Search Documents

By J. F. Olk, E. D. Spaulding, R. E. Thurmond, G. A. Komadina, R. W. Hernlund, J. A. Journeay

THE Pima pit is a 1700x1400-St oval, the long T axis parallel to the strike of the orebody. The north side of the pit is carried as a final pit slope that coincides with the footwall of the orebody. The south side and east and west ends of the pit are working slopes continually being stripped back toward the final slopes. An inclined roadway extending from the natural ground surface on a 5 pct grade down to the north- east corner provides access to the pit. This road enters the pit 130 ft below the natural surface and continues as a pit ramp on a 5 pct grade to the 3150-ft bench (roughly the base of the alluvial cover). At this point the ramp system is steepened to a 12 pct grade and continues to the pit bottom. The 5 pct grade is maintained in the alluvial section to facilitate scraper haulage out of the pit. In addition to this main access ramp, temporary working ramps in the alluvial areas allow shorter routes to dumps. These are left on top of working benches and do not change the overall working slopes. Below the base of the alluvium, haulage is by truck down to the skip loading point or up from the bottom to the skip loading point.

Jan 4, 1958

The Pinson Mining Co., which will start production in very early 1981, is the fourth Carbon-In-Pulp plant to be put into operation in the United States. The property is located in Humbolt County, Nevada, 38 km (24 miles) northeast of the town of Golconda. The famous Getchell Mine was also near Golconda and was the site of one of the early Carbon-In-Pulp plants in the 1940s. The deposit was discovered in 1971 by Reno based Cordilleran Explorations, which is founded by a consortium of Canadian mining companies. Cordilleran is a partnership consisting of John Livermore and Peter Galli. In 1972 a second but smaller deposit, called "Preble", was discovered at a location 15 miles south of Pinson. During 1980, a decision was made to place the Pinson deposit into production and Pinson Mining Company was formed. Ownership of Pinson is vested in Lacana Mining Inc. , Rayrock Mines, Inc. , Siscoe Metals, Inc., John S. Livermore, Peter E. Galli and Donald M. Duncan. Three distinct but connected ore zones occur at Pinson. Combined reserves of milling ore total 3, 200, 000 tons at an average (undiluted) grade of 4. 12 g per mt (0. 12 oz per st) Au. Initial mining will be from "A" zone which contains 1, 500, 000 tons with an average (undiluted) grade of 5. 8 g per mt (0. 17 oz per st) Au. An additional 5, 500, 000 tons of low grade ore will be mined from the Pinson deposit and processed by heap leaching. Mining reserves at Preble total at least 1, 500, 000 tons grading 2. 7 g per mt (0. 08 oz per st) Au. Production plans for the Preble deposit have not been formulated at the date of writing. Gold mineralization at both deposits is finely disseminated as sub micron sized particles. The ore at Pinson is structurally controlled and occurs in an Ordovician limestone-siltstone unit. Much of the ore has been silicified to a jasperoid. The ore zones have been entirely oxidized. Preble ore occurs in the Cambrian formation in a carbonaceous, limey shale. Only the upper part of the Preble is oxidized and amenable to conventional cyanide leaching. The Pinson ore body is adjacent to the mouth of Granite Creek in the Osgood Mountains at an elevation of 1, 615 m (5, 300 ft) with the mill being 1. 2 km (3/4 mile) from the mine at an elevation of 1, 495 m (4, 900 ft). Mine development work began in May of 1980 with ore being stockpiled for later processing. Pertinent factors affecting

Jan 1, 1981

By Wayne D. Gould

Cities Service Co.'s Pinto Valley concentrator was designed to eliminate excess capital costs without loss of efficiency. The result is a workable plant with some important innovations. These innovations, the equipment used, and plant processes are outlined. Particular attention is paid to the work efficiency and wear of the six ball mills, the largest wet ball mills made. For experiment purposes, four designs of liners were installed. The effectiveness of each design is discussed.

Jan 1, 1977

By Ta M. Li

Recent start-up of the Pinto Valley mine and mill is expected to add to domestic copper mine capacity by some 62,500 tpy. Owned and operated by Cities Service Co.'s Miami Operations, the complex lies approximately 5% miles west of Miami, Ariz. The estimated $100- million project, the largest single construction project ever undertaken by Cities Service, includes the Pinto Valley open pit mine, a 40,000-tpd concentrator, and a 10-mile slurry pipeline that will transport a 28% copper concentrate slurry to a new filter plant located in Miami. Concentrate will be treated nearby at Inspiration Consolidated Copper Co.'s new smelter complex. The current pit design contains reserves of approximately 350 million tons of ore averaging 0.44% Cu. Based on an initial production target of 40,000 tpd ore and 60,000 tpd waste, mine life is estimated at 24 years. The current stripping ratio is 1.5: 1, requiring the ultimate removal of more than 500 million tons of waste and leach-grade material.

