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By J. C. Deppe

A method is presented for calculating approximate injection rates in secondary recovery operations. The method can be applied to cases of unequal fluid mobilities, irregular well patterns and boundary patterns. The steady-state pressure distributions for the four flood patterns reported by Muskat and for five additional patterns reveal that most of the difference in pressure between the injection and producing wells occurs in regions around the wells which can adequately be described as regions of radial flow. This leads to a method of calculating injectivity by approximating the flood pattern with radial flow elements (or a combination of radial- and linear-flow elements for some patterns such as the direct line drive). Irregular and boundary patterns can also be approximated by radial and linear elements. Each of these elements can be described by radial-and linear-flow equations and the results combined as series flow resistances to give an approximate equation for the initial injection rate. The mobility ratio does not affect the initial rate; therefore, if the well pattern is one of those regular patterns for which theoretical rate equations have been derived for unity mobility ratio, the approximate initial rate equation can be improved by adjusting it to match the theoretical equation. The available theoretical rate equations are listed, including five new cases. As the flood progresses, the injectivity changes because in general the flood front will divide the pattern into areas of different fluid mobilities. Simple shapes can be assumed for the flood front so that both areas can be divided into radial- and linear-flow elements. Radial- and linear-flow equations are applied to these elements to account for the change in flow resistance behind the front. To calculate injection rates after breakthrough, it is necessary to know the sweep efficiency at breakthrough. Areal sweep data are available in the literature for a number of patterns, and sufficiently accurate breakthrough sweep efficiency can be estimated from these data if it is not otherwise available. Again, simple shapes for the flood front can be assumed after breakthrough, and injection rates can be calculated for the remainder of the flood. When areal sweep data are available, these data can be used to cbeck. the calculated injection rates after breakthrough. Injection rates calculated by this approximate method compare favorably with available model data. INTRODUCTION When the fluid mobilities in the swept and un swept regions are equal, the injectivity will not change as the flood front advances; and for regular patterns it can be calculated by mathematical formu1as.l When the fluid mobilities in the swept and unswept regions are not equal, the injectivity will increase or decrease as the flood front advances. In this case, the injectivity has not been calculated by analytical means for any practical well pattern; and, furthermore, scale model and analog4,6 results have been published only for the five-spot pattern. The main object of this paper is to present an approximace method for calculating injectivity for the case of unequal mobilities. The method can be applied to regular, irregular and boundary patterns. Before the approximate method is discussed, the analytical formulas for equal mobilities will be summarized, and the analytical solution for radial flow with unequal mobilities will be used to show how the injectivity changes as the flood progresses. EQUAL MOBILITIES, REGULAR PATTERNS In a flooding operation the injectivity, the rate at which fluid can be injected per unit difference in pressure between injection and producing wells, depends on basic physical properties and, in addition, on three variables to be treated here—the area of the swept region, the fluid mobilities in the swept and unswept regions, and the well geometry (pattern,

