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By C. L. Lin

The characterization of rare-earth resources in 3D is now possible using high-resolution X-ray microtomography (HRXMT) to describe ore texture and mineral phase composition. In addition, detailed texture analysis, including grain exposure and mineral association, can be described. Preliminary examination of a sample of Mountain Pass ore is reported to describe the spatial distribution of the mineral phases (calcite, barite and bastnaesite), particularly the grain size distribution of bastnaesite. The examination includes analysis of selected particle size classes to determine the appropriate size for liberation of the rare-earth mineral bastnaesite. Good liberation is expected to be achieved if the material is ground to a top size of -150 µm.

By Wei Li

Carbothermic reduction kinetics of ilmenite concentrates catalyzed by sodium chloride and the microwaveabsorbing characteristics of the resulting reductive products were investigated; the reduction degree of the reaction was deduced to be . Results show that the activation energy is 112.03 kJ/ mol when NaCl is used as catalyst, lowering to 23.11 kJ/mol for the final stage activation energy using sodium silicate as a catalyst. There is a sharp change in the reduction rate constant at temperature ranges of 1,223 K - 1,273 K and 1,373 K - 1,423 K. Microwave-absorbing characteristics of reductive products were measured by the method of microwave cavity perturbation. It was found that microwave-absorbing characteristics of reductive products obtained at temperatures of 850° C, 1,100° C and 1,150° C show sharp changes. Through X-ray diffraction (XRD) characterization, it was found that the formation of Fe occurs at a temperature of 900° C during the reduction process of ilmenite concentrate. The decrease of FeTiO3 content results in the decrease of microwave-absorbing characteristics, while the increase of Fe content gives rise to the increase of microwaveabsorbing characteristics. The decreasing trend is larger than the increasing trend, which is the main reason for the sharp changes in the microwave-absorbing characteristics of reductive products at the temperature range of 850° C to 900° C. When the decreasing trend is smaller than the increasing trend, it becomes the main reason for the sharp changes in microwave-absorbing characteristics of reductive products at the temperature range of 1,100° C to 1,150° C. Kinetics results show that sodium chloride can catalyze the carbothermic reduction of ilmenite, and microwave-absorbing characteristic investigations indicate that microwave heating can be used in the carbothermic reduction of ilmenite.

By Lewis A. Riley

I desire to submit, for the consideration and information of the members of the Institute, the following data, drawings, and tables, showing what I believe will be interesting information with regard to the diamond drill, and its uses in developing mineral lands. I would first say that the results given have been obtained during the past two years by means of two drilling machines belonging to the Lehigh Valley Coal Company, operating on their coal lands in the Mahanoy, Lehigh, and Wyoming regions. 1st. A tabulated statement, giving location of borings, date, progress, total cost, itemized cost per foot, etc. 2d. Section showing strata bored in Nos. 5 and 10 holes at Mt. Carmel, see Plate VI. 3d. Section showing strata bored in No. 19 hole at Hazleton, see Plate VI. 4th. Photograph and description of drill No. 2. From the first it will be seen that the total number of test-holes bored up to May 1st of this year is 24; 9 of these are in the Mahanoy region, 6 in the Lehigh region, and 10 in the Wyoming region, in all of which cores have been taken for the whole distance. The total distance bored is 9902 feet. The majority of the holes have been put down for the purpose of proving the lower veins of the coal series, and have had to encounter the harder rocks of the coal formation. Much of the distance has been through the lower conglomerates, going in some cases through the coarse egg conglomerate, the foundation of the coal deposit, and to the green sandstone and red shale which underlie it. These lower sandrocks and conglomerates are among the hardest known to geologists, and present a formidable resistance to the exploring drill. This fact must be taken into consideratiotl in comparisons of cost of drilling, and when considered will still further improve the very favorable results I am able to show in my statement of costs. In illustration, I will cite the work of one bit when boring in the upper or softer rocks of the Wyoming region, where 280 feet were obtained without resetting, while in the Lehigh and Mahanoy regions, in the lower and harder rocks, bits set with the same quality of diamonds would only bore from 3 to 20 feet before being worn out. In this connection it may

