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By A. W. Dana, F. J. Shortsleeve, A. R. Troiano

The phenomenon of flake formation which may occur during cooling or room temperature aging of large steel sections is caused by a combination of hydrogen and stress. As such, the transformation characteristics of austenite in a particular section play a major role in the occurrence of flakes. Isothermal and continuous cooling studies demonstrated that flake formation is particularly sensitive to nature, distribution, and relative proportions of the microconstituents in the cooled sections. In the absence of transformation stresses, abnormally high hydrogen contents could be tolerated without flaking. Flakes were not found in the absence of transformation stresses. No correlation existed between average hydrogen content and flake formation where cooling stresses were low. Hydrogen in the steel was a necessary but not sufficient condition for flake formation. DESPITE a long history of laboratory and commercial investigations, the mechanics of hairline crack or flake formation in large steel sections remains unresolved. Recent publications1-5 emphasize that flaking is still a serious problem.* immediate cause of flaking is the pressure exerted by entrapped hydrogen gas that collects in small internal cavities or voids during cooling. When the temperature of steel is low enough to preclude extensive plastic flow, the cavity pressures cause local brittle fractures (flakes). 2—The microsegregation and transformation stress theory. According to this theory, flaking results from stresses arising from the volume changes accompanying the formation of martensite and/or low temperature bainite after a large portion of the section has transformed at elevated temperatures. The proponents of the hydrogen theory suggest that stresses from other sources may be additive to the stresses produced by hydrogen and may, in some cases, provide the increment of stress necessary to produce flakes. However, the critical aspect of this theory is that no stress, except that produced by hydrogen pressure, is believed to be sufficient in itself to produce flakes. For practical considerations, this means that the only safe thermal cycle is one that reduces the hydrogen content to some low critical level below which flaking will not occur regardless of the state of transformation. On the other hand, the transformation stress theory does not rule out the embrittling effect of hydrogen. This theory simply proposes that flaking does not occur in the absence of transformation stresses. With the transformation stress theory as a basis, commercial antiflaking cycles would be designed to complete the transformation of austenite prior to cooling to ambient temperatures. Both of these theories appear compatible with industrial experience. Antiflaking cycles, such as cooling at extremely conservative rates or soaking for periods of time in the upper subcritical temperature ranges prior to cooling to ambient temperatures, may allow the following: 1—diffusion of hydrogen out of the section and, as a consequence, reduction of the hydrogen content to some safe minimum value (hydrogen pressure theory) and 2—complete decomposition of the austenite at rela-

Jan 1, 1956

By Margaret G. Scroger, Luke L. Y. Chang, Bert Phillips

Using the sealed-system technique, isothermal sections at 1000°, 1400°, and 1700°C for the system Co-W-O hare been determined. The equilibrium data were obtained by microscopic and X-ray diffraction examination of samples winch had been equilibrated in pellet form fit sealed capsules and subsequcelly quenched. The only ternary phase in the system is CoWO, which mells congruentlly at approximately 1280°C. At 1000°C, this ternary phase exists in equilihrinm with all the allows and oxide compounds in the hounding binary systems. At 1400°C, liquid forms in thin oxygen-rick region near the CoWO4 composition and only one phase assemblage in the system (W + WO2 + H'5CV7) contains no In order for tungsten to be used to its full potential as a refractory metal. it is necessary that coatings be developed which will preclude oxidation of the metal. It is true that coatings now in use do protect tungsten for short periods at temperatures near 1700 °C. but no coating has been developed which protects adequately at or above this temperature where the use of tungsten is most required. This situation exists despite the great effort in recent years to develop such coatings. and it has become evident that success in this area can be achieved only after a more fundamental knowledge of the thermochemical and therrnophysical propertics of tungsten oxidation and tungsten -metal oxidation is obtained. In our 1aboratories. a project liclrriel. At 1700°C, tungsten is the ouly solid phase which is stctble, and a large range of compositions melt to two liquids, one metallic and one oxidie. The sealed-system method of etjuilibra lion prevents the determination of the partial pressure of oxygen and the total gas pressure orer the condensed phases at equilibrium. This data is not available and can be obtained only by some other method. We can generalize on these unknowns and indicate that both partial pressure of oxygen and total pressure of the gas phase must increase as compositions change from the W-Co binary toward the oxygen apex and as temperatures increase. has been initiated which is directed at providing some of this fundamental information through a study of metal-tungsten-oxygen reactions and equilibria and the properties of any intermediate phases which result. This paper is based on a part of this program in which the system Co-W-O was studied between 1000° and 1700°C. I) RELEVANT INFORMATION FROM THE LITERATURE A) The Notable Lack of High-Temperature Work on Metal-Tungsten-Oxygen Systems. It should be pointed out that there has been no published report (of which we are aware) which deals with the study of a metal-metal-oxygen system at 1700°C. Also, there has been no report on a complete metal-luugsten-oxgen system at any temperature. As a matter of fact. before this program started. The

