Mass transfer in a porous medium by thermally driven fluid convection: a numerical model and its application to the Travis Peak Formation, East Texas

J. Gerretsen; W.H. Breeuwsma; H. de Boorder; C.J. Spiers

J. Gerretsen Institute of Earth Sciences, University of Utrecht, P.O . Box 80.021, 3508 TA Utrecht, The Netherlands
W.H. Breeuwsma Institute of Earth Sciences, University of Utrecht, P. O. Box 80.021, 3508 TA Utrecht, The Netherlands
H. de Boorder Institute of Earth Sciences, University of Utrecht, P.O. Box 80.021, 3508 TA Utrecht, The Netherlands
C.J. Spiers Institute of Earth Sciences, University of Utrecht, P.O . Box 80.021, 3508 TA Utrecht, The Netherlands

Keywords: mass transfer, porous medium, fluid convection, numerical model, Travis Peak Formation

Abstract

The diagenetic change of porosity by long range solution-precipitation mass transfer in a freely convecting porous medium is investigated by numerical modelling. From the conservation of mass and energy, assuming Darcian flow and local chemical equilibrium, making the Boussinesque approximation and neglecting deformation effects, a set of dimensionless partial differential equations is derived. These are then transformed into a set of algebraic equations, using a central finite difference method. Solutions were obtained using an implicit Gauss-Seidel relaxation method as well as an explicit method employing direct matrix inversion plus time stepping. The coupling between fluid flow behaviour (determined by the Rayleigh number) and local mass balance is established through a linear relation between the relative change in permeability and relative change in porosity. The results obtained for steady state convection omitting solute transport effects are in good agreement with numerical and laboratory scale experiments reported elsewhere. When solution-phase transport is permitted the reservoir porosity shows an exponential change with time at rates twice those predicted using a simpler analytical approximation. The numerical model is used to evaluate the development of porosity in the Travis Peak Formation of East texas. This formation consists of well-sorted, fine-grained quartz arenites deposited in the Early Cretaceous. During the early stages of diagenesis, the average porosity decreased from25% to 10% as a result of quartz cementation. Explanations based on an influx of warm meteoric fluids are questionable because of the large fluid-to-rock ratios required. However, taking into account geological constraints on heat flux, starting permeability and layer thickness, our numerical simulations show that long range solution transfer in a freely convecting closed system may well explain the rapid decrease of porosity observed in the Travis Peak Formation.