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By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By A. S. Odeh

This paper analyzes the effect of limited entry to flow at the wellbore on the steady-state productivity of a well. Wells that have been opened to flow along a fraction of their productive interval are termed wells with limited entry. Previous work treated the cases of a partially penetrating well, a well producing from the central portion of the productive interval and a well in which several intervals equally spaced were open to flow. In this paper the open interval can be located anywhere within the productive interval. Thus, in a sense, it generalizes previous work. The finite cosine transform was used to arrive at a solution for steady-state flow of a slightly compressible fluid. The solution was programmed for a CDC 1604 computer. Numerical vaIues for rd = 660 ft, r, = 1/4 ft, and range of sand thickness of 20 to 200 ft are presented in graphical form. The effect of rd and r, values on the result is shown in a table. The correct calculation of skin and damage ratio in the presence of limited entry to flow is explained and illustrated by examples. Moreover, the paper shows how to calculate the net decrease in productivity due to the combined effect of limited entry and perforations. INTRODUCTION In some wells only a fraction of the productive interval is open to flow. Location of this fraction is usually dictated by formation characteristics and reservoir behavior. For instance, if a gas cap exists, the open interval is located away from the gas-oil contact to prevent any possible gas coning. Wells that intentionally have been opened to flow along a fraction of their productive formation are tened wells with limited entry. Obviously, unintentional completions of this type also exist. Limited entry to flow decreases well productivity. Magnitude of the loss depends on the fraction of the formation open to flow, on the thickness of the sand, on the location of the open interval and on the ratio of rd /r, where r , is well radius and rd is the drainage radius of the well. The use of pressure buildup data on producing wells to calculate the condition of the formation around the wellbore is an accepted practice. van Everdingenl and Hurst2 introduced the concept of she skin factor s considered to be due to a thin layer of different permeability immediately around the wellbore. These authors dealt with the case of a well of complete radial geometry, i.e., a well with open-hole completion that completely penetrates the formation. The presence of a low-permeability skin results in a loss of productivity, as does limited entry. Therefore, if pressure buildup data obtained on a well with limited entry are used to establish the presence or absence of skin (i.e., formation damage), and a correction is not made for this loss of productivity, the calculations would result in an erroneous skin value. They might indicate the presence of formation damage when in reality there is none, or they might indicate a value larger than the true value. This could lead to an incorrect basis for planning remedial measures. Muskat3 studied the problem of partially penetrating wells for the case of incompressible flow. He presented equations and figures which allow estimation of loss in productivity. Brons and Marting,4 using equations based on Nisle's work,5 studied the loss of productivity for three cases. The first was for a partially penetrating well; the second was for a well producing from only the central portion of a productive interval; and the third was for a well in which several intervals equally spaced were open to flow. Their work was for steady-state depletion-type reservoirs wherein the well radius of drainage is established and the fluid is considered to be slightly compressible. Considered in this paper is the problem of wells with limited entry in which the open intervals are located anywhere within the productive sand. The finite cosine transform is used to arrive at a

Jan 1, 1969

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener's anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,' the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.' THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.' Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969

By David B. Brooks

Identified potential resources of lead and zinc are lower, relative to reserves, than the same ratio for other metals, Either there is little material below present grades or, if it exists, there are no data on it. The author examines both these factors in detail, and also introduces a third possibility. In their 1961 monograph, The Future Supply of the Major Metals, Bruce Netschert and Hans Landsberg noted that identified potential resources (that is, known but submarginal resources) of lead and zinc were much lower relative to reserves (that is, known and supermarginal resources) than was the same ratio for other metals.' Put another way, it seemed that for such metals as iron, manganese, copper, and aluminum, slightly more favorable economic conditions or modest advances in technology would greatly increase reserves by permitting the exploitation of vast quantities of leaner or deeper or otherwise less valuable mineral deposits. But for lead and zinc, Netschert and Landsberg concluded that either: "(1) there is relatively little material below present cutoff grades; [or] (2) such material exists, but for some reason there are no data.'12 This situation, which they called "the lead-zinc anomaly'' has been subsequently discussed by other authors. The purpose of this paper is to carry the discussion further by examining the evidence in favor of (1) and (2) and by advancing a third alternative. There are at least two reasons for devoting time to the lead-zinc anomaly. First, while it is unlikely that we shall have to turn to alternative lead or zinc resources in the near or middle-term future, the longer run resource picture for the two metals is not so certain.3 Both within the United States and for the world as a whole, new discoveries will have to come at a fair pace to keep up with growing rates of consumption. Thus, it is important to see whether there exist lower grade or nonconventional potential sources of two such useful metals that we could turn to at some time in the future. The second reason for studying the lead-zinc anomaly is also related to resource adequacy, but is of more general significance. Depending upon whether the anomaly is technologic, geochemical, spatial, or temporal in origin, we shall be able to draw some conclusions about the resource picture for other metals. Can we expect the apparent pattern of lead-zinc resources to be repeated? If so, will technologic advances in either exploration methods or mineral processing be able to alter the pattern? Or is the pattern unalterably set by geochemical distribution? Most important, are metals characterized by what seems to be an anomaly, different in any way from metals for which low-grade or nonconventional sources already have come to be exploited, as the porphyry deposits have for copper. In sum, investigation of the lead-zinc anomaly represents a case study combining both physical and economic aspects that may open up a neglected area in evaluating mineral resource adequacy. WHAT IS THE LEALLZINC ANOMALY? There are two dimensions to evaluations of the potential of any mineral resource? The first involves the degree of certainty that we ascribe to the estimate: how much do we know about the size of the resource as a result of geological mapping, exploration, and mine development? This dimension is expressed by the terms measured, indicated, and inferred reserves (and, if you wish, 'undiscovered reserves'), all of which terms carry with them the implication of exploitability under current cost-price conditions. The other dimension to evaluations of a mineral resource involves the economic limits of the estimate: how will the size of the resource vary with different (usually more favorable) cost-price conditions? (This economic dimension should be understood broadly to include all factors bearing on the cost-price relationship. In this sense it subsumes technology because any resource is exploitable at some cost; the role of technology is to bring cost down.) The latter dimension is expressed in the terms potential or sub-marginal 'ore,' and is logically quite independent of the former. For example, we have relatively good measurements of the tonnage of manganese in low-grade deposits in this country, though they are too lean to be considered reserves; on the other hand, we are much less certain of our measurements of new lead and zinc deposits in Missouri, though there is no question but that there is a sizable reserve. Thus, it may be uncommon but is not a contradiction to talk of measured submarginal ore or inferred potential ore.

Jan 1, 1968

By W. G. Pfann

In zone-melting, a small molten zone or zones traverse a long charge of alloy or impure metal. Consequences of this manner of freezing are examined with impurerespect to solute distribution in the ingot, with particular reference to purification and to prevention of segregation. Results are expressed in terms of the number, size, and direction of travel of the zones, the initial intermsofsolute distribution, and the distribution coefficient. IF a charge of binary solid-solution alloy is melted and then frozen slowly from one end, as for example in the Bridgman method of making single crystals,' coring usually occurs, with a resulting end-to-end variation in concentration. Such coring, or normal segregation, is undesirable where uniformity is an object. On the other hand, for certain systems, it can be utilized to refine a material by concentrating impurities at one end of the ingot.'. ' In the present paper a different manner of freezing will be examined with respect to the distribution of solute in the ingot. A number of procedures will be indicated which have in common the traversal of a relatively long charge of solid alloy by a small molten zone. Such methods will be denoted by the general term zone-,melting, while the process described in the preceding paragraph will be called normal freezing. It will be shown that, in contrast to normal freezing, zone-melting affords wide latitude in possible distributions of solute. Segregation can either be almost entirely eliminated or it can be enhanced so as to provide a high degree of sttparation of solute and solvent. A number of simplifying assumptions will be invoked which, while not entirely realizable in practice, nevertheless provide a suitable point of departure for more refined treatments. Moreover, our own experience with zone-melting has shown that, for certain systems at least, the analysis holds quite well. The present paper will be confined to a discussion of principles and a general description of procedures. Comparison with experiment is planned for later publication. Normal Freezing Before considering zone-melting, segregation during normal freezing will be reviewed briefly. If a cylinder of molten binary alloy is made to freeze from one end as in Fig. 1, there usually will be a segregating action which will concentrate the solute in one or the other end of the ingot. If the constitutional diagram for the system is like that of Fig. 2, then the distribution coefficient k, defined as the ratio of the concentration in the solid to that in the liquid at equilibrium, will be less than one and the solute will be concentrated in the last regions to freeze. If the solute raises the freezing point, then k will be greater than one and the solute will be concentrated in the first regions to freeze. The concentration in the solid as a function of g, the fraction which has solidified, can be expressed by the relation: C = kC0 (1-g)k-1 [I] where C, is the initial solute concentration in the melt. Eq 1 is based on the following assumptions: 1—Diffusion in the solid is negligible. 2—Diffusion in the liquid is complete (i.e., concentration in the liquid is uniform). 3—k is constant. Concentration curves representing eq 1 for k's from 0.01 to 5.0 are plotted in Fig. 3. This equation, in one form or another, has been treated by Gulliver,³ Scheuer,4 Hayes and Chipman5 for alloys and by McFee2 for NaCl crystals. It is derived in Appendix I. It should be pointed out that the k which is calculated from the phase diagram will be valid only in the ideal case for which the stated assumptions are correct. In all actual cases, the effective k will be larger than this value for solutes which lower the melting point, smaller for solutes which raise the melting point, and will probably vary during the beginning of the freezing process. For simplification it will be assumed that the ideal k is valid. Zone-Leveling Processes The processes of this part are designed to produce a uniform, or level, distribution of solute in the ingot. Single Pass: Consider a rod or charge of alloy whose cross-section is constant and whose composition, C2, is constant, although permissibly varying on a microscopic scale." Such a charge might be a rapidly frozen casting or a mixture of crushed or powdered constituents. Cause a molten zone of

Jan 1, 1953

By J. H. Swisher, E. O. Fuchs

Rate equations were derived to describe the kinetics of internal oxidation of cylinders and spheres. The derived equations for cylinders were checked experimentally by means of sub scale thickness and electrical conductivity measurements on Cu-Cr alloy wires. The properties of the internally oxidized samples were examined with conductivity applications in mind. It was possible to produce uniform dispersions of Cr2O3 in copper with an initial chromium content as high as 3 wt pct. While electrical conductivities only a few pct less than that of OFHC copper were obtained, the Cr2Os particle size and spacing were too large for effective dispersion hardening. T.HE process of internal oxidation has been used widely in basic studies of the permeability of gases in metals. In a review article, Rapp1 has discussed the principles of internal oxidation in considerable detail. From a technological standpoint, internal oxidation is often considered undesirable, since it is a means by which inclusions can be introduced into an otherwise clean material. Another important aspect of internal oxidation is its use as a means of dispersion hardening a material. Broutman and Krock2 discuss this and other methods for making dispersion hardened alloys. The only internally oxidized material known to the authors which is commercially available is a Cu-BeO alloy.3'4 This alloy is made from Cu-Be alloy powder, using a so-called Rhines pack. It has a tensile strength of 80,000 psi and retains its strength at relatively high temperatures. The objectives of the present study were to derive rate equations for the internal oxidation of cylinders and spheres, to check the derived equations for cylinders experimentally, and to examine the structure and properties of internally oxidized Cu-Cr alloys. The Cu-Cr system was chosen for this study because uniform dispersions are obtainable at high alloy contents, which is a desirable characteristic in dispersion hardened materials. RATE EQUATIONS FOR VARIOUS GEOMETRIES A number of authors5--9 have derived equations to describe internal oxidation kinetics. These derivations differ somewhat in mathematical assumptions and approximations, and all except one of the derivations deal exclusively with the internal oxidation of plates. The exception is a brief treatment of cylindrical and spherical geometries given by Meijering and Druy-vesteyn9 as a part of a comprehensive paper on the general subject of internal oxidation. These authors did not obtain rate data to check their derivations, although they did show that the hardness profile across an internally oxidized sample is directly related to the rate of interface movement. For cylindrical and spherical geometries, a quasi-steady-state approximation is needed to circumvent mathematical complications in obtaining a solution to the basic differential equations. In using this approximation, we consider the concentration gradient of dissolved oxygen in the internally oxidized zone or sub-scale to be the same as the gradient which would be present if there were no movement of the subscale interface. The steady-state approximation introduces an error of about 1 pct in computing the rate of internal oxidation of an Fe-1.0 pct Mn alloy plate, if the present method is compared to the more exact method of Wagner.7'10 The details of the derivations of the rate equations for cylinders and spheres are given in the Appendix, and only the results of these derivations are given below. The final equations obtained by Meijering and Druyvesteyn9 can be shown to be equivalent to our Eqs. [1] and [2], although the two approaches are somewhat different. Cylindrical Geometry. [2] where r1 is the outer radius of the cylinder or sphere, cm, r2 is the radius of the unreacted core, cm, see Fig. l(a), D is the diffusion coefficient of oxygen in copper, cm2 per sec, %O is the concentration of dissolved oxygen at the surface of the specimen, wt pct, %Cr is the initial chromium concentration in the alloy, wt pct, and t is the reaction time, sec. Plate Geometry. The analogous rate equation for a plate has been derived previously for internal oxidation of Fe-Al alloys.8'11 For Cu-Cr alloys, we may write the same equation as follows: [3] where r1 is the half-thickness of the plate, cm, and r2 is the distance from the mid-plane to the subscale intherate is An analysis of Eqs. [1], [2], and [3] shows that for a plate the rate is completely parabolic. The initial

Jan 1, 1970

By Jei Y. Choi, P. G. Shewmon

The surfrrce-diffusion coefficients (DJ for Aulg8 on (100) and (111) surfaces of copper have been determined between 1050" and 780°C using a new avuzlysis imd experimental procedure. The results are: D, has also been determined fm cua4 at 870°C, and the values found are 4.5 times larger than those measured by the grain boundary grooving technique for the same surface orientations. This difference is felt to result from the approximate nature of the mathematical solution used in the present work. Attempts to measure D, for silver on copper and silver surfaces indicated a means of matter transport different from surface diffision was dominant in moving tracer from the source out over the surface. Cnlculations and experiment both indicate that this is the flow of silver through the vapor phase which completely masks the much smaller flow due to surface diffusion. The previous self-difhsion studies of D, for silver and copper are discussed in terms of our own analysis and found to yield values of D, factors of lo5 or more greater than those found by the grain boundary grooving tech -nique. UNTIL about 5 years ago it was widely believed that the activation energy for surface diffusion, AH, , was less than that for grain boundary diffusion, AHb,, which in turn was less than that for diffusion through the lattice, AHz.' This was concluded from various evidence that D,> Db>Dl, and one tracer study of D, for silver on silver from which AH, was inferred.2 In 1959 Mullins and Shewmon demonstrated that D, could be determined from the kinetics of the growth of grain-boundary grooves.3 Using this procedure, Gjostein measured D, on copper between 800" and 1050°C and found that the activation energy was roughly equal to AHl .4 Subsequent work on copper,5" silver,',' and goldg between the melting temperature T, and 0.87 T, confirmed that AH, as determined using the grain boundary grooving or scratch-relaxation technique was equal to or greater than AHz. During the same period, Drew and Pye again determined AH, for silver on silver using a tracer techniquelo and a mathematical solution similar to that of Nicker son and arker.' Though the values of D, Drew and Pye measured at any given temperature were about 200 times smaller than those reported by Nickerson and Parker, they again found a low activation energy of about 10 kcal, or about one fifth that found at the higher temperatures with the mass transport technique. A distinguishing characteristic of these two previous tracer studies is that they have worked at low temperatures (-1/2 T,) where they felt volume diffusion was negligible and then analyzed these data as if all tracer atoms leaving the source flowed out into and remained in a homogeneous high-diffusivity surface layer of undefined thickness. This is totally different from the model used in the mass-transport studies or the studies of grain boundary diffusion, which assume the high-diffusivity surface layer to be only a few angstroms thick. If this latter model is applied to the earlier tracer studies, it is shown that the tracer has really pe!etrated into the lattice a mean distance of 1000A. Thus the tracer distribution observed after an anneal is thought to be due to the combined effects of surface and volume diffusion. Independent of the relative validity of the two models, it seems evident to us that any comparison of the values of D, as determined in these two ways is meaningless and misleading, since the values of D, and AH, obtained in these two ways would be totally different for the same physical distributions of tracer. Once the fundamental difference in the approaches of the two techniques is established, we are faced with the question of which model better approximates physical reality. Here all the evidence seems to be on the side of the ''thin surface layer" analysis. In fact, the authors of Refs. 2 and 9 do not argue for the "thick-layer model" we have described; they simply invoke it through the equation they use to calculate D, . The primary evidence for the thin-film approach is: a) grain boundary grooves and scratches widen in proportion to tU4 and Mullins' rigorous analysis shows that this is only valid for a surface layer which is quite thin relative to the width of the groove;11 b) all accepted or seriously discussed models of solid-vapor interfaces and high-angle grain boundaries assume that the disturbed region of the interface is at most a few a0 thick. With the above in mind, it was desirable to determine D, using a radioactive tracer and a "thin-

Jan 1, 1964

By B. L. Landrum, J. Simmons, J. M. Pinson, P. B. Crawford

Patentiometric model data have been obtained to estimate the effect of vertical fractures on the areas swept after breakthrough in water flooding and miscible displacement programs such as gas cycling where the mobility is near one, The data are presented for the case of the fire-spot pattern in which the cemer well is fractured various lengths and orientations, the data indicate that for 10-acre spacing, fractures extetidirrg over 1300 ft in either directior1 from the fractured well may re.srrlt in reductions in sweep efficiencics from 72 to approximately 34 per cent. However. the area swept after break through may be quite largr and only 10 or 12 per cent 1ess than would be obtained if the reservoir were trot fractured. For the specific case when the volume of fluid injected is equivalent to 100 per cent of the pattern vol-unie, the swent area may vary from 80 to 88 per cent, depending on the lenght of the fracture. The former value is that which occurs when the break through or sweep efficiency was orrly 34 per cent and the latter figrrre of 88 per cent is that which is obtained if the reservoir were unfrac-ttm'd. It is pointed out that although the sweep efficiency may he very low in vertically fractured five-spot patterrz.s, the area swept at low water-oil ratios may be only 5 to 10 per cent less than those achieved if the reservoir were unfractured. INTRODUCTION Since the initiation of commercial reservoir fracturing techniques it has been desirable to determine the effect of fractures on the areas swept after breakthrough. Most water flooding or gas cycling projects are continued for substantial periods after the brcakthrough of the injected fluid. Although the sweep efficiency serves as one criterion for rating various flooding patterns. the area swept after breakthrough for various water-oil ratios or percentage wet gas, if cycling. is of perhaps more importance than the sweep efficiency alone. Sweep efficiency data on the vertically fractured five-spot have been presented3. Previous work on the line-drive pattern has shown the effect of vertical fractures on the area swept after breakthrough for the case in which the distance between injection and producing wells divided by the distance between adjacent input wells was equivalent to 1.5 (see lief. 2). The data indicated that for the line-drive pattern it may be desirable to flood or cycle substantially perpendicular to the fractures in order to achieve the greatest recovery for the smallest volume of fluid injected. For this study the center well of a five-spot is assumed as the fractured well. All fractures were assumed to originate at this well and extend into the reservoir for various distances and orientations. All the fractures are straight and are of large permeability compared to the matrix proper. These data are presented to aid the engineer in estimating fractured five-spot pattern performance. ANALOGY The potentiometric model was used in making this study. The model used was 20 20 in. by approximately 1-in. deep. For certain portions of the study one corner of this model was considered to be an injection well and the opposite corner a production well. To simulate vertical fractures a copper sheet was soldered to the wire well and made to conform to the desired length and orientation. In other studies the same model was used except that the four corners of the model might be considered as the corner wells of a five-spot pattern and a fifth well was placed in the center of the model. The well placed in the center of the model was fractured. The total fracture length is L and the well spacing. d. The complimentary fracture angles will be obvious from Figs. 3 and 4. The data obtained on the potentio-metric model assumes the pay to be uniform and homogeneous, the mobility ratio is one, steady-state conditions exist and gravity effects arc neglected. The permeability of the fractures is very great compared to that of the matrix proper. The po-tentiometric model has been used widely both in water flooding and gas cycling projects, and may be used for miscible displacement; how-ever. it is believed that the poten-tiometric model data are more properly applicable to gas cycling than water flooding because the model as-

By R. R. Judd, H. W. Paxton

The rate of dissolution of cementite was studied in three low-carbon materials: a zone-refined Fe-C alloy, an Fe-0.5pct Mn-C alloy, and a commercial low-carbon steel. The materials were spheroidized, ad then held isothermally at temperatures above the Al. The isothermal anneal was interrupted periodically by a water quench and the specimens were analyzed by quantitative metallography for the amount of aus-tenite formed during the anneal. The results of this study were compared with an analytical model for the process, which assumes that carbon diffusion in aus-tenite is the rate-controlling step for the cementite dissolution process. The correlation between the model and the experimental data is excellent for the zone-refined Fe-C alloys; however, the Fe-0.5 pct Mn-C alloys and the commercial steel deviate from the calculated model. This deviation is thought to be a result of manganese segregation between the carbide and the matrix. The rate of nucleation of austenite at carbide interfaces was reduced by the manganese addition and enhanced by the presence of ferrite-ferrite grain boundaries. PREVIOUS investigations of the nucleation and growth of austenite from ferrite-carbide aggregates are not entirely satisfying for at least one of several reasons. The most prevalent of these is a lack of quantitative data. Engineering studies have been run on many steels with little control over important parameters such as composition and initial aggregate structure. The data obtained are valid only for material with identical chemistry and thermal history. A more informative approach to the problem of aus-tenitization would be to determine the mechanism that controls the rate of solution of carbide in austenite and how it is modified by alloying elements. This information could then be used to calculate an austeniti-zation rate for any material, provided its composition and structure are known. The object of the present work is to establish the rate-controlling step for cementite dissolution in Fe-C austenite and to investigate the modification of this rate by small manganese additions. The composition and structure of the material used were carefully controlled and all measurements were designed to allow a quantitative analysis of the kinetic process that controls the austenitization rate. A MODEL FOR DISSOLUTION OF CEMENTITE Cementite dissolution has been analyzed mathematically by a model that approximates the material used in the experiments. This model postulates a regular ar-array of identical cementite spheroids with 4 C( diam, embedded in a grain boundary- free ferrite matrix. The analysis provides a detailed description of the dissolution of one carbide spheroid and a generalization of the solution by summation over all the carbides in the material. The carbides may be isolated by defining identical, space-filling cells of ferrite around them. If the cell dimensions are greater than the diameter of the austenite sphere resulting from complete dissolution of the carbide, and no interaction (through diffusion in ferrite) takes place between cells during the dissolution process, the model need concern only one cell, since the solution in each cell is identical. In the experimental material, the dimensions of the cell, the carbide, and the final austenite sphere are approximately 24, 4, and 8 p, respectively; use of the single cell is therefore justified. The experimental observations are made on the austenite nodules that form around each carbide during the dissolution process. The model concerns the growth of these austenite nodules. The attendant shrinking of the carbide can be obtained from the same analysis by an extension of the calculations. Several a priori assumptions are necessary to make the analysis of the growth problem tractable. They are: 1) carbon diffusion through the austenite nodule is the rate-controlling process; 2) local equilibrium exists at all interfaces, 3) the austenite nucleus that forms on each carbide instantaneously envelops the carbide; 4) during the austenite growth process, the diffusion flux of carbon in ferrite is insignificant; 5) a quasi-steady state exists in the austenite concentration field; that is, at any instant during the dissolution process, the austenite carbon concentration gradient closely approximates that for a steady-state solution; and 6) the effects of capillarity on the dissolution rate of the carbides can be neglected. Referring to Fig. 1, a mass balance at the y-a interface for an infinitesimal boundary movement gives: Where rb is the outer radius of the austenite shell, C1 and C are carbon concentrations at the interface in austenite and ferrite, respectively, see Fig. 2, is the diffusion coefficient of carbon in austenite for the concentration of carbon at the interface, and t is time. The fifth assumption permits the austenite carbon concentration to be approximated by the Laplace solution for the spherical case. Therefore, where C(Y) is the carbon concentration at r, and A and B are constants. Local interfacial equilibrium fixes the boundary conditions for the diffusion problem. They are:

Jan 1, 1969

By R. L. Moment

The anisotropic elastic behavior of rolled beryllium sheet has been measured, using a pulse echo technique, and compared with X-ray diffraction data. Calculated elastic stiffness constants compared favorably with published values for beryllium single crystals which were attributed to the strong (0002) rolling plane texture. Variations of Young's modulus in the yolling plane could be associated with the velative distribution of (0002) planes out of their ideal position in the rollitzg pkule. WHEN a metal is subjected to cold working such as drawing, forming, or rolling, a crystallographic texture develops which can significantly alter its physical properties. One method for detecting this texture is X-ray diffraction, but Alers and Liu' have recently pointed out how the prediction of anisotropic physical properties from pole figures alone is not always accurate due to differences in interpretation. Variations in Young's modulus with orientation or, more completely, the values of the effective elastic constants of the worked metal, also serve to indicate the presence of a texture. In fact, as Alers and Liu' pointed out, calculated variations in Young's modulus for assumed orientations, when compared with experimental data, can be used to eliminate some of the uncertainty in interpretation of X-ray pole figures. Thus, elasticity measurements can serve not only to clarify any unusual elastic behavior of worked metal, but also to detect and in part determine the nature of its texture. X-ray determination of the texture of rolled beryllium has been reported by Smigelskas and Barrett,2 who found a strong texture of (0002) in the rolling plane with (1070) planes normal to the rolling direction. In the case of metal rolled at room temperature, they reported that [1010] directions also appeared at positions 60 and 120 deg from the rolling direction in the rolling plane, while in more recent work Keeler3 found these directions were also tilted towards the rolling plane. The texture for beryllium rolled at 80O0C, however, only showed (1010) planes normal to the rolling direction and the spread of (0002) planes out of the rolling plane was less. In looking for elastic anisotropy one might consider unidirectional rolling of a metal as introducing an or-thorhombic symmetry through reorientation of the grains, since the three deformations, compression, extension in the rolling direction, and extension in the cross direction, are orthogonal to each other and unequal in magnitude. Thus the rolled sheet could be treated like an orthorhombic single crystal and the nine stiffness constants of the elasticity tensor used to calculate the anisotropy of Young's modulus, the shear modulus and Poisson's ratio. In this case we could write: which is symmetric about its diagonal. Borik and Alers4 have recently used this approach on rolled die steel with very good results. They found, however, that instead of displaying orthorhombic elastic symmetry their specimens could be considered tetragonal in which case Cr1 = c22, c13 = Ca, and c44 =cjj. This conclusion was made solely on the basis of the measured tensor elements, and serves to point out the advantage of this method for studying the anisotropy of rolled metals. Their calculated values for Young's modulus as a function of angle in the rolling plane also checked very well with direct measurements made on different specimens using the resonance technique. In the present study, cross-rolled beryllium was used which had been unidirectionally rolled about 11 pct for the final reduction. This imparted a slight anisotropy in the rolling plane which was detected both by X-ray techniques and elasticity measurements. For purposes of discussion in this paper, the rolling direction is that direction in which the most reduction passes were made and cross direction is the normal to the rolling direction in the rolling plane. It was also decided to consider the rolled sheet as displaying orthorhombic symmetry for the purpose of obtaining elasticity samples with the direction defined as in Table I. Any change in the final symmetry attributed to the sheet would then be made on the basis of the measured elastic stiffnesses. The final data would then be compared with that expected from the X-ray study and that reported for beryllium single crystals. EXPERIMENTAL PROCEDURE Rolling Schedule. The samples used in this study were taken from a large sheet which, because of its size, had to be unidirectionally rolled for the final reduction. The resulting texture was that of cross-rolled metal with a slight unidirectional texture superimposed. A cast beryllium ingot, 9.500 in. sq by 3.325 in. thick, was cross-rolled to 81 pct reduction followed by unidirectional rolling for an additional 11 pct to give a total reduction of 92 pct. The thickness of the final sheet ranged from 0.265 to 0.280 in. Reduction up to 67 pct was done at 980°C and the final 25 pct at 870°C. Analysis for metallic impurities showed aluminum 0.06 pct, iron 0.19 pct, and silicon 0.11 pct, giving a beryllium purity of 99.64 pct.

Jan 1, 1968

By B. E. Sundquist

The various methods based on solution models for obtaining free energies of mixing from miscibility-gap data have been applied to a number of binary-alloy systems. For nine of these systems there exist experimental thermodynamic data that permit a comparison of the results to experiment. It was found that the method of van der Toorn and Tiedema almost invariably leads to results that are physically unacceptable and that vary drastically with small changes in the miscibility-gap parameters. The subregular solution model is found in all cases, except the Al-Zn, Fe-Cr, and Cu-Pb systems, to exaggerate the free energy of mixing by 30 pct or more. The model developed by Lumsden is found to give results that are often in excellent agreement with experiment and which exaggerate the free energy of mixing by no more than 30 pct. These results and others give evidence that the Lumsden treatment of the effect of unequal atomic sizes and of imperfect configurational randomness due to deviations of AB bond energies from the mean of AA and BB bond energies is adequate for most systems. ANALYTIC expressions are frequently proposed for the dependence on composition of the activities of the components of a solution. Because the development of solution theory is incomplete, these expressions contain parameters which must be determined by experiment. The measurement of activities is often difficult and consequently such measurements are less readily available than are measurements of phase equilibria which, under certain conditions, can also be used to evaluate these parameters. For example, suppose it is known that two structurally dissimilar phases, each of known composition, in an n-com-ponent system are at equilibrium at a given temperature and pressure. n equations can be set up in terms of these parameters expressing the equality of the chemical potential of each component in the two phases. In addition, one can write the Gibbs-Duhem equation for each phase that also contains these parameters. Thus, if these n + 2 equations contain n + 2 parameters, these parameters can be determined (at the temperature in question) from the phase diagram alone. If the average number of parameters in each expression for the activity of a given component in a given phase is V then there will be 2nV parameters involved. Equating 2nV to n + 2 shows that, for n + 2, V = 1. If the temperature dependence of each parameter were to be expressed in some explicit form one could use equilibrium conditions at a number of temperatures to increase V. The situation is much improved when the two phases in equilibrium are structurally similar. It can then be assumed that, stably or metastably, two phases will become one at higher temperatures. Thus the number of parameters involved becomes nV instead of 2nV. Hence, V = 2 for n = 2 using only one temperature. (It is implied here that the activity expressions used are valid over the entire composition range.) In this investigation only the equilibrium of two structurally similar, two-component phases (miscibility-gap systems) will be considered. The various proposed solution models will be applied to a number of these systems and the results compared with available experimental results. All of the analytic expressions that have been proposed for the free energy of mixing of a two-component system are of the form where ?Gmix is the free energy of mixing per mole of solution, N1 and N2 are the mole fractions of components 1 and 2, respectively, and f(Ni, T) is some function of composition and temperature. In the "ideal" solution model f = 0. In the "regular" solution model f = a constant. Since these two models permit only a symmetric equilibrium diagram they will not be considered further here. The simplest model that permits a nonsymmetric miscibility envelope is the so-called "subregular" solution model proposed by Hardy.1 This model gives where the Ci(T) are functions of temperature only. The same expression for f is obtained from the "linear a function" model proposed by Darken and Gurry2 and applied to miscibility-gap systems by Wriedt.3 This model requires that the a function defined by be a linear function of composition (yi is the activity coefficient of component i). This model is not purely hypothetical for it has been found2 to hold true for a number of systems. It is readily shown3 that the f(Nl, T) obtained from this model is of the form given in Eq. [2]. It will be noted that the subregular solution model contains only two parameters and hence both of them can be determined at any desired temperature below the critical temperature, Tc, for a miscibility-gap systems in the manner described previously. At T, the two constants can be determined by equating the second and third derivatives of ?Cmix with composition to zero. Another two-parameter model was proposed by Lumsden4 who set

Jan 1, 1967

By H. J. Ramey

The wellbore acts as a storage tank during drawdown and build-up testing and causes the sand-face flow rate to approach the constant surface flow rate as a function of time. This effect is compounded if non-Darcy flow (turbulent flow) exists near a gas wellbore. Non-Darcy flow can be interpreted as a flow-rate dependent skin effect. A method for determining the non-Darcy flow constant using this concept and the usual skin effect equation is described. Field tests of this method have identified several cases where non-Darcy flow was severe enough that gas wells in a fractured region appeared to be moderately damaged. The combination of wellbore storage and non-Darcy flow can result in erroneous estimates of formation flow capacity for short-time gas well tests. Fortunately, the presence of the wellbore storage eflect permits a new analysis which can provide a reasonable estimate of formation flow capacity and the non-Darcy flow constant from a single short-time test. The basis of the Gladfelter, Tracy and Wilsey correction for wellbore storage in pressure build-up was investigated. Results led to extension of the method to drawdown testing. If non-Darcy flow is not important, the method can be used to correct short-time gas well drawdown or build-up data. A method for estimation of the duration of wellbore storage effects was developed. INTRODUCTION In 1953, van Everdingen and Hurst generalized results published in their previous paper3 concerning wellbore storage effects to include a "skin effect", or a region of altered permeability adjacent to the wellbore. Later, Gladfelter. Tracy and Wilsey4 presented a method for correcting observed oilwell pressure build-up data for wellbore storage in the presence of a skin effect. The method depended upon measuring the change in the fluid storage in the wellbore by measuring the rise in liquid level. To the author's knowledge, application of the Gladfelter, Tracy and Wilsey storage correction to gas-well build-up has not been discussed in the literature. It is, however, a rather obvious application. Gas storage in the wellbore is a conlpressibility effect and can be estimated easily from the measured wellbore pressure as a function of time. Several approaches to the wellbore storage problem have been suggested. As summarized by Matthews, it is possible to minimize annulus storage volume by using a packer, and to obtain a near sand-face shut-in by use of down-hole tubing plug devices. Matthews and Perrine have suggested criteiia for determining the time when storage effects become negligible. In 1962, Swift and Kiel' presented a method for determination of the effect of non-Darcy flow (often called turbulent flow) upon gas-well behavior. This paper provided a theoretical basis for peculiar gas-well behavior described previously by Smith. Recently, Carter, Miller and Riley observed disagreement among flow capacity k,,h data determined from gas-well drawdown tests conducted at different flow rates for short periods of time (less than six hours flowing time). In the original preprint of their paper, Carter et al. proposed that the discrepancy in flow capacity was possibly a result of wellbore storage effects. Results of an analytical study of unloading of the wellbore and non-Darcy flow were recorded by carter.14 In the final text of their paper, Carter et al.!' stated that they no longer believed wellbore storage was the reason for discrepancy in their kgh estimates. In view of the preceding, this study was performed to establish the importance of non-Darcy flow and well-bore storage for gas-well testing. In the course of the study. a reinspection of the previous work by van Everdingen' and Hurst' was made, and the basis for the Gladfelter, Tracy and Wilsey' wellbore storage correction was investigated and extended to flow testing. WELLBORE STORAGE THEORY As has been shown by Aronofsky and Jenkins,11-12 Matthews," and others, flow of gas can often be approximated by an equivalent liquid flow system. The following developnlent will use liquid flow nomenclature to simplify the presentation. Application to gas-well cases will be illustrated later. First, we will use the van Everdingen-HursP treatment of wellbore storage in transient flow to establish (1) the duration of wellbore storage effects, and (2) a method to correct flow data for wellbore storage. DURATION OF WELLHORE STORAGE EFFECTS When an oil well is opened to flow. the bottom-hole pressure drops and causes a resulting drop in the liquid level in the annulus. If V. represents the annular volume in cu ft/ft of depth, and p represents the average density of the fluid in the wellbore, the volume of fluid at reservoir conditions produced from the annulus per unit bottom-hole pressure drop is approximately: res bbl-- (V, cu ft/ft) (144 sqin./sq ft) psi -(5.615 cu ft/bbl)(pIb/cuft) ........(I)

Jan 1, 1966

Dr. Healy's paper presents a concise state-of-the-art description of mechanistic, thermodynamic models available today for design, interpretation, and trouble-shooting flocculation processes and problems. Coagulation by manipulation of inorganic electrolyte concentrations is controlled largely by adjustment of electrostatic repulsive forces, guided by well understood theory. For simple solids in simple electrolytes, existing models are capable of predicting the influence of potential determining ion and one dominant, non-reacting, symmetrical electrolyte concentration on floc stability quantitatively. Concentration changes required to coagulate and disperse can be estimated. Convenient, easily understood means are available for summarizing the effects of key variables, (e.g., pH, ionic strength) on dispersion stability, and estimating tolerance to unintentional changes (Matijevic coagulation domain diagrams). These models have not been developed to the point that mixed unsymmetrical electrolytes can be easily handled. They are capable of describing two- solid heterocoagulation, but not “n-solid” heterocoagulation. In combination with recently developed computer codes for simultaneous computation of solution equilibria, ion exchange and electrical double layer properties (1,2), these models .should be capable of describing simple clay coagulation systems. This has not been done. Models developed for polymer flocculation are valuable interpretive tools, have some qualitative predictive value, but are less potent in quantitative needs. Most real systems probably involve more than one mechanism of floc stabilization. Little has been done toward developing combined models, even in the simplest systems.

Jan 1, 1979

The sum of $100 was appropriated to the War Minerals Committee for expenses of letter paper, postage, etc. The report of the Treasurer was accepted and ordered filed. Upon the recommendation of the Committee on Membership, sixty-eight Members, two Associate Members, and ten Junior Members were elected. The Secretary presented a letter from the office of the Chief of Ordnance, U. S. A., offering him a commission in the Ordnance Officers' Reserve Corps, and asking him to submit to the governing body of the Institute a request for release from his contract with the Institute, in order that he may accept the commission in question. The following minute was then passed. "The Executive Committee is of the opinion that the Secretary of the American Institute of Mining Engineers can be of more use to the Nation in his present situation, in view of the fact that there is no possible substitute for him in this position, than he could be if he left to accept a commission as an officer in the Ordnance Department, and this Executive Committee requests that an executive officer of the Institute go to Washington and confer with the Chief of Ordnance, requesting a withdrawal of the offer to the Secretary of the Institute and presenting the names of substitutes therefor." The payment of 'a special clerk for the Committee on Increase of Membership at the rate of $100 a month was ordered continued for a further period of six months.

Jan 10, 1917

No greater opportunity for public service has ever been presented to the engineers of the United States, as a class, than the campaign to make thrift a permanent American habit, conducted through the Savings Division off the Treasury Department. The engineer owes a duty to his community, to his country, by reason of the very fact that he is an engineer. By reason of his position and influence, his education and experience, he owes to his country the duty of public service. The public understands that the opportunities of the engineer have allowed him to equip himself to handle logically and properly questions affecting the public. He has been trained to maintain a constructive viewpoint. His work is constructive and he builds for the future. The qualities that the public deems necessary for public service have been bred in him. The time has gone by when the professional man can perform his whole duty to himself and his community by shrouding himself and his calling in mystery and locking himself away from the public in office or laboratory. The duty of public service is calling for every man whose training has fitted him to perform that service. The engineers of the country have demonstrated their capacity and their willingness for public service. Throughout the war period they, have been found in every branch of governmental and. civilian activity which could contribute to national success, doing their share to promote national efficiency. Their duties are not over.

Jan 7, 1919

Engineers and masters of enterprise are waking fast to the realization that there is something more in the relations of employer and employee than mechanical output, which can be measured mathematically, and that the human side of service must receive greater consideration for the future. So much has been said and written on this subject that it has passed into a truism. Should not the same element, long neglected, be considered as of even greater importance than questions of "administration and membership, in the plans of engineering societies? Should mutual service and interest end with mere technical output by members and the rendering of care and management by officers? The world is recognizing, as never before, obligations for service to fellowmen clue from all, high or low, in rank or wealth. Our technical societies, organized for professional protection and advancement, are, insensibly to themselves, almost without conscious intent, widening their field of service to members and dealing heartily with questions broader than technique. Those who are doing such service find unconsciously more and more satisfaction in work so rendered. The growth of knowledge that comes to subaltern engineers or veterans by converse and contact with their fellows, working along and versed in the same subjects, brings interest and friendship. In this way are built some of the warmest friendships of life, coming as incidental and pleasurable result of meetings undertaken for other purposes. Should not the friendly purpose, the desire for service one to another, and es-

Jan 1, 1919

By A. G. Metcalfe, R. P. Elliott, F. A. Crossley

THE texture method (utilizing monochromatic copper radiation) was applied to determine the orientation of the columnar grains of two vacuum cast beryllium ingots of 3 in. diam. Samples were mounted in a fixture as illustrated in Fig. 1, which permitted rotation and translation in order to approximate the method used for wires. The specimens were aligned so that the major axes of the columnar grains were parallel. Rotation was around the growth direction. After each translation the specimen holder was rotated 2 deg (1 deg for the samples from the second ingot) until a range of 30 deg on either side of the vertical was covered. The speed of translation was 1 mm per sec. A representative Debye pattern is shown in Fig. 2. The pattern was compared with theoretical patterns for various orientations. Also shown in Fig. 2 is the disposition of reflections on the (10i0), (0002), and (1011) Debye rings for the two possibilities that growth is either in the <10i0> or <ll30> direction. It is apparent that no significant preference for the direction of columnar growth is indicated. It is considered that the lack of a preferred orientation is due to the occurrence of the phase transformation (reported by Martin and oore&apos; to occur above 1250 "C) which masked the original solidification orientation. This research was supported by the United States Air Force under Contract No. AF 33(616)-5911, monitored by the Materials Central, WADD, Wright-Patterson Air Force Base.

Jan 1, 1962

By Leland O. Erdahi

Many problems have surfaced in our economy during this decade, and the mining industry has certainly had its share: huge capital outlays for environmental controls, volatile markets, double-digit inflation, inadequate capital markets, political uncertainties-plus shortages of energy, manpower, supplies, and equipment. All these and other problems have left their visible marks on the economy of our industry. Solutions are slow in coming; perhaps, in some instances, there are no right answers. However, it appears that many companies are using joint ventures to an increasing extent in efforts to reach partial solutions to some of these problems. A joint venture does present an economic alternative that should be examined-especially when trying to answer questions arising within the current economic context. The dictionary defines "venture" as an undertaking involving chance, risk, or danger. The word was originally applied to hazardous undertakings involving delivery of cargoes to distant ports and subsequent disposition of the merchandise, but it is now applied to any project of limited scope and temporary duration. When two or more entities join in such a project, it becomes a joint venture, and this is the context in which I have used the term. Joint ventures may be formed for exploration, for development of a new ore body, or for expansion of an existing operation. Each requires different approaches for negotiating and drafting the agreement governing the conduct of the joint venture.

Jan 9, 1975

By C. S. Desai

INTRODUCTION Behavior of joints in rock and interfaces in structures and geological media subjected to static and cyclic loading play an important role in analysis and design of structures founded on rock and soil foundations. The objectives of this paper are (1) to describe a device that can permit laboratory testing of joints and interfaces under translational and torsional motions, (2) to present procedures for constitutive modelling of joints and interfaces with a typical example of modelling of a concrete-sand interface, and (3) to give brief details of the proposed research plans for cyclic testing and modelling of joints in concrete as a simulation of joints in rock. The subject of testing and modelling of interfaces and joints is wide in scope, and in view of space limitations, it is not possible to provide a comprehensive review herein. Hence, only a few references, particularly relevant to the ongoing research by the authors and co-workers are included; a review of the subject can be found in (Desai, 1981) and (Heuze and Barbour, 1982). Although there can be (minor) differences in modelling for the behavior of joints and interfaces, the basic procedures can be considered to be essentially similar. Now onwards in this paper, the term joints will be used to imply both joints and interfaces. TESTING DEVICE Appropriate laboratory (or field) testing is an important and indispensable ingredient for constitutive modelling of joints. A new device has been developed for static and cyclic testing of

Jan 1, 1984

"The earth is the Lord&apos;s and the fullness thereof." Science knows no national boundaries, knows no country. These views might be taken as premises for a discussion of the development of the mineral resources of the world. Yet how far man is removed from such broadminded ideals! In this day of jealousy and dread, of political machinations and statesmen&apos;s maneuverings, of rantings and crass ravings against fellow-beings, man&apos;s attitudes towards God&apos;s gifts are but the measure of the smallness of man. That the exploitation of mineral wealth should be for the common good, none will deny, but what is meant by "common"? Is it for the common good of The Pennsylvania State College, Pennsylvania, the United States of America, or the world? If man is big enough and honest enough to state categorically that by "common," as used in the context above, is meant that the utilization of the mineral wealth should be for the mutual benefit of all mankind, and that all concerned strive to see that such a viewpoint is executed, then there is brighter hope for the future. It is to be hoped that the world may have at least a few years or possibly a generation of peace. What can be done in these years to work towards the ultimate goal of human improvement? The work of statesmen in the drafting of international agreements and the easing of small frictions which appear between nations, as they

Jan 1, 1950