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By Roger Potvin

Abstract The demand for pure zirconium and titanium metals in Germany increased considerably during the war. Pure zirconium was used in flash bulbs, in vacuum tubes, and in time fuses for bombs, where it has a decided advantage because it gives no gas in burning. Under the form of alloy, it was used with other rare elements for making substitutes for platinum; it was also used as a scavenging agent in high-grade steels. Metallic titanium was mainly used in connection with the manufacturing of special alloys. The authors were sent to Germany by the Department of Reconstruction and have investigated the German process developed for producing these rare metals. They describe the procedure and special equipment used for their commercial production in Germany during the war. General Metallic zirconium and titanium were .produced on a commercial scale in Germany by the thermal reduction, with metallic sodium, of potassium fluozirconate and titanium chloride, respectively, using a mixed potassium and sodium chloride flux. According to the information gathered, the sole German producer of these rare metals in pure form was the Deutsche Gold und Silber Scheideanstalt (commonly called Degussa), at their Werk II, 215 Gutleutstrasse, Frankfurt/Main, which was visited by the authors on September 18th, 1945. As far back as 1934, Degussa was carrying on active research on the manufacture of zirconium, and nearly one ton of the pure metal had been produced before September, 1939. Concurrently, a quite similar process was worked out for the recovery of titanium and it was in commercial operation in the year 1938, during which the production totalled about half a ton (metric). The demand, especially for pure zirconium, increased considerably during the war, attaining a total of about 48 tons during the period October, 1939, to the end of 1944, and reaching a peak of more than 15 tons in 1943. In 1944, the plant was slowed down due to the frequent and disastrous bombing by the Allies, especially in March and September.

Jan 1, 1946

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is 'uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b'e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970

By R. L. Whiting, H. J. Ramey

The basic study from which this paper was prepared was started as the result of the growing need throughout the world for increasing quantities of energy in all forms. Quite obviously, natural forms of energy that are readily available at low development cost are those in greatest demand. The underdeveloped countries — and particularly those having little or no petroleum resources — are the countries in which the most interest is being shown in the newer energy sources. One of the least expensive energy sources is natural geothermal steam.'-* Although this form of energy has been recognized for centuries, it has been only during the past 20 years that serious efforts have been made to harness it. Natural geothermal steam energy in Italy, New Zealand, Mexico, Japan, and California is now being produced through wells to drive turbines and generate electricity. Further, active exploration for natural geothermal steam is being conducted in Hawaii, Fiji, Taiwan, Chile, Russia, Greece, and Katanga. It is surprising to find that most geothermal steam exploration is in the "steam seep" stage. That is, surface studies are made and exploratory wells are drilled in the general area of steam seeps. However, in the larger geothermal steam areas, there have been efforts to apply the most modern geological and reservoir engineering principles in order to define the reservoir parameters, particularly those relating to estimates of reserves and future productivity. This paper is concerned with the development of appropriate equations and techniques to facilitate these estimates. Production of natural steam or hot water presents problems different from those experienced in the production of oil and gas. For example, steam or hot water systems may be essentially single-component systems, while hydrocarbon systems are most frequently multicomponent fluid systems. Heat effects are much larger for water than for hydrocarbon systems; and the natural steam production may or may not be isothermal, while production of petroleum reservoirs is considered normally to be isothermal. Petroleum reservoir engineering principles may be applied to natural steam or hot water reservoirs if the inherent differences in the systems are considered. The basic considerations involved in geothermal steam reservoir engineering are: thermodynamics, physical and thermal properties of water, materials and energy balances, fluid influx, and performance matching and predicting. Thermodynamics Fig. 1 is a pressure-temperature diagram for the liquid-vapor region for pure water, showing the critical point and five other points representing possible initial conditions for a geothermal steam reservoir. To generate a physical appreciation for the mechanics of natural steam production, it is helpful to consider

Jan 1, 1970

By D. S. Pye, J. P. Gallus

Successful hydraulic pressure treatment of oil and gas wells that have long producing intervals, multiple pay zones, fluid thief zones, or natural or induced fractures has long been a serious problem plaguing the petroleum industry. High fluid-injection rates, straddle packers, ball sealers, and either liquid or solid additives to the treating fluids are being used to cope with this difficult and costly problem.l-6 The use of ball sealers and straddle packers is limited, in practice, to wells that have been completed with perforated cemented casings or liners. Well stimulation with ball sealers and straddle packers is usually successful as long as the cement remains competent. The other techniques of diverting are used with all types of completions. However, there are two significant disadvantages of the high rate method: excessive horsepower requirements, and the need of large treating-fluid volume. Consequently, most well stimulation techniques that involve diverting depend upon ball sealers or granular materials. Liquid diverting agents, and some of the solid ones in use today, frequently will cause formation damage. On the other hand, the most popular particulate diverting agents often are so soluble in the treating fluid that they become largely ineffective; their particle size is severely reduced as they dissolve while being transported through thousands of feet of pipe to the formation face down hole. In our attempts to deal with the shortcomings of these diverting agents, we experimented with a large variety of potentially suitable deformable materials the solubility of which could be controlled. Following are the criteria for the diverting agent sought: 1. The material must be effective in reducing fluid loss to thief zones, including existing fractures and very high permeability layers in the formation to be pressure treated. 2. The material must have enough strength to bridge under the treating pressure. 3. The material must be insoluble or slowly soluble in the treating fluids so that the particles retain sufficient size to be effective after they reach the formation face. 4. The material must be completely soluble in the produced oil or condensate liquid so that it can be removed readily; it must not cause formation damage. A number of products consisting of various polymers blended with waxes and other solid hydrocarbons were examined. All these materials satisfied the criteria for a diverting agent and also exhibited some degree of plastic deformability. On the basis of initial tests of strength and hardness, several blends of wax and polymer were selected for extensive testing in the laboratory and the field. These compounds have congealing temperatures ranging from 140 to 190F; they are insoluble in water and soluble in oil. They conformed, therefore, to the criteria specified for a theoretically superior diverting agent. Laboratory and field tests were conducted using these wax-polymer materials to demonstrate that the use of a deformable diverting agent can significantly improve fluid diverting performance. Data in this

Jan 1, 1970

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By F. W. Jessen, James N. Howell

The accumulation of paraffin deposits in tubular goods has been recognized as a major production problem since the inception of the petroleum industry. This problem is not limited to any particular geographical area nor is it limited to a specific type of crude oil.' Generally speaking, "paraffin" deposition pertains to the deposition of any predominately organic material in flow lines, and possibly even at the sand face, which would hamper the production of oil. In some fields, a continuous effort is required to remove deposits of paraffin and in order to accomplish this, many unique methods have been devised. The best solution to this problem, however, is to prevent the formation of such deposits. One method which has been tried in a number of fields is the use of plastic pipe. The purpose of this investigation is to compare the relative effectiveness of several plastic materials to aid in the reduction or prevention of paraffin accumulations in surface flow lines. COMPOSITlON OF PARAFFIN DEPOSITS By definition, paraffin deposits are those materials which are insoluble in crude oil at the prevailing producing conditions of temperature and pressure. Such deposits1 s usually consist of small particles of petroleum wax intermixed with resins, asphaltic material, and crude oil. They may also contain a variety of foreign materials such as sand, silt, water, various metal oxides, sulfates and carbonates of iron. barium, and calcium. The petroleum waxes deposited in flow strings usually consist of both a "hard" and a "soft" wax fraction. These waxes are largely aliphatic hydrocarbons with smaller amounts of aromatic and naphthenic compounds. Nathan' has classified the hard and soft wax fractions. The aliphatic hydrocarbons present are those of high molecular weight with high melting points. Reistle3 pointed out that these high molecular weight compounds first separate from the oil due to a sharp decrease in solubility as the melting point increases. The identification of the resins and asphaltic materials rests, at present, on an arbitrary solubility procedure. Under certain conditions, materials which are insoluble in pentane (ASTM D-893) are defined as resins and asphalts. Subgrouping of these materials is made on decreasing solubility in benzene and carbon disul-fide. Shock' found some correlation be-tween the solvent response and the pentane insoluble content of paraftins: higher pentane insoluble fractions are less soluble in any of the commonly used commercial solvents. PARAFFIN CONTROL METHODS The methods used in oil fields to prevent and remove paraffin accumulations can be grouped into four general classes: (1) operative methods, (2) physical methods, (3) chemical methods, and (4) combination of any of these. Operative methods attempt to prevent the formation of paraffin deposits while the other methods are concerned primarily with the removal of these deposits. Plastic coated pipe has been used for a number of years to prevent cor- rosion in wells, and in manv instances paraffin deposits have -been greatly reduced. Field observations have indicated that plastic coated pipe not only reduced paraffin accumulation but in some cases eliminated deposition completely; however, data are needed to demonstrate the relative effectiveness of plastic materials. Deposition Apparatus The pipe used to determine the effect of velocity on rates of deposition was %- and 2-in. nominal diameter, and 5 ft in length. Steel, butyrate, rigid PVC, kralastic resin-type plastic pipes, epoxy coated pipe, PVC lined glass fiber pipe, and aluminum pipe were tested. Steel pipe was used as a control. Fig. 1 is a schematic diagram of the apparatus showing the relative position of the separate units making up the equipment. In order to facilitate the installation and removal of the test pipes in the apparatus, O-ring seals capable of sustaining pressures of 50 psi were provided at each end. Test pipes were submerged in a cold water bath maintained at or below room temperature by circulating water through copper cooling coils packed in ice. A hot water bath equipped with immersion-type heaters, stirrers, and a thermoregulator was used to maintain the temperature of the oil prior to introduction into the piping manifold. The capacity of the oil reservoir was 30 gal. A 33-gal/min centrifugal pump, capable of producing turbulent flow velocities in the test pipes, was used to circulate the oil through the system when using %-in. pipe; and a 70-galjmin centrifugal pump was used in later tests using 2-in. pipe. A by-pass arrangement made it pos-

By W. K. Godfrey

The highest compressive strength cement has the highest bond strength in tests in which the cement is subjected to a confining pressure. After perforating, the bond strength is reduced to nearly zero when the pipe is supported by weak cement. Perforating does not affect the bond strength, however, when the pipe is supported by strong cement. Pipe supported by weak cement is damaged by perforating with expendable capsule jets, but is not damaged by perforating with the hollow carrier gun. High strength cements are recommended for oil wells that are to be perforated. Introduction The purpose of this work is to determine the effect of jet perforating on the bonding strength of oilwell cement at simulated down-hole conditions. Bond strength is a good criterion for determining the effectiveness of cement in performing its main function, i.e., that of isolating zones. According to the literature on the subject, the optimum cement strength for perforating is low and should not exceed 2,000 psi compressive strength. This conclusion was based on the appearance of bullet and jet perforations in neat and gel cements largely done in the absence of a confining pressure more than 15 years ago. Discussion Literature A relatively weak cement has been recommended in the literature as having optimum properties for perforating. In 1947, Oliphant and Farris tested bullet perforating of neat cements at various curing times.' Some of the tests were made at down-hole conditions. They reported that the optimum cement strength for perforating was about 2,000 psi compressive strength. Enlarged holes occurred when strength was too low, and the cement shattered and cracked when the strength was too high. In 1951, Morgan and Dumbauld tested bullet and jet perforating of neat and gel cements at surface conditions.' They reported that optimum cement has a compressive strength less than 2,000 psi. In their tests at atmospheric pressure, high strength cement shattered and cracked when perforated. Thus, the optimum cement strength was based on the appearance of neat and gel cement after perforating. In 1953, Clark showed a relation between cement strength and fluid shutoff.' He concluded that a 500 psi compressive strength is required for good fluid shutoff and that maximum bonding ability is developed at approximately 1,000 psi compressive strength. In 1964, Bell and Shore invalidated most of the conclu sions by the previous authors when they demonstrated that atmospheric pressure tests cannot be used to determine casing deformation and damage that will result from perforating under down-hole conditions.' They showed that the higher the hydrostatic pressure, the more restricted will be the expansion of gases generated by the charge. Less casing deformation and damage occurs under down-hole conditions than at atmospheric pressure. In recent work, Bearden et al. reported that jet perforating at surface pressure with the hollow carrier gun caused the cement sheath to shatter and crack.' The perforating, however, did not seriously affect the pressure required to leak past the casing cement bond. Only three cementing mixtures were tested, and presumably they had strengths in excess of 2.000 psi. Bearden et al. also reported that the hydraulic bonding strength increased as the compressive strength increased. Their hydraulic test showed that approximately 1,000 psi pressure is sufficient to break the casing cement bond for a well aged neat Portland cement sheath. Unfortunately, the tests were not run with a confining pressure, so Bearden et al. were merely measuring the strength of their outer 8%-in. casing. In our investigation, we measured the hydraulic bond strength of cement to pipe under a confining pressure and found that the bond strength was not limited to 1,000 psi. Cement Bond The bond strength is a good criterion for measuring the effectiveness of cement in performing its main function, that of preventing interzonal communication of fluids behind the casing. Measuring bond strength after perforating should be a good quantitative method of determining optimum cement properties, and should be a better method than that used by previous investigators,11 ' who simply observed the appearance of the cement after perforating.

Jan 1, 1969

By J. E. Strassner

Oilfield emulsions are stabilized primarily by film-forming asphaltenes and resins containing organic acids and bases. Adding inorganic acids and bases radically changes the physical properties of these films and their emulsion-stabilizing properties. Interfacial films show one of three different physical characteristics when retracted in pendent drop tests. These compressed films have rigid, soap-type or minimum film properties depending on the quantity of asphaltenes and resins in the crude oil and on the pH and composition of the brine. There exists for each crude oil-brine system an optimum pH range over which the adsorbed film exhibits minimum contracted filtn properties. In this range, intmfacial tension is high — frequently near its maximum value — indicating the absence of highly surface-active specier; crude oil-brine emulsions generally show minimum stability; and surfactant requirements for breaking these emulsions are significantly reduced — sometimes no surfactant is needed. About two-thirds of the world's crude oil is produced as emulsions that must be treated (demulsified) to be marketed.' Approximately three-fourths of all domestic crude oil produced must be treated. The percentage of crude requiring treatment increases as fields become older and more water is produced. Demulsification most frequently is attained through use of surfactants, heat and electric treaters. It is estimated that over 75 percent of all oilfield emulsions are broken by chemicals generally containing alkylene oxide condensates. Although acids and bases are known to affect emulsion stability:-' they rarely are used in the oil field except in batch treatment of the most severe emulsions. Nevertheless, pH adjustment by using acids or bases in demulsification has some advantages over other methods. Mainly, it is cheaper. Acids and bases frequently are cheaper to use than surfactants, or can appreciably reduce the amount of surfactant required for demulsification. Secondary advantages are that less oil is lost by emulsi-fication into the aqueous phase, and that less corrosion is encountered when the optimum pH is basic. Limitations to the use of pH include (1) use in brines containing high concentrations of reactive ions, (2) closer supervision for pH control than is required for surfactants and (3) need for corrosion protection when the optimum pH is sufficiently acidic. These factors indicate that the economics of pH con trol in demulsification will be maximized when relatively large treating facilities are needed, when relatively large surfactant concentrations are required to break an emulsion, when a relatively low concentration of the aqueous phase is emulsified in the oil and when the emulsified aqueous phase contains relatively low concentrations of reactive ions. Because there are no broad guide lines for using pH control in breaking oillield emulsions (and because the limited guides available are highly specific and frequently contradictory), this paper will attempt to clarify the principles involved in using acids and bases to break emulsions. These principles also should be useful in refinery separations and in other oilfield applications where stable or unstable petroleum emulsions are involved. Principles of Emulsion Stability Oilfield emulsions generally occur as water droplets dispersed in oil (w/o) and occasionally as oil droplets in water (o/w). These emulsion droplets are usually in the 0.1- to 10-micron range. However, more coarsely dispersed water droplets frequently are present in the emulsion. Pure hydrocarbons and water will not form stable emulsii except in extreme dilutions where the large distance brtween droplets inhibits coalescence. An emulsion breaks because interfacial tension acts to minimize the surface area of the dispersed drops by coalescence. However, emulsions can be stablized for long periods of time by the presence of a third phase that adsorbs at the oil-water interface and inhibits coalescence of the dispersed phase."' Emulsions generally are stabilized by (1) repulsive charges on the surfaces of the dispersed phase and (2) adsorbed films that, being preferentially wetted by the continuous phase, act as a physical barrier to inhibit contact between the dispersed droplets. Both these factors generally are important in stabilizing and in breaking o/w emulsions. However, repulsive charges are less effective in stabilizing w/o emulsions which generally are stabilized by adsorbed films.V or this reason the nature and importance of these films at oil-water interfaces were examined closely; as will be shown, pH changes were found to affect the films significantly, and this work led to laboratory tests of pH- adjustment in emulsion breaking. This paper will present evidence to show that emulsions are stabilized primarily by films that form around droplets

Jan 1, 1969

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By G. W. Binkley, R. E. Collins, G. K. Dumbauld

A mathematical analysis has shown that the primary factors affecting the deposition of cement in unfractured perforations during squeeze-cementing operations are: the properties of the cement slurry, the geometry of the perforations, and the filtration time. The validity of the analysis has been substantiated by laboratory investigations. The information presented in this paper makes possible the prediction of the rate of deposition of cement in and about unfractured perforations under given squeeze-cementing conditions, the proper filtration time to control the amount of deposition to any desired value, and the deposition properties needed in cement slurries to restrict to any desired degree the formation of nodes of cement .Solids inside the casing. INTRODUCTION The deposition of solids against a permeable medium by the process of filtration is an important property of a cement slurry. General recognition of the role of filtration in the use of cement in wells is evident in view of the fact that several patents on low-water-loss cements have been issued during the past few years. In the conventional, high-pressure squeeze-cementing technique, a large volume of cement slurry is usually displaced into the area surrounding the perforated interval after the formation has been fractured hydraulically.&apos; Near the end of the job, the pumping rate is slowed or stopped intermittently in an effort to obtain a high pressure in the wellbore. The way in which a high pressure is obtained is not understood thoroughly. but it is be- lieved to be caused by the deposition of a rigid mass of compacted cement particles either in the fractures of the formations or inside the casing opposite the perforated interval. In a method of squeeze-cementing introduced several years ago, a small amount of cement slurry is squeezed into the perforations at a low pressure to avoid fracturing the formation. The filling of the unfractured perforations with cement particles by the process of filtration is important to the success of this technique. Early in the development of this low-pressure squeeze-cementing technique, laboratory and field-size experiments showed that conventional, neat cement slurries were unsatisfactory if the tubing was extended into or through the perforated section of the casing. The extremely high filtration rate of neat cement slurries caused the deposition of a compacted mass of cement inside the casing and made it impossible to remove excess cement by reverse circulation and difficult to withdraw the tubing. Because the need for cements with a reduced filtration rate was obvioils and urgent, modified cements containing 12 per cent bentonite were used until research was completed on modified cements containing 25 per cent bentonite.< These modified cements were useful in the solution of the immediate problem, but the following questions remained unanswered: (I) what is the optimum filtration rate of cement slurries for this application, (2) how long should the squeeze pressure be applied. and (3) how great are the effects of squeeze pressure and well temperature on the rate of deposition? Furthermore, the relationship of the filtration properties of cement slurries to the dimensions of the perforations and the wellbore was unknown. In order to obtain information relative to these basic considerations, a systematic evaluation of all the factors involved in the deposition of Cement during low-pressure squeeze-cementing operations was initiated. Although the work was directed toward an evaluation of the factors influencing the deposition of Cement in the low-pressure squeeze-

By A. S. Odeh

The mechanism of two-phase flow in porous media has been a subject of wide controversy. One of the properties essential for understanding the dynamic behavior of two-phase flow is relalive permeability. Relative permeability to a certain phase is defined as the ratio of the effective permeability of that phase to its permeability when it is the only fluid present and powing. In this research, a theoretical analysis was made to determine the effect of viscosity ratio between the non-wetting and the wetting phase on relative permeability. Experimental work was conducted to test the validity of the derived equations. The experiment was conducted on four natural cores. Four oils were used as the non-wetting phases with a viscosity range of 0.42 to 71.30 cp and two wetting phases with a viscosity range of 0.86 to 0.96 cp. Oil and bring were made to flow simultaneously at various ratios, and relative permeability curves were constructed. A total of eight relative pertileability cycles representing eight viscosity ratios were run oil each sample. It was found that relative permeability to the non-~cletting phase varies with viscosity ratio. The relative effect of this variation on relative permeability values was a function of the sample&apos;s single-phase permeability, decreasing with its increase. It was concluded that, for .samples of single-phase permeability over I darcy. the effect of viscosity ratio could be disregarded, and relative permeability would be, in effect, a function of satrtration only. INTRODUCTION Two-phase as well as multiphase flow occurs in many fields of science. This type of flow is of particular interest in petroleum production. The knowledge of relative permeability, which describes the dynamic behavior of two-phasc as well as multiphase flow, is essential for solution of problems arising in that field. Thc relative permeability ot a porous medium to a given phase in multiphase flow. is generally considered to be only a function of the saturation of that phase, independent of the properties of fluids involved and ranging in value from zero to unity. Work by Leverett&apos; and Leverett and Lewis&apos; apparently supports this concept. In his experiments Leverett used a clean, packed unconsolidated sand of high permeability (3.2 to 6.2 darcies) with two phases (water and oil) flowing and a viscosity ratio range of 0.057 to 90.0. His results showed that the wide range of viscosity had practically no effect on relative permeability-saturation relationship. Recently accumulated evidence from work performed by several laboratories and a paper by Nowak and Krueger,2 in which relative permeability to oil of a few core samples in the presence of interstitial water was considerably greater than single-phase permeability to water, cast some doubt on the conclusions reached by Leverett&apos; and subscribed to by a large number of individuals in the oil industry. One explanation advanced to explain this behavior states that it is caused by the variable extent of hydra-tion of clay minerals present in the sand. The greater the water saturation, the greater will be the area of contact between water and clay minerals; therefore, the greater will be the extent of swelling with corresponding reduction in permeability. Yuster4 presents another explanation for the recently accumulated evidence. Utilizing Poiseuille&apos;s law, he analyzed concentric flow in a single capillary where the non-wetting phase flows in a cylindrical portion of the capillary and concentric with it. The wetting phase flows in the annulus between the non-wetting phase and the capillary wall. The equations obtained indicate that relative permeability to the non-wetting phase is a function of saturation and viscosity ratio. Although Yuster&apos;s equations show that fractional rel-ative permeability to oil could be greater than unity, as was indicated by the data of Nowak and Krueger,1 they failed to present an explanation to the experimental data of early investigators such as Leverett.1 Due to the importance of relative permeability in understanding the flow behavior of petroleum reservoir fluids, this work—theoretical as well as experimental —was undertaken to determine whether relative permeability is a function of saturation only as was concluded by Leverett1 or a function of saturation and viscosity ratio as was theorized by Yuster.4 THEORETICAL ANALYSIS An equation will be derived for the rate of oil flow through a porous medium that is initially filled with water. Based on this equation, an analytic expression for relative permeability will be developed. The porous medium will be assumed to consist of .straight circular capillaries of different radii. It will also be assumed that there are no interconnections among the capillaries and no mass transfer across the oil-water interface. Consider a porous sample initially saturated with a wetting phase (water). As a non-wetting phase (oil) is

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.&apos;, n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " &apos;.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.&apos;,&apos; Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a&apos;=-n;s/= nD,(qo);"; and b&apos; = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By J. V. Vogel

Jan 1, 1969

By C. S. Matthews, M. J. F. Rosenbaum

The purpose of thir work wax to lcarn it~lzut infori~lation could he obtained from various typs of pilot water floods and to attempt to find the optunum pilot patter11, for a revervoir which had previously been depleted by a solution gas drive. The study was made in the laboratory with mathemetical methods a dynamic analog and a potentiotnetric analog. Results werp tested against the field llistorics of a nrrnlber of pilot water floods. At a reasonable valrre of currzulative injection, the total production rate for the one-injector five-spot should reach about 6.5 per cent of injection rate, and for a four-injector five-spot, about 9 per cent. Accurate estimates of ultimate recovery cannot be made on the basis of such snzall prorluction rates. However, with a pilot composed of nine ir1jector.s and 16 producers the production rate is approximately 50 pcr cent of injection rate at a reasonable value of camulative injection. Sonle inforn~ation for extended performance predictions might he obtained from such a large pilot. These conclusions were drawn on the basis of results obtained for unit mobility ratio, and a sturly using tlre potentiometric analog was made of the effect of other mobility ratios to determine the range of applicability of these predictions. For the four-injector, five-spot pilot with the ratio of production to injection rate (before water breakthrough) is about twice that for with it is about two-thirds; and with M0= 10, it is about one-third For high mobility ratios, it was found that the production rate increased considerably as water-cut increased. These result can be used to modify, qualitatively, the inter.pretntions based on curves for the unit rnobilit\. ratio CaSeS. It was found that the maximum ratio of production rate to injection rate obseriled in field pilot floods was of rhe scime order as that prerdicted by these methods. The time required to reach thisr maximum did not generally agree with the time predicted for a homogeti~orir reservoir. The differcrlce between predicted and observed time of response gives an indication of the permeability profile and of the condition of the producin,g wells. Pilot water floods of the pattern type are generally carried out in reservoirs which have been depleted by solution gas drive and are at low pressure. Under these conditions, oil and water can be considered incompressible. It is assumed that, as the water is injected, an oil bank forms ahead of it and that there is a distinct interface between the water zone (or bank) and the oil zone (or bank) and between the oil zone and the region ahead of the oil zone. It is further assumed that only gas is mobile in the unflooded (gas) region, only oil is mobile in the oil bank and only water is mobile in the water bank. The saturations and the mobilities associated with each zone are assumed uniform. We idealize our reservoir to be homogeneous, horizontal and of constant thickness. Effects of gravity within the producing layer are assumed negligible. If the actual time-dcpendent flow problem is approximated by a acries of steady-state problems. the potential and stream function in the oil bank and water hank satisfy Laplace&apos;s equation in two dimensions. We can therefore use a poteiitiometric analog of this system. Potentiometric models have yielded uscful results in this laboratory&apos; and clsewhere in the study of a variety of secondary recovery problems. For the case where M = I, we generally prefer to use theoretical mcthods as well as a simpler dynamic analog. Except where otherwise noted, the ratio, side of five-spot/wellbore radius. is taken to be 3,600. a figure which corrcsponds to a normal-size wellbore in a 10-acre well spacing. THEORETICAL EVALUATION OF VARIOUS PILOT PATTERNS, Mw0 = 1 <&apos;he theoretical models which we used to examine the performance of various pilots are shown in Fig. 1. Image theory was used to determine the ratio of production rate to injection rate as a function of the volumc of the flood. The ratio of production rate to injection rate was chosen because this is an easily measurable quantity which is characteristic of a pilot

By R. J. Watson, A. H. Juch

About half a million sucker-rod pumps are installed in oil wells in the U. S. alone. In Venezuela, too, the system is widely used; some 5,000, or 90 percent, of Cia. Shell de Venezuela&apos;s wells produce a total of 400,000 BOPD by this method. Most of the crude pumped is viscous, gassy and contains relatively small amounts of free water. API gravities vary from 90 to 16O; dead oil viscosities vary from 10 to 10,000 cp at the pump; and GOR&apos;s range from 100 to 2,000 cu ft/bbl. Pumps are set at depths ranging from a few hundred to 6,000 ft; the average setting depth is about 2,500 ft. From the literature, it appears that although recent years have seen significant progress toward understanding the rod pumping system as a whole, relatively little attention has been paid to those key items, the sucker-rod pump and the subsurface gas separator or gas anchor. Perhaps because of proration in the U. S., pump manufacturers have seemingly concerned themselves more with the durability of their product, achieved mainly through robust design and metallurgical know-how, than with its working efficiency. In 1963, CSV commenced a major rehabilitation and expansion of its heavy oil fields along the Bolivar Coast. The advent of the more efficient gravel-packed completion and of large-scale thermal recovery (mainly steam soak) operations resulted in well potentials *Now with B. I. P. M., The Hague, The Netherlands. greater than pump capacities. Hence, an urgent need arose to improve over-all pump efficiencies and to attack those special problems related to the production of both the extremely viscous and the hot, steam-laden crudes that formed an increasing proportion of the total stream. There followed a detailed investigation and testing program, carried out in close cooperation with a major pump manufacturer. This culminated in the introduction to the oil industry of a new line of sucker-rod pumps. Early Investigations and Experiments Field Tests Extensive field tests were carried out in three primary Bolivar Coast wells with an in-situ dead oil viscosity ranging from 400 to 6,000 cp. In these installations provision was made to (1) monitor bottom-hole pressures below, in and above the pump by means of pressure transducers, and record casing- and tubing-head pressures continuously; (2) measure accurately the annulus gas, as well as measure the tubing gas and liquid production from the well; (3) take special PVT samples of the well fluid; (4) measure power consumption of the prime mover; and (5) measure the rod loads at the polished rod. A typical test installation is illustrated in Fig. 1. It was established from the pressure transducers that with viscous oils, there is considerable flow resistance across the pump and gas anchor assembly. Pressure surges were observed over each pump cycle,

Jan 1, 1970

By T. Seldenrath

In the development of a fluid -operated hammer drill&apos; for accelerated penetration of hard rock formations in oil wells, a research investigation was conducted to evaluate the percussion effects obtained with different design characteristics and to determine the possibilities of percussion in the low frequency range. Tests were conducted on granite blocks and comparable impact forces were measured with a load cell under selected test conditions. These full-scale laboratory tests provided an evaluation of the effectiveness of percussion which was further supported by actual downhole field performance. While much pertinent data have been presented by other investigators the method of evaluation described in this article resulted in good correlation between laboratory and field performance and may be applicable in other low frequency percussion developments. EXPERIMENTAL METHOD For these tests the bit was held stationary and the test block was rotated and forced upward against the bit by a hydraulically-lifted rotary table. "Weight on bit" was calculated from pressure readings on the fluid system of the lifting cylinders—corrected for tare and friction. Percussion was obtained with several tubular hammers of different weights up to 320 lb. These were lifted mechanically and allowed to drop by gravity from various heights onto a slidably-mounted bit sub or "floating anvil" for calibration of the load cell response with known kinetic energy of the hammers. During evaluation of percussion effects, the hammers were hydraulically operated to provide a range of percussion frequencies up to 1,020 blows per minute delivered to the anvil. To obtain comparable test readings, the load cell of the strain gauge type, was attached to the bottom of the anvil or bit sub in place of the bit. The load cell rested on a typical granite test block mounted on the drilling table. The latter was hydraulically supported as in the actual drilling operation. The effect of support resistance was the same for all tools when calibrating. Impact forces so determined werethusdirectly comparable with one another for the purposes of this investigation. When a roller bit was substituted for the load cell for actual drilling, the impact force would probably be reduced due to the resiliency of the bit body, legs. cones and teeth and the penetration of the teeth into the rock. However, since the bits and rock specimens were uniform in these tests, an evaluation of actual tool performance, in terms of parameters previously determined with the load cell at the selected standard conditions of calibration, proved satisfactory. Throughout these tests, 8¾-in. standard tricone, hard rock toothed roller bits and carbide-insert roller bits were used. Rotary speeds were 50 and 100 rpm; static weight on bit was applied up to 40,000 Ib, and percussion frequencies up to 1,020 blows per minute were available. During this investigation it was found that toothed bits on which the teeth had developed flat ends about 3/16 in. wide did not change appreciably for the duration of a test. Hence, all toothed bits used in this study were in this condition. Conventional reference curves obtained in these tests show that increasing weight on hit by 2:1 yielded an increased penetration rate of approximately 2.7:1, while an increase in rotary speed of 2:1 netted an increased penetration rate of roughly 1.7:l. Results are thus of the same order as those reported for hard rock drilling by other investigators." CALIBRATION Under the selected standard test conditions previously described, with the lifting table hydraulically supported, and the anvil interposed between hammer and load cell, the hammers were dropped from known heights. Thus, with the kinetic energy of the hammer known, the corresponding maximum impact force shown by the cell was determined. (It may be of passing interest to note here that special drop tests with the hammers showed that no appreciable reduction in impact force resulted from introduction of the anvil or hit sub.) From these calibrations, it was possible to determine the theoretical kinetic energy available in the hammer from the maximum impact force shown by the load cell while operat-

By C. D. Hall, F. E. Dollarhide

Fluid Ioss agent.s for crude oil and for water have been studied in dynamic tests. A treatment using a spearhead with a fluid loss agent followed by plain fluid appears feas ible in crude oil, but not in water. An equation for spearhead depletion shows that spurt loss relative to fracture width must be low, if the portion of spearhead fluid in the treatment is to be small. The presence of colloidal matter in crude oils aids the fluid Ioss agent. Unlike in kerosene, where flow limited the agent deposition, in crude oils the filter cake continually formed and leak-off declined. The volume-time relation varied somewhat for different crudes, but was best described by a square root of time function. Spurt loss was inversely proportional to agent concentration. After the fluid loss agent initiated the filter cake, the crude oil colloids built on it effectively. A 2-minute or a 5-minute spearhead with double the normal agent concentration gave the same fluid Ioss curve as the same concentration did for a 30-minute test. The agents tested in water gave fluid Ioss plots on which, for the first few minutes, volume was proportional to the square root of time, but later became proportional to time. For fracture area calculation the customary square root of time function is a satisfactory approximation. Leak-off rates and spurt losses were higher in water systems than in oils. The spurt Ioss tended to be inversely proportional to concentration. In spearhead tests, the filter cakes were not eroded by water flow. However, the rather high spurt loss values make spearhead treatments impractical for water-based fluids. Introduction The effects of dynamic testing conditions on the performance of fluid loss agents in kerosene have been studied previously.&apos; We have extended the work to include crude-oil- and water-based fracturing fluids. An understanding has been gained of the mechanisms of formation and functioning of the filter cakes of fluid loss agents. The practical aspects of evaluating performance of agents in relation to fracture area calculations also are considered. The feasibility of using the fluid loss agent in a spearhead stage of the treatment is examined further for both types of fluids. Experimental Procedure The dynamic fluid loss tests were performed in an apparatus similar to the high-pressure apparatus described in a previous publication.&apos; A fracturing fluid was circulated over a rock surface located in a closed pressurized loop. The fluid flowed axially over the cylindrical surface of a core 2 in. in diameter X 3.5 in. long, mounted (with the flat ends sealed off) in a pipe, with 0.117 in. annular clearance. The filtrate was collected in a central hole in the core and led through valves to graduated cylinders. Provision was made for changing quickly the circulating fluid during the test (spearhead runs) without interrupting the filtration pressure. The only modifications were to add heating tapes and water jackets for the tests with crude oils, all conducted at ISOF, and to change all parts exposed to the test fluid to stainless steel for the tests with water-based fluids. The latter tests were made at room temperature, 80F. Three crude oils were tested. A mixed crude, obtained from a local refinery, contained a considerable amount of light ends. For safety reasons, it was stripped to 250F vapor temperature before use in the fluid loss tests. The other two oils were used as obtained from lease tanks. One was a greenish-brown, 37" API paraffinic crude, and the other was a black, 32" API asphaltic crude. The fluid loss agent for oil, here designated for brevity as Agent A, was Adomite@ Mark II*, a granular solid commercial agent, the same as previously tested in kerosene.&apos; Three different compositions of fluid loss agents were tested in Tulsa tap water. Agent B was adomit& Aqua*, a solid commercial fluid loss agent, comprising clays and hydrophilic gums principally derived from starch. Agent C was a mixture of three parts of Agent B with two parts of silica flour. Agent D was Dowel1 J137, a mixture of guar gum and silica flour. The test cores were cut from contiguous blocks of Berea or Bandera sandstones. For the oil tests, the cores were oven dried, evacuated, saturated with kerosene, and the kerosene permeability was measured. The cores used with the water-based fluids were pretreated by saturating with 3 percent calcium &loride solution to minimize pemeability damage by the fresh water due to clay migration. The

Jan 1, 1969

By H. D. Hodges, J. K. Godbey

In order to better understand the fracturing process, bottom-hole pressures were measured during a number of typical fracturing operations. A recently developed system was used that allows simultaneous surface recording of both the bottom-hole and wellhead pressures on the same chart. The results from six fracruring treatments are summarized on the basis of the pressure data obtained. Al-though no complete analysis is attempted, the value of accurate pressure measurements is emphasized. Important characteristics of the bottom-hole pressure record do not appear at the wellhead because of the damping effect of the fluid-filled column. In four of the six treatments described, the formations apparently fractured during the initial surge of pressure with only crude oil in the well. The properties of the fluids used during the treatments are given and the fluid friction losses are obtained directly from the pressure records. This technique is also shown to be adequate for determining when various fluids, used during the process, enter the formation. INTRODUCTION Hydraulic fracturing for the purpose of increasing well productivity is now accepted in many areas as a regular completion and workover practice. Numerous articles have appeared in the literature discussing the various techniques and theories of hydraulic fracturing&apos;. In general, three basic types of formation fractures are recognized today. These are the horizontal fracture, the vertical fracture, and fractures along natural planes of weakness in the formation&apos;. Any one or all three of these fracture types may be present in a fracturing operation. However, with only the wellhead pressure record as a guide, it is difficult at best to determine if the formation actually fractured, and is almost impossible to determine the type of fracture induced. These difficulties arise in part because the wellhead pressure record, especially when fracturing through tubing, does not accurately reflect the pressure variations occurring at the formation. Several factors contribute to this effect and preclude the possibility of using the wellhead pressure as a basis for accurately calculating the bottom-hole pressure. These factors are: 1. The compressibilities of the fluids which damp the pressure variations. 2. The changes in the densities of the fluids or apparent densities of the sand-laden fluids. 3. The flowing friction of the various fluids and mixtures, which is dependent on the flow rates and the condition of the tubing, casing, or wellbore. 4. The non-Newtonian characteristics of a sand-oil mixture and its dependence upon the fluid properties, the concentration of sand, and the mesh size used. 5. The unknown and variable temperatures throughout the fluid column. Because of these reasons it was determined that in order to obtain a more accurate knowledge of the nature of fracturing, the bottom-hole pressure must be measured along with the pressure at the surface during a fracturing treatment. Even with accurate pressure data, a reliable estimate of the nature of fracturing is still dependent upon knowledge of the tectonic conditions. However, the hydraulic pressure on the formation is basic to any approach to a complete analysis. In order to accomplish this objective a system was developed to record the wellhead and bottom-hole pressures simultaneously at the surface. By recording both pressures on a dual pen strip-chart recorder, it was possible to greatly expand the time scale so that rapid pressure variations would be faithfully recorded. By such simultaneous recording, time discrepancies inherent in separate records are eliminated, thus overcoming one of the most difficult problems associated with bottom-hole recording systems. This paper illustrates the results obtained by using this system during six typical fracturing operations. All of these tests were taken in wells that were treated through tubing. By a direct comparison of the wellhead and bottom-hole pressures, the importance of obtaining complete pressure information during a fracturing treatment is emphasized. THE INSTRUMENTATION AND PROCEDURES The bottom-hole pressure measuring instrument consisted of a pressure-sensing element, a telemetering section, and a lead-filled weight or sinker bar. The pressure-sensing element used was an isoelastic Amerada pressure-gauge element. By using an isoelastic element, no temperature compensation was necessary in the tests described, since the temperature was believed to be well below the maximum temperature limit of 270°F. The rotary output shaft of this helical Bourdon tube element was coupled to a precision miniature potentiometer. The rotation of the pressure-gauge shaft thus changed the resistance presented by the potentiometer

By Karl A. Bauer, Cornelis Bezemer

The deposition of calcium carbonate scale on surface and subsurface production equipment creates an operation problem in many oil fields. The formation water in which the carbonate-scale-forming components are initially dissolved becomes supersaturated with calcium carbonate as a result of the drop in pressure during production. The continuous flow of a supersaturated solution through the production equipment results in the growth of a dense layer of calcium-carbonate crystals. For a scale layer to be built up, the supersaturated formation water should contact the walls of the production equipment. The tendency for scale to be deposited, therefore, will be low, if the crude has a low water cut and if the water is finely dispersed in the oil. A scale problem will occur, if at a high water cut part of the water is present as free water. The rate of scale deposition will then be approximately proportional to the rate of free water production. Depending upon where the formation water becomes supersaturated, scale may be deposited in the flow line only, in both flow line and tubing, and in some cases even in the perforations and in the formation near the wellbore. In the South Sumatran fields (Indonesia) the main difficulties encountered due to the deposition of calcium-carbonate scale have been restriction of flow through tubings and flow lines, wear and abrasion of plungers and liners, and stuck plungers or wellhead valves. So far, the only methods of combating the *Presently associated with Brunei Shell Petroleum Co., Ltd.. Seria. scale problem have been routine acidizing and additional well pulling. As for the pumping wells, it was estimated that some 50 percent of the total well-pulling effort was directly attributable to scale deposition. The most promising alternative was to prevent the deposition of calcium carbonate scale by means of chemicals. Inorganic polyphosphates such as sodium hexametaphosphate and trisodium polyphosphate are known to retard the formation of scale by the "threshold action". They are adsorbed on specific faces of the crystal nuclei and thus prevent crystal growth, thereby stabilizing supersaturation. Polyphosphates are effective at very low concentrations ( a few ppm), and far less than stoichiometric quantities are required to keep the scaling ions in solution. Recent investigations on barium sulfate scale1 have confirmed this mechanism. The types of polyphosphate mentioned can be applied as concentrated aqueous solutions either squeezed into the formation, lubricated down the annulus or injected via macaroni string. Several squeeze jobs with polyphosphate solutions have been carried out in the South Sumatran fields, however, with disappointing results. Lubrication down the annulus and injection through a macaroni string were not considered attractive in this area because of the kind of equipment and the degree of supervision these techniques require. Polyphosphates are also available in a granular, glassy form, which, in contrast with the readily soluble types already mentioned, show an extremely low

Jan 1, 1970