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By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy's law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.

By J. Böhlke, B. Friedrich, E. Hecker

The legislation for the disposal of heavy metals contaminated substances is still going to be tightened up in the future. The main criteria for the utilization or deposition of these residues are the content and the water solubility of these metals. Through this, the use of slags from the lead-and zinc-industry in road building may become limited or even not possible at all. From an economic point of view this would lead to Pb/Zn losses and costs for safe dumping. This paper investigates the feeding of the reducing agent via hollow electrode DC smelting and the yield of metal reduction. After carrying out thermodynamic calculations, the process window conditions for electric-arc furnace tests were determined. Doing this, the zinc could be reduced, evaporated and recovered as an oxidic intermediate product flue dust, while the lead was present either in flue dust or in metallic form. The zinc content in the final slag could be reduced by up to 90%. The slag product has undergone an eluation test which allows it to be used as building materials. Keywords: zinc reduction, lead reduction, hollow electrode, slag treatment, electric arc furnace

By Theresa Y. Schulz

It is interesting to study the noise standards that have been promulgated in the US over the last decade or so. These regulations are likely to have long-lasting impact. The Occupational Safety and Health Administration (OSHA) Hearing Conservation Amendment (March 1983) continues to have influence not only in the workplace but in the debate over new regulations. Both the Mine Safety and Health Administration (MSHA) and Federal Railroad Administration (FRA) regulatory preamble documents state the desire to be consistent with OSHA. An examination of Table 1, which compares the major components of the three regulations and the 1998 NIOSH “best practices” criteria, depicts the extent to which that intent is met. There has been some regulatory activity in the last decade which may give some hope for evolution and updating based on the wealth of science that has occurred during the last quarter of a century since the OSHA regulation was enacted. However there has also been some “back-sliding” toward more lenient standards. The MSHA noise standard made regulatory progress in September 2000 by emphasizing engineering and administrative controls, followed by personal protective equipment, in the hierarchy of noise intervention. MSHA’s requirement for technician certification (today only available from CAOHC) strengthened the training requirements for audiometric testing in hearing conservation programs and MSHA also added the requirement of dual hearing protection at 105 dB TWA. There were many subtle differences between OSHA and MSHA based on comments and a desire to clarify some of the vague aspects of the OSHA noise standard, and meet the needs of the regulated mining industry. One example pertains to the ceiling for exposures. OSHA says, “no exposures >115 dBA,” which is interpreted to mean no unprotected exposures above that level, giving credit for the assumed effectiveness of hearing conservation programs, hearing protection devices and administrative and engineering controls. MSHA specified that a “P” code1 violation be issued for any protected or unprotected exposures >115 dBA. The Federal Railroad Administration (FRA) noise standard for railroad operating employees, which went The Modern Evolution of Hearing Conservation Regulationsinto effect February 26, 2007, was expressly based on the OSHA standard but also uses MSHA for comparison. The preamble states that the FRA defers to OSHA as the “primary regulator of noise in the workplace,” but also acknowledges the need for some departure from the OSHA regulation (FRA Preamble II.B). As an example, FRA requires testing at 8000 Hz “because it will allow employers to identify hearing loss sooner.” The FRA rejected MSHA’s hierarchy of noise controls in favor of requiring specific engineering interventions and focusing on appropriate hearing protection which would still allow communication and audibility, and identification of excessive noise through employee-filed “excessive noise reports.”2 Where OSHA has no specific mandate requiring employees to take advantage of the employer-paid audiogram, it has been traditionally a condition of employment and is generally accepted that OSHA-covered workers require an annual audiogram. MSHA addressed this issue in its preamble; however, they made no significant change. MSHA employers are required to offer annual audiograms but MSHA stopped short of requiring employees to comply with annual audiometric testing. The MSHA preamble does allow that mine operators can also make audiometric monitoring a condition of employment. FRA requires employees to

By Mark Larson, Steve Iverson, Brian G. White

The authors hypothesize that excavation-induced extension fractures are caused by elastic shearing displacement that in turn causes tension oblique to a propagating shear zone. Such extension is manifested as tension on scales larger than that of microcracks. En echelon fracture patterns are a common result. FLAC modeling confirmed that localized tension is created near the corners of mine openings. In the model, tension was concentrated at the leading edge of a simulated fracture in a pattern that could promote the formation of an en echelon fracture. Particle Flow Code models confirm progressive formation of en echelon tensile failures with distance from an opening. The elastic displacements and the resulting fractures facilitate reduction in applied load at the expense of shear deformation and lateral dilation. Understanding the mechanics of fracture and deformation is vital for designing more effective ground support practices, a major objective of ground control research being conducted at the Spokane Research Laboratory of the National Institute for Occupational Safety and Health.

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity' factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse

By Richard J. Robbins

Raise and shaft drilling, a continuing development RICHARD J. ROBBINS* (Visitor) Although the past decade has witnessed many improvements in large-diameter drilling machinery for the boring of raises, there is still room for improvement both in operational use and in the design of equipment. Some of the available machines are described and illustrated, and it is concluded that the possibilities of new systems and designs should continually be re-assessed since the factors that determine their feasibility, such as bore diameter, cutter costs, and penetration rates, are changing rapidly.

By R. Karl Zipf, David Newman

The objective of this is paper is to review the current state of knowledge and practice in highwall mining (HWM). HWM has become a widely-applied method in surface mining, commonly used alone or in conjunction with contour or slot mining. It provides 800-feet to 1,200-feet of additional recovery when the economic stripping ratio is reached in contour mining or in slot mining when surface access to a reserve is limited. A significant attribute of the highwall miner is its versatility. HWM has been used successfully to mine abandoned pre-reclamation law highwalls, points or ridges uneconomic to mine by underground or other surface methods, outcrop barriers left adjacent to underground mines, separate benches of the same seam where the parting thickness or quality differences between benches render complete extraction uneconomic, previously augered areas containing otherwise inaccessible additional reserves and close or widely spaced multiple seams. The theory and design methods to assess roof, pillar, and floor stability are presented followed by three case histories. Simple design charts for sizing HWM web and barrier pillars are also presented. A recommended web pillar width may be obtained from the design charts given the overburden depth, the HWM cut width, and the mining height. Given the depth and panel width for a set of HWM cuts, another set of charts gives a suggested barrier pillar width. The case histories, from Northern and Southern Appalachia are used to illustrate the application of rock mechanics to quantify the stability of the highwall, roof, web pillars, and floor. The case histories involve 1) mining through a previously augered highwall, 2) mining under back-stacked spoil and 3) selective mining of closely spaced benches of the same seam. Because each site is unique, the appropriate pre-mining geotechnical analyses range from the calculation of roof, web pillar, and floor bearing capacity stability factors to detailed numerical modeling of the auger and underground mine workings. When operating in the vicinity of existing underground mine or auger workings, the determination of ground deformation and strains resulting from highwall mining is a necessary facet of a ground control investigation.

By M. K. Larson, J. K. Whyatt, R. B. Langston, J. C. Johnson, H. Kirsten, T. M. Brady

An experiment is described in which hollow inclusion cells (HICells) were used to measure stress in a jointed rock mass during drift development at the Stillwater Mine, Nye, MT, USA. Two HICells were installed in the footwall approximately two drift widths ahead of the face. One HICell was over cored and then immediately tested in a biaxial chamber. The other HICell was left in place and monitored as the drift was excavated in three advances, each one-half the width of the drift. Strains were recorded hourly by a datalogger. Results show that there was little stress change during the first and second drift advances, but that a large stress change occurred after the third advance. The measurements also showed that the in situ principal stress directions lined up with regional geologic structures. Stress changes during face advance were likely caused by deformation along localized joint sets and inelastic deformation near the face.

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

Problem: Blasting is a hazardous component of surface mining. Serious injuries and fatalities result from improper judgement or practice during rock blasting. This paper describes several fatal injury case studies, analyzes causative factors, and emphasizes preventive measures. Method: This study examines publications by MSHA, USGS, and other authors. The primary source of information was MSHA’s injury-related publications. Results: During the 21-yearperiod from 1978 to 1998, the mean yearly explosive-related injuries (fatal and nonfatal) for surface coal mines was 8.86 (95% CI: 6.38 -11.33), and for surface metal/nonmetal mines 10.76(95% CI: 8.39 - 13.14). Flyrock and lack of blast area security accounted for 68.2% of these injuries. This paper reviews several case studies of fatal injuries. Case studies indicate that the causative factors for fatal injuries are primarily personal and task-related and to some extent environmental. A reduction in the annual injuries in surface coal mines was observed during the ten-year period of 1989 - 1998 [5.80 (95% CI: 2.71 - 8.89) compared to the previous ten-year period of 1979 - 1988 [10.90 (95% CI: 7.77 - 14.14)]. However, such reduction was not noticed in the metal/nonmetal sector, i.e., 9.30 (95% CI: 6.84 - 11.76) for the period 1989-1998compared with 11.00 (95% CI: 7.11 - 14.89) for the period 1979-1988. Discussion: A multifaceted injury prevention approach consisting of behavioral/educational, administrative/regulatory, and engineering interventions merits consideration. Impact on industry: The mining community, especially the blasters, will find useful information on causative factors and preventive measures to mitigate injuries due to flyrock and lack of blast area security in surface blasting. Discussion of case studies during safety meetings will help to mitigate fatal injuries and derive important payoffs in terms of lower risks and costs of injuries.

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

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By Steven J. Knoll, Theodore J. Williams, Douglas F. Scott

Highly stressed rock in stopes continues to be a primary safety risk for miners in underground mines because it can result in failures of ground that lead to both injuries and death. Spokane Research Laboratory personnel investigated electromagnetic (EM) emissions in a deep underground mine in an effort to determine if these emissions could be used as indicators of impending catastrophic ground failure. Results suggest that (1) there is no increase in the number of EM emissions prior to recorded seismic activity, (2) some EM signals are generated during blasting, (3) interference from mine electrical sources mask seismic-generated EM signals, (4) EM emissions do not give enough warning (compared to seismic monitoring) to permit miners to leave a stope, (5) the distance an EM signal can travel in the rock is between 18 and 40 m, and (6) current data acquisition systems do not differentiate between EM signals generated from seismic activity and random mine electrical noise. These results preclude monitoring EM emissions as precursors of impending catastrophic ground failure.

By F. H. Deist, J. P. E. Morris, E. Georgiadis

For some years the Collieries Research Laboratory of the Chamber of Mines of South Africa has been engaged in the development and application of computer programmes to aid in the solution of rock mechanics problems. It is the purpose of this paper to introduce some of the programmes having general applicability. A system capable of predicting stresses and displacements induced by large-scale tabular excavations is discussed. A finite element programme especially designed for handling layered continuum problems, and which is being used extensively has been supplemented by an automatic mesh generation facility that reduces problem preparation times considerably. Some typical applications of these programmes are described. An entirely new approach, potentially capable of performing linear three-dimensional continuum analysis at practical cost is introduced.

By G. C. Wallick, W. R. Foster, J. G. Savins

Inasmuch as the differentiation and integration methods represent different modes of rheological analyses, a dual scheme of analysis using both methods should lead to a generalized method of data analysis. A dual differentiation-integmtion method of analysis is applied here to the Poiseuille flow of a variety of ideal Generalized Newtonian and viscoplastic models. Using machine-processing techniques, the result is a spectrum of response patterns which are expressed in terms of certain derivative functions. It is shown that these characteristic functions form the basis of a highly-sensitive analytic technique for optimizing the selection of the most appropriate functional relationship between shear rate and shearing stress. INTRODUCTION In the first paper of this series, Savins, Wallick and Foster1 presented an historical review of the salient features of the differentiation method of rheological analysis in Poiseuille flow, and also indicated how the method could be applied to problems involving plane Poiseuille flow. It was shown that the differentiation and integration methods, although basically not incompatible, do represent different modes of rheological analysis. This suggests that valuable background information regarding the probable response characteristics of real data obtained with the differentiation method can be obtained from an integration method-differentiation method analysis of the response of a variety of ideal rheological models. The present paper describes how this dual method of analysis has been applied to suites of idealized models representing a wide variety of Generalized Newtonian and viscoplastic behavior which have received attention at various places in the literature.

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By Robert G. Ditchburn, Albert Zondervan, Akira Usui, Hiroshi Shibasaki, Hajime Hishida, Ian J. Graham

Earlier reconnaissance geological survey and recent mineral exploration by the Geological Survey of Japan (now part of AIST), Metal Mining Agency of Japan (now part of JOGMEC) have revealed that hydrogenetic ferromanganese crusts are widespread over rock outcrops of the floor of the NW Pacific Ocean, south and east of the Japanese Islands, despite vigorous tectonic activity, such as subduction and backarc spreading. Deposition of ferromanganese oxides has occurred since at least the mid-Paleogene over the Philippine Sea Plate region and nearby.

By A. L. Holley

The general usage of engineers, manufacturers, and merchants, is gradually, bat surely, fixing the answer to this question. In every country rails, boiler-plates, and machinery bars, whether hard or soft, are almost universally called steel, when they are made from cast ingots. Other names for the softer steels, such as " homogeneous metal,'' "Bessemer iron," " Martin iron," and the like, have failed to obtain general recognition. The meaning of the term steel, before it was enlarged to cover newly developing varieties, has been traced, by a recent writer, down through Percy, Shakspeare, and the Bible, in a most interesting manner, from an archœological point of view. Undoubtedly, it did characterize hardness arid other qualities imparted by carbon. It is within the memory of most of us, that all steels were tool steels, and that the soft, structural varieties were introduced—varieties which harden but little, which bend cold, and which, in many physical properties, are akin rather to wrought-iron than to tool-steel. But, since both the hard and the soft steels are made by the same processes, and have their great, distinguishing structural feature in common, viz., homogeneity resulting from fluidity, it has come to pass, despite every other proposed nomenclature, that all the compounds of iron which have been cast in malleable masses, are called steel, the term wrought-iron being still confined to malleable iron made from pasty masses, and hence laminated in structure. No inconvenience has been found, so far, in distinguishing between the more or less carburized products, in general, by the terms " highsteel," "low-steel," "tool-steel," etc., and, in particular, by prefixing the percentage of carbon and other ingredients, to the terra steel. Steels which contain distinguishing ingredients other than carbon, are called "chrome-steel," "titanium-steel," and the like, just as variously compounded bronzes are called " phosphor bronze," " aluminium bronze," etc. Thus the combination of several words or symbols, and figures, may completely disclose the characters of the metal, in terms that are subject to no misunderstanding. But inasmuch as several high metallurgical authorities and clever writers have of late proposed to disturb this natural and somewhat settled nomenclature, it seems important to consider the claims of the various classifications. I shall attempt, in this paper, to show

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior