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By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

By P. D. I. Honeyman

DURING 1938 many copper companies again felt the economic pinch and smelter operations were often on a reduced basis which some- times resulted in intermittent operations and complete shutdowns. During the last half of the year production was stepped up and smelting operations resumed a more normal appearance. One of the present-day trends in reverberatory sme1ting is definitely toward high-tonnage operations. i\ t the Phelps Dodge Corporation's Douglas plant, the reconstructed 107 by 26- ft. reverberatory furnaces are operated at the rate of 1000 tons of solid charge per day. The arch, all of silica brick; is sufficiently high above the bath to give

Jan 1, 1939

Jan 1, 1887

By Mary Sue Coates

Characterization of the rock mass in which deep underground structures are to be located is of critical importance to the feasibility and design of the structures. The process involves areal studies, subsurface exploration and extensive testing to obtain comprehensive data on the rock units which will enclose the excavated structures. The Illinois Deep Hole Project provides an example of characterization of rock at great depth describing the types and variety of tests and studies which were utilized and the results obtained.

Jan 1, 1984

By Shiou-Chuan Sun

Most previous work on sedimentation of coal1 and mineral2,3 suspensions has been conducted in graduated 1-liter glass cylinders of 6-cm diam. With this type of large container it is often difficult to see through the suspension and tedious to perform a large number of tests. Furthermore, the heavy glass walls and the graduation lines of glass cylinders cause internal and stray reflections, respectively. To obviate these difficulties, an Atlab Emulsion Viewer from Arthur H. Thomas Co. was adopted as an alternative apparatus. Equipment: The viewer,4 shown in Fig. 1, consists of: 1) a stainless steel frame rack holding 21 flat-bottom Nessler tubes or an ungraduated replica 1.64 cm ID and 1.80 cm OD, 2) a movable masked 150-w lumaline lamp behind the tubes, and 3) a scaled glass panel with 100 vertical divisions in front of the tubes. The tubes are snugly held by springs in slots formed by spacer bars, which also serve as shields to eliminate stray light. The lumaline lamp is mounted behind a slit in a movable housing so that it can be positioned behind the suspension to be examined. The lowest or 100-division line on the front glass plate is leveled with the upper side of the bottom of all tubes. The scaled portion of each tube, roughly 19 cm high and 40 ml in volume, is used to study coal and mineral suspensions.

Jan 1, 1959

CONTRARY to the natural order of art, it has been discovered how to cast in moist earth in order to avoid labor and expense. This is truly a thing that many desire and few practice because it is not as smooth a way nor as easy to effect as it apparently seems. To do this, one part of fine-grained yellow tuff is taken, or some very

Jan 1, 1942

By W. F., Netzeband

SEVERAL criteria have been used more or less successfully in finding and developing orebodies in this district. Among them is the relation of the fracture to the orebodies. It has been known for some time that there was some relation, but it has been but recently. that careful study has been given to this subject. Like all the criteria used in this district, this relationship must be used with caution, for what-is true in one part of the district is not necessarily true in another.

Jan 1, 1928

By Robert M. Dreyer

Although lateritic ore deposits are relatively flat-lying, surficial ore bodies, the evaluation of lateritic bauxite and nickel deposits is among the most difficult problems confronting an economic geologist. Laterite is a soil formed under tropical conditions resulting in the concentration, within the soil zone, of certain trivalent metals - principally iron and aluminum, but also, locally, nickel and manganese. The soil zone is divided into two parts: (a) the true soil or lateritic zone and (b) the zone of partially altered bed rock or saprolite. Whereas bauxite generally is confined to the lateritic zone, some nickel deposits occur in both the laterite and saprolite zones. The evaluation of bauxite and lateritic nickel deposits thus has both similarities and differences. These ores have been formed by supergene, soil-forming solutions moving downward through zones of widely varying permeability within the weathering rock. Because the permeability varies widely, both vertically and laterally. the extent of weathering may vary greatly within short distances. Because the weathering process varies widely, the degree of metal concentration may also vary widely. It is not at all uncommon for a laterite to change, within a few centimeters, from a virtually valueless rock to a high grade ore. Moreover, the depth of weathering, and hence the depth and form of the ore profile, vary greatly. Obviously, for this type of deposit, a few grab samples or a few drill holes are virtually worthless. The evaluation of such a deposit requires a sophisticated statistical study based on thousands of carefully selected samples. As a rule of thumb, the cost of evaluating a large bauxite or lateritic nickel deposit will be about one cent per ton of ore in the ground. Thus, the cost of evaluating a several hundred million ton deposit may be considerable. The following factors must be considered during the evaluation: Type of Sampling: The best and most reliable samples for the evaluation of lateritic ores are taken along large, vertical channels in hand-dug pits. Where labor costs are high, some form of drilling may be used in place of pitting, but it is always wise to choose a drilling procedure after checking drilling results against a series of pit channel samples. The drilling may not reproduce exactly the results from pit channel samples, but it may be possible to derive a constant correction factor. If the physical character of the laterite varies within the deposit, it may, of course, be necessary to change the type of drilling, the correction factor or both. In some areas, it has been found empirically that augers, chum drills, vacuum drills, rotary drills, or core drills yield satisfactory results. The problem is to find which drilling technique gives results most similar to channel samples through the heterogeneous sequence characterizing the laterite in a given area. In lateritic nickel deposits, the drilling characteristics of the lateritic and saprolitic portions of the deposit are very different. Within the saprolite, the major nickel values are commonly found in weathered zones within less altered boulders - a type of occurrence which makes sampling very difficult.

Jan 1, 1979

The eastern part of the state of Rhode Island on both sides of Narragansett Bay, including the island of Rhode Island, is underlaid with carboniferous rocks which carry veins of anthracite. This formation extends into the neighboring portion of Massachusetts, including the area from the state line, the towns of Mansfield, Brockton and Bridgewater,: and extending probably ten miles east of the latter two towns, to Middlesboro, and to Fall River. In Massachusetts the coal formation extends over nearly the whole of Bristol, and parts of Plymouth and Norfolk Counties. In Rhode Island and Massachusetts the area covered is about 400 square miles. In both states the exact limits of the coal measures cannot be determined on account of a thick layer of drift which overlays it. Along parts of Narragansett Bay, the coal measures outcrop in the cliffs on the west side of Rhode Island, and the presence of coal here seems to have been noted as early as 1760, and in 1768 a patent was granted to parties who "were about to dig after pit, coal or sea coal" at the back of the town of Providence. In 1807-08 Benjamin Silliman, later a geologist, visited some openings,' and in 1808 a mine was opened near Portsmouth, in the northeast part of Rhode Island. Work was done here until about 1814 when the mine was abandoned. No anthracite had been used in New England at that time, all coal used came from Nova Scotia, Virginia or England, and was high volatile bituminous; neither experience nor the means of firing favored the use of the local fuel? This mine was again working in 1827, was again abandoned and operations were resumed in 1847. In 1837 a note in a magazine mentions, "the immense coal mine in Cumberland-about six miles from the city of Providence" as having a shaft 14 ft. in diameter and 80 ft. deep, that the horses then used for hoisting the coal were to be superseded by a steam engine and another shaft was to be sunk. With these improvements 30,000 to 50,000 tons were to be produced the following year at a cost of $1 per ton and a sales realization of $6.1 Hitchcock's report refers to a number of localities in both states where definite knowledge of coal existed. These are:

Jan 1, 1942

By William R. Rumbold

The Kinta valley, in the State of Perak, one of the largest of the Federated Malay States, is probably at the present time the richest alluvial tin-district in the world, Perak producing from 20,000 to 25,000 tons of tin annually, and the Kinta valley being the chief producer. The valley runs approximately north and south, and is 30 miles long by 12 wide. It is very flat, the mountain-ranges on either side rising abruptly from the plain, that on the east being the great Central range of the peninsula, and that on the west a subsidiary range marked " Kledang " on the map, Fig. 1. The valley is drained by the Kinta river, which rises in the eastern mountain range and flows south to join the Perak river, being joined by numerous streams from both mountain-ranges.

