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By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The room-temperature Knoop hardness of single -crystal titanium diboride has been determined. Variations in microhardness have been correlated with orientation and structural imperfections in the crystals. Maximum differences in hardness values of 750 kg per sq mm with respect to orientation and 450 kg per sq mm with respect to substructure were found. The effects of etchants, load on indenter, and degvee of cracking of indentation were studied. The average hardness was determined as 2800 kg per sq mm on the as-grown crystals. Annealing increased the average hardness to 3375 kg per sq mm. ThE microhardness of polycrystalline titanium diboride approximating the stoichiometric composition TiB, has been studied by several investigators. The values for the Knoop hardness number range from 2710 kg per sq mm (Khn = 2710 kg per sq mm) to 3400 kg per sq mm.'-4 Samsonov et al.' reported a Vickers hardness number of 3400 kg per sq mm (Vhn = 3400 kg per sq mm) at 120-g loads for a 98 pct Ti + B material of 96 pct theoretical density. Recently Dunegan measured the Vickers hardness and obtained 2060 kg per sq mm with a 10-g load (Vhnlo = 2060 kg per sq mm), 1425 kg per sq mm for Vhnloo, and 1320 kg per sq mm for Vhnlooo. We have obtained a Khnloo = 3000 * 350 kg per sq mm for hot-pressed polycrystalline TiB2 that was 99.1 pct Ti + B and 96.6 pct of theoretical density. The present investigation has been made on single-crystal titanium diboride boules, and is believed to be the first such study on TiB, crystals of known orientation. EXPERIMENTAL The single crystals were prepared by a Verneuil-type process using an electric arc by the Linde Division of Union Carbide Corp. The largest specimens were 6 mm in diameter by 12 mm long. The crystals were of theoretical density (4.50 g per cm3) with a Ti + B content of 99.8 pct. The major impurities present were: 0.03 pct (by weight) 0, 0.06 pct C, 0.01 pct Si, 0.05 pct Fe, 0.01 pct Cr, and 0.01 pct Ni. The crystals were boron-rich, the average boron content being 31.S7 wt pct (stoichiometric value is 31.12 wt pct), and titanium-poor, the average titanium content being 68.2 wt pct (stoichiometric value is 68.88 wt pct). Titanium was determined gravimetrically by cupferron precipitation and boron by titration of H3B03 from a NaOH-fused specimen after removal of titanium with BaC03. The outer edge of the boule accounted for some of the excess boron. An electron-microprobe analysis showed that the titanium content increased from 60.0 wt pct at the edge to 68.5 wt pct at D, ~ 1000 p, where D, = distance from outer edge (see Fig. 5). X-ray measurements indicate that the boules are single crystals with considerable substructure. Upon etching this structure is seen in the form of a Widmanstatten-type rhombohedral line pattern in the basal (c) plane and a parallel "lines" pattern in the prism (a) planes. A typical WidmanstHtten-type pattern is seen in in Fig. 1. Electron microscopy reveals that the lines are less than 1 p across, which does not allow direct electron probe or microfocus X-ray determination of their composition. The identity of the second phase has not been established. It might be a higher boride or a nonstoichiometric TiB2. On annealing above 2200°C the precipitate is dispersed and dissolves in the matrix. The best etchants found were HF/HNO/HO, KF(CN)$NOH/HO (Murakami's Etch), and A large number of other etchants were previously Studied. The acidic etchant produced an acicular or "needles" pattern in the (a) planes which is an etchant effect on the "lines" pattern.

Jan 1, 1965

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby', it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes' which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,' the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young's modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By J. M. Roberts, N. Brown

The stress-strain behavior of zinc single crystals was measured over a strain range of 10-6 to 10-2. The phenomenon of macroyielding was observed in detail and plastic strains were detected at almost zero-stress. Closed hysteresis loops were observed during loading and unloading in the strain region of about 10-5. From the hysteresis a frictional stress on the dislocation of about 6 psi was obtained. A preliminary analysis indicates that impurities are primarily responsible for the friction. Nonelastic Strains as much as 10 -4 were recovered depending on the amount of prior deformation. Part of the recovered strain occurs instantaneously upon unloading and the remainder occurs at zero stress. The time dependence of the recovered strain was measured. THIS investigation is concerned with the details of plastic deformation preceding the ordinary yield point as measured with the usual strain sensitivity of about 10-4. The approach leads to internal friction observations in the hitherto neglected frequency range below 10-1 cycles per sec. It is believed that if the phenomenon of macroscopic yielding is to be understood, then the stress-strain curve in the neighborhood of the macroyield point should be greatly magnified. It may then be possible to determine whether macroscopic yielding is a unique event or whether it is a process which begins gradually at a lower stress. In the case of low-carbon steel a unique event obviously occurs at the macroscopic yield point as indicated by a drop in the load, but copper appears to exhibit a gradual transition from the elastic to the plastic state. In zinc the yield point is rather abrupt although the data indicates that some plastic deformation precedes large scale yielding.' One of the purposes of this investigation is to determine whether there is an abrupt transition from the preyield microstrain region to the region of macroscopic deformation. Such a rapid transition would support the concept that there is a critical stress for yielding. The concept that yielding is a unique event associated with such phenomenon as activating a Frank-Read source, freeing the dislocation from solute atoms, dislocations cutting through dislocations, or dislocations moving freely by one another, has been expounded widely on theoretical grounds. It is hoped that highly sensitive measurements of strain in the neighborhood of the macroscopic yield point will shed some light on the event known as the "Yield Point". EXPERIMENTAL METHOD 1) Specimens—High-purity zinc was cast into spherical graphite moulds in air and grown into spherical single crystals by the Bridgman method under a positive pressure of Argon gas. Spectro-graphic analysis of cleaved sections from four crystals showed a purity of 99.994 pet Zn. The specimens were acid machined with an 1/8 in. gage section in a form similar to those used by Parker and co-workers.2 Bausch type grips were fastened to the specimen by Epon VI adhesive. The specimens were oriented so that only [1120] (0001) slip occurred. Fig. 1 shows two of the specimens in the grips. Prior to each test, the gage section of the specimen was given a concentrated HNO3 chemical polish followed by alcohol rinsing and air blast drying. 2) Test Method- The shear tests were performed on an Instron testing machine and the experimental set-up was made very "hard". Strain could be measured to a sensitivity of 10 -6 by means of a capacitance gage extensometer. The design and calibration of this type of extensometer to measure microstrain, as applied to pure shear and tensile tests of metals, will be the subject of a separate paper—therefore, only a brief account will be presented here. The method essentially consists of attaching a

Jan 1, 1961

By M. L. Hammond, G. M. Bowers

Silicon dioxide films have been prepared on silicon wafers by the oxidation of SiH, near 400°C. Results previously reported by Goldsmith and Kern7 have been qualitatively corrobovated using a system of different geometry, and significantly greater deposition rates have been achieved. The deposition rate is independent of thickness and nearly independent of the O2/SiH, ratio over a wide range; however, the rate is strongly temperature-dependent. The structure of the deposit depends upon the cleanliness of the substrate, and the electrical field strength of the deposited oxide depends upon the nature of the electrodes. MULTILEVEL interconnects in integrated circuits using aluminum metallization require an insulator that can be deposited at low temperature. Because the A1-Si eutectic is only 577°C, the maximum deposition temperature must be below about 500°C to prevent reaction of the aluminum with the silicon and with other materials in the integrated circuit. Many methods of depositing insulating films of SiO, and other dielectrics have been reported'-6 but the technique described by Goldsmith and Kern7 offers the simplest method of preparing SiO, films. The technique involves the reaction of SiH, and 0, to form SiO, films in the 300" to 500°C temperature range. Previous work using this gas system has been reported8 and the initial development work at Philco Microelectronics was done at the East Coast R&D Laboratories. 9 This paper corroborates some of the results of Goldsmith and Kern,7 shows that much higher deposition rates can be obtained than previously reported, and presents some observations on the structure of deposited SiO, films. EXPERIMENTAL CONDITIONS Fig. 1 is a schematic drawing of the apparatus used in this study. It differs from that of Goldsmith and Kern in that 1) the gases are mixed before they enter the reaction chamber, 2) there is no fritted glass diffuser, and 3) the wafers are stationary during deposition. The control thermocouple was in a well located 0.06-in. from the substrate, and three gas supplies were used: 1 pct SiH4 in N 2, O 2, and N 2. Water vapor must be excluded from the plumbing to prevent the formation of colloidal SiO, and the SiH4 must be diluted with an inert gas because SiH4-0, mixtures are extremely flammable above about 4 pct SiH The wafer temperature was determined by attaching a thermocouple to a test wafer and the temperature was maintained to +5 C. The conditions used in this investigation are listed in Table I. The temperature range was chosen for compatibility with the A1-Si system. The volume ratio of 0, to SiH4 is the actual volume of 0, delivered to that of SiH4, taking into account the initial dilution of the SiH4. This ratio, which was used by Goldsmith and Kern,7 is a useful indicator of the experimental conditions. The active/inactive ratio is the ratio of the volume of active gases, SiH4 and O2, delivered to the volume of dilution gas. The active/inactive ratio is an important parameter to specify for deposition rate determinations since it determines the amounts of reactants that arrive at the sample per unit time. Fairly high dilution ratios were necessary to achieve uniform deposits of SiO,. Most of the process characterizations were performed on the polished (111) face of 3 to 5 ohm-cm, n-type silicon wafers which were 0.009 in. thick; but the data approximately apply to deposition of SiO, on thin films of aluminum. It is difficult to obtain accurate deposition rate data over aluminum films because of coarsening the aluminum surface during exposure to 300" to 400°C. The deposited SiO, film fol-

Jan 1, 1969

By J. M. Dumore

If in a vertical, downward miscible displacement, the transition zone between the displacing and displaced fluids is neglected, a criterion for stable displacement can be obtained by considering a small hypothetical protrusion of one of the fluids into the other. This criterion leads to the definition of the well-known critical rate, uc = kg p/p. The consideration is further extended by taking into account the transition zone that develops as a result of diffusion and mixing. A generalization of the previous criterion leads to the definition of another characteristic rate, the stable rate, which in actual miscible drives will be less than the critical rate. In such drives, the entire transition zone is stable at rates less than the stable rate. At rates between the stable and critical rates, the displacement is only partly stable, i.e. part of the transition zone adjacent to the displaced fluid is in an unstable position. From that part of the transition zone viscous lingers will develop. At rates greater than the critical rate the entire displacement is unstable and viscous lingers will develop more strongly. Results of laboratory experiments are in agreement with the expected behavior based on the theoretically deduced stability of the displacement. INTRODUCTION The simplest form of miscible drive in an oil-bearing formation is the injection of a fluid that is completely miscible* with the oil under reservoir conditions. In general, such a fluid, a solvent for example, is less dense and less viscous than the oil present in the formation. If it is injected into a horizontal homogeneous layer, gravitational forces will lead to the formation of a gravity tongue of solvent in the upper part of the layer and the adverse solvent-oil viscosity ratio will cause viscous fingers to develop. If, however, the solvent is injected up-structure into ,a dipping layer, gravity has a favorable effect, because it tends to keep the less dense solvent up-structure. Tongue formation and viscous fingering are consequently reduced and it is even possible that they will be suppressed completely. Viscous fingering and gravity tonguing are the consequences of the instability of the displacement. A stable displacement cannot result in growing viscous fingers and/or growing gravity tongues. Since large amounts of oil can be bypassed if there is viscous fingering and/or gravity tonguing, the stability of a miscible drive is very important with respect to the recovery efficiency of the drive. The stability is of particular importance in miscible-slug drives, as it determines how quickly the miscible slug between the displaced and displacing fluids will be distorted and broken up, after which the drive is no longer completely miscible. Stability is thus a most important factor in determining the success of a miscible drive, and it is considered that the aspects of stability considered in this paper will make a useful contribution to existing theories. Consideration is given only to vertical downward displacements, in which no gravity tongues can develop and which are therefore simpler than downward displacements in sloping layers. THEORY CRITERION FOR STABLE DISPLACEMENT Let us consider a vertical column of a homogeneous permeable medium saturated with oil. A solvent less dense and less viscous than the oil is injected at the top of the column at a constant rate; in the column the velocities of oil and solvent are assumed to be uniform. Diffusion and mixing of oil and solvent will at first be neglected, i.e. we assume that solvent and oil are divided by a sharp interface. An additional assumption is that the interface is horizontal. Continuity of pressures exists at the interface, because no capillary forces are present between the two miscible fluids. Consequently, at the interface (Z = I)):** Ps = Po - P-where Ps is the pressure at the solvent side and

Jan 1, 1965

By H. D. Outmans

In steady vertical flow, the interface of an immiscible liquid-liquid displacement is horizontal for any flow rate below the critical. In nonvertical flow, however, the shape of the interface in the steady state does depend on the flow rate, and the purpose of this paper is to calculate the unsteady interfaces during the transition of one steady state of flow to another. A knowledge of these transient interfaces is of considerable importance in reservoir engineering where the calculation of breakthrough recovery depends on the instant the interface reaches the producing wells and on the shape of the interface at that time. Although the emphasis is put on transient interlaces, which eventually approach stable equilibrium, it is shown that if the displacement exceeds a critical rate no equilibrium is possible. The interface is then unstable and viscous fingers are formed during the displacement. The critical rate and the shape of the transient and equilibrium interfaces are affected by the effective interfacial tension; but since this effective interfacial tension appears in the calculations only in combination with the inverse square of the thickness of the medium, its effect in the reservoir would appear to be negligible compared to its significance in model experiments. INTRODUCTION Stability criteria and the early growth of interfacial disturbances in a plane parallel to the boundaries of a dipping formation in which oil is displaced by an incompressible fluid were described in a previous paper.l This type of instability is significant in thin reservoirs. However, if the reservoir has appreciable thickness, then interfacial stability in vertical planes, normal to the upper and lower boundaries, also becomes important (the displacement is supposed to be parallel to these vertical planes). The difference between the two stability problems is that, in the first case, the intersections of the interface with planes parallel to the boundaries are normal to the direction of the displacement; in the second case, the intersections, this time with vertical planes, are not normal to the displacement. Instead, they are tilted at an angle which depends on the displacement rate. The tilt of steady interfaces was calculated by Dietz2 who also determined the critical rate of displacement for stability in the vertical plane by assuming that this rate would coincide with an interfacial tilt equal to the dip of the formation. The critical rate thus calculated is the same as has been found for thin reservoirs (see Eq. 1.1 of Ref. 1 and of the present paper). Dietz's calculation of the stable tilt was verified by laboratory experiments and the agreement was found to be fairly good.3 It is doubtful, however, that stable tilts actually exist in the reservoir because a change in production rate is not followed by an instantaneous adjustment of the interface to the new rate but, rather, by a transition period during which the interface changes from one equilibrium tilt to the other. The principal objective of this paper has been to describe these transient interfaces without putting any restrictions on the flow conditions or the shape of the interface, as had been done previously. The second objective was to compute the critical velocity, taking into account capillary effects, and the third was to evaluate, at least qualitatively, the shape of the front at rates above the critical, again without making the simplifying assumptions introduced by previous investigators.2,3 In the following sections two examples are given of the calculation of interfacial motion. The first describes this motion for an initially horizontal interface in a dipping layer, and the second for a vertical interface in a horizontal layer. The mathematical formulation of the problem is nonlinear in the boundary conditions, and this prohibits its solution in closed form. Instead, the solution is obtained in the form of higher-order approximations. 1 Before proceeding to a description of the mathematical model, however, we define two quantities

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

By C. Chu

A theoretical investigation has been made of the forward combustion process using a one-dimensional linear mathematical model, taking into consideration the effect of the vaporization-condensation which occurs on the leading edge of the heat wave. This work involves the solution of five coupled partial differential equations. Besides the vaporization-condensation phenomenon, these equations account for conduction, convection, combustion, heat loss, diffusion and bulk fluid flow. For the one-dimensional linear model studied, the vaporization-condensation phenomenon does not induce appreciable change in the temperature at the combustion front; and its primary effect is to create a steam plateau and to increase the length of the heated zone ahead of the combustion front. This effect becomes more pronounced at lower pressures, higher porosities or reduced gas saturations. The peak temperature and the temperature profile on the leading edge of the heat wave stabilize after a certain period. The length of the steam bank remains practically constant, although the length of the water bank increases as the heat wave advances. INTRODUCTION The existence of the vaporization-condensation phenomenon in the heat-wave process and the important role played by the phenomenon have been recognized by several investigators. Kuhn and Kochl stated that steam plateaus were frequently observed on the temperature records of their experiments. The steam plateaus were attributed primarily to the vaporization and subsequent condensation of the interstitial water existing in the oil sand. Szasz2 suggested that both lighter hydrocarbons and water are vaporized on the leading edge of the heat wave, carried forward in the gas stream, and then condensed to create banks of oil and water. Martin et al suggested that the vaporization-condensation phenomenon is one of the main mechanisms of the heat-wave process, along with thermal expansion and viscosity reduction. Wilson et al. reported the existence of a steam plateau several inches in length in their small-scale tube-run experiments. However, this important phenomenon has never been taken into consideration in the numerous theoretical analyses by various authors. 5 The purpose of this work was to study the thermal aspects of a linear heat wave, taking into consideration the vaporization-condensation on the leading edge of the wave, to determine the effect of this phenomenon on the temperature profile of the reservoir, and to investigate how this effect varies when other process variables are changed. THEORY We consider a reservoir of porous medium of cross-sectional area A, extending from x = 0 to x = L. This reservoir contains, aside from the solid matrix itself, a gas phase and a "combined liquid phase" which is a combination of two immiscible liquid phases — namely, an oil phase and a water phase. The oil present in the reservoir is assumed to consist of three fractions, a noncondensable gas, a nondistillable residuum, and a vaporizable oil fraction which may be present in both the gas phase and liquid phase. Before the heat-wave process begins, preheating has taken place and has imparted an initial temperature distribution T,(x) to the reservoir. At the start of the process, a stream of oxygen-bearing gas is introduced through the face at x = 0. This gas supports the combustion of the residual fuel and supplies the heat throughout the process. In order to develop a tractable system of equations, the model properties are postulated as follows: (1) the system is isotropic and homogeneous; (2) there is a uniform fuel content throughout the reservoir; (3) combustion takes place in a moving vertical planar region of infinitesimal thickness; (4) the temperatures of the fluids and the solid matrix are identical; (5) radiation is negligible; (6) the gas and liquid saturations are uniform throughout the reservoir and remain unchanged

Jan 1, 1965

By R. A. Morse, C. R. Holmgren

The production of oil by water flooding can be substantially increased by the maintenance of free gas saturation in the reservoir during the flooding operation. This effect is accomplished by the alteration of oil relative permeability characteristics and the occupation by gas of pore space that would otherwise be filled with residual oil. The amount of reduction In residual oil can be calculated from appropriate water-oil relative permeability characteristics. This paper presents experimental data in support of the foregoing conclusions and an example of the calculations. The microscopic pore saturation concepts of the mechanism are discussed. A method of practical application to field floods is presented together with discussion of certain limitations. INTRODUCTION The presence of free gas has been reported by a number of investigators to significantly affect the oil recovery which can be obtained from sandstone flow systems by water flooding.1,2,3,4,5 The effect of gas, noted in every instance, has been to cause lower residual oil saturations than could be obtained by water flooding the same systems in the absence of free gas. The degree of improvement in recovery has been observed to vary widely, depending on the systems used and the conditions of the tests. The increased oil recovery obtained because of the presence of gas during a water flood has been variously attributed to changes in physical characteristics of the oil, selective plugging action of the gas, inclusion of oil mist in the free gas phase, and the additional sweeping or driving action of the free gas. All but the first of these suggestions imply changes in the displacement mechanism. The change in viscosity and inter-facial tension of the oil phase, within the pressure range used for all the experimental work, is certainly not sufficient to account for the differences in residual oil saturation noted dess there is a drastic change in the displacement process. One other effect which logically seems capable of causing differences in residual oil saturation of the magnitude noted in the experimental work is that of simple replacement. In a water-wet system containing oil, water, and gas, it is to be expected that the gas will exist inside the oil. This is the position of minimum free surface energy, since the gas-oil interfacial tension will be less than the gas-water interfacial tension. There is no apparent reason to expect that the existence of free gas within the oil phase should alter the saturation at which the non-wetting phase (now oil and gas) should become discontinuous and hence trapped so as to be unrecoverable by direct displacement by water. If this is the situation, then trapping of a certain percentage of gas saturation during water flood should result, at infinite water-oil ratio, in a like reduction of oil saturation below that attainable by flooding in the absence of free gas. It is visualized that the gas will exist as bubbles inside the discontinuous residual oil as illustrated in Fig. 1, with the size of the oil bubbles being substantially unchanged due to the presence of the gas. As a practical matter, it can be anticipated that the presence of a free gas saturation inside the oil phase will reduce the relative permeability to oil which will exist at any particular water saturation. This reduction will be caused by two factors — -the addition of the gas-oil interface, and the reduction of area available for oil flow in the pores containing gas. This reduction in oil permeability at any particular water saturation will result in water breakthrough at a lower water satu-

Jan 1, 1951

By A. D. Mutch

IT has long been known that there are wide variations in the thermo-electric potential of pyrite. In the last few years a study of this variation and other properties of pyrite was carried out at the University of Toronto by F. G. Smith on specimens of pyrite from many loyalities. As a result of these studies the pyrite geothermometer was developed by Professor Smith. The calibration of the pyrite geothermometer is based on the assumption that "crystals of any one electronically conducting mineral species deposited at a high temperature have a more positive thermoelectric potential than crystals deposited at a low temperature, and the thermo-electric potential varies continuously between any given limits of the temperature of deposition." The cause of the variation was postulated to be crystal discontinuities, such as lineage boundaries. As yet this postulated relationship has not been established as fact. On theoretical grounds it is indicated that the thermo-electric potential of pyrite or any other partial conductor is dependent upon a number of factors as well as the temperature of formation. For this and other reasons there is ground for doubt as to the validity of the relationship postulated above. To date a large number of readings have been made with the pyrite geothermometer which have been recorded in terms of the calibration of the instrument in degrees centigrade. So far most of the pyrite tested by this technique has been in association with gold ore. The values for the temperature of formation obtained in these tests appear to be reasonable and, in relation to geological problems, to vary in the right sense. Determinations on some specimens not in association with gold ore have given readings that appear to be much too high, taking into account the probable maximum temperature of the host rock. To sum up, although many determinations made with the pyrite geothermometer appear to give reasonable values for the temperature of formation of the pyrite, there are at the same time other readings which seem anomalous. On the basis of an examination of available results of work with the pyrite geothermometer, two problems must be considered: 1—the validity of the calibration of the pyrite geothermometer; and 2— the nature of the distribution of the thermo-electric potentials of pyrite in relation to the specific problems that have been examined. In this paper the academic problem relating to the validity of the calibration of the pyrite geothermometer will not be discussed. Instead, the variations of thermo-electric potential of pyrite in association with gold veins will be discussed with regard to specific examinations. The first of these two examinations deals with the distribution of thermo-electric potentials of pyrite in association with a gold vein and was carried out in the McIntyre Porcupine Mine, Schumacher, Ont., in the summer of 1949 as part of a study with this technique. The second problem deals with variations of thermo-electric potential of pyrite in gold ore specimens from all over the world. The specimens used in this study were part of the private collection of Frank Ebbutt, geologist for Howe Sound Exploration Co. Results of Detailed and Reconnaissance Studies In discussion of the results of determinations made in these two studies the values of thermo-electric potential in millivolts will be used. It will be noted that in some of the diagrams the determinations are recorded in terms of pyrite geothermometer temperatures. Fig. 1 is a calibration chart relating pyrite geothermometer temperatures and thermoelectric potentials. A full discussion of the technique is given in the original paper by F. G. Smith.' Briefly, the determinations are made by placing two stainless steel probes, one hot and the other cold, against the surface of the pyrite crystal being tested. The thermoelectric potential that is developed is read with a null-point potentiometer that is calibrated in what

Jan 1, 1953

By A. E. Deruyttere, J. Van der Planken, M. Laurent, Van den Bergen

FahRENHORST and schmid1 observed that zinc single crystals work hardened less rapidly when strained in liquid air (- 185°C)than in a bath at -82°C, whereas at higher temperatures the rate of work hardening decreased with increasing temperature, as would be expected. Cadmium and magnesium showed no such decrease at -185°C. At that time the observed anomaly for zinc at liquid air temperature probably seemed insignificant. However it later was confirmed2 by experiments in liquid nitrogen (-196°C) and in the mixture solid carbon dioxide-acetone (-77"C) and therefore appeared to be real. seeger3 then suggested that the anomaly might be due to the different wetting of the zinc crystals by the cooling media. Recently a new confirmation was obtained,4 however the cooling media again were different: the rate of strain hardening was found to be lower in liquid nitrogen and liquid oxygen than in pentane cooled to various temperatures down to -126°C. Ekperiments will now be reported in which the medium surrounding the specimen at the different temperatures was the same, namely gaseous air. The single crystals were made from "Overcor 99.99" zinc. They were grown in a vertical traveling furnace on seeds of nearly the same orientations. The diameter of the crystals was 5 mm and the length between shoulders 140 mm. The brass shoulders were stuck to the crystals by means of araldite. A thin steel wire was fixed to each shoulder and served to fasten the specimen to a Houns-field tensile testing machine. The crystals with the shoulders and part of the wires were surrounded by two concentric cylindrical containers. The coolant. either liquid air or ground solid carbon dioxide, was poured into the outer container only. During cooling the containers rested on a support which was removed when the straining was started. In order to check the temperature which the crystals would attain inside the inner container, a hollow bar of zinc in which a thermocouple was fitted was first mounted in the apparatus as a substitute for a crystal. It appeared that a constant temperature, respectively - 183° and -72°C, was attained inside the bar, if a soaking time of the order of 1 hr was allowed and if the outer container was constantly kept filled. Accordingly, this procedure was adopted for every tensile test. To take account of the large scatter, fourteen tensile tests were performed with liquid air and seven with solid carbon dioxide. The orientation of the crystals and the results are presented in the table, in which the symbols have the following meaning: 1 : temperature x : initial angle between basal plane and specimen axis : initial angle between slip direction and specimen axis a : shear strain at fracture 0: average rate of strain hardening = —-——- 100 t0 and Te representing respectively the critical shear stress and the shear stress at fracture. Despite the scatter of the a- and 8— values which is of the same order of magnitude as in the work reported by Seeger and Trzuble,4 it is evident that the strain hardening rate is significantly lower at -183°C thanat-72°C. The table also contains the average values calculated from Seeger and Trauble's results at the corresponding temperatures: z.e., four results at -183oC and two at-70°, -71°C. These authors calculated 9 in a slightly different way, but this is unimportant. The agreement between the a-values shows that both sets of experiments are comparable despite the differences in experimental techniques. The rates of strain hardening also agree and it may therefore be concluded that the anomaly is not

Jan 1, 1962

By David E. Jones, Dean K. Hunt, C. Y. Chen

INTRODUCTION Of all the numerous geological hazards that threaten the well-being of urban areas in the United States, probably none is so widespread, persistent, and diversified as surface subsidence (HRB-Singer, Inc., 1977). Simply defined, subsidence is the vertical displacement or sinking of the ground surface caused by either natural phenomena or man's activities. The downward movement, however, can be accompanied by horizontal movement, strain, tilt and even by a locally upward movement. Damage to structures and the environment can result from any of these movements. Extracting subsurface materials, fluids and solids, accounts for most man-induced subsidence in the United States. Among all the mining-related subsidences, the collapse of voids created by underground coal mining has been the major cause in inflicting surface damage (Comptroller General of the United States, 1979). Subsidence from coal mining may occur within a few weeks or be delayed for years, depending upon the mineral layer's depth below the surface, the overlying rock strata's characteristics, the extent and methods of mining that were employed, and the time deterioration of pillar and mine structure. Unless underground resources are not mined or control measures are implemented to prevent or minimize damage, some degree of surface subsidence and its accompanied deleterious effects are often inevitable. The ways to control the subsidence and minimize surface damage may include: 1. Precautionary measures built into new structures or surface features. 2. Preventive works applied to existing structures or surface features. 3. Mine design incorporating special underground layouts. 4. Any combination of the above measures. Upon the enactment of Public Law 95-87, the Secretary of the Interior, through the recently created Office of Surface Mining (OSM), was authorized to promulgate rules to regulate mining reclamation including subsidence control. Proposed on September 18, 1978, these rules were finalized, following public comment and hearings, on March 13, 1979, as part of the permanent regulatory program for the regulation of surface mining and reclamation operations which include the surface effects of underground mining. On January 28, 1981, Secretary Watt of the Department of the Interior issued an order to re- quire all agencies to identify with recommendations all regulations which are believed to be excessive, burdensome or counterproductive. Also on February 17, 1981. President Reagan issued Executive Order No. 12291 requiring all Federal agencies to conduct a regulatory review to make a determination that each promulgation of a regulation is clearly within the authority delegated by law and consistent with Congressional intent (Federal Register, 1981). As a result, OSM initiated the regulatory reform to revise the permanent regulatory program. Following a brief discussion of the technical aspects and the effects of subsidence on man and his environment, this paper presents a historical overview of how rules and regulations are used to govern the subsidence related problems. The development of the regulation of subsidence under Public Law 95-87, the Surface Mining Control and Reclamation Act of 1977 (SMCRA or the Act) are also discussed, including the new regulations being developed under the regulatory reform program. SOME TECHNICAL ASPECTS Am EFFECTS OF FINE SUBSIDENCE An extensive historical review of mining subsidence is given by Zwartendyk (1971) and Shadbolt (1978). Comprehensive technical presentations have been given by Henry (1956), King and Whetton (1957), Hall and Orchard (1963). Muller, et al. (1968). Grard (1969), Voight and Pariseau (1970). Kapp and Williams (1972), Cummins and Given (1973), Brauner (1973) , and NCB (1975). A theory of surface subsidence due to underground mining was perhaps first fundamentally stated by a French engineer, Toillez, in 1838, and formulated by a Belgian engineer, Gonot, in 1839 (Goldreich, 1913, cited by Zwartendyk, 1971). Since that time,

Jan 1, 1982

By Louis A. Rosales, Kanji Ono

The anomalous behavior of hydrogen in iron is examined and a new model is proposed It is postulated that hydrogen single and di-interstitials are in equilibrium with each other. When the binding enthalpy of the di-interstitial, B, is assumed to be about 10 kcal per mole, the predicted temperature dependence of the solubility agrees reasonably well with the reported data. Effective diffusiuity is calculated assuming the di-interstitials to be immobile. Since the number of mobile single interstitials is greatly reduced at lower temperatures, the effective diffusivity is decreased. A good agreement in the temperature dependence of diffusivity between theory and experiment is provided with B - 10 kcal per mole. The predicted diffusivity is also a function of total concentration of hydrogen and this appears to be Partly responsible for the large scatter in the reported data. HYDROGEN is known to form an interstitial solid solution with iron.''' At elevated temperatures, it has been well-established that hydrogen enters iron in the dissociated form and occupies the interstices, and that diffusion of hydrogen in iron is via the interstitial mechanism. The concentration, c, permeability, P, and diffusivity, D, of hydrogen in iron have been separately determined and are consistent with each other under the steady-state condition for temperatures above approximately 400°C; that is, the relationship P = c-D holds. At lower temperatures, however, anomalous behavior of hydrogen in iron has been observed by many investigators. The results of experimental studies4-'' of the diffusion of hydrogen in iron are summarized in Fig. 1, in which the values of D are plotted against the reciprocal temperature. Although there is an increasing divergence in observed values of D with decreasing temperature, the values of D at temperatures below approximately 200°C are definitely small as compared with the extrapolation from high-temperature data. The lines shown bracket the region containing the most probable data. The observed values of c6," are plotted against the reciprocal temperature in Fig. 2, where the dashed lines represent Geller and sun's'' most probable isobars at 1 and 100 atm. At high external hydrogen pressure and low temperatures, the values of c observed are higher than those expected from high temperature data. It is generally accepted that certain trapping mechanism is responsible for the anomalies, but the nature of the trapping mechanism has not been clarified. Various types of hydrogen traps were suggested in the literature, such as "rifts" in the lattice dislocations, voids, microcracks, and so forth. However, no quantitative account of the observed behavior has been given in terms of these trapping mechanisms. Formation of methane in hydrogen-charged steel was found by ~odgurski." This appears to explain the existence of the so-called "residual" hydrogen,4 but not the observed anomalies of hydrogen in iron. McNabb and Foster' proposed a mathematical analysis in terms of a trapping mechanism. However, the physical significance of the traps was not clarified. The necessity of evaluating five parameters in their theory made comparison with experiment difficult. In the present paper, a model is proposed in which the anomalous behavior of hydrogen is attributed to the formation of hydrogen di-interstitials at lower temperatures. In this model, it is postulated that single and di-interstitials are in equilibrium with each other. (The hydrogen di-interstitial is to be distinguished from a hydrogen molecule which may exist in voids.) It can then be shown that most of the anomalies can be explained by assuming that the di-interstitials are virtually immobile and that the binding enthalpy of the di-interstitial, B, is approximately 10 kcal per mole. Predictions of the theory agree with the available experimental data reasonably well. THEORY The basic postulate of the present analysis is that single and di-interstitials are in equilibrium with each

Jan 1, 1969

By T. L. Loucks, E. T. Guerrero

Pressure drop characteristics in a system composed of two adjacent concentric regions of different permeability were studied. The differential equations for continuity of mass flow in the two regions were solved using the Laplace transformation and the necessary boundary conditions to give the pressure distribution in the composite reservoir, the resulting equation for pressure drop at the inner boundary was evaluated for a variety of composite reservoirs and compared with the results for a uniform reservoir. From this study it was found that under certain conditions the permeability in both zones, as well as the size of the inner zone, can be determined from the pressure drop curve. INTRODUCTION The theory for the pressure distribution and pressure build-up behavior of a well producing a single, slightly compressible fluid from infinite and finite homogeneous reservoirs was presented by Hornerl and Miller, Dyes and Hutchinson.2 Extensions on this original work to provide improved and extended interpretations and better agreement between theory and observed results have been made by Matthews, et a1,3 van Everdingen,4 Gladfelter, et al5 Stegemeierand Matthews,6 Hurst and Guerrero,7 and Perrine.8 More recently Lefkovits, et al,9 studied pressure build-up behavior in bounded reservoirs composed of stratified layers. Houpeurtl0 has suggested various approaches to the general problem of variable permeability and porosity but presented no analytic solutions for particular permeability variations. Albert, Jaisson and Marionll studied the finite composite reservoir and presented numerical solutions to the unsteady-state case and an analytical solution valid only for large times. They also studied the so-called pseudo-steady state for several examples of radial permeability variations. Very similar examples have been treated in the unsteady state with application to pressure build-up by Loucks in an unpublished manuscript. More recently Hurst12 has presented the complete point-sink solution (valid for all times) for the infinite composite reservoir. He applied these solutions to interference between oil fields along with an even more elegant application of his explicit solution to the material-balance equation including water influx. Mortada 13 approaches the same application by avoiding the point-source limitation but gives the solution for the aquifer region which is valid only for large times. Hopkinson, Natanson and Temple14 have treated both the finite and infinite composite reservoir obtaining the pressure distribution for the inner zone valid for large times. This paper presents a theoretical study of the pressure distribution in an infinite composite reservoir composed of two adjacent concentric regions of different permeability. The object was to determine the manner in which pressure drop at the inner boundary of a composite reservoir depends upon time, the permeability of each zone and the size of the inner zone. Expressions for the pressure distribution in both zones are developed which take into account the radius of the sink and are valid for small times as well as large times. It was felt that an understanding of the pressure drop behavior in various composite reservoirs would be of assistance in the interpretation of some pressure build-up curves which do not behave according to the theory derived for uniform systems. Often the region surrounding the wellbore is either more permeable or less permeable than the reservoir because of the various drilling and completion practices. The effects of reduced permeability due to drilling-fluid invasion and of increased permeability due to fracturing or acidizing need to be more carefully defined. Therefore, an equation for the pressure drop in a composite reservoir was developed, and the effects of both the permeability in each zone and the size of the inner zone were studied. STATEMENT AND SOLUTION OF PROBLEM BOUNDARY CONDITIONS AND ASSUMPTIONS The physical system studied was a composite

By A. C. Losekamp, J. B. Conway

Thermal-expansion data for, tungsten, rhenium, tantalum, .molybdenum, niobium, W-25 pct Re, Ta-10 pct W, ant1 Mo-50 pct Re are presented covering the range from room tempature to 2500°C. In these measureMents, made in a resistively heated tungsten tube furnace operating in a helium atmosphere, data for rod and sheet specimens were found to be identical; in addition, arc-cast and sintered tungsten were found to yield essentially identical results. Optical rneasurenlents of thermal expansion .made in any atmosphere other- than vacuum are subject to a refraction error which can be quite substantial. Specimens tested in helium appear shorter than when tested in racuum and hence a special correction factor must be applied to the helium data in order to obtain accurate results. WHILE it is true that linear thermal-expansion data for many of the refractory metals have been measured to very high temperatures, it is also true that except in a few instances the data from various investigators are not in good agreement. This is particularly evident in the case of tantalum and niobium although some tungsten data have been reported which differ by as much as 40 pct from the data of other investigators. Due to the sensitivity of both tantalum and niobium with respect to impurity absorption during exposure to high temperatures, it is probable that this single factor accounts for the majority of the discrepancies in the thermal-expansion data for these metals. However, this same factor can probably not be employed to explain the existing differences in the tungsten data. In all probability, these are due to errors in the measurement technique, to material composition variations, or to changes which take place in the material during the heating process (e.g., additional densifica-tion resulting from heating a sintered specimen above the original sintering temperature). In view of the discrepancies which exist in the linear expansion data reported for many of the refractory metals, the current study was initiated in an attempt to resolve such differences. Also, no high-temperature linear thermal-expansion data were found to be available for several refractory metals. Providing such data was another objective of the current investigation. MATERIALS In this study test specimens were employed in either rod or sheet form and in several instances both arc-cast and sintered material were employed. Material compositions are presented in Table I. Helium gas was fed to the furnace at a rate of about 0.5 SCFH and no special purification procedures were employed. However, the helium contained less than 50

Jan 1, 1967

By F. G. Miller, R. C. McFarlane, T. D. Mueller

During the process of gas storage in pressure-depleted oil reservoirs, it has been observed that in some instances additional liquid oil is recovered and that the composition of the storage gas is materially altered. A mathematical study was made of the dynamic behavior of such a depleted oil reservoir undergoing gas injection. The important variable considered in this study, not included in previously published work, was that of compositional effects on the phase behavior of two-phase flow. Pressure, saturation and component composition profiles were developed for a linear, horizontal and homogeneous porous medium containing oil and gas but undergoing dry gas injection. Special new techniques were developed to overcome the problems of numerical smoothing which arise in the solution of the equations representing such systems. The method of solution includes the development of partial differential equations describing the behavior of the system, representing these equations by finite difference approximations, making certain simplifying assumptions and, finally, applying methods of numerical analysis with the aid of a high-speed digital computer. In an example calculation, results using the mathematical model are compared with field observations made on a gas storage project in Clay County, Tex. This field project involved a depleted oil reservoir used 'for gas storage and gas cycling purposes. As a result of these processes, the reservoir yielded substantial amounts of secondary oil, both in the form of stock tank oil and as vaporized products in the produced gas. The methods derived in this study may be applied to a variety of oil reservoir problems which are dependent on compositional effects. In recent years the number of oil reservoirs being used for gas storage purposes has increased greatly, and there has been at least one published account of additional oil recovery resulting from gas cycling a depleted oil reservoir after repressur-ing with dry gas for storage purposes. Additional oil recovery from oil reservoirs resulting from gas storage operations could become an important secondary recovery process. This is especially true since the use of natural gas in large metropolitan areas continues to increase and more gas storage volume near these areas is needed. These facts provided the motivation for the work reported here. This paper reports on a study of the inter-relations of composition, saturation and pressure changes which occur when hydrocarbon gas is injected into an oil reservoir system. From an understanding of the process, prediction methods may be developed for use in forecasting the secondary recovery products from gas storage operations in oil reservoirs and, consequently, .the economics of such projects can be developed. The process of storing hydrocarbon gas in an oil reservoir and the cycling process both involve the transient multi-phase flow of oil reservoir fluids with changing fluid compositions. There is a scarcity of work published on the subject. One of the first laboratory models developed to study a problem similar to the one posed here was published in 1948 by Standing, Lindblad and Parsons. l They developed a model to study gas condensate recovery by gas cycling, including the effect of heterogeneous reservoir permeability. Their results showed the compositional effects of injecting a gas of known composition into a two-phase condensate reservoir of known composition. A major finding of their study indicated that maximum oil recoveries from gas cycling projects result when low cycling pressures are used. Previous to their work it was generally considered

By L. R. Mabson, F. M. Russell

INRODUCTION Roan Consolidated Mines Limited (RCM) operates five underground mines - Mufulira, Luanshya, Baluba, Chambeshi and Chibuluma (figure 1) . Associated metallurgical plants provide for the operations of milling, smelting two refineries for copper and a cobalt plant. Primarily a producer of high quality copper (242,000 tonnes during 1980) the Company is also the world's second largest producer of cobalt metal. RCM's remaining ore reserves at 31st March 1980 were 275 million tonnes at 2.84% copper. Monthly ore production is in excess of 1.2 million tonnes. Sublevel open stoping was the choice of mining method for the first underground operations on the Copperbelt for ore with dips steeper than 30 degrees. This was for use at the Roan Antelope mine, subsequently to be called Luanshya mine. The sublevel open stoping system was planned based on the methods used in many of the iron mines of Michigan and New York and in the copper mines of Tennessee. Peterson (Ref. 1) gave the following reasons for employing sublevel stoping, reasons which are still valid today: (1) the working place could always be barred and made safe, and the sublevel exit was always at hand; (2) the working conditions were similar day by day and drilling operations were repetitive; (3) pillar spacing can be varied as conditions demand; and (4) stoping operations could be shut down completely or opened up to full capacity at short notice, without affecting grade or causing wastage of reserves. Such was the success of the method that it was adopted as the basic mining method at all the RCM mines in their initial stages. Although cut and fill, block caving, and sub- level caving methods have been used, sublevel open stoping in its many variants still accounts for nearly 90% of total ore production in the Company. The following descriptions outline some of the applications of sublevel open stoping within RCM. LUANSHYA Geology There are two main ore deposits at Luanshya: the Roan (Luanshya Mining Area), in which mining began in 1930, and Baluba, in which mining production started in 1973 (figure 2). Both orebodies occur in synclinal and variably folded basins. These basins are underlain and completely surrounded by much older schists and granites. The ore formation, an argillite, lies near the base of the sediments and is underlain by conglomerates, quartzites and arkoses. Copper mineralisation is mainly found in two well defined zones, separated by a varying thickness of pyrite mineralisation. In the eastern part of the Roan deposit only the upper orebody is present, but west of 18 shaft and at Baluba the lower orebody predominates. Locally the subjacent quartzites of the footwall formation are also mineralised with copper. The copper mineralisation is found princi- pally as disseminated sulphides, mainly chalcocite, bornite and chalcopyrite. Near the surface the sulphides have been changed to oxides. At Baluba the cobalt mineral carrollite is found with the sulphides. Mining methods Sublevel open stoping is the basic mining method. In its standard form this method is best suited to steeply inclined orebodies, with simple structures and with a strong foot- wall and hangingwall. In recent years, as more complex folding and flatter dipping orebodies have been encountered, considerable variations have been introduced. Stope drilling is effected with drifters and extension steel.

Jan 1, 1981

By L. A. Wilson, N. H. Harrison, R. R. Clay, R. L. Reed. D. W. Reed

Experiments have been performed in a linear near-adiabatic system for the purpose of extending data on reverse and forward combustion from atmospheric pressure to 1,000 psig. Results obtained from reverse combustion appear to conform qualitatively with the existing description of the process when reaction kinetics are suitably modified to account for the increase in pressure, i.e., increasing tbe pressure decreases the peak temperature and increases the combustion zone velocity. Forward combustion appears to be a fuel dominated process wherein peak temperature and combustion zone velocity are not very sensitive to changes in pressure. The moderate effects of pressure that do exist at low flux virtually disappear at high flux providing all oxygen is consumed. With this provision. increasing the pressure decreases the frontal velocity and increases the peak temperature. Results me shown graphicaIIy which demonstrate the effects of presswe on peak temperature, rate of advance, oil recovery, air/oil ratio, carbon oxides produced and temperature distributions. INTRODUCTION Numerous field tests of oil recovery using the technique of underground combustion are now in progress. Operating pressures used are always substantially in excess of atmospheric pressure. Nevertheless, the literature contains no laboratory data pertaining to the effects of pressure except for those of Martin, Alexander and Dew.1 Unfortunately, these data appear to reflect heat losses which may have obscured some of the effects of increased pressure. The underground combustion processes are exceedingly complex, and general concepts relating to them have necessarily been described in relatively simple terms. Particularly with regard to forward combustion, the interaction between multiphase fluid flow, heat transport and various rate mechanisms is so involved that to date a rigorous treatment is not available. In this paper a linear near-adiabatic system is described which was found capable of operating at pressures up to 1,000 psig and temperatures of at least 1,100 F. Using this equipment, experiments on both forward and reverse combustion were accomplished at elevated pressures and the data presented as a function of air flux or temperature. It will be assumed that the reader is familiar with the papers of Wilson, Wygal, Reed, Gergins and Henderson on forward combustion and that of Reed, Reed and Tracht3 on reverse combustion, so that it is not necessary to repeat the details of the two processes. EQUIPMENT AND PROCEDURE It was decided to study the effects of pressure over the interval 0-1,000 psig using a near-adiabatic system. Since satisfactory operation of such a system requires very thin tubing walls, it proved necessary to insert the entire combustion tube and heater assembly into a high pressure jacket in such a way that the internal tube pressure could be counterbalanced by pressurizing the annulus. This meant that the numerous heater and thermocouple wires had to pass through gas-tight seals that required considerable effort to maintain effective. An unexpected difficulty arose in connection with the nature of the annulus pressuring gas. It turned out that the composition of this gas critically affected the functioning of the adiabatic control system. Operation of the equipment at elevated pressures was not particularly difficult. The problems that did arise were a direct consequence of the large numbers of connections and seals involved. EQUIPMENT The equipment consisted of the combustion tube which fitted within the pressure jacket. This jacket was in turn mounted on a wheeled carriage which facilitated movement and provided for rotation of the

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.

By J. S. Aronofsky, A. S. Lee

Results and experimental procedures are presented covering a preliminary laboratory investigation of the compaction of reservoir rocks and its effect on porosity and permeability. "Egective" compressibility was measured by subjecting core material to an overburden load and reducing pore pressure. Preliminary results showed relatively high effective compressibilities which varied from 1.8 X 10-' pore volume/pore volume /lb / in.~ for limestones to 7.7 X 10-6 pore volume/pore volume/lb/in.' and even higher for sandstone reservoirs conmining large amounts of fine clay material. It appeared from the initiol results that the effective compressibility of the material could not be correlated directly with porosity and that other factors, such as the amount of clay material present might have to be taken into account. The work to date has indicated that effective compressibility factors will have to be measured for the particular reservoirs heing studied. Oil permeability of core materid was measured under various effective overburden loads from 0 to 8,000 psi. It has been found than reduction of permeability in clean sands was relatively small and the results agreed with published data. For sandstones containing large amounts of clay, preliminary tests indicated very large reductions in permeability with increasing effective overburden pressures. It is planned to continue laboratory work on this phase because of its importance in low-permeability reservoirs. INTRODUCTION During the past few years increasing interest has been shown in the differences obtained between conventional laboratory measurements on cores at atmospheric pressure and those when reservoir conditions are simulated. Since these data are used as the basis for calculations and the prediction of reservoir behavior, their evaluation under reservoir conditions is most important. The effect of the compressibility of the rock upon the reservoir behavior, as fluid pressure declines, is an important subject which has been insufficiently studied. The total pressure on any plane through a reservoir is the result of the grain-to-grain rock pressure due to the overburden and the pressure of the interstitial fluid on the plane. As reservoir fluid pressure declines, the net load on the rock phase must increase, and the result is the compaction of the rock structure which produces a decrease in pore volume. Simultaneously, the rock grains expand into the pore space as the fluid pressure declines. The result of these two effects is defined as the effective compressibility of the rock and is expressed in units of pore volume/original pore volume/psi. Work was started by Imperial in 1954 on the effects of pressure on the porosity of reservoir rock. These studies established effective compressibility factors for some limestones and dolomites. Since that time effective compressibilities have been obtained for other Canadian and some U. S. reservoir rocks. In conjunction with the study of porosity, an investigation has also been initiated to determine the effects of pressure on permeability. One outcrop and several reservoir sandstone cores have been tested to date. ROCK COMPRESSIBILITY Apparatus anD Procedure A diagram of the apparatus used in these studies is shown in Fig. 1. The equipment was constructed so that a uniform pressure, equivalent to the reservoir overburden, could be applied by the oil pump and transmitted on all sides of the core through the Lucite sheath. The sample was completely saturated by circulating brine through the mounted core. Pressure in