Jan 6, 1975

By P. I. Lipman

Largely forgotten by today's environmentalists and mineralogists is a pioneer scientist of the nineteenth century named Ellen Swallow. Fortunately, the memory of her accomplishments has been resurrected by Robert Clarke in his biography, Ellen Swallow: The Woman Who Founded Ecology. Her direct contributions to the field of mining included authoring First Lessons in Minerals and an analysis of the rare mineral samarskite which indicated the presence of an insoluble residue; her findings led to the eventual discovery of samarium and gadolinium. While enjoying the distinction of being the first woman student at the Massachusetts Institute of Technology, she successfully isolated vanadium in an ore which other experts had examined without detecting the metal.

Jan 1, 1974

By C. A. Shook, W. H. W. Husband, D. B. Haas

Although previous studies l,2,3 have been made, no correlations for pressure drop have been proposed. This is probably because severe particle breakage occurred and pressure drops changed substantially with time. A quantitative statement of the relationship of pressure drop to the parameters of the system is desirable for lignite since, unlike higher rank coals, lignite slurries are thixotropic. The present investigation was undertaken to quantify the pipeline behavior and required continuous monitoring of pressure drop and size distribution.

Jan 2, 1979

By C. A. Shook, W. H. W. Husband, D. B. Haas

Introduction Although previous studies1,2,3 have been made, no correlations for pressure drop have been proposed. This is probably because severe particle breakage occurred and pressure drops changed substantially with time. A quantitative statement of the relationship of pressure drop to the parameters of the system is desirable for lignite since, unlike higher rank coals, lignite slurries are thixotropic. The present investigation was undertaken to quantify the pipeline behavior and required continuous monitoring of pressure drop and size distribution.

Jan 1, 1980

By R. B. Burt, James A. Barr, I. S. Tillotson

THE pumping of solids in water suspension is an important part of many metallurgical and mining operations. In most cases, it is still in the rule of thumb category for which no universal formula has been developed, and much research is needed. Because of the limited and incomplete data available, this article may be classed as an experience paper, which is presented with the hope that some contribution will be made toward the development of the so-called universal formula. This formula, if and when developed, may be evolved from several factors, many of which are not now available for general application. The designing engineer is interested in obtaining accurate forecasts on: 1-the minimum velocities needed to prevent choke-ups in the pipeline, which in turn dictates pipe sizes, 2-power required for pumping, 3-pump selection. The basic factors for a given problem will include: 1-weight per unit of time of solids to be handled, 2-specific gravity of solids, for calculation of volume, friction and power, 3-screen analysis of solids with the colloidal acting, i.e., the slime fraction, a very important factor, 4-shape of particle or some means of determining a friction constant, 5-effects of percentage of solids, 6-development of a viscosity factor to be used in the overall calculations, 7-calculation of the lower limits of pipeline velocities permissible, 8-calculation of total head, pump horsepower, and 9-setting up of pump specifications. In certain limited cases horsepower and total heads and minimum velocities may be computed and a suitable pump selected from basic data, but in many cases, as in mining of Florida pebble, phosphate, experience rather than a hydraulic formula still should be used as a basis of selection. Pumping Florida Pebble Matrix Pumping at the Noralyn mine of International Minerals and Chemical Corp. will be used as an example. Other areas will vary as to the characteristics of the matrix, especially the slime content. A typical screen analysis of this matrix is: +14 mesh, pebble size,* 2.1 pct; -14 +35 mesh, 11.4 pct; -35 +150 mesh, 60.5 pct; -150 mesh, 25.0; total, 100 pct; moisture in bank, 20.0 pct; weight per cu ft in bank, 120 lb. The -150 mesh fraction may increase to as much as 35 pct in adjacent areas. When thoroughly elutriated, the matrix has a relatively slow settling rate, which is an important factor in permitting lower pipeline velocities without choke-ups. Exact data is not available to evaluate settling rates. For a factor of 100 a suspension of clean building sand in water is suggested. When pumping long distances, a quick settling matrix allows the coarser solids to settle out along the bottom of the pipeline, causing drag, turbulence, and increased friction. With a slow settling matrix as at Noralyn, turbulence acts to keep the solids in suspension at a lower friction head, regardless of the pumping distance. When the pebble, content of the matrix, i.e., the +14 mesh fraction, is in excess of 10 pct of the total solids, trouble may be expected from settling out even in normal pumping distances. To prevent choke-ups and maintain tonnage, an additional pump must be added in the long runs, where one pump would otherwise be satisfactory. A typical pulp handled is: total volume, 7800 gpm; water, 4500; solids pumped per hr, 4200 lb; sp gr pulp, 1.4; percent solids in pulp, 46.; pipe size, 16-in. ID; pulp velocity, 12.85 fps; probable critical velocity, 10 fps, as below this minimum -velocity choke-ups would be numerous. In calculating friction heads the Armco handbook is used where a roughness factor based on 15-year-old pipe is set up. Because the pipe used in pumping matrix is, smooth and- polished because of the scouring, action of the phosphate and its silica content, the head losses in the Armco table for water are practically the same as in pumping the Noralyn matrix through smooth pipe, plus the fact that conditions vary widely over short periods, making accurate determinations difficult to obtain. New pumps and pump, changes are being tested continuously and a wealth of data built up. This has resulted in a substantial improvement and lower relative costs in pumping matrix. The Florida phosphate industry is constantly seeking to offset higher wage and material costs with improved technique. Until a few years ago a 12-in. discharge pump was commonly used, with heads as low as 80 ft. Sizes have gradually increased and heads more than doubled. For example, the following pump was placed under test at the Noralyn mine: make, Georgia Iron Works; size, suction 16 in., discharge 14 in.; impeller, 39-in. diam; motor, 600 hp, slip ring; full load speed, 514 rpm. The results were increased head, higher capacity than the older design, with fewer pumps in the line from mine to washer.

