34761 - Polyphasic Flow Models M

Learning outcomes

The learning outcome of this course is to give the fundamental knowledge to simulate the exploitation of the hydrocarbon and geothermal reservoirs: the philosophy and methodology behind numerical simulation, differential equations governing the bi and three phase fluids flow in porous media, discretization of differential equations and their numerical integration, analysis of the typical numerical simulators architecture used in the industrial environment.

Course contents

General introduction to the study of reservoir (of hydrocarbon, water and geothermal) dynamic behavior through numerical simulators. System and model relationships, definitions and classifications. The mass balance equation. Multiphase Darcy's law. Heat transport equation: energy balance for an open system. Mathematical model of a reservoir: radial flow through porous media for slightly compressible single phase fluid.
Classification of mathematical reservoir models based on geometry and number of mobile phases. Flow model for gas fluid. Equation for a two and three phases models without mass exchange among phases. Black-oil model for heavy oil reservoirs. Volatile oil model. Compositional multiphase flow model. Model of confined aquifer. Model of a unconfined aquifer. Elements on non-isothermal model of multicomponent, multiphase fluids flow in porous and fractured media.
Basic principles of Finite Difference (FD) method for the numerical integration of the partial differential equations. Elements of convergence, consistency, and stability of the FD scheme. Truncation errors. Different grade of implicitness in the simulation with multiphase models: implicit pressure explicit saturations (IMPES), sequential method (SEQ), full implicit method (SIMULTANEOUS). Solution of linear algebraic equations systems: direct methods (Gauss elimination method, factorization method, Thomas algorithm for tridiagonal systems), iterative methods (Jacobi, Gauss Siedel, PSOR, LSOR).The forward and inverse problem. Model calibration: history matching. Sensitivity analysis.

Readings/Bibliography

1- Teacher's lecture notes.
2- W. Kinzelbach. Groundwater modeling - An introduction with sample programs in BASIC, Elsevier, New York, 1986.
3- G. L. Chierici. Principi Di Ingegneria Dei Giacimenti Petroliferi, vol. 1-2, ENI, Milano, 1991.
4- D.S.Oliver, A.C. Reynolds and N. Liu. Inverse theory for petroleum reservoir characterization and history matching. Cambridge University press, Cambridge, 2008.
5- J. Bear, Y. Bachmat. Introduction to Modelling of Transport Phenomena in Porous Media, Kluwer Academic Publ., Dordrecht, 1990.

Teaching methods

Lessons will be traditional by demonstrations on the blackboard and with exercises, also using dedicated software, on the lessons arguments.

Assessment methods

Final exam (oral).

Teaching tools

Overhead projector, Projector, Personal Computer.

Office hours

See the website of Villiam Bortolotti