Jan 1, 1907

By H. Foster Bain

THE "miracle of production." which was such an essential element in winning the European war, was nowhere more in evidence than in our Western States. In shipbuilding alone the Pacific Coast States -et a mark never before equaled, and in production of war goods of many kinds, both Rocky Mountain and Coast States accomplished more than their proportionate share if measured by population standards. This was only possible because of the building of immense new plants of many types, largely financed with Government money. Their operation has built up payrolls in the West and brought a measure of prosperity which Westerners are naturally anxious to have made permanent. A widespread doubt obtains, however, throughout the nation and even in the Western States themselves, as to whether, and if so to what extent, this may prove possible. The question has been raised as to whether the national treasury has not been raided to stock the Western ranges with a voracious breed of white elephant .

Jan 1, 1945

By R. L. Stephenson

A sampling technique has been developed for procuring a sample of sinter representative of the entire depth of the sintering bed. The sampling method involves the use of an open-bottom metal basket that rides on the grate of the sintering machine and when removed contains a sample of the sintered product. Additional data have been obtained to indicate that the tumbler test is a suitable means of measuring sinter strength.

Jan 3, 1953

By AIME AIME

THE value to the engineering profession of a liaison between the engineering societies of Russia and America, through Engineering Council, was the subject of a meeting in the Engineering Societies Building attended by over 500 persons. In introducing the subject, Mr. N. A. Stephanoff, President of the Russian Society of America, said: In Russia, engineers were divided into two classes: those who had graduated from the high technical schools and the practical engineers who had graduated from special technical schools. These technical schools were divided into three groups: The first corresponded to the German polytechnical schools with many departments, mechanical, chemical, metallurgical, mining, etc. The second group corresponded to the French special schools of the "Écoles des Ponts et Chaussées." "École des Mines." The third group was formed by the Military and Naval Academies of Engineers. In 1910, Russia's high technical schools had about 45,000 students, whose training covered a period of not less than five years, and who enjoyed all opportunities afforded by laboratories in no way inferior to those of Germany.

Jan 1, 1920

By Robert L. Kidd

ONE time or another placer mining attracts the attention of a large number of people, because of the possible low initial investment, low operating cost, and quick returns. Much has been said about sampling and operating placer deposits but many are still inclined to jump at a property without giving much, if any, consideration to proper sampling. This statement does not apply to experienced mining engineers but I am hoping that readers will tear out this article and pass it along where it will do the most good and thus help to preserve the reputation of legitimate mining. It would appear that some people have an ability to sink test pits in high-grade gravel that is positively uncanny. One pit showing high-grade values proves to some property owners and promoters that the entire property will do the same. This is

Jan 1, 1937

By Hal M. Scrugham

UNITED States Steel Co.'s Tennessee Coal & Iron Div. Wenonah mines present definite materials handling problems arising from the natural features of the operation. Trackless equipment went a long way toward supplying the answers-but at the same time gave birth to several new posers. Machines-trackless or otherwise-require maintenance and Wenonah's experience may do much to add to the body of information already available on this type of equipment. Let's look at the mines themselves. Ore is of sedimentary origin, extending over an area of several square miles. A thickness from 8 to 14 ft is mined. Bed dip varies from the horizontal to 20 pct in local rolls. Practice is to mine across the dip at 14 pct or less. A parting forms a smooth footwall in some of the mines while in others the footwall must be blasted smooth. Ore weighs 215 lb per cu ft in place and is extremely abrasive.

Jan 6, 1953

By AIME AIME

AT A meeting of the Iron and Steel Institute held in London on May 6, Dr. J. E. Stead was formally inducted into the chair by Dr. Eugene Schneider, the retiring president. After presenting the Bessemer gold medal to Harry Brearley, of Sheffield, England, for his distinguished services to the British steel industry, Doctor Stead delivered his presidential address, a masterly review of iron and steel making progress during the past 50 years, emphasizing economy in production, and pointing out suggestions for future improvement. A considerable portion of the address was devoted to blast-furnace operation.

