ABSTRACT
Every simulation study is a unique process, starting from the
geological model and reservoir description to the final analysis of
recovery factor optimizations. In petroleum engineering area, numerical
reservoir simulators are often employed to obtained meaningful and
reliable solutions for most actual cases due to extreme complexity of
reservoir systems.
In this work, a three-dimensional numerical reservoir simulator is
developed for expansion-drive reservoirs. The governing equation is
discretized using finite difference approach; conjugate gradient method
with the aid of MATLAB 9.0.0R code is used to solve the system of linear
equations to obtain reservoir pressure for each cell, until bubble
point pressure is reached; cumulative production at bubble point is
computed as sum of expansion from each cell and oil production rate is
determined at each time step. The average reservoir pressure is
determined as a weighted average based on the stock tank oil that is
left in the reservoir, and finally the recovery factor at the bubble
point pressure is computed.
Contour plots (with colour map to ease the user’s assimilation and
interpretation of the simulator results), of reservoir pressure
depletion with time were generated for different number of
finite-difference grid blocks. The results indicate that the more the
number of grid blocks used, the more accurate the numerical solution and
the more detailed the description of the reservoir fluid distribution.
The plot of average reservoir pressure against time shows a rapid
decline in the average reservoir pressure due to the negligible
compressibility associated with rock and liquid expansion-drive
reservoirs. The estimated oil cumulative production of 236MSTB was
recovered in 1180days up to the bubble point using the developed
simulator. Furthermore, sensitivity analysis was performed to
investigate the impact of key reservoir parameters the average reservoir
pressure.
CHAPTER ONE
INTRODUCTION
1.1 General Introduction
Reservoir simulation is the science of combining physics,
mathematics, reservoir engineering, and computer programming to develop a
tool for predicting hydrocarbon reservoir performance under various
operating strategies (Aziz, K. and Settari, A. 1979).
The practice of reservoir simulation has been in existence since the
beginning of petroleum engineering in the 1930's. But the term
"numerical simulation" only became common in the early 1960's as
predictive methods evolved into relatively sophisticated computer
programs. These computer programs represented a major advancement
because they allowed solution of large sets of finite-difference
equations describing two- and three-dimensional, transient, multiphase
flow in heterogeneous porous media. This advancement was made possible
by the rapid evolution of large-scale, high-speed digital computers and
development of numerical mathematical methods for solving large systems
of finite-difference equations.
Fluid flow in petroleum reservoirs (porous media) is very complex
phenomena, and as such analytical solutions to mathematical models are
only obtainable after making simplifying assumptions regarding reservoir
geometry, properties and boundary conditions. However, simplifications
of this nature are often invalid for most fluid flow problems and in
many cases, it is impossible to develop analytical solutions for
practical issues due to the complex behaviors of multiphase flow,
nonlinearity of the governing equations, and the heterogeneity and
irregular shape of a reservoir system. Due to these limitations in the
use of analytical method, these models must be solved with numerical
methods such as finite difference.
Reservoir simulation is one of the most effective tools for reservoir
engineers that involves developing mathematical equations or computable
procedure that are employed to understand the behaviour of the real
reservoir (Darman, 1999).
Today, numerical reservoir simulation is regularly used as a valuable
tool to help make investment decisions on major exploitation and
development projects. These decisions include determining commerciality,
optimizing field development plans and initiating secondary and
enhanced oil recovery methods on major oil and gas projects. Proper
planning is made possible by use of reservoir simulation; it can be used
effectively in the early stages of development before the pool is
placed on production so that unnecessary expenditures can be avoided.
When crude oil is discovered, in order to have proper understanding
of reservoir behaviour and predict future performance, it is necessary
to have knowledge of the driving mechanisms that control the behaviour
of fluids within reservoirs. The overall performance of oil reservoirs
is largely determined by the nature of the energy available for moving
the oil to the wellbore. The recovery of hydrocarbons from an oil
reservoir is commonly recognized to occur in several recovery stages.
They are: Primary recovery, Secondary recovery, Tertiary recovery
(Enhanced Oil Recovery, EOR), and Infill recovery.
Primary recovery is the recovery of hydrocarbons from the reservoir
using the natural energy of the reservoir as a drive. The term refers to
the production of hydrocarbons from a reservoir without the use of any
process (such as fluid injection) to supplement the natural energy of
the reservoir (Ahmed, 2006).