Jan 1, 1952

By R. Costantini

Long-distance transportation of solids by hydraulic pipelines holds promise of great economic benefits. In most mineral processing plants today, moving of solids in slurry-form by pipeline is commonplace. Yet in spite of this, the method is slow in being adopted on a broad scale for moving solids over distances of many miles. This is especially surprising in view of the successful realization of two daring ventures in long-distance solids pipelines in this nation within the last five years. One is the 72-mile long, 6-in. diam. pipeline of the American Gilsonite Co. which has been satisfactorily transporting 700 tpd of gilsonite from the mine at Bonanza, Utah, to the processing plant at Grand Junction, Colo., since April 1957. The other is the 108-mile long, 10-in. pipeline of the Pittsburgh Consolidation Coal Co., which has been transporting about 4000 tpd of finely crushed coal from the mine at Cadiz, Ohio, to the Eastlake Power Plant of the Cleveland Electric Illuminating Co. since January 1958.

Jan 8, 1961

By R. D. Vaughn

The analysis of laminar flow of power-law non-Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journa! bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annul us would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7. 5 per cent. INTRODUCTION Non-Newtonianism and eccentricity occur simultaneously in two engineering problems: (1) flow of lubricants in journal-bearings and pressure-reducing bushings, and (2) flow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character — often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publicationsl-4,6,7 have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda 1 and Redberger and Charles 2 have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Ca ld well 3 and Bairstow and Berry,4 which is reported by Dryden, et al. 5 Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles2 show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (k < 0.5); however, for large diameter ratios (k + l), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden,5 Tao and Donovan6 and Piercy, et a1.7 Tao and Donovan examined the case of flow in narrow, eccentric annuli (k + 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et a l. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles2 and the experimental proof of Tao and Donovan6 both suggest that the region of large diameter ratios (k + 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. This model has many disadvantages which have been pointed out; nevertheless, its simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Bird8 and Savins9 have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli.

Jan 1, 1966

By J. G. Savins

Certain types of macromolecules added to water and salt solutions flowing in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these materials. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89-in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a I-in. water line yields a throughput capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion. INTRODUCTION This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe f1ow.I Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required* to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd,3 Agoston et al., Bundrant and Matthews, Robertson and Mason,6 Ousterhout and Hall,7 Daily and Bugliarello~ Lummus, Anderson, and Fox. 9 That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels,l0 Dever, Harbour, and Seifert.11 One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver12 and Dodge.13 However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction-. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabulal5 and Granville.16 Along somewhat different lines are the drag reduction studies of Kramer.17118 He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne,19 Cess and Sparrow,20&apos;21 Sparrow, Jonsson, and Eckert.22 Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merri11,23 Dodge and Metzner, Clapp,25 and Thomas.26