By C. K. Eilerts, J. D. Ham

Laboratory research has been conducted to evaluate the characteristic effects of condensate saturation on the mobility of gas in typical reservoir rocks. A pump with two pistons provided phases in equilibrium at controlled flow rates and constant liquid-vapor volume ratios. Core samples were tested in a holder that permitted sealing steady-state phases in the pore spaces under flow test pressures for weighing with sufficient precision to give an accurate measure of the attained saturations. Parameters of the study were pressure, apparent velocity, flowing liquid-vapor volume ratio, fluid composition, core material and length-to-diameter ratio. Tests were conducted at 515 and 1,515 psia to determine the effect of pressure on the mobility-saturation relationship. Influence of the apparent velocities 0.30, 0.15 and 0.07 cm/sec and of five liquid-vapor volume ratios from 0.0001 to 0.01 was determined at 515 psia The principal fluid system was nitrogen and and separator liquid from a Gulf Coast condensate, but the effect of a condensate of different viscosity was also determined. The significance of a possible concentration of liquid near the outlet end of the test cores was investigated. Core materials included a consolidated sandstone and a low-permeability limestone. Relative mobility and liquid-vapor volume ratio relationships are concluded to be dependent on pressure, saturation and, to a lesser extent, on velocity. For each porous medium and fluid there is a minimum saturation essential to two-phase flow, and high velocities of flow have only limited effect on saturations in this range. INTRODUCTION It is now recognized that knowledge of the availability of a reservoir gas — the period that gas may be recovered from a reservoir at a given rate — is as important as the estimate of gas in place. When reservoir conditions are such that pressure decline owing to production will result in retrograde condensation, liquid saturation can increase in the structure around the production well in a way that may restrict flow capacity, and hence future availability. l Based on a numerical solution of transient radial flow of single-phase gas-condensate fluids, 2 a program for computing the accumulation of condensate in a reservoir and the effect of this condensate on deliverability has been developed. During this development a need evolved for data that described the influence of pressure, velocity of flow and condensed liquid on mobility as recovery progressed. This paper presents the results of experimental investigation to obtain insight into the mobility relationship at reservoir pressures of gas-condensate fluids. A core holder for flow tests at reservoir pressure was developed to weigh the core and its fluid contents under pressure to determine saturation. A specially constructed pump was used to drive a two-phase fluid through the core until a steady state prevailed. The core was used as a differential device, and properties measured were intensive rather than extensive. APPARATUS Fig. 1 shows a schematic representation of the major pieces of equipment used in the mobility determination. The weighable core holder is connected to a two-piston, constant-displacement pump. Attainment of steady-state flow is indicated by stability of the flow differential read from the high-pressure manometer. WEIGHABLE CORE HOLDER An important part of the data needed was the mobility-saturation relationship. This required that mobilities and saturations be measured at pressures, flow velocities and liquid-vapor volume ratios characteristic of condensate reservoirs.

By H. E. Sadler, Prof. Silliman

The research here recorded was undertaken early in the present year, and has been prosecuted steadily for about eight months. While the work has been under my constant supervision and advice, the labor has all been performed by Mr. Sadler, to whom is chiefly due the development of the successive steps which have led to the final result. The process is better than I dared to hope, and we are able to place at the command of chemists and engineers interested in the matter an apparatus of continuous and uninterrupted action, and methods of analysis by which the daily averages of the two variable and inconstant factors of illuminating gas, ammonia and sulphur, may be determined with all needful accuracy, even by those little skilled in chemical manipulation, and with very little loss of time. This research has been carried out in the laboratory of the New Haven Gaslight Company.

