Introduction to Numerical Reservoir Simulation

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Day 1 :MAIN PHYSICAL LAWS
Porosity
Darcy’s law
Relative Permeability
Capillary pressure
The continuity equation

Day 2 :
SLIGHTLY COMPRESSIBLE MONOPHASIC FLOW
From physical case to mathematical model
From math model to numerical model
Study of stability and convergence of numerical methods
Build a numerical simulator using “SCILAB software” and show numerical experiences

Day 3 :
SIMULTANEOUS FLOW OF 2 IMMISCIBLE FLUIDS INCOMPRESSIBLE, HORIZONTAL
Without capillary-pressure
From physical case to math model
Study of the saturation equation “The Buckley-Leverett equation”
Study of stability and convergence. Build a numerical simulator and show numerical experiences
2-D problem front tracking and grid effects
Study of the five – Spot pattern – Build the math model and the numerical model
Present numerical experiments – Front tracking – Grid effects
Compare the results with solution of equivalent “moving boundary problem”

Day 4 :
SIMULTANEOUS FLOW OF 2 IMMISCIBLE FLUIDS INCOMPRESSIBLE, HORIZONTAL
With capillary-pressure
From physical case to math model
Study of the saturation equation with capillary pressure
Study of the “boundary conditions”
Build a numerical simulator and present numerical experiments

Day 5 :
THE BLACK-OIL MODEL
Thermodynamic model for the two phases flow of two components (oil and gas)
Build the mathematical “black-oil model”
Derive the numerical model
The IMPES method

Langue

Français & Anglais

Public visé

Students in “Reservoir engineering”, Students in “Applied mathematics”.

Durée prévisionnelle

This integrated week and the integrated week “Use of Numerical Simulation for Reservoir Modeling” are generally coupled and presented jointly to constitute a double integrated week (30 hrs).

Moyens Pédagogiques

slides.

Prérequis

Objectifs

Modern numerical simulators are high performance tools and more and more user-friendly. However, it could hazardous to trust blindly this tools, ignoring the main problems which are hidden at the core of each math model and which may lead to erroneous results. We present 4 different basic cases of flow of fluids through porous medium. For each one we present the physical case, we build the math model and we derive the numerical model by discretising space and time, and we compute the solution. We show the main critical points of the different step which brings about the development of a numerical simulator.