The second law of thermodynamics determines the practical limits of operating systems. However, within these limits, conditions leading to optimum performance can be found.

In reservoir analyses the conditions or variables which are controllable are somewhat limited. These include well head pressure, production or injection rate, number of wells and production or injection rate, number of wells and their locations and the recovery technique. The efficiency of reservoir exploitation decreases as the entropy generation increases. Since entropy generation translates into irreversible loss of fluid energy, the operating conditions of a reservoir should be selected to minimize the entropy generation over the productive life of the reservoir.

In this paper, it is shown how entropy generation function is calculated and used as a guideline for selecting the conditions leading to high ultimate recovery. This is accomplished by calculating the cumulative entropy generation over the reservoir volume and the production period and by determining the conditions minimizing the entropy generation.


The amount of oil and gas which may be recovered from a reservoir is a widely varying quantity, dependent partly on the particular conditions imposed by nature on the underground structural trap and on the properties of the contained fluids, and subject further to the controls exercised by the operator in its development and operation. The most important factors which influence the recovery of oil are (a) the characteristics of the productive formation, such as the permeability, porosity, and structural configuration, (b) the properties of the reservoir fluids, and (c) the operating controls, including control of the available driving mechanisms, the rate and location of production of reservoir fluids, and the pressure behavior. However, only the production rate can be externally controlled once the locations of the wells are fixed. Many authors recognized very early the role of production rate on the ultimate oil recovery and production rate on the ultimate oil recovery and concluded that there exists a maximum rate of production that will permit reasonable fulfillment production that will permit reasonable fulfillment of the basic requirements for efficient recovery. Increase in the production rate beyond this maximum value will usually lead to rapidly increasing loss of ultimate recovery, and reduction in rate below this maximum will not substantially increase the ultimate recovery of oil. Considerable controversy exists concerning the degree of efficiency attributable to rates, however, everyone recognizes the importance of using efficiently the in-situ reservoir energy.

Versluys and Schilthius investigated the reservoir energy changes that occur during the course of production. Schilthius based his study on an imaginary thermodynamic engine in which net change in energy is equivalent to that in petroleum reservoirs. His analysis provided an explanation of the energy supplied by various sources, including the expansive energy of the oil and the gas with which it is associated, both dissolved and free, the energy supplied by water drive, and the energy of gravity. However, his approach did not include the loss of fluid energy due to irreversible processes, and is only applicable to macroscopic processes and volumetric reservoirs. Lacey and Sages applied thermodynamic concepts to analyze the energy relations in a flowing well and demonstrated the usefulness of these concepts.

P. 285

This content is only available via PDF.
You can access this article if you purchase or spend a download.