditions for both the fluid and the geomechanical parameters, as well as different boundary and initial conditions; therefore, it can be used as a benchmark to test fully numerical models. Graphical results are shown to illustrate practical cases with extraction and injection of fluid into a reservoir using real data. This work is a current research in progress.
机译:本文介绍了解析方程换算的新的热多孔弹性模型,以描述由流体注入/提取在热储产生的岩石变形,使用径向坐标。该模型被完全耦合在等温条件下多孔弹性的,但如果本地热非平衡(LTNE)被认为是热解偶联。未耦合模型描述流体和导电对流热在根据线性Biot理论线性变形的多孔岩石中的流动。流体流可以是达西型或非达西的。有13个未知数在该模型:流体压力,在孔隙中的流体含量的变化,固体骨架,径向和切向应变和应力,孔隙率,固体,流体速度和岩石和流体温度的变形速度的径向位移,分别。除的温度,所有的未知量是半径和时间f(R,T)的明确的功能。考虑LTNE,有固体骨架和液体之间的有效体积传热Q_(SF)[W /米〜3]。孔隙率被估计为流体的压力和温度的函数。固体岩石u_r的径向变形是不旋转的矢量场,其结果,流体含量ζ_f的变化,变得正比于孔隙压力P_F,这是使用经典泰斯模型计算。在这些条件下,ζ_f的扩散方程被集成在解析形式以获得固体径向位移u_r(R,T)。与所有的未知数的联立方程,系统立即解决了圆柱坐标。一旦获得了流体速度,流体温度可利用扩散对流方程的一个新的解析解来计算。这种径向thermoporoelastic模型是说教,实用,简单易用。它允许探索用于流体既和地质力学参数,以及不同的边界和初始条件不同的条件;因此,它可以被用作基准测试充分数值模型。图形结果被示出以说明实际例提取和流体注射到使用真实数据的储存器。这项工作是正在进行的研究现状。

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