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By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By C. Richard Tinsley

INTRODUCTION The economic analysis (Chapter 3), the engineering studies (Chapter 10), the credit structure (and the consequential funding sources) - Chapter 11, and the overall feasibility structure for any venture are all directed to determining one major decision element: How much and how certain is the reward for taking these risks? Risk assessment is a surprisingly weak area of analysis and is usually addressed in a checklist fashion. It is much preferable to deal within a risk system so that the inevitable tradeoffs among risks are correctly made. DEFINITION The first step toward risk definition must be to ascertain all of the risks to which a project or a company is exposed; otherwise one will remain ignorant of the possibility of a financially crippling loss until it occurs. (Carter and Crockford, 1974). However, simply stating what "risk" is can lead to debate. For example, risk could be (adapted from Vaughan, 1982): -the chance of a loss - uncertainty of loss -possibility of loss - uncertainty -dispersion of actual from expected results - probability of an outcome different from the one expected - possibility of an occurrence of an undesirable contingency -a condition in which a possibility of a loss exists. For the minerals industry financier, the last definition is probably the most appropriate. However, from a mineral company's point of view the definition might well include the possibility of not achieving the expected financial return. RISK CLASSIFICATION Risk identification will be readily agreed as the all-important first step. There are five major "branches" of risk classification. These are: -Statistical -Modellers -Checklist -Project Financing -Insurance The Statistical set discovered probability theory and any risk discussion soon deteriorates into a mathematical jungle (Megill, 1977; Hartman, 1976; Reutlinger, 1970; and Pouliquen, 1970).Their use of terminology tells its own story: coin toss (binomial distribution), gamblers' ruin, delphi (oracle) techniques, monte-carlo simulations, random walks, etcetera. These techniques inadequately represent the judgements necessary in an increasingly complicated and interrelated world. The risk Modellers have turned to the computer to handle these inter-relationships but soon find barriers because of "simultaneity". Certainly the computer has its uses to conduct various analyses (marketed as "sensitivity" analyses) but very often one finds that this involves changing one or two variables at a time, all other things being equal. Unfortunately, in a modern and complex world all other things do not remain equal. The statisticians will, no doubt, jump to their own defence by citing this

Jan 1, 1985

Jan 1, 1966

By Lester A. Blackner

Discussion of the paper of LESTER A. BLACKNER, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 102, June, 1915, pp. 1249 to 1290. SIDNEY J. JENNINGS, New York, N. Y.-In the historical part of the development of the caving system discussed by Mr. Blackner, I notice the absence of one man's name, Charles Henroten. Mr. Henroten used the caving system in South Africa in the. Kimberly mines, and realized from his work there that ground would cave when properly prepared. I think it is due him that his name should be mentioned in connection with an exposition of this system in America.

Jan 12, 1915

By R. E. Salvoti

IN underground coal mining, the increasing trend towards mechanical methods is ever apparent. Figures for 1939 showed that 28 per cent of the total bituminous coal production was mined mechanically 1940 statistic will reveal an even higher figure. Factors causing this trend are varied, but the important are the following;

Jan 1, 1941

Jan 1, 1967

By G. W. Josephson

JUDGING by the progressive atmosphere prevailing in the nonmetallic mineral industries during the past year, postwar conditions were healthful though inflationary. Demand for most industrial mineral products has been exceptionally high and many new production records were attained. Severe shortages of some commodities existed, especially building materials and fertilizers. Production costs and prices increased and profitable operation was general. Under these conditions expansion programs were the order of the day. Ample funds were available to finance the purchase of good equipment; and, as wages and other operating costs were increasing, primary emphasis was placed on attaining maximum efficiency in new installations. These efforts were hampered by shortages and slow delivery of desirable equipment, so compromises in design were often necessary. However, on the whole, production practice improved.

Jan 1, 1948

By Robert A. Laurence

Ore deposits in the Southern Appalachians are ( 1) sedimentary or syngenetic, ( 2) epigenetic, and ( 3) residual. In general, deposits characteristic of high temperature and pressure are found in the Blue Ridge and Piedmont provinces and those of low and intermediate temperature and pressure, including the sedimentary ores, are found in the Valley and Ridge and Appalachian Plateaus provinces. Residual deposits are present throughout the area. Recognition of several periods of intrusion and metamorphism in the Appalachians has changed former concepts which held that most mineralization was of late Paleozoic age in a zonal pattern including all four provinces. Many deposits probably are of early or midPaleozoic age. Similarly, recent studies in geomorphology indicate that the formation of residual deposits is a continuous process and not related to specific cycles of peneplanation.

Jan 1, 1968

By F. R. Morral

INDUSTRY has yet to find a universal solution to the problem of engineer personnel selection. Today, the choice of the right man for the right job is even more pressing than ever before. The age of the hard apprenticeship seems to have passed. In its place one finds the interviewer who must determine through personal contact and evaluation of college grades whether a graduate engineer will fit into his company's scheme. The problem, as it is constituted today, may be broken into four parts: Need for better use of human resources (there is a shortage of engineers, scientists, and skilled workers), productivity with higher efficiency, encouragement of personal pride in work performed, and employee's happiness on the job and away from it.

Jan 4, 1953

By G. P. Halliwell, C. R. Austin

The investigation described in this paper deals with the development of high-temperature alloys of the Konel series over a considerable period of time at t,he Research Laboratories of the Westinghouse Electric and Manufacturing Co. The word ''Konel" has been coined to designate a class of alloys which are essentially nickel-cobalt-iron with other elements added, usually in small quantities. Most of these alloys contain titanium, usually about 2.5 per cent. The main consideration related to strength at high temperatures but the thermionic characteristics of the alloys was also of considerable importance. It is, however, with the mechanical properties at elevated temperatures that we are herein concerned. Much attention has also been devoted to their age-hardening characteristics. There is little need to stress the utilitarian aspect of this subject, as it has been discussed frequently. Alloys exhibiting superior properties at normal or elevated temperatures rapidly find many suitable applications. There may be some question, however, as to what constitutes a "superior alloy," or an alloy that may have good service possibilities at high temperatures. The problem is complex and various means have been employed to predict the useful life that may be expected of a material. In recent years the "creep limitJ' has been used as the best means of evaluation. Such tests necessarily are prolonged and hence collection of data is very slow. In a general survey of many alloys therefore the creep test is not desirable and recourse must be had to much shorter time tests in order more rapidly to select alloys which appear to show promise. For this reason the present survey has been made using the high-temperature tensile test and a bend test developed by Howard Scott.' In the tensile test the conditions have been standardized for all tests, so that values obtained are at least comparable, one alloy with another, although the absolute values recorded merely indicate the mechanical properties at the given temperature under a definite rate of loading.

Jan 1, 1932

By GORDON H. FISHER

During the year 1945, the drilling pace in West Texas increased above that in the year 1944, and represented the highest number of well completions since 2941. The 1680 new wells drilled 8,287,958 ft. of hole for a per well average of 4933 ft. This depth is approximately 30o. ft. deeper than the average for the year 1944. Although the deepest well drilled in West Texas (Phillips Petroleum Company's Ada Price No. 1, in Pecos County) was completed during the year. 1944 to a depth of 15,279 ft. and tested the Ellen-burger horizon, the producing depth record for West Texas was set during the year 1945 with the completion of Amerada Petroleum Corporation's Jones No. I-A, in the Jones Ranch field, Gaines County, which now is producing at 11,422 ft. from the Devonian formation.

Jan 1, 1946

Jan 1, 1968

Jan 1, 1968

By C. D. Thurmond

Jan 1, 1968

By Thomas B. Douglas

INSTRUMENTATION in the process industries can no longer be regarded as a convenience, but rather an absolute necessity. Although many chemical processes must already be conducted with instruments, every properly designed application of automatic process control will improve operation: 1) the product will be more uniform and of higher quality; 2) the manual labor saved will reduce cost; 3) uniformity of flow and uniform control of process will increase production; and 4) surges will be eliminated, making it possible to operate equipment near ultimate capacity at all times. Industrial instruments fall into two general classifications—those that measure and those that measure and control. The cement industry has been using instruments for a number of years, particularly in the burning process, primarily for indicatlng and recording. Automatic process control makes additional use of these instruments, and others, to control variables. Assisted by the instrument manufacturers, engineers at Ideal Cement Co. achieved considerable progress in determining how well the usual recording instruments could be made to control various phases of cement-making. The results of these experiments were used to make the new plant at Houston as wholly automatic as possible. The original Houston plant, built in 1937 by Gulf Portland Cement Co., consisted of only one 8 x 220-ft kiln and the necessary grinding mills and accessory equipment and had a capacity of 900 bbl per day (300,000 bbl annually). Ideal Cement Co. purchased this plant in 1940 and almost immediately started plans to increase its production. In 1941 a 9 x 220-ft kiln was installed and grinding and storage capacity were increased. The growing demand for cement in the Houston area necessitated a third kiln (9 ft 6 in. x 250 ft) in 1947. This brought the plant up to its present capacity of about 1.3 million bbl per year. Calcium silicates in cement are produced in a burning operation at high temperatures from raw mix of argillaceous and calcareous materials that have been crushed, mixed, and ground to a fine powder. The composition of this mixture must be kept consistent within narrow limits. Raw mixing and grinding may be done either wet or dry, but in both instances the materials must be correctly proportioned, finely ground, and thoroughly intermixed before entering the kiln. As the raw mix passes through a long horizontal rotary

Jan 1, 1959

Jan 1, 1965

By Robert Pack

INTRODUCTION SOONER or later in the development of any natural resource it becomes highly desirable to know the quantity of this resource in the country as a whole, as well as of the part that is being developed, for the general course and. conduct of the development work must be governed to some extent by the total supply available. An accurate estimate of the quantity of any natural resource is difficult to make; yet if one is diligent enough one can obtain a pretty accurate idea of the quantity of marketable timber, the acreage of tillable land, or the horsepower that may be developed from the streams, for these are things that may be measured. But any attempt to estimate the quantity of some mineral in the ground appears to enter the realm of imagination and it seems that the estimate can be nothing more than a blind guess. It may appear to be especially futile to attempt to determine the quantity of oil and gas that is available in the ground, for these minerals are so vagrant that even if the quantity now available should be known quite exactly, the quantity that will eventually be obtained may be much less, for certain losses in the extraction of both oil and gas are unavoidable, and just what these losses will be cannot be predicted. Though necessarily inaccurate, estimates of such mineral reserves are, however, of distinct value, for they summarize the existing knowledge of the deposits of the mineral and thus enable those who are interested in some industry that depends in one way or another on this mineral to formulate a rational commercial policy. Some time ago, when the price of gasoline suddenly rose in a rather spectacular manner, the writer was one of the U. S. Geological Survey geologists called upon to help to estimate the quantity of oil that could be obtained in the United States, for the fear had become widespread that perhaps the rate of increase in the price of gasoline was a measure of the rate of depletion of the supply of petroleum. It thus became his

Jan 8, 1917

Jan 1, 1897