Jan 1, 1965

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

A 1,500-ft experimental well was used to study the pressure gradients occurring during continuous, vertical, two-phase flow through 1-in., 1 1/4-in. and 1 1/3-in. nominal size tubing. The test well was equipped with two gas-lijt valves and four Mathak electronic pressure transmitters as well as with instruments to measure the liquid production rate, air injection rate, temperatures and surface pressures. Tests were conducted for widely varying liquid flow, rates, gas-liquid ratios and liquid viscosities. From these data, an accucrate pressure-depth traverse was construcred for each test in each of the three tubing sizes. From the results of these tests, correlations have beer] developed which allow the accurate prediction of flowing pressure gradients for a wide variety of tubing sizes, flow conditions, and liquid properties. Also. the correlations and equations which are developed satisfy the necessary condition that they reduce to the relationships approprate to single-phase flow when the flow rate of either the gas or the liqutid phase becomes zero. All the correlations involve only dimensionless groups. which is a condition usually Sought for in similarity analysis but not always achieved. The correlations developed in this study have been used to calculate pressure gradients for pipes of larger diameter than those upon which the correlations are based. Comparisons of these calcuclaed gradients with experimetally determined gradients for the same flow conditions obtained from the literature indicate that extrapolation to these larger pipe sizes is possible with a degree of accuracy sufficient for engineering calculations. The extent of this extrapolation can only he determined with additional data from larger pipe diameters. INTRODUCTION The accurate prediction of the pressure drop expected to occur during the multiphase flow of fluids in the flow string of a well is a wideiy recognized problem in the petroleum industry. The problem has been brought even more into prominence with the advent of tubingless or slim-hole completions which use small-diameter tubing. Many of the correlations which give reasonably accurale results in the lager tubing sizes are greatly in error when applied to small-diameter conduits. Small-diameter conduits are defined as 1 1/2-in. nominal size tubing or smaller. The study of the pressure gradients which occur during multiphase flow of fluids in pipes is exceedingly complex because of the large number of variables involved. Further difficulties relate to the possibility of numerous flow regimes of widely varying geometry and mechanism and the instabilities of the fluid interfaces involved. Consequently, a solution to the problem by the approach normally used in classical fluid dynamics based on the formulation and solution of the Navier-Stokes equation has not been forthcoming. This is primarily the result of the nonlincarities involved and the difficulty of adequately describing the boundary conditions. As a result of the foregoing, most investigators have chosen semi-empirical or purely empirical approaches in an efford to obtain a practical solution to the problem. Much of the previous work in this area was done in short-tube models in the laboratory. A number of problems arise, however, when attempts are made to extrapolate these laboratory results to oilfield conditions where a much longer tube is encountered. In those few studies where data taken in long tubes were utilized, the data covered only a limited range of the variables, and as a result inaccuracies are introduced when the correlations are extended outside the range of the original data. Also, as a consequence of the limited amount of data available for these studies, the effects of several important variables were overlooked. The problem of predicting the pressure drop which occurs in multiphase flow differs from that of single-phase flow in that another source of pressure loss is introduced, namely, those pressure losses arising from slippage between the phases. This slippage is a result of the difference between the integrated average linear velocities of the two phases, which in turn is due to the physical properties of the fluids involved. In contrast to single-phase flow. the pressure losses in multiphase flow do not always increase with a decrease in the size of the conduit or an increase in production rate. This is attributed to the presence of the gas phase which tends to slip by the liquid phase without actually contributing to its lift. Many investigators have attempted to correlate both the slippage losses and the friction losses by means of a single energy-loss factor analogous to the one used in the single-phase flow problem. In an approach of this type, hourever, many of the important variables, such as

Jan 1, 1966

By L. L. Melton, W. T. Malone

Fluid mechanics research conducted with non-Newtonian fluid systems now permits prediction of the behavior of these fluid systems in both laminar and turbulent modes of flow through circular pipes. Present work concerns non-Newtonian fluid systems currently used in the hydraulic fracturing process. During fracturing treatments, an unsteady-state condition may frequently be encountered arising from. the reaction rate of a chemical additive. This condition must be evaluated in order to predict the actual behavior of a particular fluid during field application. Design and operation of the apparatus used to determine fluid-flow behavior permit obtaining data under such non-equilibrium conditions. This paper shows methods used to obtain rheology measurements, develop hydraulic relationships and evaluate chemical reactions producing unsteady-state conditions. Engineering application of this research is illustrated by employing measured rheological values and developed hydraulic retationships to produce frictional pressure loss (psi/100 ft) us flow rate (bbl/min) charts of common tubing and casing sizes for an example fracturing fluid. How these charts and chemical reaction rate information are then combined to predict actual turbulent hydraulic behavior during unsteady-state field conditions is also discussed INTRODUCTION Many fluids used in hydraulic fracturing contain chemical additives which impart non-Newtonian fluid properties that may drastically alter their hydraulic behavior. Equally drastic alteration in wellhead pressure, injection rate and hydraulic horsepower requirement may result from these fluid properties. Prior research conducted to relate non-Newtonian fluid properties with hydraulic behavior has not as yet produced a universal relationship, particularly for the turbulent flow region. which of the many Possible non-Newtonian fluid properties is responsible has not been conclusively established. A systematic description, suggested by Metzner, of the many possible non-Newtonian fluid properties exhibited by real-fluid behavior, and a current discussion of theoretical and applied aspects of non-Newtonian fluid technoloy can be found in Handbook of Fluid Dynamics. f Little or no research has previously been attempted with fluids exhibiting time - dependent properties. Addition of chemicals during a fracturing treatment is often accomplished by continuously mixing and displacing the fluid. This produces a time-dependent effect or unsteady-state condition while the fluid is progressing through surface and wellbore conductors. This condition is due to solution or chemical reaction of the additive. Considerable departure from conventional methods of obtaining and interpreting data was found necessary to consider these conditions. Therefore methods were developed to obtain hydraulic behavior information under these complex, unsteady-state conditions. Relationships presented in this paper to predict hydraulic behavior of non-Newtonian fluids in circular pipes were obtained by constructing and operating a small pipeline apparatus in the manner of a pilot-plant study. These relationships are suggested as scaleup equations and are not proposed as fundamental rheological parameters. While perhaps deficient from a fundamental research viewpoint, a pilot-plant study does permit the determination and convenient evaluation of variables pertinent to a process. A pilot-plant study can result in a valid engineering application procedure even when fundamental relationships are still undefined. An excellent series of articles by Bowen has appeared in the chemical engineering literature.2-8 These give a thorough review of proposed hydraulic relationships and their limitations for non-Newtonian fluid behavior in circular pipes. A graphical method is presented to scale up data for a fluid exhibiting an anomalous hydrau1ic behavior in the turbulent flow region. Considerable assistance has been obtained from these articles to interpret the anomalous behavior noted during this investigation. These articles also provided assurance that a pilot plant is a practical approach to evaluate the hydraulic behavior of non-Newtonian fracturing fluids. _____________

