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By K. E. Brown, J. P. Brill, A. R. Hagedorn, T. C. Doerr

A recent correlation for multiphase vertical flow by Hagedorn and Brown1,7 has been used to examine the effect of numerous variables such as pipe size, gas-liquid ratio, liquid flow rate, liquid viscosity, liquid surface tension, oil API gravity, water cut, etc., on flowing pressure gradients. Most previous correlations were derived by using a form of the general energy equation which assumed negligible changes in kinetic energy. Under certain flow conditions this can lead to serious errors in predicting pressure traverses. Examples of traverses calculated both with and without the kinetic energy term are included here. The Chew and Connully correlation for calculating changes in viscosity with changing pressure and temperature has been extended so that the effect of a changing viscosity with depth on pressure gradients can also be predicted. Examples illustrating the effect of tubing size show the importance of this correlation in determining pipe sizes for initial well completions. Limitations on production rates in small pipe sizes from excessive friction losses can be predicted with greater accuracy. The combined use of a vertical-flow correlation with a horizontal-flow correlation provides a method for determining the maximum flow rate possible from both flowing and gas-lift wells. Examples are included to illustrate application of the combined use of vertical and horizontal-flow correlations in optimizing production rates and minimizing excessive costs from over injection of gas in gas-lift wells. INTRODUCTION The problems of multiphase vertical and horizontal flow are immediately encountered in any producing well. Fig. 1' shows three stages of production: flow in porous medium, vertical flow and horizontal flow. All three stages affect the production rate from a well. If we are confronted with a particular well and consider only the variables involved in the vertical and horizontal stages of Fig. 1, we should be capable of calculating the flowing bottom-hole pressure necessary to produce a particular flow rate. A change in any of the variables results in a new solution to the problem. Recent approaches in developing horizontal and vertical-flow correlations have improved to the extent that the solution can now be obtained with more confidence than previously. VERTICAL AND HORIZONTAL FLOW CORRELATIONS Since Poettmann and Carpenter's' original work in multiphase vertical flow, there have been many additional vertical-flow correlations developed which have greatly improved the accuracy of pressure-loss calculations. These