Jan 1, 1965

By G. C. McCartney, S. J. Kidder

The Helen Mine, of the Algoma Steel Corporation, in the Michipicoten district, Ontario, Canada, has produced more than 6,240,290 tons of iron ore. Prior to and during World War I, 2,823,369 gross tons of brown ore were shipped, and from 1939 to the end of the 1944 season, 3,416,921 gross tons of siderite ore were produced from open-pit operations. Brief descriptions are given of the nature of the ore, the mining methods employed and the manner of treatment of the ore. Shipment of the finished product, known as Algoma sinter, is made to blast furnaces in both Canada and the United States. The iron-ore bodies—i.e., the oxide ores of the Old Helen and the siderite of the New Helen—are a part of a tabular shaped area of iron formation that extends over a length of more than 100,000 ft. and has a maximum width of 1000 ft. The ores are considered to be a product of introduction of iron-bearing material accompanied by replacement of the rocks already present. It is shown that introduction took place subsequent to the development of the major folded structures. It is believed the iron-bearing material emanated from an igneous source. Introduction The Michipicoten mining district derives its name from the Indian word1 meaning "place of bold promontories" or "region of big places," and anyone who has visited this part of Canada will agree that the district is well named. In 1897, there was active prospecting for gold in the district and the Ontario Bureau of Mines2 opened a recording office at the Hudson's Bay post at Michipicoten River. In the summer of 1897, Ben Boyer, probably searching for gold, discovered an outcrop of brown iron ore at the east end of a small lake, less than 8 miles, in an air line, northeast of the nearest point on Michipicoten Harbour. In the following year, extensive surface exploration and diamond drilling disclosed a commercial body of nonbessemer brown ore, possibly 700 ft. long and 200 ft. wide, of about the following analysis:3 Fe (natural), 57.15 per cent; S, dried at 212°F.. 0.113; SiO2, dried at 212°F., 4.00; P, dried at 212°F., 0.125. The property (Figs. 1-3) was taken over by E. V. Clergue and ultimately was transferred to the Algoma Steel Corporation. The Algoma Central Railway shortly afterward built its line from Michipicoten Harbour to the mine, together with an ore dock at the Harbour. Thus, within three years of its discovery, the mine had adequate shipping facilities and a market for its ore. Production of Brown Ore and Pyrite The first shipment of brown ore was made in July 1930. By 1939, the mine was shipping at the rate of 170,000 long tons

Jan 1, 1949

By S. J. Kidder, G. C. McCartney

The Helen Mine, of the Algoma Steel Corporation, in the Michipicoten district, Ontario, Canada, has produced more than 6,240,290 tons of iron ore. Prior to and during World War I, 2,823,369 gross tons of brown ore were shipped, and from 1939 to the end of the 1944 season, 3,416,921 gross tons of siderite ore were produced from open-pit operations. Brief descriptions are given of the nature of the ore, the mining methods employed and the manner of treatment of the ore. Shipment of the finished product, known as Algoma sinter, is made to blast furnaces in both Canada and the United States. The iron-ore bodies—i.e., the oxide ores of the Old Helen and the siderite of the New Helen—are a part of a tabular shaped area of iron formation that extends over a length of more than 100,000 ft. and has a maximum width of 1000 ft. The ores are considered to be a product of introduction of iron-bearing material accompanied by replacement of the rocks already present. It is shown that introduction took place subsequent to the development of the major folded structures. It is believed the iron-bearing material emanated from an igneous source. Introduction The Michipicoten mining district derives its name from the Indian word1 meaning "place of bold promontories" or "region of big places," and anyone who has visited this part of Canada will agree that the district is well named. In 1897, there was active prospecting for gold in the district and the Ontario Bureau of Mines2 opened a recording office at the Hudson's Bay post at Michipicoten River. In the summer of 1897, Ben Boyer, probably searching for gold, discovered an outcrop of brown iron ore at the east end of a small lake, less than 8 miles, in an air line, northeast of the nearest point on Michipicoten Harbour. In the following year, extensive surface exploration and diamond drilling disclosed a commercial body of nonbessemer brown ore, possibly 700 ft. long and 200 ft. wide, of about the following analysis:3 Fe (natural), 57.15 per cent; S, dried at 212°F.. 0.113; SiO2, dried at 212°F., 4.00; P, dried at 212°F., 0.125. The property (Figs. 1-3) was taken over by E. V. Clergue and ultimately was transferred to the Algoma Steel Corporation. The Algoma Central Railway shortly afterward built its line from Michipicoten Harbour to the mine, together with an ore dock at the Harbour. Thus, within three years of its discovery, the mine had adequate shipping facilities and a market for its ore. Production of Brown Ore and Pyrite The first shipment of brown ore was made in July 1930. By 1939, the mine was shipping at the rate of 170,000 long tons

Jan 1, 1949

By P. R. Sperry, M. L. Holzworth, P. A. Beck

The basic work of Z. Jeffries 1,2,3 has long ago established the main features of grain growth in the presence of a dispersed second phase. Working with sintered specimens of initially fine grained tungsten, to which various amounts of thoria had been added, Jeffries found that grain growth was inhibited, that is, practically prevented, up to a certain annealing temperature. When this temperature, which increased with the thoria content, was exceeded, extremely large grains developed abruptly from the fine grained matrix. such a a temperature" was later found by Gross-mann~3,14 in certain types of steel, while ~~i~ showed15 that in other steels grain growth was gradual, without inhibition and abrupt coarsening. Later work demonstrated the connection between coarsening and aluminum additions. The viewpoint that the direct cause of inhibition and coarsening in aluminum killed steels is a fine dispersion of aluminum oxide21 appears to be held quite generally, although some doubts have been voiced even very recently, 20 In steels with Ti additions the titanium carbide phase is considered responsible for the inhibition effects found.20 The coarsening temperature increases with the titanium content. That coarsening may occur, as a result of, certain heat treatments, even in low carboil rimmed sheet steel, was shown by Samuels. He also detected coarsening in a steel ingot of similar composition, after giving it the same heat treatment as that used by him for the sheet material. In this instance the identity of the inhibiting phase has not been determined. However, Tangerding found23 that even the few small carbide particles, which occur in carbonyl iron, have a very marked inhibitive effect. As a result of an oxidizing anneal at 850°C, large grains begin to form at the surface of the carbonyl iron specimen, and gradually grow inward as the subsurface oxidation of the carbide particles progresses and eliminates the obstruction. The carbide particles Can be removed also by annealing in hydrogen, with similar results. But if the oxidizing anneal of 10 hr at 850°C in air is followed between in hydrogen for 75 hr at the Same temperature, grain growth is more hibition usually the whole specimen is transformed into a single crystal (approx. 1.5 cm X 5 cm). The reversed procedure, that is, hydrogen annealing followed by oxidizing annealing leads to smaller grains. Tangerding arrived at the logical conclusion that there must have been in his specimens some additional obstruction to grain growth hibition from a minor impurity, other than carbon. It seems likely that this obstruction was caused by an oxide formed during the oxidizing anneal and gradually reduced rtain the subsequent hydrogen-annealing. Other instances of grain growth inhibition of varying severity, associated with a dispersed second phase, have been described by several authors. Notable examples: lead with 0.06 pet Cu or Ni,24 cartridge brass with 0.12 pct Cr,25 or with up to 0.15