By M. H. Gaskell, D. M. Kehn, G. T. Pyndus

A correlation of the bubble point pressure for black oil systems is developed using the standard physical-chemical equations of soiutions. The correlation is based on 158 experimentally measured bubble point pressures of 137 independent systems and is expressed in terins of the usually measured field pnrameters— flash separation gm-oil ratio, rank oil gravity, total gas gravity, and reservoir temperature. The data were obtained on systems produced in Canada, Western and Mid-Continent01 United States, and South America. The average error (algebraic) in the representation is 3.8 per cent, and the maximum error encountered is 14.7 per cent. INTRODUCTION In the absence of experimentally measured properties of reservoir fluids, it is often necessary for the field engineer to make estimates regarding the fluid properties based on the usually measured producing parameters. To aid in these estimations, various correlations have appeared in the literature in recent years. Among the pertinent properties of interest is the bubble point pressure. A correlation for this parameter has been reported by Standing'. However, this correlation was based essentially on California produced crudes and this limitation was pointed out with its presentation. The correlation presented in this paper utilized data on crude oil systems from Canada, Wes- tern and Mid-Continental United States, and South America. CORRELATION DEVELOPMENT The basic assumption used in this development is the same as employed by Standing', There is a wide variety of ways to combine these parameters; however, in this instance the combination was made on the basis of Henry's law2. Accordingly, the relationship proposed is Although Eq. 2 defines an individual system, it is of limited value since H' is a function of gas-phase composition and the system temperature. It was observed that for the systems where the bubble point was measured at several temperatures that the ratio of the bubble point pressures and the ratio of the corresponding absolute temperatures (R) were practically identical. Thus, for correlation purposes the bubble point pressure may be taken as a direct function of the absolute temperature. This relation is valid only for those systems that are not near the critical point. Accordingly, this correlation will be inadequate for systems in the region of the critical point. The solubility of the various hydrocarbons found in the gas phase increases with the molecular weight. Thus, the saturation pressure should be inversely related to the gas gravity. Applying these principles to Eq. 2 and rearranging terms gives: The variables 02 the left side of Eq. 3 were designated as the "hubble point pressure factor". The number of mols of tank oil per barrel is a function of the "mclecular weight" of the tank oil. Although the tank oil is a complex mixture, it was assumed for the purposes of this correlation that a unique molecular weight could be assigned to a given oil. This was designated as the "effective molecular weight", and was related to the oil gravity, This empirical relationship was developed simultaneously with the correlation by assuming values of M,. and working to obtain a smooth curve for both the correlation and the effective molecular weight. The relationship between the oil gravity and the effective molecular weight used in this correlation is shown in Fig. 1. The effective molecular weight is somewhat higher than the molecular weight of the C fraction. The difference between these values is largest for the low-gravity systems. It is noted that this effective molecular

By T. Egleston

IF we may characterize the aim of metallurgists twenty years ago by any one point towards which their efforts were especially directed, we should say it was the idea of adapting '' waste products" to some useful purpose, while the energy of to-day seems rather to take the direction of so arranging processes as to have no "waste products." The iron-master of this decade no longer speaks of the waste gases

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

THE Institute assembled in the rooms of the Geographical Society at the Cooper Union, Tuesday evening at 8 P.M. President Raymond called the meeting to order, and introduced Mr. Abram S. Hewitt, who welcomed the Institute to New York. President Raymond, in behalf of the Institute, replied. The President then read the following report of the Council for the past year. The Council respectfully report that the American Institute of Mining Engineers has held four meetings-at Wilkes-Barre, Bethlehem, Troy, and Philadelphia, respectively-all of which have been well attended, and socially and professionally most successful. The proceedings of these meetings having been published in the Engineering and Mining Journal, and sent to all members and associates, are sufficiently well known. Forty-Bur papers, by twenty-six authors, have been read. These papers embrace a wide range of subjects, and prove the practical character of the proceedings of the Institute. The finances are in a satisfactory condition. By the report of the Treasurer it appears that $1290.10 have been received, $519.90 expended, and that $770.20 now remains in the treasury exclusive of fees for 1872. This fund, it is hoped, will be so increased by voluntary subscriptions as to enable us before long to issue a volume of our most important transactions in a permanent form. The Council has made a favorable arrangement with the Scientific Publishing Company, publishing the Engineering and Mining Journal, by which that journal became the organ of the Institute for the first publication of the proceedings, papers, and notices to members. This arrangement it is proposed to continue through the present year unless the Institute shall otherwise direct. I t is not intended to supersede the publication of an annual or occasional volume, but to maintain an interest in the Institute, and to serve the convenience of members while our funds do not permit a more ambitious publication.

