Higher order time discretization of compartmentalized reservoirs

Wang, Dan (2016) Higher order time discretization of compartmentalized reservoirs. Masters thesis, Memorial University of Newfoundland.

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Abstract

Reservoir tank modeling has traditionally been employed to simplify complicated reservoir simulation models and to reduce computational time whilst maintaining model accuracy. In this thesis, we refine this concept by replacing a simple tank model with a system of ordinary differential equations (ODEs) to model the dynamic changes of well inflow, aquifer influx, fluid compressibility, and pore volume. A dual time step method is used to solve the system of equations, which is not included in the existing model. Well transmissibility and aquifer sizes are kept constant during small time steps in which pressures and flow rates are solved. The new pressure is then used to update the well indices and aquifer size over larger time steps. This new model is transient during a single large time step calculation and hence represents an enhancement over standard finite difference method formulations. The reservoir is subdivided into a number of subvolumes representing individual reservoir compartments and aquifers, which may or may not be in communication. Using the concepts of transmissibility and compressibility, the complex 3D reservoir system is converted into a model that establishes flow into wells and between compartments. Pressure loss due to friction along the well is also fully integrated in the model. The multiple reservoir compartments and flowing wellbore are coupled to provide influx and inter-compartment fluid transfer. Employing the fourth-order Runge-Kutta Method, the ordinary differential equations generated by the system of reservoir units, are solved accurately and efficiently. The new method is verified by comparing it with a standard reservoir simulation launcher (Eclipse Trademark of Schlumberger Technology Corporation). Case studies are utilized to illustrate the results of the method which predict oil/gas production with water encroachment from an aquifer. Sensitivity analysis is performed to understand the relationships between input variables and output results in the model. For black oil reservoirs, this model incorporates wellbore friction and up to fifty reservoir compartments, which allows us to more accurately predict the reservoir performance. In addition, this model incorporates and compares the effects of compressibility for gas reservoirs, the results show that for those gas reservoirs with high rock compressibility, the gas reservoir model with water compressibility and pore volume term considered must be used in order to obtain more realistic simulation results.

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