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By G. Thodos, W. F. Stevens

The point-source function introduced by Horner' us a solution to the general unsteady-state equation for the flow of fluids through porous media has been utilized to calculate pressure profiles for adjacent wells as a function of time. By trial and error, the time at which the pressure waves meet to cause interference can then be calculated. For this calculation, the time of interference is arbitrarily defined as that time when both pressure waves exhibit a pressure decrease of 25 psi ar the same point within the formation. To illustrate the method, an example involving two adjacent wells producing at different rates has been worked out and is presented in detail. INTRODUCTION The initiation of production of a new well is usually accompanied by pressure drawdown measurements in order to establish the extent and characteristics of the formation. The interpretation of such pressure drawdown data is based on mathematical developments involving a single well in an infinite reservoir. If more than one well is present in a reservoir, the possibility of interaction between wells exists. Therefore, care must be taken in interpreting the pressure drawdown data. It becomes important to be able to determine when this interaction, or interference, becomes significant. This paper presents a method for the prediction of the approximate time of interference between two such adjacent wells. The basic differential equation describing the pressure distribution existing during unsteady-state flow of a slightly compressible fluid has been solved by Hor-ner.' for a constant production rate from a circular homogeneous reservoir of infinite extent. The solution utilizes the point-source function to define the pressure at various points within the formation as a function of time. The resulting expression is: q = production rate, STB/D ,;= formation volume factor, dimension-less µ = fluid viscosity, cp k = formation permeability. md H = formation thickness, ft C - fluid compressibility, psi' F = formation porosity, dimensionless R = distance from centerline of well, ft T = production time, hours Ei(—u) = Ei-function of U Eq. 1 may be used to calculate the pressure profiles generated during production from a single well in an infinite reservoir.

By Stephen C. Tadolini, Gabriel S. Esterhuizen, Anthony T. Iannacchione

A Major Hazard Risk Assessment (MHRA) was developed in Australia after a series of mine disasters in the 1990’s. A MHRA is used to help prevent major hazards, i.e. fire, explosion, wind-blast, outbursts, spontaneous combustion, roof instability and chemical and hazardous substances, from injuring miners. A MHRA is a structured process that identifies the characteristics of major hazards, assesses and ranks the risk they present, and evaluates engineering and administrative controls to mitigate them. These controls typically consists of a broad spectrum of prevention, monitoring, first response, and emergency response techniques and helps to move an operation from a reactive to a proactive approach towards safety. This paper documents a MHRA performed at an underground mine where strata instabilities and fire hazards may threaten the condition of its escapeways. The objective of this MHRA is to 1) identify what hazards could affect the egress through the mine’s escapeways, 2) determine what unwanted events pose the greatest threat for the mine, and 3) recommend a plan to prevent or recover from the potential disruption of egress through the escapeway. The plan provides information on the key existing controls that should be monitored and audited, and makes recommendation of new potential controls to further reduce related risks. By documenting the use of MHRA to this specific ground control issue, this paper provides a framework for others to judge the merits of this approach and to help design and perform these activities.

By Kenneth L. Cashdollar

This paper is an overview of and introduction to the subject of dust explosions. The purpose is to provide information on the explosibility and ignitability properties of dust clouds that can be used to improve safety in industries that generate, process, use, or transport combustible dusts. The requirements for a dust explosion are: a combustible dust, dispersed in air, a concentration above the flammable limit, the presence of a sufficiently energetic ignition source, and some confinement. An explosion of a fuel in air involves the rapid oxidation of combustible material, leading to a rapid increase in temperature and pressure. The violence of an explosion is related to the rate of energy release due to chemical reactions relative to the degree of confinement and heat losses. The combustion properties of a dust depend on its chemical and physical characteristics, especially its particle size distribution. In this paper, the explosion characteristics of combustible dusts will be compared and contrasted with those of flammable gases using methane as an example. These characteristics include minimum explosible concentration, maximum explosion pressure, maximum rate of pressure rise, limiting oxygen concentration, ignition temperature, and amount of inert dust necessary to prevent flame propagation. The parameters considered include the effects of dust volatility, dust particle size, turbulence, initial pressure, initial temperature, and oxygen concentration. Both carbonaceous and metal dusts will be used as examples. The goal of this research is to better understand the fundamental aspects of dust explosions.

