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By M. R. J. Wyllie, Michael A. Torcaso

With the continued deep drilling of today, increasing numbers of high pressure and high temperature gas-condensate reservoirs are being discovered. Correspondingly, the ranges of properties of gas-condensate reservoir fluids are also being increased. The literature1*'." contains several excellent reviews of the property ranges in presently known condensate reservoirs. When one examines these property ranges, it becomes apparent that the need for reliable data is great if the engineer is to evaluate properly or appraise a gas-condensate reservoir. It is the purpose of this paper to present phase-behavior data that will point out some of the important variables that influence recovery from gas-condensate reservoirs produced by pressure depletion. All these variables may be resolved into two major categories: the hydroc:arbon composition of the reservoir fluid and the physical properties of the reservoir. But the variables which we will consider are those which are usually determined from well tests shortly after discovery and are, consequently, readily available to the engineer. They are as follows: (1) the producing separator gas-stock-tank liquid ratio, (2) stock-tank liquid gravity, and (3) reservoir temperature. Laboratory depletion studies have been performed on several reservoir fluids to illustrate the effect of changes in the cronsidered variables upon ultimate recoveries. The deviation factors, Z, of a series of reservoir fluids were determined experimentally to illustrate their order of magnitude and their effect upon the calculation of in-place reserves existing at high pressurcs and temperatures. The procedures followed in conjunction with the performance of these studies and their associated calculations are illustrated in Fig. 1. For the purpose of this paper, the depletion recoveries are expressed only in terms of pcr cent of initial stock-tank liquid, with the abandonment pressure assumed to be 500 psig. VARIATION OF RECOVERY WITH INITIAL PRODUCING SEPARATOR GAS-STOCK-TANK LIQUID RATIO The producing separator gas-stock-tank liquid ratio has long been one of the principal criteria in assumptions and generalized correlations' used for the estimation of ultimate recovery from gas-condensate reservoirs. Fig. 2 presents a plot of the cumulative recovery of stock-tank liquid at abandonment as a function of the initial producing separator gas-stock-tank liquid ratio. The graphical illustration represents the results of 44 laboratory depletion studies performed on actual gas-condensate fluids. These data are presented not only to illustrate the general trend of ultimate recovery increase with initial producing ratio increase but to emphasize the considerable variation in possible recovery at any given producing ratio. Table 1 presents the properties of two actual reservoir fluids chosen to illustrate the approximate extremities of producing ratios for gas-condensate systems. The fluids designated as A and B exhibited initial producing ratios of 3,400 and 114,000 scf/bbl, respectively. Fig. 3 presents a graphical comparison of the cumulative stock-tank liquid recoveries, calculated from the well-stream compositions and produced volumes for each fluid during depletion. It is to be noted that Fluid A exhibited a recovery of only 16.5 per cent when produced to an assumed abandonment pressure of 500 psig while the corresponding recovery for Fluid B was calculated to be 62.2 per cent. This difference in recovery, which exemplifies the general trend of recovery increase with initial producing ratio increase, is readily explained by consid-

By M. R. Tek, K. H. Coats, D. L. Katz

The nature and the limits of validity of Darcy's law US applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the ,8 factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been conridered. In light of the current numerical results the significance and linlitation of the rate of flow function Y proposed by Smith" has been discussed. INTRODUCTION The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments, Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (Dvp/u), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis' reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots.' The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer." The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. Some fluid dynamicists define turbulence as a flow

By Kenneth L. Cashddollar, Terry G. Montgomery, Eric S. Weiss, John E. Going

The Pittsburgh Research Laboratory (PRL) of the National Institute for Occupational Safety and Health (NIOSH) and the Mine Safety and Health Administration (MSHA) conducted joint research on dust explosions by studying post-explosion dust samples. The samples were collected after full-scale explosions at the PRI, Lake Lynn Experimental Mine and after laboratory explosions in the PRL 20-L chamber and the Fike 1-m3 chamber. The dusts studied included both high and low volatile bituminous coals. Low temperature ashing for 24 hr at 515°C was used to measure the incombustible content of the dust before and after the explosions. The data showed that the post-explosion incombustible content was always as high as or higher than the initial incombustible content. The MSHA alcohol coking test -was used to determine the amount of coked dust in the post-explosion samples. The results showed that almost all coal dust that was suspended within the explosion flame produced significant amounts of coke. Measurements of floor dust concentrations after LLEM explosions were compared to the initial dust loadings to determine the transport distance of dust during an explosion. All of these data will be useful in future forensic investigations of accidental dust explosions in coal mines or elsewhere.

By Ancel St. John

At the New York meeting of the Institute of Metals Division in February, 1927, Jeffries and Tarasov presented a paper on Tungsten and Thoria,' in which the experimental facts were interpreted in accordance with the prevailing point of view that the thorium is present as the oxide, thoria. In discussing that paper the writer of this article stated that his own investigations, which had been unavailable to Messrs. Jeffries and Tarasov, showed that the so-called "thoriated" tungsten filament failed to disclose any sign of the oxide when subjected to X-ray diffraction analysis, but did give plenty of evidence of the presence of metallic thorium and, in certain cases, of a material believed to be an alloy of tungsten in thorium. Since these results were completely at variance with the results reported in the paper under discussion and with other papcrs which had preceded it from time to time in the past, it was felt that further discussion should be withheld until the new evidence could be presented adequately. Arrangc-mcnts were therefore made to present that evidence at this meeting. Material Examined The material exalllined was high-ernission filament such as is used in radio tubes, supposed to contain about 0.75 per cent. thoria. The actual analysis was not stated. Scope of the Investigation The investigation was undertaken because of a feeling that the thorium present in filamentary material of this type exists as metallic thorium or as an alloy of thorium and tungsten and not as the oxide. Attention was therefore directed to determining: 1. The minimum amount of thoria detectible in a mechanical mixture of thoria powder and finely divided tungsten. 2. The amount of t.horia detectible in the filament. 3. The condition of any thorium present in other form than as thoria. 4. The amount of thorium dissolved in the tungsten.

By Richard A. Thomas, Michael J. Sapko, Gary L. Mowrey, William D. Monaghan, Michael A. Trevits

Over the years, more than 20,000 mine seals have been erected in underground coal mines in the United States. Seals are used extensively in underground mines to isolate worked-out areas, active mine fire zones, and to control water inundations. Seals are most often built directly in the mine and can be fabricated from blocks made of wood or cementitious material. Recently, several explosions occurred within sealed areas of underground U.S. coal mines. These explosions, believed to be initiated by lightning strikes on the surface, destroyed numerous seals and caused considerable damage external to the sealed area. The National Institute for Occupational Safety and Health is conducting research to develop design guidelines, to investigate noninvasive techniques to characterize seal strength properties, and to evaluate seal test methods. As part of this work, a 30-ft wide, 16.1-ft tall and 4-ft thick seal was built in an underground experimental mine using cement and foamed water. Two types of noninvasive techniques are currently being investigated, namely the Schmidt Hammer for measuring compressive strength and ground penetrating radar (GPR) for detecting the presence of anomalies (e.g., voids, discontinuities) within the seal. Once these noninvasive tests were completed, the seal was subjected to destructive explosion testing. This study presents the results of the Schmidt Hammer tests, GPR scans, and the characteristics of seal failure during explosion testing.

By Steven J. Page, William A. Heitbrink, Andrew B. Cecala, Edward D. Thimons, John A. Organiscak

Miners at noncoal surface mining operations are often exposed to high levels of respirable dust. In an effort to lower the respirable dust exposure of these surface miners, the National Institute for Occupational Safety and Health (NIOSH) has been conducting research to address this problem in a practical and economically viable manner. One successful effort deals with lowering the dust exposure of equipment operators in enclosed cabs. Many types of surface mining equipment utilize enclosed cabs to protect equipment operators from dust exposure. Normally when the equipment is new, the cabs are fairly airtight. These tightly sealed cabs, combined with good filtration systems, generally provide the operator with good dust protection. However, most mining equipment is older, and as aging occurs, many components of the enclosure deteriorate. The structural integrity of the cab diminishes and the effectiveness of the air filtration system fails. NIOSH has been successfully researching costs-effective methods to improve both filtration effectiveness and cab integrity of these older cabs in order to provide a healthier work environment for equipment operators. Dust sampling records indicate that drill operators and helpers have the highest dust exposure of all workers at surface mining operations. Since much of the overburden contains a high percentage of silica, the health hazard associated with this dust can be even more serious. NIOSH research is addressing techniques to lower respirable dust levels at surface drilling operations. INTRODUCTION NIOSH's mission is to assure a safe and healthy work environment for the working men and women of this nation. The primary emphasis of NIOSH's Pittsburgh Research Laboratory (PRL) is mining health and safety research. This report focuses on two areas of research

By R. L. Perrine

This paper presents results obtained by consider ation of unstable miscible displacement within a porous medium as a quasi-turbulent displacement process, that is, a process characterized by fluctuations around a simpler, mean flow behavior. The instability usually results from the miscible displacing fluid having a viscosity lower than that of the displaced fluid. Such instability is evidenced in suitable experiments by the presence of viscous fingering. A unified theoretical relationship applicable to both stable and unstable displacement is derived. Parameters in the theory are obtained by empirical means. Although the theory describes an idealized conceptual model, agreement with experiment is quite reasonable up to moderately adverse viscosity ratios, such as 17:1. INTRODUCTION Many experimental studies of miscible displacement in porous media have been conducted with prediction of reservoir displacement efficiency as the ultimate objective. Most such studies have utilized lower displacing than displaced fluid viscosity, scaled to potential reservoir fluid pairs. Theoretical approaches have been largely limited to unit viscosity ratios, however, in spite of the necessity for an understanding of the mechanism of the unstable, adverse viscosity ratio displacement process. An obvious reason is the difficulty of describing in mathematical form the viscous fingering characteristic of these conditions. Observation of experiments conducted with dyed fluids in transparent systems suggests an analogy between unstable miscible displacement and turbulent flow in a pipe. In both cases there are fluctuations around a simpler, mean flow behavior. An important difference is that flow behavior of interest in the porous medium is entirely transient, contained within a transition zone between displacing and displaced fluids. Transient behavior complicates description in that coefficients in the equations become variables rather than constants. In the study reported here, the analogy with turbulent flow has been used in treating unstable miscible displacement as a quasi-turbulent displacement process. The purpose has been to derive, even if restricted to an idealized conceptual model, a unified theoretical relationship applicable to both stable and unstable displacement. A relationship meeting these specifications up to moderately adverse viscosity ratios, such as 17:1, is presented. One fluctuation parameter in the theory and dispersion coefficients are obtained by empirical means. The idealized theory is compared with experimental results. UNSTABLE MISCIBLE DISPLACEMENT AS QUASI-TURBULENT DARCY FLOW The miscible displacement of one fluid by another within a porous medium is considered in this study. Flow conditions are such that Darcy's law is applicable. It is further assumed that, by the stability criterion proposed by perrine,1 initial flow conditions lie well within the regime of instability. Thus substantial viscous fingering is assured. We wish to show how this flow regime can be represented as quasi-turbulent. That is, the Reynolds number for the established flow conditions is below that for inertial or turbulent flow within a porous medium, and lies within the regime for which Darcy's law is valid. Yet flow behavior can be described as the combination of some relatively simple average result, and characteristic fluctuations that are superimposed on the simpler behavior. Stated another way, flow behavior includes the movement of layers of fluids with different velocities past or over one another. Such descriptions are characteristic of turbulent pipe flow. The fluctuations in the present case are a direct consequence of the local viscous fingering which accompanies the unstable displacement process. Should displacement become stable, fluctuations would die out. It is of particular importance to note that fluctuations such as these can interact in a way that contributes to material transport by the basic flow. The basic transport equations required for engineering calculations must be modified to reflect this fact.

