Wave propagation in an hydrocarbon reservoir during exploitation: A a preliminary, integrated study

INTRODUCTION Problem of reservoir estimation. The optimal exploitation of hydrocarbon reservoirs requires the accurate estimation of the reservoir's characteristics. Placement of wells, injection of gas and water, and production rate of hydrocarbons depend on the correct assessment of the reservoir properties. Furthermore, the field's properties change over tim e as reservoir pore fluid is removed. I advocate to assess a reservoir's state by an integrated inversion of combine well test, well log, and seismic data. This paper is result of my exploratory reading and discusses the physics of reservoir flow and seismic wave propagation in porous rocks. The paper includes simple finite difference simulations for reservoir fluid flow and wave propagation. Overview over various sections. Inversion. The section on inversion considers when inversion problems should be integrated and when they should be separated. Reservoir flow simulator. The section on reservoir flow simulation canvasses the fundamental equations based on Darcy's law, mass conservation, and gas-oil-water mixtures (black oil model). Additionally, the section introduces a simple simulator for a single phase fluid that I implemented. Wave equation for porous rocks. The third section considers wave propagation in a porous rock medium. Central to the section is Gassmann's velocity expressions. Additionally , the section discusses Biot's derivation of frequency dependent wave equation for a saturated porous rock. The section discusses a simple implementation of an acoustic wave simulator. A first experiment. The final section simulates the fluid flow and seismic time-lapse experiments over a simple reservoir model. For lack of time, the example currently simplifies much of the theory discussed in the paper. The historic success of simple models in seismic analysis encourages such a simplified first attempt. Darcy-Gassmann-Elastic formulation Several competing physical models of porous rocks exist. The models usually vary in their assumptions and their mathematical sophistication. A scientist ought to choose the most parsimonious model for the experiment. The popular Darcy-Gassmann-Elastic formulation combines the feasible state of the art of all three fields into a single model. The formulation of the reservoir flow and Gassmann's elastic parameters are directly based on macroscopic models of porous rock. However, it is unclear 2 if the combination of the three formulations is computationally feasible or parsimonious. The formulation and implementation of the seismic and well simulation is my first step towards a future inversion of experimental field data. All simulators are implemented in Jest (Schwab and Schroeder, 1997), an inversion framework. The simulators …