Course overview
The course gives the theoretical basis and practical fundamentals for the mathematical modelling and numerical simulation of fluid flow in petroleum reservoirs. The governing laws and equations required for the modelling of single-phase and multi-phase flow in porous media, such as mass conservation, Darcy, equation of state, rock compressibility, capillary pressure and relative permeability, are reviewed. By combining these laws and equations, the corresponding partial differential equations are derived. The numerical methods for solving the governing partial differential equations are presented. A particular attention is given to the internal and external boundary conditions, and initial conditions. It is also demonstrated how numerical simulation can help us to forecast the reservoir performance in response to different field-development scenarios. The role of input data of reservoir simulators on the accuracy of prediction is another aspect which is reviewed in this course. It is also discussed how to reduce the inherent uncertainties in the input data, using inverse modelling techniques, known as history matching. Through several exercises and assignments, an overview of a commercial reservoir simulator is given.
Course learning outcomes
- Explain the mathematical and computational concepts behind commercial reservoir simulators
- Explain the physical laws that govern fluid flow in porous media
- Formulate single-phase and multi-phase flow in petroleum reservoirs
- Solve the governing partial differential equations using finite difference methods and interpret the potential numerical errors
- Treat internal and external boundary conditions and initial conditions
- Explain iterative matrix solvers and Understand the fully implicit and IMPES solution strategies for solving flow equations
- Write a program for simple problems
- Use a commercial reservoir simulator for studying the reservoir performance in response to different development strategies
- Develop some experience with history matching a reservoir simulation model
- Demonstrate the ability to work cooperatively in groups for the assignments