# Flow and Transport
Through Porous Media II

# Multidimensional
Displacement

# Instructor: G. J.
Hirasaki

## Finite Difference
for Fractional Flow Equation

### Differential equation

Up stream weighting

Explicit or Implicit

Truncation error

Stability analysis

Time step selection

## Dispersion

### Mechanisms for dispersion

One dimensional convection with dispersion

Estimation of dispersion coefficient

Mixing zone growth

Finite slug

## Hydrostatic Fluid Distribution

### Capillary pressure
definition

Capillary pressure curves

Scaling of capillary pressure

Hydrostatic fluid distribution

Three phase distribution

Reservoir seals

Outflow boundary condition

Methods of measurement

Capillary pressure models

Effects of wettability

## Finite Difference in
1-D with Capillary Pressure

### Differential equation
and boundary conditions

IMPES formulation

Semi-implicit formulation

Block tridiagonal matrix

## Multidimensional, Multiphase
Displacement

### Generalized material
conservation equations

Hydrocarbon phase behavior

Particular fluid systems

## Finite Difference Solution
in Multidimensions

### Finite difference
in time

Regular grid spacing

Variable grid spacing

Material balance check

IMPES formulation

Semi-implicit formulation

ADI

Preconditioned Conjugate Gradient

## Reservoir Geometry
and Properties

### Curvilinear coordinates

Cylindrical r-z coordinates

Reservoir geometry

## Well Models

### Relation with grid
block

Well impairment

Saturation dependence

Well common to several grid blocks

Vertical lift performance

Oil-water coning model

## Reduction to Two Dimensions

### Averaged conservation
equations in two dimensions

Vertical equilibrium

Stiles-Hearn model for layered formation

Page maintained by: G. J. Hirasaki, gjh@rice.edu

Last updated: May 22, 2001
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