Jan 1, 1949

By M. L. Holzworth, Philip R. Sperry, Paul A. Beck

INTRODUCTION THE basic work of Z. Jeffries1,2,3 has long ago established the main features of grain growth in the presence of a dispersed second phase. Working with sintered specimens of initially fine grained tungsten, to which various amounts of thoria have been added, Jeffries found that grain growth was inhabited, that is, practically prevented, up to a certain annealing temperature. When this temperature, which increased with the thoria content, was exceeded, extremely large grains developed abruptly from the fine grained matrix. Such a "coarsening temperature" was later found by Gross mann13,14 in certain types of steel, while Bain showed" that in other steels grain growth was gradual, without inhibition and abrupt coarsening. Later work16,17,18,19,21 demonstrated the connection between coarsening and aluminum additions. The viewpoint that the direct cause of inhibition and coarsening in aluminum killed steels is a fine dispersion of aluminum oxide21 appears to be held quite generally, although some doubts have been voiced even very recently.20 In steels with Ti additions the titanium carbide phase is considered responsible for the inhibition effects found.20 The coarsening temperature increases, with the titanium content. That coarsening may occur, as a result of certain heat treatments, even in low carbon rimmed sheet steel, was shown by Samuels,22 He also detected coarsening in a steel ingot of similar composition, after giving it the same heat treatment as that used by him for the sheet material, In this instance the identity of the inhibiting phase has not been determined, However, Tangerding found 23 that even the few small carbide particles, which occur in carbonyl iron, have a very marked inhibitive effect. As a result of an oxidizing anneal at 850°C, large grains begin to form at the surface of the carbonyl iron specimen, and gradually grow inward as the subsurface oxidation of the carbide particles progresses and eliminates the obstruction, The carbide particles can be removed also by annealing in hydrogen, with similar results. But if the oxidizing anneal of 10 hr at 850°C in air, is followed by annealing in hydrogen for 75 hr at the same temperature, grain growth is more spectacular; usually the whole specimen is transformed into a single crystal (approx. 1,5 cm X 5 cm). The reversed procedure, that is, hydrogen annealing followed by oxidizing annealing leads to smaller grains. Tangerding arrived at the logical conclusion that there must have been in his specimens some additional obstruction to grain growth resulting from a minor impurity, other than carbon. It seems likely that this obstruction was caused by an oxide formed during the oxidizing anneal and gradually reduced during the subsequent hydrogen-annealing. Other instances of grain growth inhibition of varying severity, associated with a dispersed second phase, have been described by several authors. Notable examples: lead with 0.06 pct Cu or Ni,24 cartridge brass with 0.12 pct Cr,25 or with up to 0.15

Jan 1, 1948

By B. C. Blake

IN general, billet-type or long slender ingots are used when it is desired to produce directly from the ingot in one conversion a product of medium or small cross-sectional area. They are designed to eliminate the blooming and billet-mill stages of the usual procedure. As used at Connors, they constitute a means of keeping a continuous rolling mill busy in the production of high-quality small rods, small angles, hoop stock, baling ties and concrete reinforcing rods without the need for a blooming or billet mill. They represent sound steel with the best surface that is commercially practical to use in the rolling of small continuous mill products.

Jan 1, 1947

By William E. Ford, Edward Salisbury Dana

Secondary Twinning. - When there is reason to believe that the twinning has been produced subsequently to the original formation of the crystal, or crystalline mass, as, for example, by pressure, it is said to be secondary. Thus the calcite grains of a crystalline limestone often show such secondary twinning lamella?. The same are occasionally observed (Ilc, 001) in pyroxene crystals. Further, the polysynthetic twinning of the triclinic feldspars is often secondary in origin. This subject is further discussed on a later page, where it is also explained that in certain cases twinning may be produced artificially in a crystal individual - e.g., in calcite (see Art. 282).

Jan 1, 1922

By Karl A. Bauer, Cornelis Bezemer

The deposition of calcium carbonate scale on surface and subsurface production equipment creates an operation problem in many oil fields. The formation water in which the carbonate-scale-forming components are initially dissolved becomes supersaturated with calcium carbonate as a result of the drop in pressure during production. The continuous flow of a supersaturated solution through the production equipment results in the growth of a dense layer of calcium-carbonate crystals. For a scale layer to be built up, the supersaturated formation water should contact the walls of the production equipment. The tendency for scale to be deposited, therefore, will be low, if the crude has a low water cut and if the water is finely dispersed in the oil. A scale problem will occur, if at a high water cut part of the water is present as free water. The rate of scale deposition will then be approximately proportional to the rate of free water production. Depending upon where the formation water becomes supersaturated, scale may be deposited in the flow line only, in both flow line and tubing, and in some cases even in the perforations and in the formation near the wellbore. In the South Sumatran fields (Indonesia) the main difficulties encountered due to the deposition of calcium-carbonate scale have been restriction of flow through tubings and flow lines, wear and abrasion of plungers and liners, and stuck plungers or wellhead valves. So far, the only methods of combating the *Presently associated with Brunei Shell Petroleum Co., Ltd.. Seria. scale problem have been routine acidizing and additional well pulling. As for the pumping wells, it was estimated that some 50 percent of the total well-pulling effort was directly attributable to scale deposition. The most promising alternative was to prevent the deposition of calcium carbonate scale by means of chemicals. Inorganic polyphosphates such as sodium hexametaphosphate and trisodium polyphosphate are known to retard the formation of scale by the "threshold action". They are adsorbed on specific faces of the crystal nuclei and thus prevent crystal growth, thereby stabilizing supersaturation. Polyphosphates are effective at very low concentrations ( a few ppm), and far less than stoichiometric quantities are required to keep the scaling ions in solution. Recent investigations on barium sulfate scale1 have confirmed this mechanism. The types of polyphosphate mentioned can be applied as concentrated aqueous solutions either squeezed into the formation, lubricated down the annulus or injected via macaroni string. Several squeeze jobs with polyphosphate solutions have been carried out in the South Sumatran fields, however, with disappointing results. Lubrication down the annulus and injection through a macaroni string were not considered attractive in this area because of the kind of equipment and the degree of supervision these techniques require. Polyphosphates are also available in a granular, glassy form, which, in contrast with the readily soluble types already mentioned, show an extremely low

Jan 1, 1970

By B. A. Eaton

The subject of many discussions and technical papers in the last 20 years has been the prediction of the well-bore pressure gradients that are required to induce or extend fractures in subsurface formations. The subject merits this attention because of the frequently recurring problems that arise from an inability to predict fracture pressure gradients. Encountered in several common types of operations in the oil industry are problems associated with the prediction of formation fracture pressure gradients. When wells are being drilled in both new and old fields, lost circulation is often a very troublesome and expensive problem. Complete loss of circulation has been disastrous in some cases. Many times, such disasters could have been avoided if techniques for calculating fracture pressure gradient had been employed in the well plans, and if casing strings had been set, and mud weight plans had been followed accordingly. In areas of abnormally pressured formations, the prediction of fracture gradients during the well-planning stage is extremely important. In fact, it is as important as the prediction of formation pressure gradients, which has received a great deal of attention in recent years. There are several published methods used to determine fracture pressure gradients. However, none of these methods appears to be general enough to be used with much reliability in all areas. In 1957, Hub-bert and Willis published a classical paper that included the development of an equation used to predict the fracture extension pressure gradient in areas of incipient normal fau1ting.l Overburden stress gradient, formation pore pressure gradient and Poisson's ratio of rocks were the independent variables that were shown to control fracture pressure gradient, the dependent variable. In 1967, Matthews and Kelly published another fracture pressure gradient equation that is different from that of Hubbert and Willis in that a variable "matrix stress coefficient" concept was utilized.3 Later the same year, Costley wrote about a similar idea.5 Goldsmith and Wilson used a least-squares curve-fitting technique and field data from the Gulf Coast area to correlate fracture pressure gradient with formation pore pressure gradient and formation depth.' They noted that the fracture pressure gradient increased with increasing depth while the pore pressure gradient remained constant. In each of these cases, the problem for which a solution was sought was to determine the bottom-hole pressure gradient required to initiate or extend a fracture. Results of the previous work show that fracture pressure gradient is a function primarily of overburden stress gradient, pore pressure gradient, and the ratio of horizontal to vertical stress. There is argument for a fourth variable in that in many cases breakdown fracture pressure gradient is greater than the fracture extension pressure gradient. However, if the fracturing fluid is able to penetrate the formation through the pores or existing cracks, there is very little

Jan 1, 1970

By D. Geoffry Minnes

Nepheline syenite is a silica deficient crystalline rock consisting of albite and microcline feldspars and nepheline, together with varying but small amounts of mafic silicates and other accessory minerals. Nepheline-bearing rocks are widely distributed around the world but only in Canada, Norway, the Union of Soviet Socialist Republics, and the United States are deposits worked commercially. Because of its low melting point and fluxing ability, nepheline syenite was investigated in the early 1900s by many students of glass and ceramics. Although the nepheline syenite deposits in Methuen Township, Ont., Canada, were discovered as early as 1897 it wasn't until 1935 that the first mill was erected to produce nepheline syenite products. In Canada, nepheline syenite deposits are worked by Indusmin Ltd. and International Minerals and Chemical Corp. (Canada) Ltd. who have combined production capacity in excess of 1800 tpd. Between 1935 and 1972 seven million tons valued at $78 million were produced from the Methuen Township deposits. In Norway, the Norsk Nefelin Div. of Elkem Spigerverket has produced nepheline syenite from a deposit on Stjernoy Island in western Finnmark since early 1960. Between 1961 and 1972 the company produced 930,000 mt with an estimated value of $17 million. Nepheline syenite has been under investigation in the Union of Soviet Socialist Republics (USSR) since at least 1928. In 1951 the first commercial alumina works was brought on stream at Volkhov, near Leningrad, utilizing nepheline concentrates from the Kola peninsula as mill feed. Since then two others have been completed and more are planned. Large quantities of portland cement, sodium carbonate, and potassium carbonate are produced in conjunction with the alumina. In the United States, nepheline syenite has been produced for many years from deposits in central Arkansas by the Big Rock Stone and Materials Co. for construction aggregates and, since 1947, for roofing granules by the 3M Co. Chap. 16 on "Feldspar, Nepheline Syenite, and Aplite" in the 3rd ed. of Industrial Minerals and Rocks (Castle, and Gillson, 1960) and Nepheline Syenite Deposits of Southern Ontario (Hewitt, 1960) contain excellent accounts of earlier commercial development of nepheline syenite as a glass and ceramic material. Therefore this chapter deals mostly with the period since 1960 and with matters not previously reported in detail. An English monograph on Nepheline-Syenite and Phonolite (Allen et al., 1968) is a complete current survey of nepheline syenite which, with its very complete list of references. is an excellent source book. End Uses Nepheline syenite from the Canadian and Norwegian producers finds use primarily in the manufacture of glass and ceramics. One producer also makes several grades of nepheline syenite that are useful as extender pigments and fillers in paint, plastics, and rubber. In the Soviet Union nepheline is used in increasing quantities in the manufacture of alumina, alkali carbonates, and portland cement and to a lesser degree it is used in the manufacture of colored container glass.

