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Chapter 11

MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

11.1. PRINCIPLES OF MATHEMATICAL MODELING OF GEOLOGIC SYSTEMS

Exploration, development, and production of hydrocarbon resources must be
based on reliable information, which helps to predict the subsurface conditions and
properties of the oil- and gas-bearing formations. Consequently, both mathematical
modeling of the processes of deposition and evolution of sediments and concurrent
development of mathematical procedures for predicting reservoir pressures, oil and
gas composition, and petrophysical properties of reservoir rocks and seals are the
goals of high priority. The increase in depth of oil and gas occurrence with con-
sequent increase in the complexity of geological and environmental conditions that
affect the exploration for oil and gas, as well as development of new on- and offshore
fields requires application of a set of mathematical models to process geological,
geophysical, geochemical, and engineering data. This will aid in exploration, esti-
mation, and evaluation of oil and gas resources, and to achieve an efficient oil and
gas field development and production (Miller and Kahn, 1965; Krumbein and
Graybill, 1969; Krumbein et al., 1973; Harbaugh and Bonham-Carter, 1974;
Rodionov et al., 1987).
The use of mathematical methods and computer techniques increases the scope of
problems that can be solved on the basis of integrated geological, geophysical, geo-
chemical, and engineering information. Mathematical methods with computer
processing of the current information accelerate the process of regional and local
prediction of oil and gas potential, that, in general, increases the economic and
geologic efficiency of exploration, development, and production of oil and gas
fields (Buryakovsky et al., 1982, 1990, 1991; Buryakovsky and Agamaliyev, 1990;
Buryakovsky, 1992).
In the field of petroleum geology, the discovery and development of oil- and gas-
bearing basins, regions, zones, fields, etc. may be considered as dealing with integral
geologic systems, the evolution, structure, and behavior of which can be predicted.
Geologic system may be defined as follows:
Geologic system is a well-organized natural assembly of interconnected and interacting
elements of lithosphere having common development history and comprising a single nat-
ural unit with properties that are not inherent in its individual elements.
An important feature of these systems in petroleum geology (i.e., basins, regions,
zones, fields, etc.) is that division into subsystems of (1) reservoir (permeable) rocks
and (2) sealing (impermeable) rocks is possible. The presence of these two subsys-
tems defines oil and gas reservoir or trap. Absence of any one of these subsystems
(reservoir rock or seal) indicates the absence of reservoir or trap.
Geologic systems of oil- and gas-bearing basins, regions, zones, fields, etc. are
parts of the more extensive systems in the Earth’s crust. Owing to the absence of