By J. H. Henderson, T. E. Morrisson

An irvestigation has been made of the production of oil through horizontal fractures of high capacity and large radius placed at the base of producing formations. The specific aitns of the study were to (I) determine by model studies the reservoir performance when gravity drainage is the only producing mechanism, and (2) develop a method of predicting such perfortnance from commonly measured reservoir proper-ties. Although the theoretical approach tailed to develop a rigorous analytic sorution to the transient problem, it (lid lead to a practical method of predicting performance. Predictions (Ire in good agreement with rates and recoveries observed in scaled-model experinzents. Capillary effects and the influence of relative permzenbil-ity are taken into account. The experimental program was mainly concerned with the influenre of fracture radius, fracture capacily and capillary hold-up on the total recovery and the rate of recovery. Much of the experimental work was done on a triangular model which represented one-eighth of a square well pattern, so constritcted that horizontal fractures of varying radii and flow capacity could be studied. An electrolytic model was used to relate the initial production rates to fracture radius, formation thickness and the drainage radius of the well pattern. The conclusions reached as a resrtlt of the work are as follows. I. The production of oil under gravity force alone into a well-propped horizontal fracture, whose radius is of the order of hundreds of feet, is a recovery method which combines high recoveries with very acceptable production rates. 2. The mechanism is effective in "dead oil" reservoirs as well as in reservoirs which possess the energy of solution gas. 3. A method of predicting performance has been developed which gives good agreement with experimental behavior in cases of practicnl interest. Even for very thick beds and large fracture radii, where actual conditions do not conform to the assumptions made, the method gives order of magnitude predictions which would not otherwise be possible. INTRODUCTION Gravity drainage of oil from a formation which has continuous ver- tical permeability over a reasonable depth interval is a surprisingly effective method of recovery. However, for a conventional well the production rates which result from gravity drainage are so low that the economics are seldom attractive. The same formation may produce rapidly and profitably by gravity alone through a high capacity, extensive (i.e., > 100-ft radius) horizontal fracture placed near the bottom of the pay section. Fig. 1 shows a schematic diagram of the plan. Energy in the reservoir gas is not a necessary condition for this recovery process. With a sufficiently large fracture, attractive production rates will result from gravity flow alone, and the producing GOR need only be the solution GOR. It is, of course, necessary to keep the fluid level in

By C. P. Besse, N. F. LeBlanc

Described in this paper are oceanographic data which should be considered by an offshore design engineer and methods for developing a design wave height from the oceanographic data. The selection of a design wave is predicated on contemplated waves which might affect the site throughout the life of the structure. Selection of a design wave height may be based on (1) arbitrarily established recurrence Frequencies of hurricanes affecting the structure (predicted wave heights are associated with the expected variations of forces resulting from these waves) and (2) a risk-type evaluation wherein all possible storms affecting the area are considered (anticipated wave heights are associated with both investment plus risk costs and expected variations of forces). It is shown how the following oceanographic predictions are integrated into design considerations: (1) a classification of storm intensity which considers all recorded storms which affected the design area, (2) the recurrence interval of storms of a given- intensity (this interval is dependent on the extent of the geographical area considered in the design problem) and (3) a forecast of all wave heights which might affect the area (geometry of a structure often necessitates consideration of waves from a multiplicity of directions). The authors believe that the described techniques can result in selecting an adequate and reasonable design wave. INTRODUCTION Since the inception of offshore operations in the Gulf of Mexico, engineers engaged in designing suuctural facilities have been plagued with the problem of selecting an adequate and reasonable design wave. In the development of any offshore structure it is mandatory that the engineer evaluate the ability of the structure to withstand the ocean waves to which it will be subjected. Selecting such design waves quite naturally necessitates a coalition of the oceanographer and the design engineer. The oceanographer must provide a detailed knowledge of scientific principles which govern the behavior of waters in the Gulf of Mexico. He should also have an adequate knowledge of the manner in which design waves are utilized by the engineer. Although the design engineer's primary responsibility is applying the oceanographer's specialized knowledge in the creation of real structures, it is important that he possess some knowledge of related oceanographic principles to reasonably evaluate and apply the recommendations of the oceanographer. In the Gulf of Mexico it is the hurricane wind waves which generally govern the design of an offshore facility. The oceanographer must therefore develop techniques for predicting the heights, periods and frequency of all hurricane waves which might affect a particular structure. From this mass of oceanographic data, the design engineer must select the design waves which will apply to his particular design. PAST STUDIES ON FREQUENCY AND AMPLITUDE OF HURRICANE WIND WAVES Past oceanographic studies on the frequency of hurricane wave heights in the Gulf of Mexico have been devoted largely to predicting the recurrence interval of hurricanes which will generate maximum significant waves of given heights. The maximum significant wave height is the average height of the highest one third of the waves in that portion of the storm producing maximum wave heights. Since these waves occur over a relatively small portion of the storm (Fig. 1) and since the paths of hurricanes vary considerably (Fig. 2), the recurrence frequency of such heights is largely a function of the extent of the geographical area considered. In establishing the frequency of maximum significant waves for the entire American Gulf coast, the major fully developed hurricanes which affected the coastline from BrOwnsville, Tex., to Key West, Fla., were considered (Fig. 2). These Storms were selected and described by C. L-

By W. E. Brigham, P. W. Reed, J. N. Dew

By H. N. Mead

In a reservoir when gas comes out of solution and rises, additional pressure is created because of the change in position of this gar in the bounded volume. If this pressure effect is not taken into account as a pseudo-influx ill mate rial balance calculations on reservoirs in which there is evolving gas, an error is introduced that is directly proportional to the length of oil column and amount of gas evolved and inversely proportional to the reservoir pressure. In reservoirs with small oil column this pseudo-influx is of little importance. The larger the oil column the more important the effect becomes. The most important application, however, will be for reservoirs with declining pressure in which increasing water entry has been indicated by material balance calculations. It could be that this indication is the result of the cited pseudo-influx and not water entry at all. This paper attempts to explain this phenomenon in relation to material balance calculations and prevents an approximate method of determining tile pseudo-influx. INTRODUCTION Only recently has the pressure-volume relationship of gas rising in a liquid appeared in engineering literature, although its effect has been discussed for several years—especially among engineers engaged in drilling operations. The writer published a paper in 1957 in which this phenomenon was examined in relation to blowouts in drilling wells.' Also, in 1957 Stegemeier and Matthews' authored a paper in which the relationship was presented with respect to pressure build-up tests when shutting in producing wells. In this paper the effect will be called "pressure inversion" which is descriptive of the phenomenon. Fundamentally, the effect just mentioned is the result of changing the position of a quantity of energy contained within the gas itself (as a result of its compression) within the bounded volume in which the gas exists. If the gas were allowed to expand "beyond all bounds" there could be no pressure inversion effect. This is because all of the energy contained within the gas as a result of compression would have been re- PRESSURE INVERSION A phase that has not been discussed in the literature is the effect of pressure inversion upon material balance calculations in reservoirs in which the reservoir pressure drops with reservoir withdrawal and is below the bubble point. This action releases solution gas which, after the critical gas saturation has been reached, will tend to rise and collect at the top of the reservoir. The pseudo-influx caused by this effect could be great enough in reservoirs of large oil column and high permeability to render invalid any analyzer studies made on them — if pressure inversion has not been taken into account. Most suspect would be those reservoirs with large oil column in which increasing water entry has been predicted but the bottom wells have not yet produced water. Example 1 Simply stated, this phenomenon exists in oil reservoirs because of the difference in density and expansibility between gas and oil. For example, if a bubble of gas exists at the bottom of a 1,000-ft column of oil having a gradient of 0.30 psi/ft with the pressure at the top of the column zero, the bubble of gas will be compressed to a pressure of 300 psi. If temperature and the combined volume of the oil column and the gas bubble remain constant, as the gas bubble rises in the oil column it will have the same volume and consequently the same pressure at any point. Under these conditions when thc bubble reaches the top of the oil column, the pressure will be approximately 300 psi at the surface and approximately 600 psi at the bottom of the oil column. If it is assumed that the oil is incompressible the pressures will be exactly 300 and 600 psi, respectively.

By H. S. Drinker

THE first discovery of zinc 011 the property now worked by this company was made by the celebrated mineralogist, Prof. William Theodore Rapper, in 1845. Different claimants kept the property in continual litigation till 1861, when everything was satisfactorily settled by the purchase of the land by the company, who have worked it ever since. The mines are situated in a valley, four miles south of Bethlehem, Pa., in Lehigh County. The valley is from two to three miles broad, and is bounded 011 the north and south by syenitic hills. Syenite underlies the valley, and upon this is deposited the Potsdam sandstone, then a layer of slate, and, finally, a dolomitic limestone, belonging to the Chazy or Black River formation, in which the zinc deposits are inclosed. The rocks occur in folds, and have evidently been subjected to tremendous pressure from below, the zinc deposit being found in an anticlinal axis, in nearly vertical veins. I t is supposed that the zinc was originally disseminated through the

By T. Egleston

The importance of making analyses of gases in furnaces which are used for metallurgical purposes is every day growing more and more evident. It is the only method of understanding the reactions that take place in the furnace, and of economically conducting the operations both with regard to the fuel used and the reactions which take place on the bodies to be subjected to the influence of the heat and gases. As a knowledge of the composition of gases is becoming every day more necessary to the proper conduct of furnace operations, it seems desirable that furnace managers should generally know that the analysis of gas for commercial purposes is neither difficult, tedious, or expensive, and that it does not necessarily imply the use of corrections requiring difficult instrumental observations and long and tedious mathematical calculations. Any method, therefore, which will tend to render these analyses simple will also tend to having them made and repeated as frequently as the analyses of the ores and other materials charged in the furnace. They should be made even more frequently, as their composition is affected by any change in the condition of the furnace, and a knowledge of their composition will give a ready clue to the unseen and otherwise not easily detected changes which are taking place. The only practicable method of making industrial analyses of gas is that of measuring volumes in graduated tubes. The methods by

By G. Pizzi, G. M. Ciucci, G. L. Chierici

The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and produclion measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available. INTRODUCTION A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows. 1. A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.'-' 2. A reliable value for the reserves can be obtained only if reservoir data are very accurate'- or if past production performance has been subjected to abrupt variations in the production rate."' 3. No unique value for the reserves can be obtained from reservoir past production performance. This conclusion has been based upon theoretical considerations" and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented. THEORETICAL CONSIDERATIONS As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gp, Wp,) and n output variables (p,), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multi-variable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production G,(t) and W,(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "black-box It has been demonstrated" that for a blackbox the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance. When W,(t) is known, the determination of G from

By Edmund C. Perhin

At the suggestion of some members of the Institute, attention is called to the record of the working of Dunbar Furnace during the twelve months ending in Jaunary, 1874. During this period, with a product of over eleven thousand gross tons, not a single ton of