Jan 1, 1967

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 J. L. Huitt, D. K. Lowe

This laboratory flow study covers propping agent transporl in horizontal fractures as influenced by the characteristics of the propping particles, fluid and fracture. Correlations are presented for the transport of particles, deposition and fingering through dunes. For particles moving individually, the article velocity in some cases may be low compared to the hulk average fluid velocity; in other cases, the particle velocity may exceed the bulk average fluid velocity. At high propping agent concentration or low fluid velocity, the likelihood of particle deposition and dune formation increases. Fingering and channeling accompany dune formation. Dune formation can be limited to the outer region of tile fracture by adjustment of pump rate, fluid viscosity and particle concentration. A method is presented by which pump rate and fluid vircosity may he selected to control dune formation for given propping agent concentrations. INTRODUCTION The area and flow capacity of a fracture predominantly control the stimulation derived from hydraulic fracturing. Generation of fracture area exposes the rock matrix to a flow channel; the flow capacity of the fracture controls the flow through the channel to the wellbore under a given pressure gradient. This paper pertains to an important factor that affects the flow capacity of a fracture: the transport of the propping particles in the fracturing during the hydraulic fracturing treatment. With a better understanding of particle transport, fracturing treatments may be designed to obtain more effective distribution of the propping agent. RELATED STUDIES In recent years, the approach to obtaining high fracture flow capacity has been partial monolayer propping. Three papers1-3 have dealt with various facets of this concept. However, in some papers dealing specifically with particle transport, the results generally indicate that packing the propping particles within a fracture is inevitable. In early work&apos; with a sand slurry flowing in a pie-shaped flow cell, qualitative results showed that particle deposition in a fracture during transport should be expected. In other studies"" correlations based on slurry flow in vertical linear flow cells showed particle deposition was primarily a function of fluid velocity. In a recent paper the rate of sand advance (movement of dunes) in a horizontal linear flow cell was discussed. Subsequently, a method was given for designing fracturing treatments, based on the extent of sand advance during a treatment. In this work, particles whose diameter was small relative to the fracture width (i.e., dl W< 0.2) were primarily considered. The particle transport approaches that of sand transport in a stream bed. The industry trend, however, has been to use larger size propping agents. That is, particles with diameters approaching fracture widths predicted by Perkins and Kern.&apos;&apos; This trend has led to generally better fracturing treatments with particle relative sizes in the range 0.2 <d/W < 1.0. In all of the particle transport studies previously cited, the fluid characteristics were discussed. However, little or no attention was given to the parzicle characteristics. In this study the particles. as well as the fluid and fracture, are considered. VARIABLES AFFECTING PARTICLE TRANSPORT In the exploratory work to set LIP a program for this study, it was noted that particles within a batch moved at different velocities in a horizontal linear flow cell. In some cases the particles moved independently. In others there was particle interference. Also, particle deposition and fluid fingering occurred in some cases (Fig. 1). As a result of observing the easily distinguishab&apos;le types of particle movement, the particle variables as well as the fluid variables were included. In addition, the fracture width was included because the fluid velocity profile surely must affect the movement of the larger particles differently than that of smaller particles. Particle variables were density, diameter (based on a sphere of equal volumetric displacement), long and short dimensions, drag coefficient and velocity. Fluid variables were density, viscosity, yield shear strength and velocity. Fracture variables were the width and the angle between the plane of flow and a horizontal plane. Two factors which may prove to be important were omitted because of the complexity resulting from the parameters cited above. These are the fracture-surface roughness and gross irregularities that cause changes in the direction of flow. EXPERIMENTAL EQUIPMENT AND PROCEDURE A linear parallel-plate flow cell (Fig. 2) was used in the study. Lucite plates 1 in. thick formed the test section and permitted a viewing section 11 ft long and 10 in. wide. Spacing between the plates was adjusted with shims to give fracture widths 1/36 to 1/2 in. The model could be tilted to an angle of 45" with the horizonltal plane. Fluid flow was maintained with a Moyno positive displacement pump. Single particles were placed in the flow stream with a particle injector. A .4 - in. diameter plunger moving at a constant rate in a

Jan 1, 1967

By J. L. Huitt, B. B. McGlothlin

The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed. INTRODUCTION One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deform able particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed. BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al.&apos; In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al.2 in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies,3,4 methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with de-formable proppants, Kern et al. considered proppant particles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al.&apos;0 reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion. PROPPANT PARTICLE CRUSHING—-EMBEDMENT For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study4 it was shown that the Hertzian4 loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or: Lc/dp2=C ............(1) A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study3 of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer&apos;s metal penetration hardness relationships: d1/dp=B 1/2[L/dp2]m/2..........(2) In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1. A STANDARD DEFINITION FOR PROPPANT LOADING STRENGTH Eq. 1 is useful in appraising propping agent strength," but it is strictly applicable only when the area of contact between a particle and a fracture face (or loading plate)

Jan 1, 1967

By L. R. Raymond, J. L. Hudson

This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well-bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time. Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed pertneability value. From the slope of the injection-rate curve. a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result. Graphs of pressure and injection rate us functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can he used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested. The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility. INTRODUCTION To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimu- lation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists. Several techniques for determining reservoir transmissi-bility from well tests have been presented in the literature. 1,2,3,4 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry Out. and this paper contains the first available method for the analysis of constant-pressure well tests. Determination of wellbore damage from transient well tests has been the subject of several papers."" From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage. All previous studies of well testing to determine wellbore damage have been based on the two-zone perrneability model. In this model the damaged zone has a permeability k,, extending to a radius r,,, and the formation permeability k obtains from r, to the drainage radius r,.. Consequently, there is a discontinuity in permeability at r = r,,. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests. ANALYSIS OF CONSTANT-PRESSURE WELL TESTS The mathematical analysis associated with the injection of fluid at constant wellbore pressure into a single-zone, horizontal reservoir completely filled with a fluid of small and constant compressibility and constant viscosity is given in Appendix A. In this analysis it is assumed that the well is located at the center of an undamaged, circular drainage area. From this analysis, the formation permeability can be obtained as follows. 1, Estimate a value for the formation permeability k. 2. Prepare a plot of injection rate q vs