Jan 1, 1975

By H. J. de Haan, J. van Lookeren

In view of their size and favorable characteristics, Shell's heavy-oil fields on the eastern coast of Lake Maracaibo, Venezuela — known as the "Bolivar Coast" — are obvious candidates for the application of thermal recovery methods. During the last decade various methods have been tested, such as steam drive,', steam soak and in-situ combustion.3 Steam soak was discovered as a promising production method rather accidentally in 1969, during early steam drive testing in the Mene Grande Tar Sands1 When steam erupted at the surface due to breakdown of the overburden, the injection wells were back-flowed to relieve the reservoir pressure. This resulted in high oil production rates, all the more impressive because the reservoir is unproducible by primary means. It was concluded that injection of limited amounts of steam might be a very effective method for stimulation of heavy-oil wells. To obtain information that would be more widely applicable, testing of the process was continued in the eastern part of the Tia Juana field (Fig. 1). Here even more favorable results were obtained than in Mene Grande. This created sufficient confidence to prompt a large-scale project, which was considered essential for an adequate evaluation of ultimate recovery, steam requirements, mechanical problems and economic prospects. To obtain an early answer on the ultimate recovery a fairly depleted area was selected in the western part of the same field ("A" in Fig. 1). The first steam was injected in March, 1964. This paper describes the performance until the end of 1966. The production mechanism and well inflow performance are discussed in some detail. In view of the favorable results obtained so far, steam soak operations have expanded considerably since the start of this project. Presently, five other projects are under way, of which two are about the same size as the one under discussion, with further extensions being programmed. Description of the Project Reservoir Data Shell's part of the Main Tia Juana reservoir has a proven area of 8,800 acres and an average net oil sand thickness of 130 ft. It contained an initial quantity of 2,750 million bbl of stock tank oil (STOIIP), with an API gravity ranging from 10 to 15 API and a viscosity of 100 to 10,000 cp (at 122F). As a geological unit it is known locally as the Lower Lagun-illas member of the Lagunillas formation, which is early Miocene in age. The sand bodies are believed to be distributary channel sands deposited in a lower coastal plain. Most of the channel sands have lateral and some vertical communication. The field was developed mainly in the period from 1936 to 1950. The ultimate primary recovery is estimated at 18.1 percent of STOIIP, of which 12.5 percent STOIIP had been produced by the end of 1963 from some 540 wells. By then the average pressure had decreased from an initial value of 960 to 550

Jan 1, 1970

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts'1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By C. S. Smith

The partial persistence of grain size and grain shape on melting and resolidifying crystalline substances, as well as the general effects of pre-solidifi-cation and of superheating on nuclea-tion rate, have been attributed to the presence in the liquid of crystalline impurities bearing some structural relation to the principal solid and hence capable of serving as nuclei for its crystallization. That such lattice matching does sometimes occur is well established, but it is surely improbable that a compound possessing both high-temperature stability and the requisite structural similarity should be naturally available in almost every system. It is now suggested that a mechanism for producing appropriate nuclei exists in the crystallization of all but absolutely pure substances. Impurities can he of many kinds. Some will give rise to compounds that are less soluble in the solid crystal than in the liquid. A . crystal forming from a melt or solution containing these will be supersaturated in some degree, and the foreign atoms will commence to segregate during or after solidification. They do not necessarily form pure, unstrained, crystals of the precipitating compound with its normal composition and structure. Generally—at least in the metallurgical examples that have been most studied —the first recognizable nuclei have lattice coherency with the surrounding matrix and have practically the same crystal structure and lattice spacing as the material in which they form, differ- ing only in composition. An extremely thin oxide layer formed under appropriate conditions on or in a solid metal will tend to be coherent with the metal lattice, and the first few atom layers of the oxide in contact with the metal will differ in both composition and structure from massive crystalliue oxide. It will resemble the metal more closely than the oxide. If it did not subsequently change on melting, such an oxide film would constitute an almost perfect "template" or two-dimensional matrix to hold a few atoms of the primary metal in the exact array needed to form a nucleus for solidification. Any precipitating material will adopt the correct spacing over a few atom diameters, and with appropriate substitution of other atoms of the correct sizes a precipitate can match the parent lattice over large areas of cohererlce without excessive strain. In metals, the componentsof a host of oxides, silicides, borides, nitrides, carbides, sulphides, and other compounds are always present in minute amounts. Some of these will be eliminated because of extreme insolubility in the liquid, while others will remain soluble in the solid; occasionally, however, particles will be formed in the solid by coherent precipitation—not of pure substances, but of whatever assortment of atoms best satisfies the joint requirements of availability, affinity, and appropriate average atom size. Of these, many will disappear on melting, but a few will persist unmelted as little rafts of complex composition, maintaining in the liquid a surface of the exact geometry needed to nucleate the solid on subsequent cooling. Their number and size distribution will determine the resulting grain size; the dimensions of the largest will determine the degree of undercooling that can occur before solidification commences. A similar process may operate in the case of phase transformations in solids. The coherent precipitation of supersaturated minor constituents in a low-temperature phase should facilitate the nucleation of this phase on subsequent cooling after transforming into another phase at higher temperatures. At first sight this hypothesis may seem little different from the older ones. It should therefore be emphasized that it does not depend on chance to provide the right compound to form a nucleus, but postulates that every crystal, containing minute amourlts of any of a wide range of impurities, automatically engenders particles having the correct surface structure to serve as nuclei for subsequent solidification. It could operate in any system, metallic, organic, or inorganic. The suggested mechanism is closely analogous to the production of antibodies from antigens in living organisms—indeed, it was a description of the matrix theory of this process that suggested to the writer its crystalline analogue.

Jan 1, 1950

By E. T. Turkdogan, L. E. Leake

A number of measurements have been made on the vapor pressure of pure iron at 1600°C. Experiments were carried out by the transportation method in which a sample of iron is exposed in a furnace to a stream of pure argon, metered at a predetermined flow rate for a specified period of time. The vapor pressure was obtained from the weight loss of the sample. A detailed diagram of the apparatus used for the experiments is given in Fig. 1. It consisted of a horizontal molybdenum-wire-wound furnace fitted with a recrystallized alumina tube 1 1/8 in. internal diam. The boats, 1 by 3/16 by 1/8 in., were fired in argon at 1600°C to constant weight before use. After this treatment, subsequent heating of the boats to 1600°C gave little or no further change in weight, e.g. ±0.05 mg in 24 hr. The furnace and reaction tube were separately fed with argon from two independent flowmeters. These were connected to a common supply source via an argon purification furnace containing metallic titanium sponge at 700°C, and an anhydrone drying-tower. A rotary displacement-type meter was included in the gas train to provide a direct means of measuring the total volume of gas passed through the reaction tube. The material used was vacuum melted high-purity iron in the form of wire 2mm in diam. The following impurities were present in the iron: 0.008 pct C, 0.002 pct Si, 0.005 pct Mn, 0.008 pct S, 0.001 pct P, 0.01 pct Ni, 0.001 pct Cr, 0.006 pct Cu, and 0.001 pct Al. Samples consisting of three small pieces of this wire were laid end to end in a recrystallized alumina-combustion boat, and were separated by small fragments of alumina. The wire samples were then melted in argon to form spherical beads 2 to 3 mm in diam. After weighing, the boat with its contents was placed on the boat carrier and introduced into the cool end of the reaction tube. The entire furnace system was then flushed with argon for 30 min. At the end of this period, the flow of argon to both furnace and reaction tubes was adjusted to the desired level; then the boat was slid rapidly into the hot-zone of the reaction tube. After a known volume of gas had passed through the reaction tube, the boat was withdrawn quickly to the cool end of the furnace. When quite cool, the boat was removed from the fur-mace and placed in a desiccator for subsequent re-weighing. The semi-micro balance used in these experiments had a sensitivity of 0.005 mg. The above procedure was repeated at several flow rates within the range of 25 to 300 ml per min. The flow of argon in the annular space between the two tubes was at a rate of 300 ml per min in all experiments. During all the experiments the furnace temperature was maintained at 1600° ± 5°C by means of a temperature controller. The temperature of the reaction zone was measured with a Tinsley high precision disappearing filament pyrometer which was initially calibrated against a Pt-13 pct Rh/Pt thermocouple; the errors due to temperature measurements were within * 5°C. RESULTS Assuming that the iron vapor is in the monatomic state, the vapor pressure can be calculated from the weight loss of the sample and the volume of the carrier gas. The results obtained are plotted in Fig. 2 against the rate of flow of argon through the chamber containing liquid iron beads. At low flow rates, the thermal diffusion of iron gives an apparent high vapor pressure, but at high gas flow rates, the carrier gas is not saturated with the vapor, and therefore, low vapor-pressure values are obtained. This is now a well-known phenomenon. There is a distinct inflexion of the curve at about 120 to 160 ml per min rate of argon flow and the vapor pressure of iron within this

Jan 1, 1961

Edward Dyer Peters, the only child of Henry Hunter Peters and Susan Barker Thaxter, was born in Dorchester, Mass., June 1, 1849. From his father he was a descendant of the Peters family of Ipswich and Andover, Mass., whose earliest ancestor settled in Essex County in 1659; while upon his mother's side he descended from several old Hingham families, as well as from the Quineys and from Governor Bradford. Between the ages of fourteen and sixteen he was a student at the Episcopal School for boys in Cheshire, Conn. Near the school was an old tin mine, and he used to spend his Saturday afternoons exploring it. When Edward was sixteen, his father sold his property in South-borough, and for the next three years lived in Europe. Sept. 26, 1865, Edward entered the Royal School of Mines at Freiberg, Saxony. In the summer of 1867 he joined his family on Lake Geneva, and spent a part of the season in that vicinity, going to Chamounix and taking other trips. Extract from a letter to his father: Elbingerode, Harz, Aug. 30, 1868: I left Freiberg with my friend Lilienthal, on Wednesday the 19th of August, reached Leipzig in the evening and spent the night in that city: the next morning we took the cars and in the afternoon reached Eisleben, in Prussia, which was to be our first stopping-place; there are immense copper-mines and smelting-works at this place, and the method of working the mines is very peculiar ... The next morning we got up at five and spent the whole day in the smelting-works where I obtained a number of drawings of the furnaces they use here and a good many valuable data. Saturday morning we got up at four o'clock, and descended a mine about three miles from the town; the Director of this mine was one of the most intelligent and agreeable men that I ever met; he accompanied us in the mine and explained everything that was new to us. The system of mining at Eisleben is peculiar to this town, and is not used at any other place in the world; the copper ore comes in narrow, flat veins eighteen inches high, at the utmost, consequently the men work lying flat on their left side and using the pick with both hands: the ore is carried out of the side passages into the main ones, in very low waggons about twelve inches high, and four by two feet; the boys who pull these waggons have a board buckled to their left thigh and their left arm; they pass their bare foot through a strap in the waggon and wriggle along on their side dragging the waggon after them, with their foot, almost as fast as a man can walk above ground. In the afternoon we walked over to Hittstadt, about twelve miles, and remained there Sunday and Monday. Monday night, at ten o'clock we went out to one of the smelting-works, to see the refining of the copper; this is only done at night, so we worked there from ten in the evening till eleven the next morning, and came home all blackened up and with blistered hands, for our skin was not quite so tough as that of the workmen: at noon the same day we took the stage to Ascherls-leben, and then the train to Stassfurt, where there are immense salt-mines, as well as factories for the manufacture of bromium, which latter process is, however, kept a profound secret, so we had very little hope of seeing anything but the salt mines; we were talking with our landlord about our disappointment, that evening, when he told us that the director of the Bromium works was sitting in the next room with no company but his glass of beer, so we went over to him, introduced ourselves as Americans, and actually succeeded in persuading him that it could do his business no earthly hurt if he showed us his works; at last he consented, after making us give our word of honor

Jan 1, 1919

By G. C. Wallick

Since the appearance of the paper, "Solution of the Equations of Un-steady State Two-Phase Flow in Oil Reservoirs," by W. J. West, W. W. Garvin, and J. W. Sheldon,' a two-fold investigation of this subject has been carried out. One objective of the investigation has been to deter-mine the feasibility of solving such problems 7on a medium-size com-puter such as the Datatron*, and the other objective has been to in-vestigate the application of such cal-culations to experimental and theo-retical petroleum reservoir research. In the first Datatron calculations, the fluid and rock properties published by West, et al, were used, together with the published equations describ-ing the system. Details of the formu-lation not given in the original paper are discussed in the Appendix to this note. Reference should be made to the subject paper for the complete equations and defintion of symbols. An unexpected result of this in-vestigation was the discovery that the linear solution published by West was in error. Thus, in addition to describing the Datatron solutions and to discussing certain numerical diffi-culties which will be encountered if one uses the published method of solution, the purpose of this note is to indicate the nature of this error. LINEAR FLOW Since the linear case requires a minimum amount of scaling, a fixed-decimal point Datatron program was written for the one-dimensional flow problem and an attempt was made to duplicate the solution described by West. In the case described, fluid was produced at a constant rate, Q, until such time as well pressure reached 0.04. Production was then continued at constant pressure. From the constants and curves given by West it was determined that the ini-tial constant production rate could be approximated by Q = 0.007. An ini-tial dimensionless time step ?t = 0.434 X 10 - "as used, and each suc-cessive time step was doubled until a value of = 0.444 was reached. This constant interval was then used for the remainder of the solution. In subsequent solutions, several varia-tions in the time schedule were em-ployed, including smaller time steps and slower rates of increase in the time steps. In all cases, almost identical results were obtained regardless of the time schedule employed. However, as described below, it was noted that the time schedule had some influence on the rate of convergence of the solutions. As a check on the accuracy of the solution, the cumulative production at each time step was calculated using the two methods described in the Appendix. Satisfactory agreement was observed with the differences in these two values of the order of two parts in 50,000. It should be noted that the mass balance check as described is of questionable value, particularly with regard to the well pressure and saturation. This is especially true in the radial solution where pressure and saturation values near the wellbore would make only a negligible contribution to the numer-ical integration. It is believed, how-ever, that such a comparison is ot value in determining the over-all accuracy of a solution. In comparing the Datatron solu-tion with that published by West it was discovered that in the later stages of depletion, the pressures near the well declined more rapidly in our solution than in the West solution, and that the limiting well pressure of 0.04 was reached at an earlier time than that originally reported. It thus became evident that it would be impossible to duplicate the production schedule described by West and a constant rate of production was maintained until the well pressure was equal to 0.0. A representative comparison of the results published by West with those obtained in this investigation is shown in Fig. 1, which is a plot of GOR as a function of cumulative recovery. These two curves should be in agreement until a cumulative recovery is reached which corresponds to a well pressure of 0.04 — for the Datatron solution, a recovery of approximately 5.6 per cent. Actually, a major disagreement is evident. Subsequent correspondence

