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By Julian Szekely

Through the simultaneous statement of Maxwell's equations. the turbulent Navier-Stokes equations and the differential thermal energy balance equation, a mathematical representation has been developed for heat transfer and fluid flow in electric arc furnaces. In broad outline the theoretical predictions appear to be consistent with experimental measurements. A discussion is presented of the general arc furnace control and optimization problem, together with the potential for the incorporation of the mathematical model given in the paper, into future control and optimization schemes. ELECTRIC ARC FURNACE STEELMAKING accounts for about 24% of the total steel produced in the U.S., consuming about 550kw-hr/ton of steel which amounts to about 1.4x1010 kw-hr annually. The percentage of steel produced by the electric arc furnace route has doubled since 1960 and is expected to increase further in the foreseeable future, particularly with the more extensive use of direct reduction technology. Table I shows, in terms of percentages, the principal items that contribute to the cost of running an electric arc furnace. It is seen that in addition to the fixed costs (labor, depreciation, taxes etc.) electrode costs and power consumption are the dominant inputs, and it follows that process changes that would ultimately reduce any of these cost components would have a significant impact on the efficiency of the operation. There are three main areas where progress in arc furnace design and operation must be directed in the next decade (Committee on Technology, 1981). 1. Increased furnace productivity 2. Reduction in processing cost 3. Improvement in the thermal efficiency of the furnace An estimate of the current operating efficiency of the electric arc furnaces may be obtained by comparing the theoretical minimum energy consumption per ton of steel with those achieved in operational practice. Theoretically 330-360 kw-hrs of electricity are required to melt one ton of cold scrap. For superheating, 8-12 kWh per 100°F are required. The actual energy requirements are given in Table II. It is seen that furnaces currently operate at 70-80% efficiency, with the major heat loss from the furnace resulting from the waste gases (Committee on Technology, 1981). While it is apparent that operational experience has produced a technology that is reasonably energy efficient this has been achieved in the almost complete absence of any detailed knowledge concerning the fundamental heat transfer mechanisms occuring in the furnace. The purpose of the present paper is to present a case for the usefulness of mathematical models in increasing the thermal efficiency of furnaces by investigating these heat transfer mechanisms and then combining this knowledge with existing electrode regulator mechanisms to produce truly efficient power cycles for melting and refining. In particular, existing mathematical models describing convection, radiation, and electro-magnetism in the furnace should be employed, and the development of optimization models which balance the cost of electrodes and energy against the thermal efficience of the furnace should be undertaken. Recent work in this laboratory (Szekely, McKelliget, 1981, 1982, 1983; Szekely, McKelliget, Choudhary, 1983) has made a useful start towards solving the problem of heat transfer within the electric arc furnace but the work still needs to be directly related to existing furnace power cycles and tested against plant scale measurements.

Jan 1, 1984

By C. A. Hartnagel

The production of petroleum in New York in 1940, totaling 4,999,000 bbl., was only slightly under the amount produced in each of the previous three years. The year 1940 started auspiciously with a posted price on Jan. I of $2.75 a barrel. Four price reductions, beginning in May, resulted in August in a low of $1.85 a barrel, after which two increases brought the year's closing price to $2.15 a barrel. The favorable crude price at the beginning of the year stimulated an increased drilling program, especially in the water-flooding districts. In the Allegany County region, which accounts for about two-thirds of the state's oil production, 886 wells, including water-intake wells, were drilled; 200 more than in the preceding Year. During the closing months of the Year there was a marked decline in the number of wells drilled. The unfavorable position in which the industry found itself before midsummer was due largely to the loss of export markets for its high-grade lubricants, constituting approximately 25 per cent of its business. As a result of this situation, runs to refineries were curtailed as much as 30 Per cent at the middle of the Year. Improvement in market conditions toward the end of the Year found the stocks of available crude at an almost record low. Deep DRILLING with the gradual exhaustion of some of the important natural and flood-oil-produc-ing areas of the Allegany and Bradford pools, overproduction will not be a serious problem in the future. The possibility of finding new territory or deeper producing sands has been further lessened by the drilling of additional deep wells for gas in and about the present oil fields. Many of these wells drilled to the Oriskany sand-stone were over 4000 ft. deep and have tested the entire thickness of the Devonian formation, the upper 2000 ft. of which contain all the important oil-producing strata in the state. Water-flooding It is thus evident that the problem of the New york oil producers is not one of find-ing new supplies but of obtaining as much 6 oil as possible from the old developed fields that during the 60 years of their life have 1 produced I 3o,ooo,ooo bbl. of oil. Although a few floods were in operation before I9I9, when the production of oil by flooding was 1 made legal, the output for that year amounted to only 85I,000 bbl. From 1919 I on there has been an almost constant increase, which during the past four years has averaged well above 5,000,000 bbl. annually. During the last 22 years, which constitutes the period of important flooding operations, 651337,000 bbl. of oil have been produced in the state. Careful estimates indicate that between one-third and one-half of the oil fields are being flooded or are already watered out. Some of the flooded and watered-out areas include territory with unusually thick sands, which were highly productive during the early history of the fields. From a recent study of operations in the New York oil fields, it is estimated that about 65,ooo,oo bbl. of oil