By A. Eilers

Although the process to which I refer in this paper has been in successful operation for nearly five years, during which time it has been introduced, superseding all other processes having in view the same end, in almost every lead refinery in the country, no description of it, giving economical data, has ever appeared in print, nor has the process been known in its details to any considerable number of engineers beside those conducting it at their works. A discussion of this subject at the present time becomes especially interesting in view of a late publication in the Prussian ministerial organ for Mining and Metallurgy, by Dr. Wedding, in which the method of treating the zinc-silver-lead alloy by distillation, as finally settled upon at Tarnowitz, is very minutely and fully described. It is the more interesting, because in that article reference is made to the American method in an unfavorable light, while, at the same time, it is clear from the article itself, that the most important details of the process, besides the one that it is conducted in black-lead retorts, mere not at all understood. In publishing herewith the details of our American method, one of my objects is to invite comparisons between our simple and direct process and the elaborate one at Tarnowitz. In extracting the silver from work-lead by means of zinc, it is always the intention, in this country, to obtain a zinc-crust so rich in silver that the rich lead resulting from subsequent distillation

By Fred H. Poettmann, A. L. Benham

correlation of waters and identification of mixtures of two and three waters is important in secondary recovery evaluation studies and studies involving underground movement of waters. The importance of such studies suggests the need for a method to correlate a great number of water analyses to accurately identify and improve the understanding of mixtures of waters. Geochemical analyses of waters furnish a quantitative measure of each of the ions present in a water. Table L shows a portion of the data on many oilfield water analysis report forms in use today. Under "parts per million" are listed the quantitative amounts of each ion in milligrams per liter. Following the work of Stabler' and Palmer", some laboratories have reported additional data to indicate the reaction capacity, or reacting value of each ion. Table I lists data under two subheads for the "reacting value". Under the first subhead, the reacting value is reported in gram equivalents per million, hereinafter called equivalents per million. This value is determined by multiplying milligrams per liter of the ion by a factor equal to the reciprocal of the equivalent weight of the ion. Under the second subhead (per cent) is listed the percentage of each ion based on the total equivalents per million. Sodium is not usually an analyzed value in routine analyses, but is determined by the difference between total negative equivalent per million values and the sum of all of positive ion values for which analyses were made. This difference is reported as sodium, hereafter labelled "sodium". On this basis, the subtotals of the equivalent per million and per cent reacting values of the positive and negative ions are equal. CORRELATION OF WATER ANALYSES DATA Previously reported methods for correlating oilfield waters have used part of the data in Table 1, and can be classified into two categories. Correlation by Chemical Character Correlation methods using the chemical character of waters, as represented by the per cent reacting values of the ionic constituents, have been used by Palmer2 and Tickell. These methods have the limitation of neglecting the ionic concentration of the waters. This limitation can be serious in areas where waters have the same chemical character, but differ in concentration. Correlation by Concentration of the Ionic Constituents The Reistle' and the Stiff methods use the ionic concentration in parts per million and equivalents per million. These methods are effective in differentiating waters of similar chemical character and varying concentration, as in the highly saline waters of the Mid-Continent area. These methods have the disadvantage that they correlate waters by comparing many graphs of individual water analyses to determine the similarity to, or the variance from "type" waters. PROPOSED METHOD OF CORRELATING WATER ANALYSES DATA Correlation graphs presented in Fig. 1 represent water analyses data as points to facilitate the correlation of waters. The graph on the left of Fig. 1 is a plot of per cent reacting value of magnesium vs calcium. The right