Jan 1, 1958

By J. E. Drury, W. M. Byers, E. J. Lynch

Measurements made with starch ~~~~s indicate that the Presence of starch serves to depress the streaming potential of a clay mud system. Measurements with pure starch slurries show that the addition of NaCl or CaO reduces the streaming potential significantly. The addition of NaOH, however, causes only a minor reduction in potential even when there are large changes in mud resistivity. INTRODUCTION In their excellent study of the streaming potential, Hill and Anderson' proposed that the presence of conductive solids within the filter medium will reduce the generated potential. This theory was demonstrated with measurements on shaly sandstone cores having various "b" factors; the cores with the higher negative b factors showed markedly lower potentials. (The factor b was originally defined by Hill and Milburn2 in an expression relating the resistivity of a shaly sandstone to the resistivity of the interstitial water: log F, = log F,, + b (log 100R,)'. 'he factor b, therefore, is a measure of the contribution of the conductive solids to the total conductivity of the sample. It has been found experimentally to be directly related to the amount of chemically exchangeable ion per unit pore volume.) In the logical extension of this hypothesis to the streaming potential created by filtration through mud cakes, they suggested that the presence of nonconductive starch in a drilling mud would have the opposite effect; i.e., it would cause the streaming POtential to be increased. The high streaming potentials that they observed with lime muds were attributed to this cause. A cross-plot of some of their results which are relevant to this discussion is given in Fig. 1. The lime-mud curves and untreated-mud curve are taken from curves given in their paper. The gyp-mud line was estimated from their statement that the measured streaming potential for gyp muds in the range of 1.5 to 2.0 ohm-m was approximately 18 mv/1,000 psi. These gyp-mud potentials were the lowest that they reported for any of the bentonitic-clay muds, and were the only ones which were less than the untreated-mud potentials. This very low streaming potential of gyp muds has also been observed in field studies.' By way of comparison, a U. of Texas publication4 gives the approxi-ate compositions for lime and gyp muds shown in Table 1. These materials are added to a bentonitic-clay mud base. It can be seen that both of these muds contain significant amounts of calcium salts and that the gyp mud has the higher concentration of starch. It would appear from this and from the data shown in Fig. 1 that starch may well be the cause of a streaming-potential reduction, rather than a potential increase. EXPERIMENTAL A series of streaming-potential experiments has been performed using a cell of a design similar to that reported by Wyllie.5 Calomel electrodes were used in both the mud slurry and the filtrate. Pressure in the cell was generated with high-pressure nitrogen. The primary objective of the investigation was to determine the effect of starch on the potential. Five different slurries were made which ranged in composition from untreated ben-tonitic mud (Baroid Aquagel) to a pure starch suspension (Baroid Im-permex). The intermediate slurries were prepared by mixing together a 9-lb/bbl clay mud with a 12-lb/bbl starch suspension in the ratios 1:3, 1:1 and 3:1. When starch was used alone, it was necessary to use an 18-Ib/bbl mixture, since leaner mixtures would not form a suitable filter cake. The clay mud used in the experiments was aged for three months before use. In addition to this series of measurements on the starch-clay mud mixtures, other experiments were performed to determine the effect on the potential of the absolute starch and Aquagel concentration, and the effect of adding various chemicals. RESULTS The effect of starch on the streaming potential is shown clcarly in Fig 2. Increasing percentages of starch resulted in n continually decreasing

By Steve H. Carpenter, Henry E. Otto

The explosive welding of metals is dependent upon the production of a jetting action caused by the collapsing of one metal plate against another. Successful welds are generally accomplished if the yield strength of the metals is in the range of 10,000 to 90,000 psi and the sonic velocity of the metal is greater than the detonation velocity of the explosive if direct contact explosive is being used.' Should the detonation velocity exceed the velocity of sound in the metal it may still be possible to obtain the jetting action and a good weld. However, in most cases where a high detonation velocity is used complications arise because of reflected shock waves which tear the bond apart as fast as it is put together.' Explosive welding of lead presents several problems since its yield strength and sound velocity are very low. Various values have been published3-5 for the velocity of sound in lead ranging from 2000~ to 23004 m per sec. Most of the high-order explosives have detonation velocities on the order of 6000 to 8000 m per sec, which precludes their use. The dynamites have a lower detonation velocity of around 2800 m per sec which is still somewhat too high. Lower-order explosives such as ammonium nitrate (1070 m per sec) must be used to weld lead in the as-received condition if the explosives are used in direct contact. Rather than use low-order explo'sives it was decided to alter the sonic velocity of the lead. The sonic velocity is directly related to the modulus of the material according to the following expression: Fig 1—Interface of explosive weld of lead to steel. Lead is on top As-polished Magnification 75 times as well as the yield strength. Bolling et al. 6 show that the shear modulus of lead single crystals increases from about 0.72 X1011 dynes per sq cm at 300°K to about 0.98 X1011 dynes per sq cm at 0°K, an increase of approximately 3 5 pct. This gives an increase in the sonic velocity of around 700 m per sec. Hence, the sonic velocity of lead at cryogenic temperatures is approximately equivalent to the detonation velocity of the low-order dynamites. We have obtained high-quality lead to steel explosive welds using a 40 pct dynamite in direct contact with the lead. Prior to detonation the lead was chilled with liquid nitrogen (78°K) to increase the strength and sonic velocity. Welds were made while the lead was cold. Specimen sizes were 3 by 6 in. A preset angle of 5 deg with a 0.10-in. standoff at the base was the geometrical setup used. The amount of explosive used for optimum welding of an 1/8 -in. -thick lead sheet to a steel plate was found to be 7 g per sq in. A PETN sheet explosive line wave generator was used to insure a linear detonation front through the dynamite. A photomicrograph of a lead-steel weld is shown in Fig. 1. The typical wave effect that constitutes a good explosive weld is present. When tested in shear, the weld failed in the lead, indicating that the bond is stronger than the lead base metal. Higher-order explosives were also tried without success. We believe this indicates the importance of matching the detonation velocity and the sonic velocity for successful explosive welding. Note Added in Proof. High quality explosive welds of lead to steel have recently been obtained at ambient temperature using a low velocity (1000 M per sec) free running dynamite. The weld interface obtained is comparable to Fig. 1. 'S. H. Carpenter, R. H. Wittman, and R. J. Carlson: Proceedings of the First International Conference of the Center for High Energy Forming, Syracuse University Press, syracu.se, N. Y., in press. 'A. HI Holtzman and G. R. Cowan: Welding Risearch. Council Bull., No. 104, April, 1965. 'Metals Handbook, 8 ed., p. 1062, Metals Park, Ohlo. 'J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger: Phys. Rev., 1957, vol. 108, pp. 196-216; 'L. V. Al'tshuler, K. K. Krupnikov, B. N. Ledener, V. I. Zuchikhin,

Jan 1, 1968

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953