Jan 1, 1941

By A. J. Teplitz, J. K. Rodgers, E. M. Pohoriles

This note is presented in order to call attention to a newly developed laboratory apparatus that appears to have interesting possibilities for the study of lost circulation of the pressure-parting type, for a more realistic evaluation of sealing materials for this type of loss, and for investigation of other aspects of hydraulic fracturing. A study of lost circulation, conducted jointly by operating divisions of the Gulf Oil Corp. and the Gulf Research & Development Co., has been in progress for the past few years. Earlier phases of the study dealt with mechanical factors contributing to loss of returns in laminar type sediments.' One aspect of this type of loss which has been widely discussed in the literature and elsewhere concerns the geometry of the fractures into which such losses occur. This subject is not merely a philosophical one, but has an important bearing on procedures for combating lost circulation difficulties and on other well operations. The further course of the collaborative studies previously mentioned has produced some information on this subject which, though limited in amount, is believed to be significant. In several typical cases of lost circulation in laminated shale and sand formations, the wells have been surveyed with instruments2,3 capable of detecting the points of loss with considerable accuracy. These wells were located in the Gulf Coast of Texas and Louisiana, in the Texas Panhandle, and in the Rocky Mountain area. In each of these instances the loss was shown to be occurring at some distance removed from the bottom of the hole and sharply confined to a very narrow interval, less than 1 ft in thickness. It is rather difficult to imagine that fractures of a vertical nature' would be of the limited extent indicated by the surveys in these wells. Furthermore, the high rates of loss at relatively low pressure differentials observed in some of these instances together with the narrow intervals involved would appear to require the radial flow pattern which would be associated with a more or less horizontal fracture plane. In view of the foregoing observations and records of successful squeeze cementing operations, in attempting to construct a laboratory apparatus For simulating pressure induced lost circulation, it was decided that the design should be based on a horizontal type of fracture. It was realized that5,6 Vhe production of horizontal fractures in a formation with non-penetrating fluid requires some mechanism for transmitting vertical components of the hydraulic forces to the plane of parting. This was accomplished, as will be evident in the description of the apparatus that follows, by providing recesses in the wall of the borehole which are believed to be representative of wellbore configuration found in Gulf Coast wells. The possible influence of such borehole irregularities on both pressure fracturing and the treatment of lost circulation appears to have been neglected in many studies of these subjects. It is believed that the present apparatus, incorporating features that take into account some of the factors mentioned, will provide means of gaining a further understanding of pressure induced fracturing and possibly for more realistically evaluating the numerous sealing agents, particularly the non-time-setting materials employed in treating the pressure-parting type of loss. DESCRIPTION OF APPARATUS The test cell used in the laboratory investigations is shown in Fig. 1. A schematic diagram of the entire system is shown in Fig. 2.

Jan 1, 1956

By M. E. Learmont, R. J. Lipp, I. Iwasaki

In the selective flocculation of iron ores, the concentration of alkaline earth ions in pulp solutions plays a critical role. Sodium silicate, alone or with sodium tripolyphosphate, has been used as a dispersant. When Ca+ + concentration exceeds 15 to 20 ppm, however, only a strong complexing agent, such as ethylenediaminetetraacetate (EDTA) was found to be effective (Heerema, Lipp, and Iwasaki, 1979). Some iron ores release Ca+ + in excess of 20 ppm. With ores that contain gypsum, the Ca+ + concentration may reach several hundred ppm. The purpose of this investigation was to compare the effectiveness of EDTA with nitrilotriacetate (NTA) in countering the adverse effects of Ca+ +, particularly at high Ca+ + concentrations. Emphasis was placed on the use of NTA since it is more cost-effective than EDTA. It is also used in detergents in some countries (Malaiyandi, Williams, and O'Grady, 1979). NTA, like EDTA, forms a soluble complex with Ca+ + with a 1:1 molar ratio. Its structure and the value of log Kca are given below together with EDTA (Shibata, 1963). [ ] For experimental materials, an equal weight mixture of Lac Jeannine hematite and a high-purity quartzite from Thompson, MN, both ground to - 30 µm (- 560 mesh) was used. Selective flocculation test conditions and procedures were identical to those used in previous investigations (Heerema, Lipp, and Iwasaki, 1979). The optimum level of starch addition for the above mixture was determined to be at 300 g/t (0.6 lb per st). Initially, a series of selective flocculation tests were performed on the mixture pulped with 10-3M CaC12 (40 ppm Ca + +) at pH 11. With no NTA present, flocculation of the entire suspension resulted. The selectivities achieved in tests with 90, 100, and 150% of the stoichiometric amount of NTA were virtually identical to each other and also to the selectivity of separation obtained in the absence of Ca+ + Such an observation could have been expected since Ca+ + concentrations up to a few ppm may be tolerated in selective flocculation (Krishnan and Iwasaki, 1982). A similar series of tests were performed at 10-2M CaC12 (400 ppm Ca+ +). The results are shown in Fig. 1 as grade¬recovery curves. For comparison, the results obtained in the absence of Ca++ are included. At 90% of the stoichiometric amount of NTA, a large enough concentration of uncomplexed Ca+ + was left in solution to cause indiscriminate flocculation. Note in this figure that NTA is capable of countering the adverse effect of Ca+ + even at this high concentration when it is used in excess of stoichiometric amounts. The free Ca+ + concentrations at 100 and 150% are calculated to be 2.5 and 0 ppm, respectively. [ ] The relative effectiveness of NTA and EDTA was then compared at 100% of the stoichiometric amount using 10-2M and 10-3M CaCI2 (Fig. 2). EDTA appears to be slightly more effective than NTA. The free Ca++ of 0.02 ppm in 10-2M CaC12 with EDTA compared to 2.5 ppm free Ca+ + with NTA might account for the difference. As evident, prohibitively high additions of EDTA and NTA were required to complex high concentrations of calcium ion. The use of both of these agents would result in the accumulation of complexed Ca+ + in recycle water.