Jan 1, 1920

By John Howe Hall

The recently announced run of three years, nine months and eleven days made by a crucible steel melting furnace of the Columbia Tool Steel Co., which is claimed as a world's record, brings forcibly to our attention the great improvements that have been made in the design, construction and operation of the Siemens regenerative crucible melting furnace since its introduction in this country. Credit for this advance should be given to the furnace designer, the manufacturer of refractories, and the operators, of the furnaces, whose persistent efforts and intelligent co-operation in attacking the problem have resulted so satisfactorily. There are three factors that determine the life of a crucible furnace, or any other furnace for that matter: Design, nature of refractories, and conditions of operation (including the nature of steel melted); and to some extent these factors are interdependent. Thus, for instance, if a crucible furnace is to be operated single turn and allowed to cool off considerably at night, in order to save fuel, the use of clay-brick melting holes may be advisable, since silica brick is not well adapted to endure repeated heating and cooling. But the total life of a clay-brick melting hole is necessarily short. Again, if local conditions such as danger of flood make necessary the building of the furnace largely above ground, so that the radiation of heat is promoted, the cooling down of the furnace over the week ends, when no steel is melted, will be considerable—and the contraction of the furnace that results tends to wrack it to pieces. The character of the metal being melted affects the life of the furnace to a great extent. Low-carbon steels and steels made from iron and charcoal require higher temperatures and much longer melting time than high-carbon steel or steel made largely from scrap; the life of the furnace will be shorter, and the number of heats melted will be much less, when such materials are melted. The figures available, showing the life of furnaces, are for this reason especially not strictly comparative, since the variations in the steel melted undoubtedly affect the life to a greater or less extent. Probably, however, the method of handling is as important a factor

Jan 1, 1914

By AIME AIME

AN unusual interest in the question of orienting the young college man in the mineral industry was shown in a well-attended session* of the Engineering Education Committee on Monday afternoon. About seventy-five employers and educators of mining engineers were present and took part in the discussions.

Jan 1, 1929

By Theodore B. Comstock

The paper of Mr. S. F. Emmons on the structural relations of ore-deposits, presented at the Boston meeting in February last, having been, as I am informed, unavoidably delayed in publication, was not distributed in the preliminary edition to members until immediately before the sheets of Volume XVI. of the Transactions, containing it, were sent to press. Consequently, I saw it for the first time too late to offer any comments which might have accompanied it in that volume. This is my justification for present-

Jan 1, 1889

The members of the Institute have probably seen in the daily papers notices of the plans of the Secretary of the Navy to. form an Advisory Board to assist the Government to make available the latest inventive genius of the country. Secretary Daniels has appointed Mr. Thomas A. Edison Chairman of this Advisory Board and has officially invited the Institute to secure the selection of two of its members to serve. on this Board. The Secretary in his letter states: "I feel that the work your Institute has done has been such as to give it the right to be in a way officially represented, and the Navy Department desires in this way to testify to its own appreciation of the splendid work for our country that your Institute has done. I have the emphatic approval of Mr. Edison, and he agrees entirely with me that your Institute should he represented in this way and that no better method of getting the kind of men we need could be devised." The invitation of the Secretary of the Navy has been officially accepted and steps have been taken to nominate the two members. Since the Constitution provides for no meeting of the Board of Directors until September, and as Secretary Daniels urged early action, the matter was discussed at a special meeting of the Executive Committee of the Institute, at which were present as many members of the Board of Directors as were in New York City at the time. Invitations were also extended to other members of the Institute who happened to be in the vicinity. At this meeting it was decided to submit the matter by a special letter-ballot to the Board of Directors and in doing so to suggest or nominate five members of the Institute, accompanying this nomination with the statement that the Directors might vote for two of the members so nominated or for any other members of the Institute not so nominated. It was voted at this meeting that it. was the sense of those present that in view of the fact that this committee was an advisory one the type of men to be chosen should be men of administrative or executive ability, cap-

Jan 9, 1915