By Floyd C. Kelley

The literature of the last decade is rich with information relating to the cause and means of control of grain growth in pure metals, but is deficient concerning the role diffusion plays in grain growth, although during this period many new products that depend on diffusion for their properties and success have been developed. Among these are cementation products, produced by calorizing, chromizing, and carbonizing, or by mixing, pressing, and sintering powdered metals such as Syke's iron-molybdenum die material, Genelite, and Elcon Metal (copper, tungsten) etc. This is a fertile field for new developments, but before it can be utilized to the fullest extent there must be a thorough invest,igation of the processes by which diffusion and grain growth take place. Grain growth plays no small part in the process and certainly the physical properties of these products depend largely on the grain size and state of equilibtiuni produced. The field of investigation does not end here, but may be extended to the effect of diffusion on impurities, segregations and dendrites in the broad field of ferrous and non-ferrous metallurgy. A number of years ago the author investigated several of these cases and noted, with striking regularity, the pronounced effect of diffusion in promoting recrystallization and grain growth. An example of this phenomenon is given in his paper on chromizingl which contained photomicrographs of large radial or columnar crystals produced by diffusion of chromium in the solid state. Another manifestation of this effect was discussed by Austen,2 who showed the part hydrogen plays in the decarburization of steel and the effect of diffusion upon the grain structure. Diffusion of Metals in Iron It seems to be a general law, whenever two metals are brought into intimate contact at a temperature at which diffusion takes place, that a comparatively rapid, or abnormal, grain growth results. The grains

By G. W. Tracy, R. D. Carter

Numerical calculations were made to determine the behavior of reservoirs with high-pressure drawdown and wide well spacing where the initial productivity is low and the wells are completed by hydraulic fracturing. The two-phase flow equations were solved for the flow into a single well. This well was assumed to be producing from a reservoir with hydraulically created horizontal fractures (four different systems with fractures were studied). For comparison purposes, additional two-phase flow calculations were made assuming a reservoir with uniform rock properties. The two-phase flow results were also compared with the conventional calculation methods, which do not include the effect of saturation gradients resulting from a simultaneous flow of oil and gas which are normal to this type reservoir. It was found that the conventional methods predict (1) a high and too optimistic value of ultimate recovery, (2) a high producing rate and a high reservoir pressure at a given oil recovery and (3) a low trend of gas-oil ratio with oil recovery. Included in the two-phase flow calculations were provisions to control the oil production rate by an allowable rate and, also, by a gas-oil ratio penalty rule. For the systems with hydraulic fractures, the producing rate was controlled by the gas-oil ratio penalty rule for most of the life. This is in contrast to the system with uniform rock properties which went "on decline" almost immediately. An unexpected characteristic of the systems which included fractures was the early rise in producing gas-oil ratio from 730 cu ft/bbl to approximately 1,200 cu ft/bbl, followed by a "leveling off" before the normally expected gas-oil ratio rise began. Additional features which are a result of hydraulic fracturing are (I) greater ultimate recovery, (2) higher average producing rates and (3) a lower average reservoir pressure at a given oil recovery. INTRODUCTION Some oil fields discovered during the past few years are producing from certain volumetric ally controlled reservoirs (often referred to as solution or internal gas- drive reservoirs) which are characterized by high-pressure drawdown at the wells. Since the available pressure drawdown at a well is limited by the static reservoir pressure and the producing rate is controlled by the available drawdown, wells completed in this type of reservoir usually produce at a rate less than the allowable from the time of completion. Because of this, this type of reservoir is referred to as a low productivity reservoir. Economic considerations require the use of wide well spacing and well stimulation by hydraulic fracturing to make commercial wells in this type of reservoir. Performance predictions for volumetrically controlled reservoirs have been made using a combination of two standard equations. 1. The "Schilthuis" or "Muskat" type material balance equation is used to relate the average reservoir pressure and the cumulative oil recovery. 2. The results from the material balance equation and the productivity factor as described by Pirson' are used to relate the cumulative recovery with producing rate and time. The material balance equation assumed uniform pressure and liquid saturation conditions throughout a reservoir. The steady-state radial flow formula allows for a pressure gradient toward a well but assumes uniform liquid saturation. These calculation methods are adequate for application to reservoirs wherein the drawdown at the well to realize satisfactory producing rates is small compared to the total pressure. In low productivity, volumetrically controlled reservoirs, the pressure drawdown at the well is large cornpared to the total pressure. Although a precise number cannot be given for the magnitude of a large pressure drawdown, values in excess of 1,000 psi would definitely be included. For practical considerations, this usually occurs when the formation flow capacity is less than about 100 md-ft. However, this limit of formation flow capacity will vary with the well producing rate. The low pressure in the neighborhood of the well which results from a high drawdown causes evolution of large volumes of gas. This causes the gas saturation to be higher near the well than at a greater distance—-hence, a non-uniform gas saturation. Also, the relationship between the relative permeability to oil (K/K) and gas saturation is nonlinear but decreases approximately in an exponential way with increases in gas saturation. Because of this, the following chain reaction is established.