Jan 1, 1967

By K. E. Brown, A. R. Hagedorn

Continuous, two phase flow tests have been conducted during which four liquids of widely differing viscosities were produced by means of air-lift through 1%-in. tubing in a 1,500-ft. experimental well. The purpose of these tests was to determine the effect of liquid viscosity on two-phase flowing pressure gradients. The experimental test well was equipped with two gas-lift valves and four Maihak electronic pressure transmitters as well as instruments to accurately measure the liquid production, air injection rate, temperatures, and surface pressures. The tests were conducted for liquid flow rates ranging from 30 to 1,680 BID at gas-liquid ratios from 0 to 3,-270 scf/bbl. From these data, accurate pressure-depth traverses have been constructed for a wide range of test conditions. As a result of these tests, it is concluded that viscous effects are negligible for liquid viscosities less than 12 cp, but must be taken into account when the liquid viscosity is greater than this value. A correlation based on the method proposed by Poettmann and Carpenter and extended by Fan-cher and Brown has been developed for 1¼-in. tubing, which accounts for the effects of liquid viscosity where these effects are important. INTRODUCTION Numerous attempts have been made to determine the effect of viscosity in two-phase vertical flow. Previous attempts have all utilized laboratory experimeneal models of relatively short length. One of the initial investigators of viscous effects was Uren1 with later work being done by Moore et al.2,3 and more recently by Ros.4 However, the present investigation represents the fist attempt to study the influence of liquid viscosity on the pressure gradients occurring in two-phase vertical flow through a 1¼-in., 1,500 ft vertical tube. The approach of some authors has been to assume that all vertical two-phase flow occurs in a highly turbulent manner with the result that viscous effects are negligible. This has been a logical approach since most practical oil-well flow problems have liquid flow rates and gas-liquid ratios of such magnitudes that both phases will be in turbulent flow. It has also been noted, however, that in cases where this assumption has been made, serious discrepancies occur when the resulting correlation is applied to low production wells or wells producing very viscous crudes. Both conditions suggest that perhaps viscous effects may be the cause of these discrepancies. In the first case, the increased energy losses may be due to increased slippage between the gas and liquid phases as the liquid viscosity increases. This is contrary to what one might expect from Stokes law of friction,&apos; but the same observations were made by ROS4 who attributed this behavior to the velocity distribution in the liquid as affected by the presence of the pipe wall. In the second case, the increased energy losses may be due to increased friction within the liquid itself as a result of the higher viscosities. The problem of determining the li- quid viscosity at which viscous effects becomes significant is a difficult one. Ros4 has indicated that liquid viscosity has no noticeable effect on the pressure gradient so long as it remains less than 6 cstk. Our tests have shown that viscous effects are practically negligible for liquid viscosities less than approximately 12 cp. Actually there is no single viscosity at which these effects become important. These effects are not only a function of the viscosities of the liquids and of the gas but are also a function of the velocities of the two phases. The velocities in turn are a function of the in situ gas-liquid ratio and liquid flow rate. Furthermore, the role of fluid viscosities in either slippage or friction losses will depend on the mechanism of flow of the gas and liquid, i.e., whether the flow is annular. as a mist, or as bubbles of gas through the liquid. These mechanisms are also a function of the in situ gas-liquid ratios and the flow rates. It would thus seem that the best one could hope for is to determine a transition region wherein the viscous effects may become significant for gas-liquid ratios and liquid production rates normally encountered in the field. The viscous effects might then be neglected for liquid viscosities less than those in the transition region but would have to be taken into account when higher viscosities are encountered. There are numerous instances where crude oils of high viscosity must be produced. The purpose of this study has been to evaluate the effects of liquid viscosities on twephase vertical flow by producing four liquids of widely differing viscosities through a 1 % -in. tube by means of air-lift. The approach used in this study was as follows:

Jan 1, 1965

By M. H. Harris

A solution has been obtained to the problem of calculating flow into a cased and perforated well. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. Computer experimentation indicated that the results are within 3 per cent of the exact solution. Computed results are presented as an apparent skin effect, on a series of dimensionless working curves. Productivity ratios can be rapidly calculated from these data for the wide range of wellbore and reservoir properties actually encountered in field practice. Any reasonable vertical unisotropy ratio can be included in the computation. Productivities can be calculated for wells perforated in a regular pattern, a single horizontal plane or a vertical line on one side of the casing. Solutions for asymmetrical perforation patterns can he easily obtained from the working curves. Solutions for flow into sells completed with a horizontal notch are also provided. Results show that productivity can be increased by extending perforation penetration. This is especially true for shallow penetrations. The highest productivity is obtained when perforations are arranged in horizontal planes, as opposed to a vertical line on one side of the casing. Four or five perforations in one plane will approach the maximum productivity. The effect of perforation hole diameter is small, and is rioticeable only in shallow penetrations. INTRODUCTION The perforating method of well completion has been successfully and widely used in most producing areas. In the past, the desired perforation results were achieved by simply shooting numerous large holes in the casing. A perforating scheme for an area, or particular well, was established by evaluating two types of experimental data: the well flow index and the productivity ratio.&apos; 3 The well flow index test is a means of determining the relative flow capacity of perforations in a linear system. This test also gives information on the perforation size, shape and hole damage which can be expected under well-bore conditions. However, relative flow data from this test cannot be accurately tarnsformed into the radial wellbore system. Thus, no true indication of the productive capacity of a perforated well can be obtained from the well flow index test. A well productivity ratio is derived from electrolytic models built to simulate perforated wells. Available productivity ratio data 2,3 are limited in that all important variables are not extensively evaluated. For example, data are limited to well radii of 3 and 6 in., and to maximum perforation penetration of 1 ft. Practically no information is available on the pattern of flow into a perforation. The effect of various perforation patterns on well productivity has not yet been determined and the effect of perforation diameter has not been thoroughly studied. Also, it will be shown that this type of electrolytic model data is probably in error by as much as 10 per cent or more. Modern completion techniques such as limited-entry perforating, single-plane fracturing, steam and hot air injection and chemical consolidation of incompetent formations all rely on injection and/or production from a limited type of completion. These completions may consist of several high-capacity perforations or a horizontal notch which is equivalent to an infinite number of perforations in one plane. Proper design of these new completion techniques requires, in part, accurate estimates of a well&apos;s productive capacity. Data on perforated and notched well productivity have been determined in this investigation. Results are presented as a function of the pertinent variables. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. DESCRIPTION OF PROBLEM PRACTICAL APPLICATION The computed results can be applied to wells which meet several general specifications. An external drainage radius of the well must be known or assumed, but the well need not be drilled on a regular pattern. The well must be cased and cemented through the entire producing interval. And, the casing must be perforated with one or more horizontal planes of perforations. The perforation pattern itself must conform to three geometrical requirements. 1. The perforations in a plane must divide the plane into equal angular segments (Fig. 1). Four perforations per plane would be 90" apart. 2. Perforations in a plane must be directly above or beneath perforations in adjacent planes. For two shots per plane, perforations would lie in the BB&apos; plane (Fig. 1). 3. Horizontal planes must have equal vertical spacing and be separated from the top and bottom of the formation by one half the spacing interval. Single planes of perforations should be in the middle of the formation. This is shown in Fig. 2 where h is the formation thickness in a single plane conlpletion or the spacnig interval in a multiple plane completion. The spacing interval at the top and bottom of the formation may vary somewhat without causing an appreciable error in the productivity calculation if the formation is reasonably thick and there are many horizontal planes of perforations. A special provision has been made to calculate the productivity ratios of wells with uneven spacing intervals, or for the case where a single plane of perfora-

Jan 1, 1967

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner&apos; makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,&apos; is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors&apos;&apos; derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel&apos; terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones&apos;" initiates steady-state

Jan 1, 1967

By D. J. Weintritt, J. C. Cowan

Methods of studying oilfield mineral .scale deposition in the laboratory do not work for barium sulfate because only small nonadhering crystals ore formed. On the other hand, barium sulfate scale found in down-hole or surface equipment is strongly adhering and may contain very large crystals. Results suggest that most of the difference derives from the extremely low .solubility of barium sulfate. Firm adherence of scale and the consistent development of oriented crystals 100 microns and larger suggest a relationship between scale adherence and crysta1 growth. Data from this study indicate some reasons for barium sulfate&apos;s occurring as a deposit in oilfield waters. The unique characteristics as well as the associative properties of barium sulfate scale as related to calcium carbonate and calcium sulfate ere shown. INTRODUCTION The first observed deposition of barium sulfate scale in oilfield production equipment is unknown but probably coincides closely with the beginnings of the oil industry itself. Moore&apos; described barite oolites in some producing wells in the Saratoga field, Tex., in 1914. Currently, positive identification of barium sulfate deposition is recorded in most of the major oil-producing areas of the United States. As efforts continue to identify the composition and functions of the materials found in scale deposits, the geographic and economic importance of the part played by barium sulfate will become even more important. This belief is based on the following Facts. 1. Many oil fields in the U.S. are in or entering their mature phase and the volume of produced water is increasing; thus, the cumulative effects of low-solubility minerals become more significant. 2. Secondary recovery techniques and increased emphasis on waste disposal systems require controlling the behavior of all constituents of water to prevent formation plugging. 3. The more general use of instrumental analysis has reduced the time and improved the accuracy of complete scale and water analysis. 4. Once formed, barium sulfate scale is resistant to present methods of chemical removal; therefore, costly mechanical methods are necessary. Thus, new methods of prevention and control will require specialized chemical techniques and better knowledge of the causes of scaling. Consider the results of some simulated field deposition studies illustrating this need (Fig. 1). The studies utilized a Scale Deposition Test Cell* and each coupon was exposed to 8,000 ml of a 300 me/liter solution of the various types of mineral scale. All tests were conducted at 140F. Only the calcium sulfate and calcium carbonate deposited scale. The solution containing 300 me/liter of barium sulfate exhibited copious amounts of precipitate, but none of the precipitate adhered. The fluids from the effluents were also allowed to impinge on glass slides. Fig. 1 shows the relative adherence of the three types of scale on unetched glass. The barium sulfate failed to deposit in the same manner as the calcium carbonate and calcium sulfate solutions.

By B. Farshadi, B. Asi, M. J. Habibian

"Dare-Zereshk deposit is one of the deposits supplies ore for Taft copper Complex in Iran Yazd province. This deposit is situated underneath a village the same name. Prior to mining activities, the village and its agricultural lands should be dislocated and deserted. This paper discusses about sustainability factors in this area including: Social and environmental effects of mining, dislocation and substitution of communities, created and lost jobs, financial and economic factors, quality of life index, infrastructures and post-mining land use. Studies have been performed by coupling Geographical Information System (GIS) with decision support tools such as Multi Attribute Decision Making (MADM), Through these studies revealed that considering the infrastructures developed for mine and plants, earned incomes and changing the community, mining activity in this area not only increases the social and regional sustainability but also improves it to a higher level."

Jan 1, 2011

By A. K. Sinha

The annual production and productivity of underground coal mines in recent years declined from 334 Mt (368 million st) and 14.5 t (16 st) per man per shift in 1969 to approximately 254 Mt (280 million st) and less than 8 t (9 st) per man per shift in 1977. Productivity is still hovering at about 7.25 t (8 st) per man per shift. According to US Bureau of Mines, the estimated US coal reserve is about 396 Gt (437 billion st), 68.65% of which is obtainable by underground mining methods. Approximately 153 Gt (169 billion st), or about 85.2% of the high Btu premium coking coal of the eastern US, would need to be extracted by underground mining methods. It is thus apparent that under- ground mining will continue to play a major role in total US coal production, which is expected to rapidly increase to about 1.1 Gt (1.2 billion st) by 1985, with about 606 Mt (668 million st) being contributed by underground mines. Production Potential of Continuous Mining The production potential of a continuous mining section depends primarily on the producing ability of the miner, transporting ability of the face haulage, and the matching of the two systems. The producing ability of the continuous miner depends on its actual cutting ability and the time available for cutting coal. The performance of 10 continuous miners operating in coal seams of various thicknesses were monitored in Pennsylvania and West Virginia, using continuous electrical power analyzers and time studies. The recordings on current and power strip charts yielded an accurate analysis of the cutting, trimming, and idle times of the machines on a full shift basis. Continuous miners of various models and sizes from 112-298 kW (150-400 hp) were monitored. Based on actual cutting time, the average cutting ability of the machines, as shown in [Fig. 1], ranged from

Jan 1, 1983

By C. T. Philipp

Recycling of waste is much preferred over disposal. This paper discusses the Enviroscience, Inc. (ESI) process, now being commercialized by MetWool, Inc., to recycle hazardous wastes using an extractive metallurgical process which is followed by vitrification of non-reducible metal oxides. In this process, volatile and reducible metals are reclaimed as their respective oxides and elements.

Jan 1, 1995

By H. Y. Ran

Magneto-flotation is a recently developing technology of mineral processing. This technology combines the traditional magnetic separation with flotation and provides a magnetic and buoyant force compound field to separate different minerals based on the differences of magnetism and floatability between useful minerals and gangue minerals. Magneto-flotation is applicable to separate ferromagnetic from nonmagnetic minerals, especially to separate magnetite from floatable gangue minerals. This magneto-flotation column is equipped with pulse electromagnetic field in the middle upper part, a bubble producer and upwell water inlet in the bottom. The pulse time of electromagnetic field in the column can be optionally adjusted and the maximum intensity of pulse magnetic field can reach 35mT. Pulse magnetic field can not only restrain magnetic minerals from entering into the froth layer, but also destroy the magnetic agglomeration to ensure a higher recovery and a higher concentrate grade. The results of experiments with magnetite show that pulse magnetic field has remarkable influence on flotation process. Compared with single flotation, magneto-flotation column can improve the recovery of magnetite by ten percent. After one time?s magneto-flotation processing, the grade of iron concentrate can increase from 65.4% to 69.5%, the content of silicon oxide in iron concentrate decreases from 7.4% to 2.8%, and the total recovery is above 96%.

Jan 1, 2014

By James K. Gowans

Polaris Mine, a Cominco Ltd. property located on Little Cornwallis Island, Northwest Territories, Canada, (Lat. 75°30&apos;), is the world&apos;s most northerly base metal mine. Polaris Mine, which commenced operations in late 1981, is characterized by its unique process barge. The lead/zinc concentrator, powerhouse, shops, offices, dry and warehouse have all been incorporated on a 400 ft. long by 100 ft wide by 65 ft high barge. This process barge was constructed in Southern Canada, at Trois Rivieres, Quebec, then towed 3500 miles into its final resting place on the high arctic. This paper describes the unique design of the barge concentrator and deals with the start-up and continuing operation of the Polaris Concentrator.

Jan 1, 1984

By James T. Bartis

Review of Key Issues Affecting the Prospects of CTL in the United States ?Issues of concern to the public - Impacts of coal mining - Water use - Greenhouse gas emissions ?Issues of concern to investors - CTL production costs - Oil prices - How greenhouse gas emissions will be managed ?RAND recommendations

Jan 1, 2009

By K. T. Mau

Hawaii is located approximately 2,500 miles from the mainland, but has basic needs for its thriving developing community. Cement is one of these needs Cement production in Hawaii is not without handicaps. The necessary raw materials are practically non-existent except for limestone. Even at that, the available limestone is marine in origin, coralline in nature and amorphous in characteristics - unlike calcite which is normally the calcium carbonate source for cement manufacture. There is no clay or shale for the argillaceous portion of cement raw mix. Hawaii being volcanic in origin is too young geologically for clays and shales to evolve and whatever there is, most likely is washed into the ocean.