Jan 1, 1985

By John K. Hammes

INTRODUCTION This introductory paper presents a description and definition of what the finance function is and what it specifically means for the mining industry. In its simplest terms, finance is, "management of money matters". As an area within the discipline of business administration it draws heavily on the related fields of economics and accounting, and to a lesser extent on marketing and production. MINING FINANCE DEFINED In preparing to write about what finance means to the mining industry, I asked a number of mining people the question, "What does mining finance mean to you?" Most responded that mining finance was "How a company borrowed money for mine development", and perhaps half those questioned included "raising equity" in the definition. It is not surprising that the mining industry concept of finance is the providing of funds needed for the objectives of the business, for that was once a view shared by authorities in the field of business administration. Further, it is certainly the area where much of the emphasis has been placed in the past ten to fifteen years as the industry struggled with the development of more remote and more refractory or lower-grade orebodies while profitability and internal cash flow were below expectations. No wonder project finance became such a popular topic. Twenty years ago it is probable that the emphasis would have been on mine valuation, for that subject was the area of finance then most often examined in industry publications. Papers concerning the pros and cons of payback, internal rate of return, and discounted cash flow appeared regularly. Let's examine the following situations, each the result of a financial decision: - Funding the exploration program in a developing country was accomplished by buying the next six-months budget needs in local currency. One week later the currency devalued 30 percent. If the purchase had been delayed or the local currency borrowed short term, a substantial saving would have been made in funding the program. - A major mining company borrows heavily to finance both expansion of its primary mining business and its entry into several new industry segments. When markets for all of the commodities it produces turn down for a prolonged period, there is concern over the adequacy of cashflow to cover debt service in addition to other company needs. The company's financial officers, however, had arranged very large committed credit facilities from numerous financial institutions which assured the availability of funds for several years. This enabled the company to implement a strategy to conserve cash, sell assets and survive until conditions improved. Further, short term suppliers of credit also were comfortable with the assurance that longer term credit was there to support them. -A medium size mining company financed several mines independently with limited obligations on the part of the parent company. The company decided to refinance the operations under one agreement. More flexible terms, lower interest cost and a longer tenor financing were achieved in return for assuming the risk as a direct obligor. - The exploration and development group of a large mining company proposes to develop a new mine in a country in which the company does not presently operate. When the investment is rejected they are advised that one reason was that the reinvestment assumption inherent in the discounted

Jan 1, 1985

By R. V. Higgins, A. J. Leighton

A fast method is needed for calculating thoroughly the performance of two-phase flobr~ in reservoir rock with complex geotrietry. The authors present such a method and .slzow its accuracy by romparison with laboratory performrrnce of a five-spot pattern. In making the performance c.alculations, the octant of the five-spot pattern was divided into four channels. The computer tinle required for the culculation was one rllinrcte. This is rorighly about minute per channel. INTRODUCTION By using an electronic computer it is now possible to make reservoir performance calculations in which fewer assumptions and more significant variables are included than was possible with a desk calculator. These performance calculations include such variables as the properties of the reservoir rock and its contained fluids, properties of the rock-fluid system and even different well-spacing patterns. Usually, the more variables that are included the higher the computer cost—and time on the computer is expensive. As a result, a short procedure is needed so the many variables will be included and accurate performance calculations will result. If a reservoir is composed of alternate layers of permeable and impervioi~s rock, and if each conducting layer has a different relative permeability, the combined computer cost for calculating each layer by the present long computer programs (which includes different well-spacing patterns and other variables) would be expensive. The performances of complex spacing patterns in a field often are studied by a potentiometric model, but in these model studies the analogy is to the flow of only a single phase. This paper presents a procedure to calculate the performance of a five-spot pattern with two phases flowing using a potentiometric model as a guide for the dimensions of channels and other related data. The time required to calculate the complete performance is about one minute on the IBM 7090 or four minutes on the IBM 704. The procedure can be extended to calculate the performance of more complex well spacings or an entire field with little modification. The procedure has been tested on the performance of the laboratory water floods of a five-spot pattern reported by Douglas, et alThe range of viscosity ratios in the laboratory experiments is from 0.083 to 754, which is extensive. The accuracy of the performance calculations is excellent as shown by the plotted points in Fig. I. The recovery as influenced by the geometry of the five-spot, taking into account the deviation from true radial character, has been predicted by Aronofsky and Ramey." The authors used a potentiometric model to determine the sweep efficiency to breakthrough of the flooding agent. Dyes, Caudle and Erickson,' by means of a laboratory model, show the influence of mobility ratio on recovery after breakthrough of the injected material. Dyes, et ai, used the X-ray shadowgraph technique and miscible phases in their studies. Craig, Geffen and Morse from the analysis of the performance of their laboratory model correlate many variables, including average saturation of a flooding agent determined by permeability relationship. Craig, et al, used X-ray shadowgraphs to determine the sweep efficiencies in sandstone models. In this report the sweep efficiency is not needed, and the important effect of continuously changing saturation gradients before and after breakthrough

By R. B. Rosene, G. L. Foster, A. R. Hendrickson

he properties of some of the common fracturing oils, such as sand-falling rate, fluid loss and viscasity, are a function of the three major constituents of the oil. These are: asphaltic material, parafin waxes and a base oil. The base oil can be either high or low viscosity. Asphaltic material increases viscosity by thickening the oil, decreasing the rate of fall of sand through the oil. at temperatures up to 200" F. When large arnorrnts of parafin wax are present, much of the wax i.s not dissolved, but is present in the form of rnicroscopic crystals. 7'his, of course is limited to temperatures below the melting points of waxe.s. As a result, parafin waxes clo not function primarily as thickener.7, but rother as bullting materials. The functiori of wax, without asphaltic material, in a low viscosity base oil is uniquely unlike that of wax with asphalt coexistent in the oil. The resulting difierence in wax crystal size governs the sand-falling rate to a large extent. An ideal type of fracturing oil is one containing neither asphalt nor waxes. In such cases, the viscosity and resulting low sand-falling rate are apparently due to soluble resin- ous hydrocarbons, which are compatible with formation oils. INTRODUCTION Since the introduction of hydraulic fracturing as a method of stimulating production from oil and gas wells, a variety of fluids have been employed to open the fractures and carry the propping agent. Such fluids include gels, emulsions, and oils. In the latter category, the use of refined oils has increased tremendously, and it is probably safe to assume that such oils represent more than one-half of the total fluid used in fracturing. The general acceptance of refined oils for fracturing can be accounted for on the basis of their relatively low cost and general applicability. To minimize transportation costs, such refined oils are generally obtained within the local areas of operation. As a result there are several kinds of oil used in different areas, with a wide variation in the basic composition. These types may vary from a fair grade of lubricating stock to a highly viscous cut-back asphalt. or road oil. Originally, little attention was paid to the composition of the oils used for fracturing, and any oil which would carry sand was considered satisfactory. Recently, however, service companies and well operators have become more concerned with the type of oils used for fracturing. With this in mind, the present work was undertaken to evaluate and compare many widely used fracturing oils to determine which constituents were most desirable for fracturing purposes. Some of the important properties of fracturing fluids are sand-falling rate, viscosity, and fluid loss. Other properties, that are actually of no less importance, include flash point, pour point, emulsifying tendencies with formation brines, and compatability with the formation oils. This discussion has been limited, however, to the first mentioned properties in order to give some idea of the general composition of the refined oils, how they function, and why. PROPERTIES OF FRACTURING OILS The properties of fracturing oils are a function of the three major constituents of the oil. These may be designated as: (1) asphaltic material, (2) paraffin waxes and (3) a base oil, which may be of either high or low viscosity. The asphaltic material clas-

Jan 1, 1956

INTRODUCTION Besides the European export credit agencies covered in Ted Rides' paper in this Chapter, other agencies are also active (see Appendix) but the most notable for mining projects are The Export-Import Bank of the United States ("US Exim") and the Export Development Corporation ("EDC") of Canada. Mexico's Fomex is basically a short-term trade-finance fund administered by the Central Bank. US Exim This independent agency can provide loans, guarantees, and insurance. Like all export-credit agencies, its mandate is to support the export of goods and services from the US as a means of competing against other countries' products. If a piece of mining equipment can only he made in the US, the US Exim may very well not provide any financial assistance. (It is important not to place the order for any item for which export credit is sought because, once ordered, the situation is no longer competitive in US Exim's eyes.) Direct Credits and financial guarantees ("buyer credits") are commonly in amounts greater than 85 million and for terms longer than six years. An example here is the $48.5 million provided to PT International Nickel Indonesia (see Robert de Gavre's paper in Chapter 12). US Exim usually requires a 15% downpayment and, therefore, finances up to 857 of the goods; less if the US content is lower. The dollar funding can he US prime, London Interbank Offered Rate (LIBOR), or other sources. Exim can fund in either or both of the following ways: 1. Under a US bank Letter of Credit ("L/C") 2. Reimbursement to the buyer/borrower via a US bank account. US Exim will, without charge, issue a preliminary commitment. It will, however, need to approve the various credit agreements and prefers to tie other parallel financings into one loan agreement. US Exim's total commitments are large, up to $5R billion in aggregate under various programs. US Exim has been the world's leader in medium-to long-term minerals project financings/ co-financings but suffers from (i) aggressive foreign export-credit competition whereby other nations mix in soft-loans or aid programs ("mixed credits") to increase the percentage financed and lower the interest margin and (ii) an imbalance in its own cost of funds. A common US Exim package would be as follows: 15% Banks under US Exim guarantee, floating rate over prime or LIBOR. 35% US Exim funding, fixed rate 35% Pefco funding, fixed rate 857 Drawn down pro-rata under US bank L/C 15% Cash down payment (may have been financed within a project/corporate credit) 100% Repayment usually begins six months after planned start-up in equal semi-annual instalments, with the banks usually paid out first, Pefco next, and US Exim last. Medium-term credits ("supplier credits") are issued for US equipment exports for terms up to five years, again for 85% of the equipment costs although the exporter is expected to bear at least 10% out of that 857 for its own risk. The buyer is required to be a first-class credit such as some governments or highly credit-worthy companies. Otherwise a bank L/C would be required. (This may be wrapped into an overall project-finance package for a minerals development. The project-finance banks provide an L/C to US Exim instead of funding that portion themselves.) US Exim guarantees 100% of the political risk and either 85% or 95% of the commercial risk for

Jan 1, 1985

By Bernard Greifer, Walter Rose

The purpose of this note is to call attention to a source of difficulty which can be responsible for inaccurate estimates of wetting liquid pressure gradients in mixture flow experiments of the Hassler1 type. It has been our experience occasionally to observe what were indicated to be negative pressure gradients, and these were regarded as anomalous in the sense that physically they seemed to contradict the requirement that the flux be in the direction of the potential field. At first it was thought that our scheme of assembling barriers and core sample led to such asymmetry in the distribution of isobars that the manometric leads at each end of the core were responding to internal pressures (within the core sample) which could be either positive or negative with respect to each other, and which in fact might tend to reflect on different effective core lengths in an unpredictable fashion as the wetting liquid saturation was changed. However, no compelling evidence of this possibility has been established. In addition, we were cognizant of the requirements to be satisfied in selecting manometric instrumentation to minimize the delay in response of the manometer to the differential pressures being measured, and were thus assured that our observations of anomalous pressure gradients could not be explained by faulty instrumentation. What we suggest is that if a leak sink occurs in the fluid lines connecting the core to either side of the differential manometer, errors exceeding 100 per cent may result in the estimation of wetting liquid pressure gradient, even though the leak is of such small magnitude that its existence would tend to be obscured by evaporation effects. This is because in a system with leaks at the specified places, the manometer rec- ords at steady state the pressure drop across the manometer barrier elements in addition to the pressure drop across the core sample. This possibility will be illustrated below analytically and by numerical example for the special case where the leak occurs on the high presure side of the core, since we are especially desirous to explain the significance of our observations of the so-called negative pressure gradients. It will be indicated, however, that leak sinks on the low pressure side of the core can account for observations of anomalously high values of pressure gradient, and that multiple leaks on both sides of the core can provide for some compensation so that the errors in pressure estimation are reduced. However, the major point to be emphasized is the fact that the impractical-ity of detecting the small leak sinks which give rise to the difficulties makes it a complicated task for the experimenter in a particular case to know with certainty that his estimation of pressure gradient lies within the limits of error which can be tolerated. Fig. 1 shows the electrical analog of the flow system we have employed in our studies. The inflow and outflow barriers. Rbl and Rb2, the manometer barriers, Rm1, and Rm2, and the core sample, Rc— for a particular fluid saturation and distribution— are all designated as resistance elements; the flowmeter is designated by an ammeter, A; the pressure source is designated by E; and the manometric device is designated by the voltmeter, V. Included in the circuit are the variable resistances, Rx and Ry, which may be regarded as the leak sinks, and which, in general, can vary in magnitude from zero (i.e., a large hole or shunt in the system) to infinity (i.e., no

Jan 1, 1950

By R. Adair, W. R. Hudspeth, W. T. McDaniel

ANEW method for concentrating the flake mica either from present washing plant tailings or from new feed has been developed. In this paper, flake mica refers to that which occurs in weathered granites, alaskites, pegmatites, and schists in a form too fine to be considered sheet mica. It ranges in size from 1 in. or more down to 200-mesh or finer and occurs with kaolin, quartz, and partially kaolinized feldspar. Scrap mica, a term often used indiscriminately to describe everything other than sheet mica, will be used to denote the waste product from sheet mica mines and fabricating plants. Both flake and scrap mica are used in the mica grinding plants to produce wet-ground or dry-ground mica, although some flake mica recovered from clay mining operations is fine enough to be marketed without grinding. Until 1930, ground mica was made almost entirely from scrap. From 1930 until 1935 a gradually increasing amount of flake mica was mined, and most of this was sold without grinding. A large percentage of this mica was recovered from clay washing plants. In this type of operation the recovery of any sheet mica was .of secondary importance and was considered a byproduct. North Carolina produces more flake mica than any other state, accounting for 73 pct of the total domestic production.' In the following review of current practice in jig plants, there is no intention to disparage these operations. Within the limitations under which they were built, they are examples of mechanical ingenuity. The term jig plant is a carryover from early practice since there are no jigs in operation at the present time. Current practice, as shown in Fig. 1, is based on successive stages of differential crushing with rolls followed by trommel screens to remove the more easily crushed gangue minerals. The oversize mica product then is usually dried, and passed through another set of dry rolls and a final screen to remove the remainder of the grit. This process is effective in recovering up to 50 pct of the mica in the original ore, the balance being lost in the screen undersize, usually —% in. Jigs and tables were at one time used to treat this screen undersize and were capable of recovering a part of the mica larger than about 60-mesh.V ine mica lost in these plants is normally washed away in streams and can be considered irrecoverable. There are ten or more washing plants in the North Carolina area that are losing approximately 50 pct of the mica in the feed. Since the three cooperating agencies, the Asheville Minerals Research Laboratory of North Carolina State College, the North Carolina Dept. of Conservation and Development, and the Tennessee Valley Authority, are concerned with conservation of minerals, they have investigated means for improving the efficiency of these mica plants. The mica industry has been cooperating fully with the laboratory to establish a more efficient method of recovery for flake mica. Choice of Methods The initial investigation was concentrated on finding a means of reducing the losses from plants now using the conventional flowsheet shown in Fig. 1. To accomplish this it would be necessary to collect the screen undersize products through the plant and remove from them the mica from Vs in. down to

Jan 1, 1952

By B. H. Sage, W. N. Lacey

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By H. H. Evinger, M. Muskat

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By W. Hurst, A. F. van Everdingen

A distillate-bearing sand complex is often made up of sand stringers of different permeabilities. In order to take into account the influence of the different permeabilities, "parallel flow" is defined, and this concept is used to compute the recovery efficiency of recycling such a sand complex. In the first approximation the position of the wells with respect to one another is not considered. In order to compute the effect on the recovery efficiency of the position of the wells, the area of a field is considered to be made up of rectangles; each rectangle containing one input well in the center and two producers located symmetrically with respect to the input well. Formulas are given from which to obtain the pressure and streamlines in a steady-state flow. A method is devised to compute rapidly the successive positions of the dry gas front. If the field is irregular in shape, pressure and streamlines can be obtained by a potentio-metric electrical model study. By using the concept of "parallel flow" and the results obtained by mathematical analysis or by electrical model study for a homogeneous formation, the effects of different permeabilities and of the location of the wells can be established. From these studies it is apparent that the efficiency of recycling can be profoundly influenced by differences in permeability among the various parallel strata. Introduction With the discovery of an increasing number of gas-distillate fields in the Gulf Coast, engineers have had occasion to give more thought to the performance of these reservoirs, as evidenced by the literature published in recent years. In the majority of studies published so far the formations are considered to consist of uniform, homogeneous sand. In this paper the authors wish to bring out the effect of variations in the permeability of the formations on the over-all recovery efficiency of wet gas in cycling operations. The importance of the permeability profile is clearly indicated by the fact that in gas cycling, highly permeable stringers in an otherwise tight sand can allow complete displacement of wet by dry gas in these stringers long before the wet gas in the tight portions of the sand is displaced. This by-passing will be reflected by a reduction in the condensate content of the production sooner than can be anticipated from a mathematical analysis or an electrical model study on uniform sands. Electrical model studies or mathematical analyses cannot take into consideration the manifold variations of permeability within the reservoir. Experimental as well as analytical difficulties make it necessary to consider the prototype for either of these studies as a perfectly uniform sand. Mathematical analyses are applicable only when a reservoir can be divided into units of simple geometrical form, of uniform thickness throughout. Electric model studies are capable of giving information on reservoirs of any shape or thickness, but it is essential that the sand be considered homogeneous, so that three-dimensional flow can take place. The method of approach in the following

Jan 1, 1946

By Fred C. Bond

The Standard method of determining the crushing resistance of rocks consists of crushing prepared shapes under slow compression, and expressing the ultimate crushing resistance at the load causing failure in pounds per square inch of cross-sectional area perpendicular to the crushing force, with the height approximately equal to the diameter. One-inch cubes or cylindrical drill cores are commonly used. Cubes and drill cores are cut by a highspeed steel disk with diamond dust embedded in the edges, and running under a water spray. such a saw will cut one square inch or more of hard stone per minute. An oiled, spherical, swivel compression block of small diameter should be used to equalize the pressure. Each sample is crushed between sheets of cardboard or blotting paper extending about one-half inch beyond the edges of the stone. A cloth is wrapped around it to prevent dangerous explosive shattering. It is probably preferable to place the swivel block below the specimen, with either a rigid head or another swivel block above. Whatever the arrangement, the conditions should be selected that will develop the maximum crushing strength of the specimen, even though its top and bottom planes may not be precisely parallel. The cardboard pads may be dispensed with if the ends of the specimens are polished smooth. The use of lead pads was discontinued because of the observed tendency to split the material. The samples are weighed and measured before breaking, and the density is calculated. Cubes that contain bedding lanes or veinlets are usually placed with these vertical and parallel to the crushing force, in order to develop the maximum resistance possible. A number of compression tests were made on Canadian ores, by Forrest Nagler, of the Allis-Chalmers Manufacturing CO., and are listed alphabetically in Table I. These tests were made on one-inch cubes or on diamond-drill cores approximately one inch in diameter and One inch long. The drill cores represent virgin rock, while the cubes may have been previously weakened by explosives. compression tests have been made in the Allis-Chalmers Milwaukee Laboratory on a number of ores and other materials. These are listed alphabetically in Table 2. In test NO. 1339, on limestone from the Hanna Coal Co., comparison was made between 2 by 2-in. diamond-drill core segments and one-inch cubes cut from the cores in the same strata. Results for the cylinders are tabulated directly below those for the cubes. The bedding planes were normal to the compressive force in breaking the cylinders and parallel in breaking the cubes, which accounts for the lower strength obtained from the cylinders. The percentage of net linear compression at the ultimate pressure was measured in test No. 1055 for Fontana TV A quartzite as 0.30 for cube A, and 0.37 for cube D.