By P. B. Baxendell

The performance of a water-drive reservoir having a gas cap depends primarily on the movement of the gar-oil and oil-water contacts. The movement of the contacts during production depends in turn on fluid withdrawals and how the reservoir pressure changes as fluids are produced from the reservoir; that is, on how effectively the aquifer maintains pressure by replacing withdrawals. inasmuch as pressure changes, fluid withdrawals, contact positions, and produced gas-oil and oil-water ratios are interdependent, the analysis and prediction of the performance of a reservoir produced in a given way must take into account this interdependence throughout depletion. This paper presents an analysis which, within the limitations of the assumptions made, yields an engineering approach to predicting future performance based on reservoir pressure and production history. The most significant assumption is the method of extrapolation of future gas-oil and water-oil ratios. The extrapolation procedure smoothly increases both ratios to preselected values as the remaining oil column undergoes a specified decrease in thickness. This preselection is made on the busis of previous field experience in depletion of similar reservoirs under similar conditions. For computing future performance a vdumebic balance L combined with the differential equation defining pressure distribution in the aquifer to obtain positions of water-oil and gas-oil contacts. From these positions are extrapolated produced water-oil and gas-oil ratios. Reservoir performance can be investigated when oil production rates are dependent upon various factors including the performance of the reservoir itself. Examples of practical application of the procedure are included. INTRODUCTION To predict performance of water-drive reservoirs with gas caps and thin oil columns, it is necessary to describe the motions of the fluids within the reservoir during the entire production period to depletion. These motions depend on the pressure changes and on the withdrawal of oil, gas and water. Production of oil from the oil zone primarily causes water to move in to take its place; production of gas from the cap tends to cause oil to migrate into its place. In addition, the volumes of oil and gas remaining in the reservoir depend on changes in the pressure, since a decrease in pressure causes fluid expansion, gas liberation and oil shrinkage. A method of relating the future pressure to total withdrawals is used to describe the motions of fluids within the reservoir under conditions arising in possible modes of production. The analysis is based on two relationships and will reduce the problem to one amenable to digital computation. The first of these concerns the dependence of the pressure distribution in the entire aquifer furnishing the water drive upon the total reservoir withdrawals. This dependence is dictated by the permeability distribution and the extent of the aquifer; at present, such information is most readily obtained from the performance history by means of the resistancecapacitance reservoir analyzer. The second relation involves withdrawals, pressure in the reservoir, and movement of oil, gas, and water within the reservoir. The analysis is subject to certain simplifying assumptions that are necessary to permit solution of the problem. A comparison of the methods of this paper with those presently practiced is pertinent. One method of analysis is to use the reservoir analyzer to predict reservoir behavior based on aquifer characteristics determined from production history. Inasmuch as the total withdrawal rate depends upon the gas-oil and water-oil ratios, which depend in turn upon, among other things, the positions of the gas-oil and water-oil contacts, these ratios must be assumed in advance. In this paper these ratios are, instead, related to the computed positions of gas-oil and water-oil contacts. Thus, our method can be applied to problems in which the oil production rate is limited by produced gas-oil ratio, or to problems in which it is desired to determine the variable gas injection rate that will maintain the gas-oil or water-oil contact stationary. These problems cannot be worked satisfactorily on the analyzer. Another method presently used is based on a paper by Hurst.' Since his procedure is dependent upon using the solution of the heat flow equation, which requires constant permeability within the aquifer, and our procedure recognizes variations of permeability in

By John S. McCartney

This paper focuses on the seasonal thermo-mechanical response of two energy foundations installed at the new Denver Housing Authority Senior Living Facility in Denver, Colorado. The two drilled shaft foundations, which have diameters of 36 inches and depths of 45 ft and are end bearing in the Denver shale formation, include a closed-loop series of polyethylene tubes through which fluid is circulated to exchange heat with the surrounding ground. The tubes within the foundations are coupled together with the conventional ground source heat pump system for the building and were installed to evaluate the heat exchange response of the foundations as well as any thermo-mechanical soil-structure interaction effects. A series of vibrating wire strain gages and thermistors were installed at different depths in the foundation to record the thermo-mechanical strain and temperature at different depths. Also, pipe-plug thermocouples are used to measure the inlet and outlet temperature of the heat exchanger fluid entering each of the foundations, which is necessary to evaluate the total heat exchange for the foundations and the efficiency of the heat pump. This paper will describe the energy foundation construction processes, the strain distribution and ambient temperature profiles during building construction and the seasonal strain and temperature distributions during heating and cooling of the building. The data indicates that typical heat exchange associated with heating and cooling operations leads to strains which are within acceptable limits, and that the foundations can provide a clear option for absorbing the base heating and cooling load for the building.

By Thomas E. Marshall, Michael Dunn, L. J. Prosser, Anthony T. Iannacchione

During the past few years, the Pittsburgh Research Laboratory of the National Institute for Occupational Safety and Health (NIOSH) examined and characterized conditions at a majority of the underground stone mines in the United States. Observations at these mines revealed a limited degree of roof monitoring beyond visual inspection and sounding. When monitors are used, they typically require the miner to measure movement at the roof. If conditions are unstable, the mine rmay be in a hazardous situation while recording data. Based on this scenario, researchers surmised that a simple, inexpensive monitor with the capability of recording data at a distance from the mine roof would be a safer way to gain the information. Additionally, more widespread use of monitors could potentially lead to better understanding of roof movement in general. A monitor to meet this need was designed, tested, and subsequently improved as experience was gained in its’ use at a number of underground stone mines. The Roof Monitoring Safety System (RMSS) can provide an initial indication of movement in roof beams. By understanding and measuring roof movement in underground mines, the potential for injuries and fatalities to mine workers from falls of ground can be reduced. Also, officials at a mine with a history of data are better prepared to make a decision on remedial actions in the event of ground falls. This paper will outline the evolution of the RMSS and how it can be used in a comprehensive proactive ground control safety program. Also included is a case history describing how the RMSS was used in an evaluation of the effectiveness of a mechanical impact scaling machine at an operating limestone mine.