By Michael J. Jorgensen, Pranathi B. Aedla, N. K. Kittusamy

Risk factors associated with the development of muscu­loskeletal discomfort and disorders during the operation of heavy mobile equipment include whole-body vibration and awkward and sustained joint postures of the shoulders, neck, and trunk. Cab design may influence awkward postures of the joints, and task duration may influence duration of exposure to awkward and static postures and whole-body vibration. To reduce exposure to risk factors related to the interface between cab design and task, it may be necessary for manufacturers to address cab design. This study assessed the repeatability of a cab design checklist developed to evaluate various design characteristics that can influence exposure to risk factors for musculoskeletal discomfort. The ability of the cab design checklist to identify posture-related deficiencies of design was also assessed. The checklist was used by two administrators across 10 pieces of heavy construction equipment. Video analysis was performed to quantify postures of the neck, shoulder, and trunk; correlation analysis was used to determine whether specific questions from the checklist were associated with the identification of awkward postures. The repeatability assessment resulted in kappa coefficients ranging from 0.52 to 1.0 (good-to-excellent reproducibility) across each piece of equipment, and an overall kappa coefficient of 0.77 (excellent reproducibility) when considering all equipment together. Results from the correlation analysis showed that shoulder flexion posture was correlated with scores from the cab design checklist. However, results of the cab design checklist were not significantly correlated with shoulder abduction or awkward postures of the neck and trunk. Results suggest that the cab design checklist may be useful for identifying cab design characteristics that need further improvement and for identifying design characteristics that increase shoulder flexion. The strength of the repeatability assessment suggests that outcomes of the cab design checklist administered by different individuals may be consistent, independent of the type of equipment being assessed.

By Ankit Jha, Sudarshan Rajagopal, Purushotham Tukkaraja

Geologic structures are one of the crucial parameters in blast design. Structural geology and rock properties influence drilling patterns, blast layout, and initiation systems. A comprehensive understanding of structural characteristics is essential to achieve the desired blasting objectives. This paper aims to identify geologic features in a bench using images obtained from the drone. Images obtained from mine site are annotated for geological features such as faults and joints. Semantic segmentation of images is achieved using an encoder and decoder structure available in the machine-learning pipeline. The encoder consists of initial convolution and pooling layers to capture essential features of the geology and rock patterns from two-dimensional RGB images. Batch normalization is used to put all the features on the same scale. These images are then inputted as training data for the machine-learning algorithm. Machine learning model is trained on sub-section of interest to achieve reasonable accuracy. Initially, 1000 best annotations were used to train the model and additional samples were added later to achieve more accuracy and avoid iteration of machine learning model in wrong convergence. After the model achieves reasonable accuracy, it is used to recognize geological features on new data. Geological features identified on the new data can be used by the blasting crew in blast design and keeps the geological maps updated that can help the geotechnical team.

By J. D. Alexander, W. L. Martin, J. N. Dew

This paper presents data obtained using a flood-pot technique to determine the fuel available and the corresponding theoretical air requirements for in situ combustion of crude oils. Since the technique is relatively quick and easy, it is a practical and convenient tool for evaluating reservoirs as fireflood prospects. It is also a research tool which facilitates systematic study of the variables affecting fuel availability and corresponding air requirements. The understanding of these variables is of prime importance to those concerned with the technical and economic development of in situ combustion as an oil-recovery process. The experimental results show conclusively that the fuel available for in situ combustion is not a constant but, rather, varies with crude-oil characteristics, porous-medium type, oil saturation, air flux and time-temperature relationships. Thus, the fuel availability for specified field applications should be determined using actual reservoir crude and core material and the process conditions expected during in situ combustion in the reservoir. INTRODUCTION In situ combustion is a thermal process for recovering crude oil from reservoirs. The thermal energy released during the combustion of a small amount of the oil in place aids in the displacement of the remaining oil. Numerous articles have been published describing the in situ combustion process giving detailed results of laboratory and field experiments.10 In order to engineer an in situ combustion project, a number of important factors must be considered and determined. These factors include: (1) the amount of fuel consumed per unit of reservoir volume swept by the combustion zone, (2) the composition of the fuel consumed, (3) the amount of air required to consume this fuel, (4) the portion of the reservoir swept by the combustion zone, (5) the appropriate air-injection rates and pressures, (6) the amount of oil that will be recovered, (7) the rate of oil production and (8) the operating costs. Nelson and McNiell1 recently have described a procedure which utilizes laboratory combustion-tube data as a basis for the calculation of some of these design factors. Various authors have attempted to describe the in situ combustion process mathematically, and considerable progress has been made. Analytical solutions to the problem of heat transfer from a moving combustion front have been obtained for linear and radial systems."-' All of the published results involve the assumptions that: (1) fuel concentration is constant throughout the reservoir, or that fuel concentration is inversely proportional to the velocity of the front for a given rate of oxygen consumption; and (2) the fuel reacts instantaneously with injected oxygen, while liberating a constant amount of heat per unit weight of fuel at all temperatures. It seems both desirable and reasonable to test the validity of these assumptions experimentally. This paper presents laboratory data which were obtained by means of a "fire flood-pot" method for determining fuel availability and composition, and the corresponding theoretical air requirements for in situ combustion of crude oils under variable conditions. The mechanics of the method are similar to a conventional tube-run experiment.' The important differences involve the size of the reservoir model used and the method for providing the experimental environment. The new method subjects conventionally-sized core samples or unconsolidated sands to a programmed environmental sequence similar to that experienced by a similar volume of rock during the approach and passage of a combustion front in a long tube or in an oil reservoir undergoing in situ combustion. Restored-state samples can also be used. The small samples and relatively simple techniques involved allow an experiment to be set up, run and calculated in about three 8-hour days. This is a considerable improvement over long-combustion-tube techniques which can require several days to run and several more work days to set up and calculate. All the runs presented were run at 40-psig injection pressure. Pressure was not considered as a variable for these experiments, since we previously had found that it had only a small effect on fuel availability up to 600 psig.APPARATUS AND MATERIALS APPARATUS The fire flood-pot apparatus consists of a consolidated

By D. H. Gray, G. Bergamini, I. Fatt

A method developed by soil scientists for measuring permeability anisotropy of soils has been adapted for use in studies of sandstone permeability aniso-tmpy. Studies on Berea and Bandera sandstone show that permeability of these materials decreases upon application of simulated overburden pressure. Permeability reduction of Berea and Grubb sandstone cores subjected to simulated overburden pressure is shown to be a function of the ratio of radial to axial stress. INTRODUCTION The effects of mechanical stress on reservoir rock parameters are now generally accepted as being important in reservoir engineering calculations. In several oil fields the unique behavior of the reservoir has been attributed to the influence of overburden pressure or internal fluid pressure on rock permeability or fluid content. l Although the gross effects of overburden pressure on permeability, porosity, waterflood efficiency, electrical resistance and sonic velocity have now been established,3-9 there are some very interesting, and perhaps important, details of rock behavior under stress that have not heretofore been studied. In this paper we will show that permeability anistropy of several sandstones is a function of overburden pressure. We will also show that permeability reduction of cylindrical samples of two sandstones, when subjected to mechanical stress, is a function of the ratio of radial to axial stress. Most studies of overburden pressure effects made in the past have attempted to duplicate reservoir conditions by applying hydrostatic external pressure on all surfaces of the sample. Assuming perfect elasticity, that is, no viscoelastic flow during geological time, reservoir rock in situ cannot be under hydrostatic stress as is apparent from the value of 0.25 for Poisson's ratio for most rock. In the absence of tectonic forces the horizontal stress component If there are directional permeability effects, as has been reported from field and laboratory studies, l0,11 then one would expect hydrostatic stress as used in the laboratory to give a different permeability reduction from that occurring under reservoir stress conditions. The influence of stress on directional permeability was measured by a modification of the method first described by Maasland and Kirkham for use on soil samples.12 Their method permits calculation of the permeabilities along each of the three mutually perpendicular axes of a cubic sample. The modification reported in this paper extends the method to observing these permeabilities when the sample is under hydrostatic stress. The Hassler sleeve type of core holder is satisfactory for studying overburden pressure effects on permeability if a known force is applied to the end plugs. Wyble6 used a sleeve core holder but did not load the end plugs. In this paper we combine sleeve pressure and axial force to give permeability changes which we believe are close to those occurring in reservoirs when reservoir pressure changes. The combination of sleeve pressure and axial force assumes, however, that the sleeve pressure simulates both vertical stress and horizontal stress in one direction. METHOD PERMEABILITY ANISOTROPY The Maasland and Kirkhaml2 method of measuring permeability anisotropy uses a cube of porous material which is Open On three faces and has discs with a Center hole for an air inlet cemented to the other three mutually perpendicular faces (Fig. 1). The rate at which air pressure falls in a bottle of known volume, and pressure slightly above atmospheric, when the bottle discharges through each disc, is

