The late A.F. VanEverdingen in finishing a brilliant career as a petroleum reservoir engineer, (1) reported that in the United States there are 300 billion barrels of oil left in the ground, of which 120 billion barrels are recoverable. This latter figure is equal to all the oil produced to-date since Colonel Drake produced oil in Pennsylvania in 1859.

This sizable amount of oil is the challenge to this industry to recover this oil, and can well be our future reserves. This paper deals with this problem, and to recover this oil in abandoned and producing oil fields. The method of recovery is to locate areas in these fields where in-fill wells can be drilled that showed the least oil production in a fields history.

This is accomplished by conformal mapping and stream-line flow from the reservoir itself to the producing wells. Where there are gaps in the mapping of the stream-lines, such designates areas of incomplete recovery and the regions where oil can be produced.

This can be simply stated that between every producing well, residual oil is left in the ground; this subject will be discussed further with illustrations.

Fig. 1 shows a circular reservoir, reproduced as a conformal rectangle, in which four wells are producing, each located in the center of a quadrant. It shows the vast gaps in plotting the streamlines along the major axis OX, and OY that defines areas of unproduced oil. Five additional wells can be drilled to produce this oil.

The application of conformal mapping and streamline flow have been discussed in the literature (2,3,4). The complications of reproducing these stream-lines is now performed by computer programming, as well as reproducing the field proper to a conformal rectangle, where all the work is done.

In this connection we have the writer's (5) own development of reproducing the potential problem, which is programmed; also the Schwartz-Christollel Method, by Gilicz, (6) a Hungarian, that is not yet completely programmed. Both of these methods are on a par with each other.

In all these respects this paper discusses reservoir simulation that apply to oil and gas fields to find new reserves.

These gaps as in Fig. 1, apply areally in a reservoir, it now must be specifically interpreted within these areas to determine where to drill infill wells. The drainage formulas (7,8) reported in the literature apply.

Fig. 1

Stream-lines for Four Wells Producing in a Circular Reservoir For All Wells. (Ref. 4.)

Fig. 1

Stream-lines for Four Wells Producing in a Circular Reservoir For All Wells. (Ref. 4.)

Close modal

Thus Fig. 2, is a straight line, joining two producing wells, for which we wish to determine the distance between the wells where the slope is zero and residual oil exists.

Fig. 2

Location of residual oil between two producing wells.

Fig. 2

Location of residual oil between two producing wells.

Close modal

The velocity of Well 1, in this figure, directed toward the well itself, is q1/2 π r1, and for the opposite Well 2 its velocity is q/2 π (R−r1) when we equate these two terms gives the distance

q1r1=q2Rr1r1=R/(q2+1)q1
(1)

where R is the distance between well.

If we have other wells removed beyond this straight line, Fig. 3, its velocity is expressed by its rate /2 R and the distance its normal, is removed from a point X on the straight-line, is expressed as

Fig. 3

Contribution of fluid flux of exterior well along straight line.

Fig. 3

Contribution of fluid flux of exterior well along straight line.

Close modal
q3(xx0)/R2R=γ02+(xx0)2
(2)

WHERE :

This is its velocity along the straight-line. Thus adding up all the contributions from Wells 1, 2, and 3, and choosing any X, by the Method of Divided Differences (2), the null sequence can be determined where the well is drilled. If a sloping formation is encountered, its hydrostatic heads of fluid can also be incorporated in these calculations.

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper Is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL.

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