Jan 1, 1947

By Rex W. Woods, Morris Muskat

A leastmsquare analysis procedure has been developed and applied for the study of the deviations in estimations of oil in place as given by the material-balance equations. The data used were those obtained from field observations on the Jones sand in the Schuler pool, Arkansas, and the Monroe dolomite in the Reed City pool, Michigan. Possible effects of water intrusion were taken into account by expressing the cumulative water influx in terms of various functions previously proposed in the literature. Formulas were developed and values calculated for the minimum deviations and minimal percentage deviations in the calculated volumes of oil in place from the average values, as could be obtained by suitable choice of the water encroachment and initial gas-cap volume parameters. The results show that the fluctuations in these calculated volumes are very insensitive to the values chosen for the rate of water intrusion and initial gas-cap volume, and hence cannot be safely used in discriminating between spurious values for these parameters and such as actually pertain to the producing reservoirs. Moreover, the exact form of the water-intrusion function seems to have but little effect on the fluctuations in the computed oil in place. Accordingly, it is concluded that the material-balance method does not of itself provide a satisfactory criterion for determining the basic physical unknowns of producing reservoirs or in making conclusive decisions regarding the production mechanism, unless independently established geological control data are available for eliminating unreasonable values for the reservoir parameters, even though they may still satisfy the material-balance formulas. If, however, from core or logging data the initial oil in place and the gas-cap volume can be established in advance, the material-balance formulas can be inverted to find the water intrusion. Moreover, by determining by such calculations the water-intrusion coefficient, the iuture production performance can then be predicted by the aid of the materiaI-balance formulas for specified operating conditions. This type of application may be of particular value in predicting the results of Pressure-maintenance operations. Introduction The evaluation of the forces acting upon an oil reservoir is a problem of considerable interest to the operator as an aid in determining the proper method of operation for the reservoir to obtain an optimum recovery of oil. In many pools, the nature and magnitude of the forces acting upon the reservoir remain unknown until an appreciable amount of ultimate recovery is obtained. To be of value to the operator, a reliable interpretation of reservoir performance should be available in the early life of the pool to permit an optimum plan of operation. Progress has been made in an understanding of reservoir behavior and the importance of the different factors involved. The material-balance method of estimating oil in place has been proposed as a tool in analyzing reservoir-performance problems.l The solution of such problems by this method ordinarily involves two or more unknown values relating to the nature of the reservoir, and the results

Jan 1, 1945

By M. Muskat, H. H. Evinger

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By W. N. Lacey, B. H. Sage

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By P. K. Foster, A. McNabb

A consideration of the literature shows the inadequacy of Fick's Laws to describe the diffusion of hydrogen in steels below 400°C. These laws are modified an the assumption that hydrogen is delayed at fixed sites in the lattice. Approximate and exact solutions of the resulting nonlinear system are derived for simple geometrical shapes. The results qualitatively account for the observed anomalous behavior. Experimental methods for verifying the theory are suggested. 1 HIS paper presents a new analysis of the diffusion behavior of hydrogen in steel based on a physical model which supposes that hydrogen atoms wander in a random manner through the crystal lattice, but tend to get trapped or delayed at certain fixed sites uniformly distributed throughout the metal. These sites, which will be called traps, are regarded merely as potential wells of significantly greater depth than those encountered in regular regions of the crystal lattices and no assumptions are made concerning their nature or origin. The results of experimental studies of the diffusion of hydrogen in iron and steel have usually been reported in the literature in terms of a diffusion constant D derived under the assumptions that the hydrogen concentration C is governed by Fick's laws.1 Fig. I is a composite of published graphs of the man. ner in which the values of D, so derived, vary with temperature. It is convenient to consider this material in two categories; the high temperature results above 400°C, and the results at lower temperatures. The graphs 2, 3, 4, 5 in the first class lie within a factor of three of each other and are relatively consistent compared with the low-temperature values. There is an increasing divergence in values of D with decreasing temperature till at room temperature they are spread over three orders of magnitude. Small values of D have been obtained for work-hardened specimens.' It is evident that D is a function of other variables besides temperature in this range and that these neglected variables are in some way connected with the work hardening experienced by the specimen. In view of evidence for an interaction between hydrogen in solution and dislocations9'10 and adsorption on crack surfaces,' some doubts must be entertained about the validity of Fick's laws and their associated physical model of noninteracting particles in random motion through the medium. More direct evidence of their inapplicability to the diffusion of hydrogen in steel was first produced by Darken and smith." Consider the permeation of hydrogen through a plate of thickness a under a boundary concentration Co at the ingoing, and zero at the outgoing, face. If Fick's first law1 is valid, the steady state flux P, through unit area is DCo/a. In addition, the concentration C varies linearly throughout and Qo, the mean quantity of hydrogen in the medium, is co/2. Compare Qo with Q1 the mean quantity required to saturate the same specimen to a uniform concentration G. In this case Ql = Co and hence the ratio

Jan 1, 1963

By M. Muskat, H. H. Evinger

ALTHOUGH the shooting of oil wells for the purpose of increasing production has been practiced since 1866, present-day shooting technique has been arrived at almost wholly by a process of trial and error. The difficulties attending either a theoretical analysis of the problem or an experimental attack become apparent when one actually embarks on a theoretical investigation or attempts to formulate an intelligent experimental program. The literature on the subject consists mainly of descriptions of current practice, scattered eye-witness accounts of events following the shooting of a well, and vague speculations on the mechanical processes involved. In contrast to quarry blasting, the results of oil-well shooting cannot be determined by means of visual inspection, and it is perhaps for this reason that only one attempt at what approaches a direct experimental attack has been reported in the literature.1 In these experiments, charges of liquid nitroglycerin were exploded in holes drilled in a sandstone outcrop. In order to observe the character and extent of the resulting fractures, the rock was blasted away so as to expose the original shot holes. After all this had been done it was found impossible to distinguish the fracturing due to the original shots from that due to the subsequent blasting. The enlargement of the holes due to the pulverizing action of the shots was. measured and an attempt was made to determine the effectiveness of 'sand tamping. Only five shots were made and few definite conclusions could be drawn. Some small-scale experiments to determine the effect of tamping were performed by Snelling and Hall,2 Small charges (20 grams) of dynamite were detonated at the bottom of a cylindrical hole in a lead block and the resulting enlargement of the hole was taken as a measure of the effectiveness of the explosion. It was found that when the shot was tamped with a sufficient amount of sand or clay, the volume enlargement was approximately double that found when no stemming had been used. The properties of the explosives have been the subject of much study by the manufacturers, the U. S. Bureau of Mines, and various other agencies. For example, velocities of detonation for many commercial explosives are to be found in the Blasters' Handbook, issued by the Du Pont company. Many other properties are given in a treatise on the subject by Naoum.3 The shock wave that accompanies the detonation of high explosives has been studied photographically by Payman4 and others. The hydrodynamical theory of the shock wave has received much attention, and an extended theoretical treatment is given by Bateman.5 Two aspects of the well-shooting problem will be considered in this paper; namely, the fracturing of subsurface strata, and possible damage to casing. With respect to the former of these, several calculations have been made giving the stresses in the rocks surrounding the shot. In order to arrive at numerical results at all, however, it is necessary to introduce a great many simplifying

Jan 1, 1941

By W. Hurst, A. F. van Everdingen

A distillate-bearing sand complex is often made up of sand stringers of different permeabilities. In order to take into account the influence of the different permeabilities, "parallel flow" is defined, and this concept is used to compute the recovery efficiency of recycling such a sand complex. In the first approximation the position of the wells with respect to one another is not considered. In order to compute the effect on the recovery efficiency of the position of the wells, the area of a field is considered to be made up of rectangles; each rectangle containing one input well in the center and two producers located symmetrically with respect to the input well. Formulas are given from which to obtain the pressure and streamlines in a steady-state flow. A method is devised to compute rapidly the successive positions of the dry gas front. If the field is irregular in shape, pressure and streamlines can be obtained by a potentio-metric electrical model study. By using the concept of "parallel flow" and the results obtained by mathematical analysis or by electrical model study for a homogeneous formation, the effects of different permeabilities and of the location of the wells can be established. From these studies it is apparent that the efficiency of recycling can be profoundly influenced by differences in permeability among the various parallel strata. Introduction With the discovery of an increasing number of gas-distillate fields in the Gulf Coast, engineers have had occasion to give more thought to the performance of these reservoirs, as evidenced by the literature published in recent years. In the majority of studies published so far the formations are considered to consist of uniform, homogeneous sand. In this paper the authors wish to bring out the effect of variations in the permeability of the formations on the over-all recovery efficiency of wet gas in cycling operations. The importance of the permeability profile is clearly indicated by the fact that in gas cycling, highly permeable stringers in an otherwise tight sand can allow complete displacement of wet by dry gas in these stringers long before the wet gas in the tight portions of the sand is displaced. This by-passing will be reflected by a reduction in the condensate content of the production sooner than can be anticipated from a mathematical analysis or an electrical model study on uniform sands. Electrical model studies or mathematical analyses cannot take into consideration the manifold variations of permeability within the reservoir. Experimental as well as analytical difficulties make it necessary to consider the prototype for either of these studies as a perfectly uniform sand. Mathematical analyses are applicable only when a reservoir can be divided into units of simple geometrical form, of uniform thickness throughout. Electric model studies are capable of giving information on reservoirs of any shape or thickness, but it is essential that the sand be considered homogeneous, so that three-dimensional flow can take place. The method of approach in the following

Jan 1, 1946