By C. E. Feather, G. M. Koen

The significance of the mineralogical and surface characteristics of gold grains in the recovery process by C. E. FEATHER B.Se. Hons. (Cape Town)* and G. M. KOEN D.Se. (Pretoria)* A description is given of the nature and occurrence of gold at various stages in the process of its recovery from Witwatersrand and related ores. Electron microprobe investigations show that the surface of gold grains in the ore is already coated. During metallurgical processing, further coatings, mainly hydrated iron oxides, accumulate on the grains. Theories are advanced for the formation of these coatings, and the adverse effects on metallurgical operations are discussed.

By C. P. Lazzara, R. A. Franks, G. F. Friel, J. C. Edwards, J. J. Opferman

A National Institute for Occupational Safety and Health’s (NIOSH) mine fire detection re-search project was undertaken to evaluate multiple mine fire sensor types for nuisance alarm discrimination. The response of multiple fire sensor types to three small coal fire and three small conveyor belt fires in the presence of diesel emissions was evaluated in NIOSH’s Pittsburgh Research Laboratory (PRL) Safety Re-search Coal Mine (SRCM). An array of fire sensors which included an optical and ionization smoke sensor, a chemical cell CO sensor, and Metal Oxide Semiconductor (MOS) sensors, was used to sample the diesel engine and fire source emissions. The mine fire detection experiments demonstrated the ability of a MOS sensor with a bimodal response to NOx and products-of-combustion (POC) to respond to the onset of smoldering combustion in the presence of CO and POC particulates from a diesel locomotive. As part of an in-mine evaluation in an operating coal mine, the MOS NOx responsive sensor and an ionization smoke sensor was demonstrated as a method to discriminate diesel emissions and cross-interference of H2 on a CO chemical cell fire sensor at a battery charging station. The reinforcement of mine fire sensor information with the use of multiple sensor types, such as an MOS sensor and ionization and optical smoke sensors, is shown to be important for nuisance alarm discrimination and early mine fire detection.

By R. Hemp

This paper describes in broad outline the development of a computer programme for determining the effects of changes in various factors in the condenser water circuit on the operation of a cooling plant. The programme is used to obtain design figures which result in minimum total power consumption. This was done for a range of different upcast air quantities, and the implications of low air quantities for heat rejection are discussed.