Jan 1, 1965

By J. L. Zakin, G. K. Patterson, J. M. Rodriguez

Correlation has been obtained between drag-reducing characteristics for turbulent flow in a pipe and measurable properties of several polymer solutions. Several concentrations of high molecular weight polymethyl methacrylate in toluene, high molecular weight polyisobutylene in both toluene and cyclohexane, medium molecular weight polyisobutylene in cyclohexane and benzene and low molecular weight polystyrene in toluene were studied. Data obtained in these nonpolar solvents and literature data for more polar solvents were successfully correlated as the ratio of measured friction factor to purely viscous friction factor vs the modified Deborah number vrl/D0.2 where 71 is the first-mode relaxation time of the solution estimated by the Zimm theory. A shift factor which is a function of intrinsic viscosity 1/(4[?] - 1) allowed all the data obtained with nonpolar solvents to be correlated as a single function. For these systems, most of the data fit a single curve to within + 5 percent of the average friction factor ratio. The shift factor did not give a unique function of the data for the more polar systems. INTRODUCTION The phenomenon of drag reduction in polymer solutions was first studied by Toms1 in dilute solutions of polymethyl methacrylate in mono-chlorobenzene. The drag ratio for flow through circular tubes has been defined2 as the ratio of the pressure. drop of the solution to the pressure drop of the solvent at the same flow rate. The drag ratio is less than 1.0 for a drag-reducing fluid. Practical use of drag reduction is being made in fracturing operations in the petroleum industry.3 A more fundamental quantity is the friction factor ratio, defined as the ratio of the observed pressure drop to that predicted for a solution of the same viscosity characteristics and density at equal flow rates using the Dodge-Metzner friction factor equation4 Viscous solutions with drag ratios greater than 1.0 can have friction factor ratios less than 1.0. For practical applications, it is drag reduction which is of interest. However, for correlation the fundamental ratio is the friction factor ratio. In recent years, drag reduction has been studied extensively. Recent studies have shown that reasonable predictions of the incipience of drag reduction in polymer solutions can be made from the properties of the solutions and the flow Variables.5 However, it has not been possible to predict accurately the amount of drag reduction to be expected for a given polymer solution without any drag-reducing turbulent flow data on the same solution.6 For flow through circular tubes it is well established that there is a concentration effect and a diameter effect on drag reduction. Toms1 observed that drag reduction increases with an increase in the concentration of the solution up to an optimum concentration beyond which, due to the increased viscosity of the solutions, the drag ratio increased with an increase in concentration. Hershey 7 observed that for dilute Newtonian polymer solutions in nonpolar hydrocarbon solvents, a normal transition region may be obtained followed by a departure from the von Karman equation (on a friction factor-generalized Reynolds number chart). The point of departure is a function of diameter: the smaller tubes depart at the lower Reynolds numbers. Concentrated solutions may show no abrupt transition region, but merely an

By R. J. Brown

Design of a submarine pipeline system is governed by many factors, one of which is the effect of transverse horizontal currents on the pipeline structure itself Although this feature alone can be of utmost importance to the life span and stability of the underwater pipeline, it is usually the least recognized, with these hydro-dynamic forces being either completely overlooked or grossly underestimated. In an attempt to supply the methods and means for stabilization of sub-marine pipelines, much capital has been spent by pipeline companies. Design criteria incorporated by these organizations extend over a broad spectrum of engineering with bases varying from pure theory to cut and dry methods. A history of numerous failures has substantiated the postulate that many of these submarine pipelines have been underdesigned from the stability standpoint. By the same token, equally as many have been excessively overdesigned with resultant excess expenditures. An attempt has been made in this paper to establish the magnitudes of these hydrodynamic forces by measuring the lateral current-induced differential pressure distribution around the periphery of the submarine pipeline. INTRODUCTION The expenditure of money for research by corporations obviously requires beneficial results to justify the investment. One of the functions of the engineer is first to make the problem known and then to provide a means of solution at the least possible cost. The initial procedure is to investigate all pertinent published technical articles on the subject to determine if this problem has been previously solved. If resolution of this problem is not obtainable, the next course of action is to evaluate through experiments these forces and their magnitudes. On the specific subject of drag and lift, the accumulation of data is provided from three separate and distinct sources: from experience, from theoreticians and through experimental observations. The experience source has proved costly with money wasted either because of underdesign and failure or excessive expenditures for overdesign, and has not been sufficient to form a definite conclusion on these hydrodynamic forces. The pure theoretician is often not completely cognizant of the situation and his works bear little adaptation to the real problem. The experimentalist has his own problems with regard to obtaining results from small-scaled models and successfully adapting them to the larger prototypes. Each method has its own advocates who diligently adhere to their own separate routes as being the only means of resolving this problem. However, a review of the various methods of analysis leads one to the conclusion that if the advantages of all three are combined, a reasonable solution to this problem can be reached. Briefly then, the problem is to obtain the magnitudes of the forces on the submarine pipeline subjected to a lateral current by investigations of previous design considerations, by a study of existing theoretica1 data and by appropriate experimentation. This paper deals mainly with obtaining experimental data and the interweaving of theoretical and experience factors for resolution of these forces. APPARATUS AND PROCEDURE These tests were performed in 1961 at Collins Construction Co.&apos;s main office near Port Lavaca, Tex. Test equipment consisted of a steel tank 3 ft high by 4 ft wide by 40 ft long, with several pumps circulating the water through the tank via suction lines from the downstream portion of the tank and discharging from the pumps directly into the upstream end of the tank. For reduction of turbulence, a wire section was constmcted in the upstream portion and straightening vanes in the form of pipes, screens, etc., were used to reduce the vortex and eddy action in the tank (Fig. 1). A venturi was built at the test specimen for obtaining velocity sufficient to simulate actual conditions. This full-scale test was initiated to eliminate the error introduced in modeling and obtain a truer picture of forces actually encountered. Six- and 10-in. specimens were prepared by

Jan 1, 1967

By L. L. Melton, D. L. Lord, B. W. Hulsey

A mathematical model d1.20p/4L = A(8v)8 derived from the Blasius equation is proposed to be applicable to turbulent flow through straight cylindrical pipe for time-independent fluids which produce a diameter family of straight parallel lines on a log (dp/4L) vs log (8v/d) plot or stress-flow diagram. Such a correlation should permit scale-up with data taken from one pipe diameter for Newtonian, inelastic non-Newtonian and viscoelastic fluids, such as dilute polymer fracturing fluids, which produce considerable frictional pressure reductions. The Newtonian diameter exponent value 1.20 is shown to be empirically valid for turbulent non-Newtonian flow by application of numerical analysis methods. Multiple regression analysis is applied to a logarithmic linearization of the proposed model. An improved data fit results from further linearization achieved by taking linear terms from a generalized Taylor&apos;s series expansion about the multiple regression coefficients. Extensive experimental data obtained in five pipe diameters with water, sodium carboxymethyl-celIulose solutions, guar gum solutions, bentonite clay suspensions and calcium carbonate slurries are presented. Except for calcium carbonate slurries, which were investigated rather than time-dependent cement slurries, the fluids studied contain drilling or fracturing fluid additives. The behavior exhibited by these fluids is considered typical of most fluids encountered in drilling, cementing and fracturing operations. INTRODUCTION Considerable difficulties have been encountered in predicting turbulent flow pressure drops produced by non-Newtonian fluids flowing through straight cylindrical pipe. Correlations previously presented require extensive experimental data which represent several pipe diameters and a wide flow rate range to estimate the necessary scale-up parameters.l-7 One must implement either elaborate experimental apparatus or spend considerable time and effort to gather these data. Presented here is a correlation method which should minimize the experimental effort and data analysis normally required by utilizing flow data taken with only one pipe diameter. Turbulent flow data (up-stream and down-stream pressure and volumetric flow rates) were collected for five pipe diameters through operation of a small pipeline system having an electronic data acquisition and digitizing system. A mathematical model derived from the Blasius equation was utilized to describe the functional relationship between pressure drop and the two independent variables, diameter and average flow velocity. A correlation, which should produce a valid single-pipe scale-up, resulted from a computer-implemented statistical and numerical data analysis for several time-independent non-Newtonian fluids.

By R. A. Ritter, J. P. Batycky

A numerical technique has been developed to permit estimating the pressure gradient associated with laminar flow of thixotropic liquids through long Pipelines. For this purpose the pipeline is divided into a number of radial and longitudinal increments within which rheological properties of the fluid may be considered as constant at any time. Then, provided only that the fluid flow curve is defined at every duration of shear, it is possible to predict the instantaneous pressure gradient at any cross-section along the pipeline for each desired flow rate and pipe size. The technique consists of an iterative integration of shear rate to establish the appropriate value of the wall shear stress at each location. Consistency of fluid in the increment is determined by the flow history of that increment, while the radial flow associated with variations in velocity profile is accounted for by adjusting the width and radial position of the increment. A number of pressure profiles, computed at each of several flow rates, provide a convenient basis for pipeline design and pump selection. INTRODUCTION In recent years considerable attention has been given to predicting pressure drop associated with the isothermal laminar flow of time-independent non-Newtonian fluids in pipes and annuli. 6,11,12 The approach generally has been to develop analytical relationships between flow rate and pressure drop based on simple constitutive models which hopefully provide an approximate description of the rheological properties of the fluid. Analytical solutions are highly desirable since the influence of all pertinent parameters can be readily determined. Unfortunately, however, this approach is restricted to simple flow geometries and- frequently leads to erroneous results due to inadequacies in the model. In certain cases a solution may be obtained through applying appropriate numerical techniques.l,14 For example, a digital computer program is available for predicting the velocity profile and pressure drop encountered by any Newtonian or time-independent non-Newtonian fluid flowing under laminar conditions in a cylindrical pipe or annulus.l In this paper the consistency behavior of the fluid need only be described in terms of basic rheological data. Analyzing flow systems involving fluids with time-dependent rheological characteristics is considerably more complicated since substantial changes in consistency may occur because of sustained shear action. This sensitivity to shear frequently persists for several hours. Consequently, variations in pressure drop and/or flow rate resulting from the aging process and addition of unsheared or partially sheared fluid to the system must be considered for purposes of pipeline design. This paper outlines a numerical method for predicting the transient and steady-state laminar flow behavior of a thixotropic liquid in a pipeline of arbitrary length (i.e., at a specified constant flow rate, the instantaneous pressure gradient may be determined at any time after start up and at any location along the pipeline). Several such pressure gradient profiles, computed at several flow rates, may be combined to produce a complete portrait of the system response. This flow portrait provides a reasonable basis for pipeline design and for selecting a suitable pump characteristic. TIME-DEPENDENT RHEOLOGICAL BEHAVIOR The most familiar time-dependent rheological properties are those exhibited by thixotropic liquids. Many of these materials, particularly thixotropic crude oils, generally display an apparent yield stress in that a finite pressure gradient is required to initiate flow. Then, under the influence of sustained shear at a constant shear rate, the consistency systematically decreases to some final limiting value. The shear stress obtained at

By D. R. Pratt, R. W. Hanks

The method of Caldwell and Babbitt for detennining Bingham plastic rheological constants from engineering pipe flow data has been erroneously used in many previous applications. A reanalysis of extensive pipe flow data from the literature is performed. Critical Reynolds numbers corresponding to the laminar-turbulent transition calculated from these data are found to agree with theoretically calculated values for the entire flow range studied. Similar agreement is found for the authors&apos; own data&apos; for flow of 10 slurries between parallel plates. The Bingham plastic model is shown to be a reliable representation of the flow of non-Newtonian slurries provided it is properly applied. If the Hedstrom number He = pD2 t0/?2 > 104, then the linear approximation method of Caldwell and Babbitt is invalid for pipe flow data obtained in systems of ordinary engineering interest, and the complete nonlinear form of the pipe flow Bingham plastic equation must be used in determining rheological parameters. INTRODUCTION Many materials of engineering interest must be handled and transported as slurries or suspensions of insoluble particulate matter in a Newtonian liquid. These suspensions frequently exhibit non-Newtonian rheological behavior which is reasonably well described by the simple Bingham plastic rheological equation1 Using this particular equation to describe the laminar flow characteristics of slurries was discussed at length by Caldwell and Babbitt2-4 who considered the flow of various clay slurries and sewage sludges. The model has since been used by many others.5-7 More recently the problem of predicting the laminar turbulent transition Reynolds number for Bingham plastic fluids has been treated8 for the case of flow in pipes. This paper points out errors which have existed in the analysis of Bingham plastic flow since the work of Caldwell and Babbitt2-4 and presents a reanalysis of the laminar turbulent transition calculatiod for Bingham plastic flow in pipes. In addition, new data obtained for flow of Bingham plastic slurries between parallel plates, both in laminar flow and in the laminar turbulent transition region, will be presented and compared with the theoretical analysis of laminar turbulent transition for flow between parallel plates. THEORETICAL ANALYSIS PIPE FLOW The mathematical analysisl-4 of laminar flow of a Bingham plastic fluid leads to the following equation. where q = <v>/R is a pseudoshear rate, rw is the wall shear stress Eo = r0/rw, r0 is the yield stress and 1 is the coefficient of rigidity or plastic viscosity from Eq. 1. Caldwell and Babbitt2-4 recognized that the quartic term in Eq. 2 was small compared to the other terms whenever 5, « 1, and that for large values of 7, a plot of Eq. 2 becomes linear. The slope of such a plot with rw as ordinate is 4? and the intercept is (4/3) ro. This approximation is illustrated schematically in Fig. 1. The shaded region between the true curve and the straight-line approximation near the origin represents the contribution of the quartic term. In principle, therefore,

By J. Orkiszewski

A method i.s presented which can accurately predict, with a precision of about 10 percent, two-phase pressure drops in flowing and gas-lift production wells over a wide range of well conditions. The method is an extension of the work done by Grifith and Wallis and was found to be superior to five other published methods. The precision of the method was verified when its predicted values were compared against 148 measured pressure drops. The unique features of this method over most others are that liquid holdup is derived from observed physical phenomena, the pressure gradient is related to the geometrical distribution of the liquid and gas phase (flow regimes), and the method provides a good analogy of what happens inside the pipe. It takes less than a second to obtain a prediction on the IBM 7044 computer. INTRODUCTION The problem of accurately predicting pressure drops in flowing or gas-lift wells has given rise to many specialized solutions for limited conditions, but not to any generally accepted one for broad conditions. The reason for these many solutions is that the two-phase flow is complex and difficult to analyze even for the limited conditions studied. Under some conditions, the gas moves at a much higher velocity than the liquid. As a result, the down-hole flowing density of the gas-liquid mixture is greater than the corresponding density, corrected for down-hole temperature and pressure, that would be calculated from the produced gas-liquid ratio. Also, the liquid&apos;s velocity along the pipe wall can vary appreciably over a short distance and result in a variable friction loss. Under other conditions, the liquid is almost completely entrained in the gas and has very little effect on the wall friction loss. The difference in velocity and the geometry of the two phases strongly influence pressure drop. These factors provide the basis for categorizing two-phase flow. The generally accepted categories (flow regimes) of two-phase flow are bubble, slug, (slug-annular) transition and annular-mist They are ideally depicted in Fig. 1 and briefly described as follows. RUBBLE FLOW (FIG. 1A) The pipe is almost completely filled with the liquid and the free-gas phase is small. The gas is present as small bubbles, randomly distributed, whose diameters also vary randomly. The bubbles move at different velocities depending upon their respective diameters. The liquid moves up the pipe at a fairly uniform velocity and, except for its density, the gas phase has little effect on the pressure gradient. SLUG FLOW (FIG. 1R) In this regime, the gas phase is more pronounced. Although the liquid phase is still continuous, the gas bubbler coalesce and form stable bubbles of approximately the rame size and shape which are nearly the diameter of the pipe. They are separated by slugs of liquid. The bubble velocity is greater than that of the liquid and can be predicted in relation to the velocity of the liquid slug." There is a film of liquid around the gas bubble. The liquid velocity is not constant—whereas the liquid slug always moves upward (in the direction of bulk flow); the liquid in the film may move upward but possibly at a lower velocity, or it may move downward. These varying liquid velocities will result not only in varying wall friction losses, but also in a "liquid holdup" which will influence flowing density. At higher flow velocities, liquid can even be entrained in the gas bubbles. Both the gas and liquid phases have significant effects on the pressure gradient. TRANSITION FLOW (FIG. 1C) The change from a continuous liquid phase to a continuous gas phase occurs in this region. The liquid slug between the bubbles virtually disappears, and a significant amount of liquid becomes entrained in the gas phase. Although the effects of the liquid are significant, the gas phase is more predominant.

By J. S. Dodge, I. M. Krieger

The laminarturbulent transition was studied for monodisperse rigid polymer latices as functions of particle diameter and concentration at several tube diameters. Breaks in the graph of friction factor US Reynolds number were used to characterize the transition; rates of shear were sufficiently high so that Newtonian behavior at the high shear limiting viscosity could be assumed. No abnormal behavior was noted at concentrations below 30 volume percent. At higher concentrations, suppression of turbulence was observed with critical Reynolds numbers rising to as high as 5,500 at 50 volume percent. No definite effect on the transition was noted due to variation of particle size or tube diameter. The type of surfactant used to stabilize the latex was found to have an important influence on the critical Reynolds number. INTRODUCTION For some polymer solutions and solid-in-liquid suspensions, the transition from laminar behavior to turbulence in pipeline flow has been reported to take place at unusually low1-5 and in some cases at higher than normal6,7 critical Reynolds numbers. Extreme values of critical Reynolds numbers (NRe*) have been found to range from 1 to 6,000, as opposed to the values of 2,000 to 3,500 which are obtained for ordinary liquids. Observations have also been reported of drag reduction in fully developed turbulent flow, i.e., a decreased value of the friction factor in the Reynolds number-friction factor plot6*10-14 in colloidal and polymeric fluids. In some cases, turbulence suppression (unusually large values of Nre*) was noted to occur preceding the drag reduction,6 while a normal transition was noted in other cases of drag reduction.14 To relate the occurrence of turbulence suppression and drag reduction to the molecular or particulate structure of the fluid, it is desirable to characterize the structural variables with some precision. For most colloidal dispersions and polymeric fluids, this is very difficult; particle sizes, shapes and stiffnesses may vary over wide ranges in the same sample. Recently, however, a colloidal fluid has become available which consists of rigid spherical particles of highly uniform diameter dispersed in a simple Newtonian liquid. These are monodisperse polymer latices, prepared by carefully controlled emulsion polymerization reactions. The purpose of this research was to study the transition to turbulence in these well-characterized colloidal fluids as a function of concentration, particle diameter and tube diameter. Typical flow curves of latices of high solids content are shown in Fig. 1. While these curves were obtained with monodisperse latices, the general shape of the curve is also typical of a polydisperse latex. It is observed that a shear-thinning region occurs for low to moderate rates of shear. At sufficiently high shearing rates a limiting Newtonian viscosity is reached. The viscosity µ diminishes with decreasing volume fraction 4 at all shear rates. For 4 less than 0.25, latices are Newtonian at all rates of shear.15 An increase in average particle size (at a given extends the Newtonian viscosity region to lower rates of shear. A third factor which influences the