By F. W. Jessen, C. A. Johnson

The effect of treatment with ferrochrome lignosul-fonate on both sodium and calcium bentonites has been examined. In the early stages of treatment it appears that some base exchange of iron and chromium for sodium may occur with the sodium bentonite. Such exchange appears specific for exchange of sodium ions when the calcium ion concentration represents 40-5.5 per cent of the total exchangeable cations, and when additions of lignosulfonate are less than 1 lb per bbl. Adsorption appears entirely physical above 1 lb per bbl treatment level for all concentrations of calcium studied. Gel strength and plastic viscosity of both calcium and sodium bentonite systems were reduced with treatments of ferrochrome lignosulfonate up to 2 Ib per bbl, the greatest reduction occurring within a range of calcium concentration of 40-5.5 per cent of the total exchange capacity of the clay. INTRODUCTION The problem of control of viscosity and gel strength of drilling fluids by the action of thinners or dispersants has been studied by many investigators.1-7 In addition, much work has been done on formation of gel structure in clay suspensions. However, gel formation and structure still are incompletely understood, and the use of the various dispersing chemicals is based, to a large extent, on data almost entirely empirical in nature. In recent years the lignosulfonates have become increasingly important in the treatment and control of drilling fluids. More specifically, ferrochrome lignosulfonate has found rather wide acceptance, particularly in calcium systems.5-7 Lignosulfonates are refined lignin products made from spent sulfite liquor from which the fermentable sugars have been removed.15 The exact structure of lignin is not known; however, it is believed to be a phenolic propane type polymer which may exist as a branched chain or cross linked structure. The molecular weights of lignosulfonates probably range from 300 to 100,000 or more.15 A better understanding of the mechanism of adsorption of dispersants is essential before improvement and development of characteristics of drilling fluids and drilling fluid control is possible. This investigation was undertaken to determine the action of ferrochrome lignosulfonate on sodium and calcium montmOrillonite' LABORATORY INVESTIGATION A Stormer viscosimeter and Fann V-G meter were used to measure viscosity and gel strength. A Zeiss spectrophotometer was used for analysis of Fe and Cr and the flame attachment was employed in the analysis of Na, Ca and Mg. A General Electric X-ray diffraction unit utilizing Copper Ka radiation and a Ni-filter was utilized in the X-ray studies. PROCEDURE Two systems were studied. Predominately sodium clay, obtained from Wyoming, and a predominately calcium clay from Texas were used. These particular samples were chosen because of the extensive work of characterization completed by Mungan. Ionic base exchange capacity determined by flame photometry and total exchange capacity by the Kjehldahl method were obtained experimentally. A 7-per cent suspension of the sodium clay and a 20-per cent suspension of the calcium clay in distilled water were prepared by mixing with a high-speed mixer. The suspensions were allowed to stand for two weeks for complete hydration. Calcium chloride was added to portions of the sodium and calcium cla suspensions to obtain suspensions varying in Ca++ concentration as shown in Table I. A series of treatments was run with 500-ml portions of the original suspensions using a ferrochrome lignosulfonate. Treatment was carried out in the same way with each of the suspensions of varying Ca concentration. Viscosity and gel strength were measured and a filtrate obtained at each treatment level. Ten ml of filtrate were diluted to 50 ml, and aliquot portions of the 50 ml were taken for the Na, Ca, and Mg analysis by the flame photometer. The pH of these filtrates ranged from 7 to 7.3. Standard

By M. L. Millican

The objective of this study has been to develop a method of log interpretation in the Delaware sand whereby the effects of the shale contained within the sand can be recognized and accounted for in a quantitative solution for porosity and water saturation. Both theoretical and empirical considerations are discussed. A simplified interpretation chart is presented which provides a means of amending the conventional porosity resolution of the Sonic log to compensate for the presence of shale. The amount of shale within the sand and its degree of lamination may be inferred from a calibrated gamma ray log. The resulting porosity value may then be used in conjunction with a knowledge of the formation resistivity to determine water saturation. Of added interest, particularly in the Delaware sand, is an approximation of permeability which may be derived empirically from the simplified chart. The discussion is illustrated by field examples. INTRODUCTION The performance of the Sonic log in defining the porosity fraction in clean, consolidated formations is well known, particularly in sandstones that are well compacted and free of shale. An approach to Sonic log porosity determination in shaly sands has been recently developed.' This method involves correcting the Sonic log readings by means of an a factor, where a is the ratio of the pseudo-static SP to, the static SP, and is a function of the amount of shale present. This method is dependent upon a contrast between the salinities of the drilling fluid and the connate water in the formation, inasmuch as this contrast produces the SP effect. In wells drilled with salt mud, the contrast, and with it the means of obtaining the a correction, disappear. In the Delaware basin, the large majority of rotary wells drilled to the uppermost sands of the Bell Canyon group employ salt mud as the drilling fluid. These sands have been the objective of most of the drilling exploration in the basin to date. A comparison of porosity values in these sands, as determined by core analysis, to Sonic log readings has indicated that a correction for the shaliness of the sand is needed. In the absence of an SP curve to determine the correction factor, the porosity resolution of the Sonic log in these sands has been questionable.

By J. C. Wilhoit, E. M. Galle

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelastic-ity was used to determine the stresses within the model. Two separate problems were solved: (1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore, induced by an uneyual system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For uneyual principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. INTRODUCTION Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eeninkl have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. whitworth2 and woods3 have obtained numerical solutions. word415 obtained a three-dimensional photoelastic solution, Durelli and Deily 6 obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit7 determined the stresses around the bottom of a short cylindrical cavity. While Miles and McGuire, Harrison and Kieschnick and Hubbert and Willis 10 obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomo-geneous, permeable and anisotropic. Previous

By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By R. H. Jacoby, V. J. Berry

When dry gas is injected into a reservoir containing a volatile crude oil, a significant amount of the reservoir liquid phase may become vaporized. The resultant rich gas phase, when subsequently produced, con-tributes to tank oil production. This contribution assumes greater importance, the more volatile the oil in-olved. Oil recovery may be sub-stantially greater than that predicted by conventional frontal-drive methods, which do not consider the vaporization equilibrium between the reservoir oil phase and the injected gas. A calculation method has been (developed to account for vaporiza-. tion of the reservoir liquid phase during gas-injectiorz operations, and for the tank oil production which results from this factor. Recovery performance calculations are presented for a reservoir containing a highly volatile oil. Tank oil recovery is calculated to be about twice that predicted by the use of the conven-rional frontal-drive equations. In contrastto usual pressure maintenance performance results, in which the gas-oil ratio rises at an increasing rate after gas breakthrough, the pre-dicated gas-oil ratio rises rapidly to about 12,000 scf/bhl and then rises much less rapidly. During gas inje-tion, most of the reservoir liquid phase contacted is evaporated by the dry injection gar. The gas-oil ratio during this period is dependent upon reservoir pressure. The higher the operating pressure, the lower the gas-oil ratio. The predicted behavior i., in accordance with laboratory PVT tests made to .simulate the vaporization behavior. In addition to recovery performance predictions, results of the calculation procedure include complete wellstrearn composition data of value in the design of gasoline plant facilities often used in con-rrction with gas-injection operations. INTRODUCTION In the cycling of gas-condensate reservoirs, dry gas is injected to maintain reservoir pressure during wet gas production and to thereby eliminate or reduce ultimate loss of liquids due to retrograde condensation within the reservoir. Gas injected into crude oil reservoirs has a dual function. It displaces oil to the producing wells and at the same time serves to partially or fully maintain reservoir pressure. Oil shrinkage which would occur upon pressure reduction is thereby minimized or eliminated. Accepted calculation methods are available'= for predicting recovery performance of either gas-condensate reservoirs or crude oil reservoirs which are being subjected to gas injection. In gas-condensate reservoirs, any retrograde liquid formed does not flow, and it is necessary to account only for the vaporization equilibrium between this liquid and the injected gas. Conversely, in normal crude oil reservoirs, both the oil and gas phases flow, but it has not been considered necessary to account for any vaporization of the reservoir liquid which might occur upon contact with the dry injection gas. Recently, high shrinkage reservoir fluids known as "volatile oils" have been found in increasing amounts. These oils are characterized by tank oil gravities above 4.5" API, solution gas-oil ratios above 1,000 scf/bbl, and reservoir volume factors above two. Special techniques have been devised for predicting depletion performance of reservoirs containing such oils.74.5.1; One of the characteristics of reservoirs producing volatile oils is that the reservoir gas phase carries a significant amount of oil which is recoverable as stock-tank liquid. This unusual vaporization be-havior implies that an appreciable amount of reservoir liquid would be vaporized upon contact of the oil with dry injection gas. In a gas-injection operation, tank oil recovery would he obtained not only through frontal displacement of the reservoir liquid by the injected gas, but also through production of the rich gas phase. This means that not only are improved methods needed to predict recovery of such oils from reservoirs undergoing gas injection, but it would also be expected that high oil recoveries might be obtained by such operations. When relatively dry gas is injected in to a volatile oil reservoir, phase equilibrium between the injected gas and the reservoir oil will tend to bc established. Initially the most volatile components, such as propane, the butanes and the pentanes, will account for most of the material transferred from the oil phase to the gas phase. As the partially stripped oil phase is contacted with additional dry injection gas, the heavier intermediate components, such as the hexanes, the heptanes and the octanes, will gradually transfer to the gas phase in increasing amounts. This is because the supply of lighter components in the oil phase dwindles due to the stripping action of the injected gas. This stripping action will usually continue to be effective down

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By D. R. Babich, E. R. Bauer

Noise-induced hearing loss (NIHL) in mine workers, especially underground coal miners, continues to be a problem in the mining industry. The recently enacted MSHA noise standard, Part 62 – Occupational Noise Exposure (Federal Register, 1999), is aimed at reducing NIHL in the mining industry. The U.S. National Institute for Occupational Safety and Health (NIOSH) is conducting a cross-sectional survey of noise sources and worker noise exposures to address NIHL in various aspects of coal mining including surface mining, coal preparation plants and underground mining. In underground bituminous coal mining, noise surveys, consisting of full-shift worker noise exposure, time-motion studies and equipment noise profiling, have been completed on longwall and continuous miner sections in six underground coal mines. The studies revealed widely varying shift-to-shift worker exposures, with workers in certain occupations routinely exposed to potentially hazardous levels of noise. A summary of these studies is reported, including worker dose, source/dose relationships and equipment noise profiles.

By D. M. James, J. C. Martin

The results are presented of a study of the application of analytical methods to the solution of two-phase flow into single wells. Approximate analytical expressions for the pressure distribution in two-phase flow are found ;;; a number of conditions. The results obtained from the analytical solutions me found to be in good agreement with results obtained by finite difference techniques using a high speed digital computer. Mathematical solutions for four sets of boundary conditions are presented. All of these solutions are composed of a short-term transient plus a steady or quasi-steady state. The rates of decay of the short-lived transients are analyzed. It is found that the durations of the short-term transients may be characterized by a parameter defined as the time constant which can be determined from simple relations. It is shown also that if the outer radius is much greater than the radius of the well. the short term transients decay at rates which are proportional to the square of the exterior radius, and the rates of decay are only slightly dependent upon the radius ratio. Numerical solutions based on finite difference techniques are presented for a number of conditions. The numerical solutions are in good agreement with the predictions based on the theoretical analysis for small and moderate drawdowns. Examples involving large drawdowns indicate that the nonlinearities in the equations of flow do not appreciably alter the longevity of the short-term transients. In all cases the time required for the short-tern transients to disappear is predicted satisfactorily. INTRODUCTION The mechanism by which oil and gas flow into a single well is of vital interest to the petroleum industry. The fundamental equations of two-phase flow which describe this mechanism are nonlinear partial differential equations. Numerical solutions of these equations describing pressure transients have been obtained with the aid of electronic computers. Although solutions obtained in this manner take into account a large number of effects, the reduction of this information to useful generalities is difficult. One method of obtaining generalities is the use of linearized approximations of the nonlinear equations. Since it is possible to obtain explicit solutions of the linearized equation, general properties of the role of pressure in the flow mechanism may be ascertained. Results obtained from this approach are limited to some extent by the linearizing assumptions. The severity of these limitations may be evaluated by comparing solutions of the linear equation with numerical solutions of the more exact nonlinear equations of two-phase flow. In the past considerable amount of work has been devoted to studying pressure build-up using the single-phase flow theory. Unfortunate1y, most prep sure build-up tests involve multiphase flow. A small amount of work has been done studying pressure build-up where the flow is two-phase. The encouraging results of these studies suggest that useful results may be found from additional studies of not only pressure build-up, but also the rapid transients associated with placing a well on production. This paper presents the basic theory of the pressure transients associated with placing a well on production and with closing it in. The paper is concerned chiefly with two-phase compressible flow; however, the results also apply to single-phase flow. The results are based on analytical solutions of the flow equations, and they are verified by numerical solutions using finite difference techniques. Much of the previous work on compressible flow into wells has been confined to single-phase flow. Some work has been done on compressible two-phase steady state flow, and solutions of the equations of flow have been found by finite difference techniques using high-speed computers. Muskat1 presents some rather general solutions to the equations of single-phase compressible flow into wells. Much work has been done on pressure build-up in wells (see, for example, Refs. 2-6). Almost all of the work on pressure build-up concerns single-phase flow with the exception of Ref. 5 and part of Ref. 2. Some work has been done on pressure fall-off in injection wells.718 Muskat9 presents the solution of the equations for radial steady state two-phase compressible flow. Handyl0 extends Muskat's solution to obtain

By Antonio Raschillà

On the 2nd of June 2007 SELI S.p.A. started the excavation of Beles Tailrace Tunnel (Ethiopia). The new 8,07 m diameter DS Universal TBM utilized for the tunnel excavation was manufactured by SELI S.p.A. and allowed the installation of 30 cm thick concrete lining, contemporaneously with the excavation of 7,200 m of tunnel. The greatest part of the tunnel alignment was excavated in hard and sound basal-tic rocks. The paper describes the main steps of the tunnelling operations which led to a remarkably rapid excavation, with a peak production of 36 m / day and a final break-through achieved 46 days ahead of the contractual deadline. Furthermore the paper describes the work and logistic organization that was set up to efficiently perform the mechanized excavation in the very remote area of the project.

By Donald P. Tuchman, Robert P. Vinson, Steven J. Page

Researchers at the National Institute for Occupational Safety and Health (NIOSH) have long used stationary tapered element oscillating microbalances (TEOMs®) in laboratory settings. They have served to assess the mass concentration of laboratory-generated particulates in experimental , dust chambers and they provide a reference method for comparison with other particulate- measuring instruments. Current NIOSH research is focused on further adapting TEOM technology as a wearable personal dust monitor (PDM) for coal mining occupations. This investigation's goal is to help identify, quantify, and provide means for resolving certain TEOM- related error. The present research investigated bias caused by thermal effects on filter assemblies. New filters used in the PDM for 8 h tests show an average positive bias of 25.5 pg, while similar tests of equivalent filters used in two 1400A model TEOMs show an average positive bias of 34.3 µg. The derived bias values allow correction of previously collected biased data. Also, pre- heating the filters for 24 h at 46° C shows significant bias reduction, with PDM pre-heated filters subsequently averaging -3.3 µg and 1400A TEOM filters averaging 5.9 µg. On a single-point comparison to gravimetric sampling, a 25.5 µg bias is only significant at low mass loadings. At 2.5 mg, this bias represents a negligible 1 % of the mass measurement. If ordinary linear regression is used, the bias is still insignificant. However, if the more valid weighted linear regression is used, it gives more weight to the smaller dependent variable values, which are more impacted by the bias. Consequently, what is 1% bias on a single high-mass value can translate into a larger bias percentage at high-mass values when performing a weighted regression on data that include a large number of low-mass values.