By Kentaro Kuraji

INTRODUCTION Background Tokyo, the capital of Japan, is one of the largest cities of the world. As many as 33 million people live in Tokyo and three neighboring prefectures although the city occupies only 0.6% of the area of the country. The network of Metropolitan Expressways serves as a major artery for daily physical distribution in Tokyo. The Central Circular Route of the Metropolitan Expressway (MECCR) is located innermost among the three circular routes in Tokyo (Figure 1). Once completed, MECCR is expected to drastically mitigate traffic congestion in the central Tokyo area and provide drivers wider varieties of options in route selection. Alleviating congestion is estimated to reduce 400,000 tons of carbon dioxide emissions annually. The eastern and northern sections and part of the western section of MECCR have been completed with the total length reaching 33 km. The western section will be extended southward by approximately 4 km in the spring of 2010. An 11-km-long western section of MECCR that is currently being constructed is composed mostly of tunnels. A large number of power supply, gas supply, telephone, drinking water and sewerage pipes have been placed under the Yamatedori avenue along which MECCR is being constructed. The shield tunneling method has therefore been adopted for constructing tunnels along the route. The method involves the advancement of a shield tunnel boring machine (TBM) through the ground simultaneously assembling segmental rings within the shield. The method not only enables the building of highway tunnels more quickly and efficiently than other methods but also minimizes the effects of construction work on the surrounding area and the environment. Constructing the tunnel using the conventional cut-and-cover method might have required large amounts of time and cost because relocating the numerous objects buried under the Yamatedori avenue might have been necessary during tunnel construction. It was also considered desirable to place the tunnel at a depth of 30 m or more from surface to prevent tunnel construction from adversely affecting railways because the tunnel was expected to cross eleven railways and subways. This is one of the reasons for selecting shield tunneling as an effective method. The shield tunneling method was finally adopted for a length of 7 km in the 11-km western section of MECCR. The shield tunneling method was also employed in the Ohashi Tunnel located southernmost in the 11-km western section of MECCR. This paper describes the construction of the Ohashi Shield Tunnel.

By F. N. Kissell, C. D. Litton

Abstract-This study predicts the level of smoke that miners might meet while trying to escape a coal mine fire and describes how smoke would impede their safe escape. For this study, the authors assumed that miners exit through an escapeway adjacent to the burning entry, that some air would leak from the burning entry to the escapeway. The following conclusions were made: • A very low amount of air leakage to the escapeway can produce a critical level of visual obscurity from smoke. This shows that intake airways may be as susceptible to smoke visibility problems as return airways. • This critical level of smoke obscurity is reached much before a critical level of carbon monoxide is reached. • Small fires can cause a severe sensory irritation that further limits vision. Thus, reliable eye protection is very important. These results show that methods to guide miners through dense smoke will contribute greatly to saving lives during mine fires.

By Gerald T. Homce, Michael R. Yenchek, H. Kenneth Sacks, James C. Cawley

Abstract—Overhead electric power lines present a serious electrocution hazard to personnel in a variety of industries. Overhead lines, typically uninsulated conductors supported on towers or poles, are the most common means of electric power transmission and distribution, and are exposed to contact by mobile equipment such as cranes and trucks. Equipment contacting energized overhead lines becomes elevated to a high voltage, and simultaneous contact by personnel of the “hot” frame and ground can cause serious electrical shock and burns. Industries where risk of these accidents is greatest include construction, mining, agriculture, and communications/public utilities. An estimated 2300 accidental overhead line contacts occur each year in the U.S. This paper describes a practical low-cost concept to detect actual contact of mobile equipment with a high-voltage line and provide a warning. Accident statistics indicate that more than half of the fatalities could be prevented by such a device. Index Terms—Crane, electrical shock prevention, engineering control, mining, mobile equipment, power line.

By G. W. Holl, E. G. Fairon

A review of some aspects of shaft design by G. W. HOLL, Pr. Eng., Associate of the Mine Managers Association of South Africa (Fellow)- and E. G. FAIRON, Pr. Eng., F.S.A.I.E.E., M.I. Cert. M.E.E., M.I.Mech. E., (Visitor) The reasons for the choice of vertical shafts in preference to inclined shafts of comparable capacity are set out, and the conclusion that the former are superior in virtually all circumstances is substantiated. The shapes of vertical shafts sunk during the past sixty years are recorded, and the shapes of those sunk during the past decade are analysed. From this analysis it is clear that circular and elliptical (and quasi-elliptical) shafts are the shafts of the future and that the rectangular shape will conceivably become obsolete. The determination of the size of shaft is discussed and it is forecast that shafts of a diameter of 13 metres and over will probably be sunk without difficulty in the years to come. The depth of the shaft is determined intrinsically by the Mines and Works Regulations applicable to factors pf safety of winding ropes and the design of the winding system. The Blair winder is the most suitable winder for hoisting rock, men, and material from a depth of, say, 3000 metres on an economic basis. Tertiary shafts will, therefore, be unnecessary in future deep-level mining projects at the limit of depth now envisaged. A few other factors relating to shaft design are described.

By L. R. Raymond, G. G. Binder

One primary purpose of hydraulic fracturing as a well stimulation technique is to overcome formation damage. The literature provides ways of designing fracture treatments and evaluating their results but not of incorporating formation damage in vertically fractured wells. Results of an investigation of this problem are presented in this paper. Prediction of stimulation ratios in vertically fractured, damaged wells is accomplished with a mathematical model relating stimulation ratio to relative conductivity of fractures whose lengths are not more than about half the drainage radius of the well. Comparison of results from the new model to results in published predictions verify its utility; these results also show that the range of stimulation ratios that can be predicted for undamaged wells is extended to include relative conductivities of less than 300. This extension is important when using fracturing to stimulate wells with high production rates and high native formation permeabilities. For example, large increases in daily oil production rate can be obtained with stimulation ratio increases as low as 1.25. The importance of complete fracture fill-up (uniform proppant packing) is shown through use of the mathematical model. If, at the mouth of a fracture, only a small fraction (1/2 percent) of the total fracture length is not packed with proppant, nearly all the polential stimulation increase is lost. Proppant crushing, compaction and embedment have been shown in laboratory studies to be responsible for low fracture conductivities in wells producing from highly stressed formations. Equipment and methods for testing the effect of stress (overburden) on conductivity of fructures in consolidated and unconsolidated sands are discussed in this paper. Laboratory tests with simlilated fractures in cores from both types of formations showed that crushing, compaction and embedment seriously affect conductivity. Results indicate that similar laboratory tests should be made when accurate knowledge of fracture conductivity is needed to assure good stimulation results for important wells. The chief factor in stimulation ratio reduction was found to be overburden pressure, but the size and type of proppant and the hardness of the formation have significant effects. Fracture conductivity reductions of up to 50 percent were observed with sand propping fractures in consolidated cores; a reduction of 83 percent was measured for an unconsolidated core. The range of effective overburden pressures for which conductivities were measured was from 100 to 5,000 psi. An example fracture design and evaluation problem indicates the usefulness of considering formation damage in planning well stimulation jobs. When damage exists, but its extent and the degree of permeability reduction are not estimated from diagnostic tests, the formation permeability used in planning the job may lead to under-designing. As the example shows, too low a target stimulation ratio can lead to much lower production rates (by half) than could be attained otherwise. Solutions of equations representing several special cases of the mathematical model are presented in graphical form and details of the derivations of the equations are given in the Appendix. INTRODUCTION Since its inception in 1947, hydraulic fracturing has proven to be an effective and widely accepted stimulation technique. In the past 18 years the ability to execute a successful hydraulic fracturing treatment has been substantially increased. The development of design and evaluation procedures1,2 has been one of the major contributions to this increased skill. However, as the art of hydraulic fracturing has moved closer to a science, new problems concerning the design and evaluation of the optimal hydraulic fracturing treatment have arisen. Three questions are pertinent to these problems. I. How is a fracturing job evaluated in a damaged well? 2. What is the effect on the stimulation ratio of not filling the fracture in the vicinity of the wellbore? 3. What is the effect of overburden pressure on fracture conductivity and, consequently, the stimulation ratio? A primary objective of fracturing a well is to stimulate production by overcoming wellbore damage. Presently. however, there is no rational basis for designing or evaluating the optimal fracturing treatment in a damaged well. All present fracture design and evaluation techniques assume that proppants can be uniformly placed in fractures. This assumption may be in serious error, particularly for the portion of a fracture directly adjacent to the wellbore. In this area, turbulence of the injected fluid can cause the proppant to be swept farther into the fracture. Also, loss of fluid from the fracture to the

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink