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Nina Artamonova, Lomonosov Moscow State University (Russian Federation)
Sergey Sheshenin, Lomonosov Moscow State University (Russian Federation)
Ernest Kalinin, Lomonosov Moscow State University (Russian Federation)
Fedor Kiselev, Lomonosov Moscow State University (Russian Federation)
Leili Panasyan, Lomonosov Moscow State University (Russian Federation)
Eldar Kakushev, Lomonosov Moscow State University (Russian Federation)
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This paper presents numerical simulation of the stress and fluid pressure in porous solid rock during transient or stationary pumping. The model is based on the poroelasticity Biot's theory, which describes coupling of rock deformation and fluid flow. The model takes into account complicated structure of the real geological object. Mathematical formulation of the coupled initial boundary problem consisting of elasticity and filtration equations is given in the form of variational equations. Solution existence and uniqueness theorems are proved.
The variational problem is solved using a finite-element method and time increment approach. As a result linear system of equations with ill-conditioned matrix of block structure arises at every time step. The matrix is ill-conditioned, if time step is small and realistic rock properties are taken. Consequently, significant efforts were made to improve efficiency of solution. Several algorithms were proposed and compared.
The developed numerical simulation was tested in calculation of rock deformation that occurred during pumping from oil deposit in Russia. The calculations based on 3D Biot's model are compared with the results determined using the Biot's model in axisymmetric formulation. The conclusions concerning elaborated simulation efficiency are discussed.
Research was conducted under the financial support from RFBR (08-05-00578-a)
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