By F. H. Turan, F. W. Jessen

The gel strength and viscosity of two different suspensions of fractionated montmorillonite clay were measured by using a Stormer viscosimeter and Farm V-G meter. The amount of sodium poly-phosphate (sodium bexametaphosphate, sodium tetraphosphate and sodium acid pyrophosphate) adsorbed by the clay particles was determined. A relationship seems to exist between the amount of polyphosphate adsorbed and the nature of the surface, edge or plate, assumed to be the principal sites for selective adsorption. Reduction in viscosity and gel strength was found to be directly related to the adsorption. Both chemical bonding and physical adsorption seem involved in defloccula-tion Some indication of the axial ratios of particles of .l- to .04-micron average size is possible though study of the adsorption mechanism. INTRODUCTION AND PURPOSE A knowledge of surface areas of clay particles in a suspension and a precise determination of phosphate adsorption should provide a basis for a better understanding of reduction in viscosity and gel strength caused by molecularly dehydrated phosphates. The purpose of this investigation was to study the adsorption of sodium polyphosphates on suspensions of fractionated sodium montmorillonite. Although there is considerable uncertainty regarding details of the structure of montmorillonite, a generally accepted one is that suggested by Hofmann, Endell and wi1m.l The structure shown in Fig. 1 is an idealized one, and Marshall2 has postulated that it is possible for several isomorphous replacements to occur. Thus, aluminum may replace silicon, in which case an exchangeable cation would go along with the aluminum to neutralize what would otherwise be a net negative charge on the structure. There is disagreement among various investigators as to the particle size and shape of montmorillonite clays. Marshall2 reported the following results for the mean lateral dimensions of a Putnam clay (montmorillonite)— 3,730 A° for particles having average diameters ranging from 500 to 1,000 A, and 750 A° for those with an average diameter less than 200 A. The latter particles were estimated at 50A°in thickness, which would correspond to a stack of five unit cell layers. On the other hand, Shaw3 has interpreted micrographs as indicating that particles of montmorillonite ire readilv broken down to the individual cell layers by dispersion in water. Brindley4 and Merings indicate the ultimate particles to be of the order of 300 A° in mean lateral dimension. Van Olphen6 suggested the thickness of particles at four to five unit cell layers. It was suggested also that this number tends to become smaller with increasing dilution. Recently, Kahn and Lewis7 determined the size of sodium montmorillonite particles in aqueous suspension from electro-optical bi-refringence decay curves. The

By J. M. Smith, D. Kunii

Effective thermal conductivities of sandstones filled with stagnant fluids were measured using a steady-state technique. Data were obtained for seven sandstone samples, taken from four different locations and ranging in permeability from 18 to 590 md. The measurements with gases (helium, nitrogen, air and carbon dioxide) covered a pressure range from 0.039 psia to 400 psig. Data were taken for four liquids — n-heptane, methyl alcohol, 79.8 weight per cent glycerol-water solution and pure water at atmospheric pressure. The experimental results were used to evaluate the theoretical equations for predicting stagnant conductivities developed earlier 4 The low-pressure measurements permitted evaluation of the consolidation parameter bpDp/ks (necessary to utilize the theory) for the various types of sandstones. Using these characteristic values, the tbeoretical equations correlated well with the experimental conductivity data for the several fluids and rock samples. INTRODUCTION An aspect of heat transfer in solid-fluid systems of considerable current interest is the effective thermal conductivity of porous media. The stimulus for study of the subject arises from the need for sound procedures for designing thermal methods of petroleum production. The general system occurs when there exists a flow of fluid through the pores of the solid material. However, a logical starting point in developing a theory for predicting the effective thermal conductivity in the general system is to attack the special case when the porous solid is filled with stagnant fluid. Since the flow rates anticipated in thermal production processes are very low, such stagnant conductivities k,O are also of practical significance. Kunii and Smith4 recently reviewed the existing data for stagnant conductivities and proposed a theory for heat transfer in porous rocks. This leads to equations for predicting the stagnant conductivity as a function of the properties of the fluid and solid phases. The existing experimental information1-3,5,7,8 covered a range of porosities and agreed well with the theory. However, the available data were insufficient to examine critically the effects of two important properties on koe, — the thermal conductivity of the fluid and the pressure. The objectives of the present study are twofold: (1) to measure the effect on koe of (a) the pressure for gases, and (L) the thermal conductivity of the fluid kg for bloth gases and liquids; and (2) to determine for rocks of different porosities and permeabilities the apparent solid conductivity ks and the consolidation parameter bpDp/ks required in applying the theoletical equations. Measurements extrapolated to zero pressure are helpful in evaluating ks and the consolidation parameter. However, the extrapolations must be based upon data obtained at low pressures because in small pores the molecular conductivity of the fluid may be unusually depressed. This occurs when the mean free path of the molecules is of the same order of magnitude as the pore diameter, that is, in small-diameter pores at low pressures. The phenomenon has been studied recently by Schotte6in beds of unconsolidated fine particles. With particles in the size range of 45 to 200 microns, a significant reduction of kg with pressure was found even at absolute pressures greater than 1 atm. In the sandstones employed in the present investigation, pore diameters lower than those experienced by Schotte are likely, so that the effect would presumably be greater. SCOPE OF MEASUREMENTS Stagnant conductivities were measured for four types of sandstones using a total of seven samples. The characteristics of the samples, including porosity and permeability values, are given in Table

By E. A. Hopkin

Laboratory tests conducted by the author. together with actual field experience in Canada. have indicated the magnitudc of some of the factors affecting ability of drilling mud to clean the hole. A correlation was observed between funnel viscosity and particle slip velocity. A relationship was also observed between the Bingham yield value of the mud and the particle .slip velocity. Laburatury tests indicated little change in slip velocity with funnel viscosities up to ahout 80 sec/qt or to yield values of aboul 15 lb/100 .sq ft. The lip velocity of the partic1e.s. studied vuried from 160 ft/min with water to neerly zero for high mud viscositie. lncreasing the mud density, creating laminar annular mud flow or rotating the drill pipe Mlay also improve the carrying capacity of mud. Field tests indicated that during fast upper-hole drilling, the rate of cutting removal must he sufficien to maintain the concentration of cuttings in the annulus at less than 5 percent by volume to prevernt balled-up drill collars and .stuck drill pipe. INTRODUCTION In the Mid-Continent area, hole cleaning during rotary drilling normally involves the use of low-density drilling muds with funnel viscosities varying from 26 to 80 sec/qt. However, frequently it is necessary to raise the mud viscosity in excess of 200 sec/qt to clean the hole. In addition, field experience has indicated that during very fast upper-hole drilling, annular mud velocities considerably in excess of the maximum slip velocity of the cuttings (normally considered to be 120 to 150 ft/min) are necessary to prevent balling the bit and drill collars. In view of these variations in mud properties and circulation rates necessary to clean the wellbore, a study of factors affecting hole cleaning and the relative magnitude of each was undertaken. The study was also prompted by the knowledge that a drilling mud with properties close to those of water would drill at rates several times that of a viscous mud. The carrying capacity of these near-water muds was not clearly understood, however, and many drillers were reluctant to use them. DISCUSSION EFFECT OF MUD PROPERTIES ON DRILLING RATE The effect of mud properties on drilling rate has been studied by a number of investigators. 1t is clear from their work that mud properties close to those of water will significantly improve drilling rate and bit life. If the water-type mud will also effectively clean the hole and cause no logging or formation impairment problems, the choice of an appropriate drilling fluid is clear—use water. Often, however, a water-type drilling fluid is not capable of effectively cleaning the hole. THEORY OF PARTICLE SETTLING The forces acting on a particle that is allowed to settle through a fluid quickly reach equilibrium, and the particle settles at some constant velocity referred to as the slip velocity. The slip velocity of any particle depends upon a number of factors such as density and viscosity of the fluid, the volume, specific gravity, shape and roughness of the particle, and upon the shape and area of the projected face of the particle at right angles to the direction of relative fluid solid movement. Brown' expressed this relationship for spheres in Newtonian fluids in the following equation. where v, = slip velocity D, — diameter of sphere p, = density of spheye p, = density of liquid /a = friction factor g = constant. The friction factor f, varies as the size, shape, surface roughness and slip velocity of the body, and as the density and viscosity of the fluid varies. WaddelV ound experimentally that where dynamic similarity exists. f, was a function of the particle Reynolds number (NRe) of the sphere (Fig. 1). Fig. 1 shows that f, for spheres varies from over 10 for low NKe numbers to 0.44 for N,,. over 600.

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG's ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid' have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey' presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,