Jan 1, 1982

By Clifford R. Miercort

When it was announced that the economy grew at an annual rate of 4.7 percent in the Fourth Quarter of 1992, it appeared that our long awaited recovery from recession was here. Unfortunately that much growth proved to be unsustainable, and in the First Quarter of 1993, the number dropped to less than one percent. Today it is clear that the recovery is continuing, but at a very slow rate. One of the Most disturbing statistics during this recovery is that unemployment has not improved as one would expect but has been hovering around 7 percent for over a year, making this recovery a ?jobless? one. In a recent Harvard Business School presentation, a professor reported that the United States has slipped from its leadership position in almost every manufacturing category since World War II. From the production of cars to consumer electronics, we have lost significant world market share to others, most notably Japan and Germany. Obviously this is not new news, but the magnitude of the loss and the number of industries affected was surprising to me. The result has been that our negative balance of payments has soared, and the United States of America now has the dubious distinction of being one of the world&apos;s largest debtor nations. It has been common for politicians, and political want-a-be&apos;s, to blame all of our trade problems on industry. They say that the moguls of American industry spend too much time seeking short-term gain at the expense of long-term growth. They say that we are interested more in our own perks and economic security than in producing quality products that can compete in the world marketplace. One of the stared goals of the Clinton Administration is the targeting of strategic industries to receive help from the government so they can compete on the world stage more effectively. Personally. I think that is an oxymoron. My experience has been that whenev-

Jan 1, 1993

By E. H. Bentzen

The purpose of this paper is to explain the production of sand for glass manufacturing and the reasoning behind the sand specifications set by the glass industry. In order to discuss the production of glass sand, there is a need to understand what glass is and how it is made. Therefore this paper discusses glass, as well as sand beneficiation.

Jan 1, 1977

By E. W. Raabe

The paper discusses the increasing role of specialist grouting techniques to form water seals or cut-offs for deep basement construction. Raabe and Toth discuss the various grouting methods available for sealing applications and then concentrate on the use of Soilcrete Jet Grouting, a system particularly well suited to ground water control. The Soilcrete processes, suitable soil types and quality control methods are fully described, particularly with regard to the formation of cut-off walls and sealing slabs to prevent the progress of ground water or leachates. The authors have included case histories detailing their experience on designing and installing Soilcrete seals for various projects in West Germany. These include an underground rail project in Dortmund and a discharge structure for the Alz Canal at Burghausen.

Jan 1, 1989

By J. M. Bray, R. R. H. Cohen, P. Kiousis, S. R. Al-Abed

"INTRODUCTION Conventional tailing storage and management practices typically utilize engineered facilities, such as ring dikes and valley impoundments. To reduce the environmental costs associated with disposing of mine wastes in tailing storage facilities (TSFs), several beneficial re-use strategies have been developed over the years. For example, thickened tailings have been used for paste backfill. It is common for tails to comprise up to 60% of the material’s total weight and it has been estimated that TSF volumes can be reduced by 60% when using this strategy, (Benzaazoua, et al. 2004). Other beneficial re-use strategies have produced unpaved temporary access roads, hot and cold asphalt, chip seals, self-compacting concrete, and golf course sand traps. This project sampled mine tailings from two different TSFs in Colorado and produced structural concrete that could potentially be used for commercial foundations, sidewalks, and paved roads. The tailings were substituted for the fine aggregates typically found in conventional concrete. The two main objectives of this study were to investigate the structural integrity of the produced concrete samples and the leaching of heavy metals from the resulting concrete. The ratio of tailings to fine aggregate (T/FA) was carefully studied to find if there was a correlation between the substitution rate and the structural integrity. The potential maximum substitution rate was also investigated for the produced concrete specimens. The potential of leaching mining impacted water (MIW) was evaluated by comparing the leachability of the raw mine tailings to the encapsulated tailings by using standard shake extraction prediction tests. MATERIAL AND METHODS Materials The four components that make up the concrete mix design for this project are: cement, coarse aggregate (gravel), fine aggregate (sand and mine tailings), and water. The type I/II ordinary Portland cement (OPC), gravel, and sand came from local cement and concrete companies in Denver, Colorado. Mine tailings were collected from two different TSFs in the Rocky Mountain Region, where Pride of the West TSF in Silverton, CO will be denoted as Site A. The primary metals of interest at the mill site are gold, silver, lead, copper, and zinc. The location of Site B will not be mentioned in this report due to confidentiality agreements with the mining company"

Jan 1, 2016