NUMERICAL MODEL OF PRESSURE AND VELOCITY FIELDS IN AXISYMMETRIC FILTRATION IN AN IMPERFECTLY PENETRATED STRATUM

A mathematical model of pressure and velocity fi elds resulting from the infl ow of hydrocarbons to a well of fi nite radius from partially penetrated reservoir beds has been presented. It is assumed that two-dimensional fl ow initiated by an assigned depression in an imperfectly penetrated stratum is axisymmetric. A mathematical formulation of the problem in cylindrical geometry on the pressure fi eld in an isolated isotropic homogeneous stratum whose boundaries do not coincide with the boundary points of a perforation interval has been given. A fi nite-diff erence model has been described on whose basis a program was made up for calculation of pressure and velocity fi elds in the stratum and computational experiments were consducted which allowed identifying new regularities of fl ow of practical importance that arise in actual oil and gas reservoirs. Space–time dependences of the pressure fi eld in an oil and gas stratum and of the radial components and modulus of fi ltration velocity of hydrocarbons have been shown, which illustrate the distinctive features of two-dimensional fl ow with imperfect penetration of the stratum and basic diff erences from the well-studied case of plane radial onedimensional fl ow to the well of fi nite radius. Based on an analysis of the contour lines, new physical regularities of the fl ow have been identifi ed that are associated with incomplete perforation of the thickness of the reservoir bed. By the numerical experiments, it has been established that in axisymmetric fl ow in the stratum, vertical fl ows inevitably arise which vanish at exit from the stratum into the well. It has been confi rmed that in homogeneous incompletely penetrated reservoirs, intralayer crossfl ows arise in the near wellbore zone, and the radial component of fi ltration velocity in two-dimensional axisymmetric fl ow in the imperfectly homogeneous isotropic stratum depends on the vertical coordinate. This means that the infl ow to the well is not uniformly distributed over the stratum thickness, and the modulus of the horizontal velocity component in all the curves peaks on the boundaries of the perforation interval. In the case of two-dimensional fl ow at the center of the perforation interval equally distant from the upper and lower boundaries of the oil and gas stratum, a minimum specifi c infl ow is observed.
A mathematical model of pressure and velocity fi elds resulting from the infl ow of hydrocarbons to a well of fi nite radius from partially penetrated reservoir beds has been presented. It is assumed that two-dimensional fl ow initiated by an assigned depression in an imperfectly penetrated stratum is axisymmetric. A mathematical formulation of the problem in cylindrical geometry on the pressure fi eld in an isolated isotropic homogeneous stratum whose boundaries do not coincide with the boundary points of a perforation interval has been given. A fi nite-diff erence model has been described on whose basis a program was made up for calculation of pressure and velocity fi elds in the stratum and computational experiments were consducted which allowed identifying new regularities of fl ow of practical importance that arise in actual oil and gas reservoirs. Space–time dependences of the pressure fi eld in an oil and gas stratum and of the radial components and modulus of fi ltration velocity of hydrocarbons have been shown, which illustrate the distinctive features of two-dimensional fl ow with imperfect penetration of the stratum and basic diff erences from the well-studied case of plane radial onedimensional fl ow to the well of fi nite radius. Based on an analysis of the contour lines, new physical regularities of the fl ow have been identifi ed that are associated with incomplete perforation of the thickness of the reservoir bed. By the numerical experiments, it has been established that in axisymmetric fl ow in the stratum, vertical fl ows inevitably arise which vanish at exit from the stratum into the well. It has been confi rmed that in homogeneous incompletely penetrated reservoirs, intralayer crossfl ows arise in the near wellbore zone, and the radial component of fi ltration velocity in two-dimensional axisymmetric fl ow in the imperfectly homogeneous isotropic stratum depends on the vertical coordinate. This means that the infl ow to the well is not uniformly distributed over the stratum thickness, and the modulus of the horizontal velocity component in all the curves peaks on the boundaries of the perforation interval. In the case of two-dimensional fl ow at the center of the perforation interval equally distant from the upper and lower boundaries of the oil and gas stratum, a minimum specifi c infl ow is observed.
Author:  A. I. Filippov, O. V. Akhmetova, M. R. Gubaidullin
Keywords:  fi ltration, imperfect penetration, piezoconductivity equation, two-dimensional fl ow, fi nite-diff erence program, pressure fi eld, velocity field
Page:  955