By Thomas E. Marshall, Timothy Batchler, Anthony T. Iannacchione

As the amount of new fractured surfaces or "damaged rock layers" within roof rock increases, the stability of the rock mass decreases. While direct measurements of this phenomenon are not easily made, there is good circumstantial evidence to support this hypothesis. For example, it is common to observe increased cracks or fractures in the immediate mine roof rock before a roof fall. Likewise, roof drill holes placed in areas that later fail often reveal increased numbers and/or separations of fractures within the rock column through time. And finally, the frequency of microseismic activity, representative of rock fracturing, increases before a roof fall. For this study, more than 700 microseismic emissions were collected from two underground limestone mine roof fall areas in southwestern Pennsylvania. Microseismic events were located and magnitudes determined using the moment magnitude technique. Moment magnitude is based on the event seismic moment, which is a measure of the seismic deformation. The amount of new fracture surface length was calculated based on the stored strain energy within the rock prior to fracture. In the two case studies presented, a significant amount of microseismic activity was observed as much as two days before the first signs of failure in the roof fall areas. Additionally, results from this analysis reveal much about the behavior of strata prone to failure and allows for the construction of hazard maps based on microseismic emissions. The potential use of this technique as a means of anticipating roof falls is analyzed and discussed.

By Peter G. Kovalchik, Lawrence W. Scott, Thomas H. Dubaniewicz, Frank T. Duda

Overheating of electric cables on shuttle cars has long been recognized as a cause of premature insulation failure leading to shock and electrocution. Use of cable reels on shuttle cars can cause excessive heat build up which, in turn, causes the cable insulation to soften and become easily damaged This heat-softened insulation reduces the life of the cable. Repeated cycling of a cable in this manner can cause premature aging of the insulation; it becomes bridle, cracks and allows electrical leakage paths to farm. These leakage paths provide the opportunity for shock and electrocution to occur if miners come in contact with the damaged section of cable. It is imperative that cable operating temperatures be maintained at safe thermal limits. This paper discusses a research project conducted by the National Institute for Occupational Safety and Health, Pittsburgh Research Center to determine dynamically the conductor temperature of reeled shuttle car cables using fiber optics technology. The research portrays typical shuttle car loading cycles (both current and time cycles). Root-mean-square current loading is calculated based on the results. The thrust of this effort is to provide the scientific basis for ampacity derating factors specifically for mine machinery using reeled cables This information will reduce the probability of electrical hazards from reeled cables

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

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 PRL Lake Lynn Experimental Mine (LLEM), and after laboratory explosions in the PRL 20-L chamber and the Fike I m3 chamber. The dusts studied included both high- and low-volatile bituminous coals. Low temperature ashing for 24 h 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 with the initial dust loadings to determine the transport distance of dust during an explosion. All these data will be useful in future forensic investigations of accidental dust explosions in coal mines, or elsewhere.

By Charles Vaught, Kathleen Kowalski

Emergency personnel, like all workers, carry out their duties within an environment composed of a set of discrete elements. First, there is the emergency itself. Whether a forest fire in France, a tornado in the American Midwest, or a mining disaster in Russia, the emergency imposes certain exigencies upon the responders. Second, a social structure exists with specific social units, rules, and forms of association. An emergency response, therefore, takes place within a context of prescribed behaviors, expectations, and value judgments that are sometimes in conflict with each other. Third, there is a technology that must be understood in order to accomplish group goals. If the technology itself is implicated in the emergency, the entire emergency environment may be impacted. Clearly, a breakdown in any of these elements could result in worker injury and might heighten responder stress. This paper discusses how emergency workers not only get injured but may come to experience bum-out, post-traumatic stress syndrome, or impaired work and family relationships, even though their normal work setting (the emergency) is expected to be 'abnormal'. The authors suggest areas in each of the three environmental elements that, deserve further inquiry.

By Alan Zeni

Blind shaft drilling equipment has not changed substantially since the 1970s. Since it resides in a niche market between conventional shaft sinking and raise boring, the relatively small demand has resulted in some stagnation of development. In the 1990s the technology found a larger foothold in foundation and deep piling work for civil construction. WIRTH GmbH from Erkelenz, Germany has been servicing this market for many years with pile top drilling rigs and tools. Frontier-Kemper Constructors, Inc. recently entered into an agreement with WIRTH to develop a new generation of large diameter blind drilling equipment more specifically aimed at mining needs. The, recently completed, DHI-240 is the first rig to apply the most recent technology. This machine made its commercial debut in the fall of 2008. A description of the technology and a short case study of the first project will be described

By Bill M. Stewart, Phil W. Patton, Curtis C. Clark

Back injuries from handling materials in underground mines continue to be a major safety problem. In spite of the ingenuity of many people and the development of numerous mechanized aids, the number of materials-handling injuries remains second only to the number of roof fall injuries in underground coalmines. Relocation and repositioning of electrical cable, conveyor belt parts, and roof bolt sup-plies in particular are the sources of significant numbers of back injuries. To help reduce such injuries, researchers at the Spokane Research Laboratory of the National Institute for Occupational Safety and Health are examining Mine Safety and Health Administration accident data to determine correlations between materials-handling tasks and the number of back injuries. Also being investigated are new technologies used in underground mines in the United States. Equipment is being developed or modified that would replace the necessity of doing lifting tasks manually. A Coleman manipulator was tested, and modifications were made to make it more suitable for underground mine use. To reduce or eliminate the need to manually clean off materials that commonly plug grizzly openings, a track-guided pincher arm device was developed. Oversized rock can be broken with the pincher arms in the up position, and the arms can be lowered to grab and remove debris. The arm can also be used in a sweeping action to remove cohesive fines that may bridge grizzly openings.

By Deno Pappas, Chrisropher Mark, John Rusnak, Linda McWilliams

Mine planning for a new reserve is based on information obtained from exploratory coreholes. A critical component of an exploration program is the geotechnical evaluation. Poor assumptions about roof conditions greatly add to the risks of mining. Rock mechanics testing is central to a geotechnical exploration program. Typically, 3 to 5 uniaxial compressive strength (UCS) tests are made to characterize a particular roof unit at a given corehole. The average (mean) of these tests is taken as “The UCS” for that location. Isopach contour maps are then used to show spatial trends in roof strength. Two issues are raised by this traditional approach. The first is due to the large variability in UCS values that is typical even within a single unit from a single hole. The average UCS might be higher at Corehole A than it is at Corehole B, but the difference may not be statistically significant. The second issue is whether widely spaced coreholes can identify valid spatial trends in rock strength. The answer depends upon whether rock strength changes over distances that are longer or shorter than the corehole spacing. This is a classical geostatistical problem. While geostatics have been used to investigate many coal quality parameters, they have seldom been used to evaluate rock strength. This paper describes an extensive investigation of these issues conducted by the National Institute for Occupational Safety and Health (NIOSH) in collaboration with Peabody Energy. The study employed the Peabody Rock Mechanics Data Base which contains more than 10,000 individual test results. Data from four important roof units were subjected to statistical analysis: • Brereton Limestone above the Herrin 6 seam (Illinois) • Turner Mine Shale above the No. 9 Seam (Kentucky) • Sandstone above the Eagle Coal (West Virginia) • Shale above the Eagle Coal (West Virginia) The study did not find significant spatial trends in rock strength in any of the cases. Perhaps there are none, or perhaps the exploration coreholes were just too far apart to see them. These results have valuable implications for the design of geotechical exploration programs.

By D. K. Ingram, G. L. Mowrey, T. R. Rehak

This paper summarizes fly rock and blast area security fatalities from 1989 to 1999 and examines the causative factors. Coal and nonmetal mining used about 43 billion pounds of explosives and blasting agents between1989 to 1999. A majority of this consumption was used at surface mines. Accident data indicates that fly rock and lack of blast area security were the primary causes of blasting related injuries in surface mining. Fatal injuries due to lack of blast area security were attributed to: failure to clear blast area; failure to follow instructions; inadequate guarding; inadequate blasting shelter; and unsafe location. Seven fatalities due to fly rock and lack of blast area security were reported in surface coal mines and six in nonmetal mines. Out of these, two fatalities (one each in coal and nonmetal mines) occurred outside the mine property. In the coal mining sector, two fatalities were attributed to fly rock, and five to lack of blast area security. In the nonmetal mining sector, three fatalities were attributed to fly rock, and three to lack of blast area security. Preventive measures include: ensuring that all personnel have evacuated the blast area during shot firing; using adequate blasting shelters for employees whose presence is required in the blast area; controlling and monitoring all entrances to the blast area; ensuring that the blast is properly designed, drilled, and loaded; and emphasizing education and training to enhance skill levels for implementation of engineering control techniques.

By A. A. Stripling

The Cretaceous limestone wells of the Mara/Maru-caibo Dist. of Venezuela are extremely prolific producers. To maintain production on cessation of natural flow, large scale gas-lift operations were commenced involving high production rates on caring Flow. For the design of these gas-lift installations it was essential to have some knowledge of the pressure gradients involved in casing flow, so that the required injection pressures, optimum gas injection raws, etc., could be forecast. This paper presents a method of calculating these annular pressure gradients. Basically the method makes use of an energy balance equation coupled with an empirical energy loss factor derived from field data. The calculations have been put in a form suitable for "punch card-type" calculating machines. A set of gradient curves for Mara/Maracaibo conditions covering flow rates up to 12,000 B/D, and GOR's of 500 to 2,000 cu fd/bbl is presented. From these curves the flowing BHP can be predicted from surface data and the vertical pow performance under varying conditions of gas injection can be estimated. The method has been applied to La Paz and Mam gas-lift operations for over three years and has given consistently accurate results. INTRODUCTION The Cretaceous limestone fields of the Mara/Maracaibo area in Venezuela are characterized by the presence of widely distributed fissure systems. Under these conditions individual wells frequently have extremely high potentials and such wells are generally flowed on the casing-tubing annulus in order to reduce the pressure loss in vertical flow. To maintain production on cessation of natural flow, an extensive gas-lift system was planned. As a first approach to this gas-lift design problem, an attempt was made to construct a set of empirical flowing gradient curves from the available subsurface pressure data. Such a method has been used successfully for tubing-flow conditions in California by Gilbert'. Unfortunately, the empirical construction of casing-flow gradient curves presents additional difficulties, as pres- sure bombs cannot bc run in the casing-tubing annulus against high rates of flow. Thus, the Full flowing gradients cannot be defined by actual measurement and the best that can be done is to obtain spot pressures at the tubing shoe. Under these conditions a vast accumulation of BHP data is required to construct a set of gradients. To the La Paz and Mara fields the majority of the available flowing pressure measurements fall into a relatively narrow GOR range, in the neighborhood of the solution ratio. While there appeared to be reasonable prospects of constructing gradient curves for this limited range, measurements at higher GOR's, which were of major interest for gas-lift operations, were relatively few and the prospects of constructing empirical curves cor~spondingly remote. As an alternative approach, the possibilities of a mathematical analysis of vertical flow conditions were investigated. May and Laird2fV n 1934 presented an excellent analysis of the vertical-flow conditions in the Anglo-Iranian Oil Co.'s fields. Their analysis was based on an energy-balance equation and calculated the losses due to kinetic energy, friction and slippage separately. By combining these losses with the total calculated available energy, the required depth-pressure traverse could be deduced. On applying the method to La Paz conditions, good results were obtained for tubing flow at high tubing-head pressures. However, for lower wellhead pressures (300 psi and under) the discrepancy between calculated and measured values increased appreciably. It was considered that this was probably due to energy losses caused by slippage or liquid hang-up in a continuous gas phase, for which it was difficult to visualize any analytical approach. In 1952 Poettmann and Carpenter4 presented a method of pressure gradient calculation which, while based on an energy-balance equation similar to that employed by May and Laird, made no attempt to evaluate the various components making up the total energy loss resulting from irreversibilities of flowing fluids. Instead, they proposed a method of analysis which assumed that all significant losses for multiphase flow could be correlated in a form similar to that of the Fanning equation for frictional losses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The total available

By D. R. Wieland, A. N. Barron, A. R. Hendrickson

A definite relationship has been found between the reactivity of flowing hydrochloric acid and its shear rate in a carbonate fracture. Both flow velocity and fracture width affect the acid reaction rate. Laboratory studies were conducted on acid reactivity at different flow velocities through horizontal-linear fractures, using 15 per cent hydrochloric acid at 80' F and approximately 1,100 psi. Fracture width varied from 0.02 to 0.20 in. These data provide a new basis from which the spending time and penetration of the acid can be estimated. Equations were derived expressing the relationship between injection rate, fracture width, acid concentration, time and fracture height, for linear and radial fracture systems. Because the penetration of the acid before spending is closely related to the extent of productivity increase resulting from an acidizing treatment, these data provide a valuable insight into some of the controlling factors that must be taken into consideration during treatment preplanning. INTRODUCTION Acidizing of carbonate reservoirs to improve production characteristics has been widely practiced since 1932. Originally, it was assumed that the acid uniformly penetrated natural formation pores and flow channels, enlarging them and thereby increasing their flow capacity. Little consideration was given to the reaction rate of the acid, or how far it would penetrate away from the wellbore into the formation, before spending. It has been shown recently' that, unless fractures are present in the rock, very little penetration is attained before spending, and the benefits of the acidizing treatment are largely confined to the immediate vicinity of the well-bore. Therefore, acid treatments may be classified into two categories: (1) matrix acidizing, in which the acid flows through multiple: formation pores; and (2) fracture acidizing, in which the bulk of the acid travels through fractures in the rock, whether natural or induced. When acidizing treatments are conducted at pressures of sufficient magnitude to open and extend such fractures, it is often desirable to inject a propping agent to hold the fracture open after the treating pressure has been released, thus providing a highly conductive flow channel through the rock. In some cases where acid attack produces surface irregularities, the resulting flow passages can be sufficient to provide high conductivity without use of a propping agent. During injection, the acid dissolves the carbonate rock with which it comes in contact until it is spent. Deeper penetration of the spent acid into the formation produces no appreciable benefit (if no propping agent is used) because the unetched fracture faces will rejoin when treating pressures are released and the fracture will "heal", with negligible resultant conductivity. The spending time of the acid thus becomes important in determining how far from the wellbore the improved-conductivity zone extends. The spending time of acid after injection into carbonate rock depends on the rate at which the acid reacts with the rock. This in turn is controlled by a number of factors, as previously reported. 2-4 These include temperature, pressure, acid concentration, rock composition, injection rate and the area-volume relationship between the acid solution volume and the surface area of the formation flow channels through which it penetrates. Thus, in matrix acidizing, where an extremely large area is exposed to the acid, spending is rapid. In contrast, spending time is prolonged in open fractures, where the area-volume ratio is much lower. Thus, greatest penetration of the acid before spending will be achieved in acid-fracturing treatments where fractures are held open by hydraulic pressure. Perkins and Kern5 have presented equations for fracture-width determinations which, for hard formations such as limestone or dolomite, indicate that high injection rates and viscous fluids are required to create wide fractures. Increasing the injection rate will, in itself, produce faster reaction rates. Because this type of reaction can be considered to be first-order diffusion-controlled, '-' the rate of movement of fluid past the rock surface affects the thickness of the diffusion layer, in turn affecting the reaction rate. Staudt, et al,10 report the results of tests in which a rotating marble cylinder was immersed in acid, and the weight loss at different speeds determined. Such test conditions, however, are not truly indicative of the situation in a formation during an acid-fracturing treatment. This paper reports reaction-rate data obtained under

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant