Masters Theses


"The purpose of this investigation is to show that it is economically feasible to produce marginal gas wells in such a manner that all the gas from the edge of the field will be captured by the first row of wells. In this problem the permeability of the sand is to be variable but known, and the effects of this variable permeability on the pressure distribution, and resulting gas production, will be discussed.

In many gas fields the point at which it is generally considered unprofitable to drill new wells is well inside the boundary of the reservoir. This is due primarily to a reduction of permeability and porosity as the boundary of the reservoir is approached. The quantity of gas which is outside the economic limit is frequently quite large in relation to the amount within the drainage area of any interior well. It will subsequently be shown that all this large quantity of marginal gas will flow into the first, or marginal, row of wells as long as they are maintained at a bottom hole pressure below that which would exist at their point of location if they were not producing, i.e., capped.

Two problems have been solved. The first to show the effect of variable permeability on the pressure distribution about a single marginal well; and the second to show the pressure distribution, and consequently the production, of a line array of three wells leading into the center of the field over a period of four years as the field is depleted.

In both problems the relaxation method of R. V. Southwell has been used to determine the pressure distribution at the interior points of the drainage area. The basic idea in solving steady state fluid flow problems by the relaxation method is that the fluid mass in any closed system can neither be created nor destroyed. In other words, at steady flow conditions the total quantity of fluid, Q, at any interior point, at any instant of time, must be zero, e.g., as much fluid is flowing toward the point as is flowing away from it.

The above idea is the basis for the solution of fluid flow problems involving steady state conditions. The drainage area is to be replaced by an equivalent network of pipes through which all the gas is assumed to flow. Essentially the solution procedure is to assume values of pressure at each interior intersection of the pipes and calculate Q for the intersection using D'Arcy's Law.

Since, for steady flow the net Q = 0, it is necessary to reassign values of pressure until Q approaches zero to the desired degree of accuracy.

It has been shown by A. A. Zwierzchowski that the relaxation method is applicable to steady state fluid flow problems, so it will not be the purpose of this paper to prove the validity of the method. However, the procedure has been expanded to include variable permeability.

In the first problem of this thesis it was found that after first relaxing the entire drainage area to an approximate value it was quicker to assume a number of new simpler networks involving a few of the interior points in the original problem and solve these to completion. After this was done the values found from the simpler networks were applied to the solution of the entire drainage area. The original network solution was then completed using the values obtained from the simplifications"--Introduction, pages 1-3.


Miles, Aaron J.


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


Missouri School of Mines and Metallurgy

Publication Date



vi, 41 pages

Note about bibliography

Includes bibliographical references (page 40).


© 1950 Horace Tharp Mann, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Gas wells -- Testing
Gas fields -- Production methods
Oil sands -- Permeability

Thesis Number

T 895

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