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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 A G. L Pratt, J R. Grant

Mining companies face the ongoing challenge of sustaining and growing production. This paper outlines business investment concepts to grow reliable returns on investment from a portfolio of choices by:improved visualisation, diagnosis and tune up of the investment pipeline (pipeline management); good corporate decision making (governance) to select the right project mix, risks and sequence; and delivery strategies to enhance and reliably execute projects.

Jan 1, 2006

By Ken G. Kress

Syphons can be a simple, reliable and proven alternative to otherwise more complex pumping systems or low level outlet works. In a simple form they consist of a pipeline constructed over the top of an embankment or high topographic feature, connecting a source pond to a receiving pond or channel (see Photograph 1). The syphon action is initiated by removing air from the pipeline (priming) using simple devices which can be purchased ?off the shelf?. Once primed, the syphon flow rate can be controlled or stopped using conventional gate, valve, orifice plate or other devices. Repriming is not required even if the flow is stopped, provided the syphon is not drained. A limiting factor in considering a syphon as a design option is the maximum lift (i.e., vertical distance from source pond level to summit of syphon) which is approximately 9 metres, or less, dependent on syphon pipe features and site conditions. Pipeline syphons can be quickly constructed from readily available materials including steel, polyethylene and PVC pipe. They are particularly well suited to many of the unique conditions often encountered at minesites. This paper identifies situations that can sometimes be best resolved using pipeline syphons. It provides basic principles for pipeline syphon design and includes case histories of their successful application.

May 1, 2001

By W. J. Dick, K. G. Kress

A pipeline syphon can be a simple and reliable alternative for water conveyance as compared to otherwise more complex pumping systems or low-level outlet conduits through earthfill dams. In a simple form, it consists of a pipeline constructed over the top of a dam or other high topographic feature, connecting a source pond to a receiving pond or channel (Fig. 1). The syphon action is initiated by removing air from the pipeline (priming) using water pumps, vacuum trucks, or simple devices that can be purchased “off-the-shelf.” Once primed, the syphon flow rate can be controlled or stopped using conventional gate, valve, orifice plate, or other devices. Repriming is not required even if the flow is stopped, provided the syphon was not drained. A limiting factor in considering a pipeline syphon as a design option is the maximum lift (i.e. vertical distance from source pond water level to summit of pipeline syphon) which is approximately 9 m or less, depending on pipeline syphon features and site conditions. A pipeline syphon can be quickly constructed from readily available materials including steel, concrete, polyethylene, or PVC pipe. It is particularly well suited to many of the unique conditions often encountered at mine sites. This paper identifies situations that can sometimes be best resolved using a pipeline syphon. It provides basic principles for pipeline syphon design and includes case histories of their successful application.

Jan 1, 2005

By Boger D. V

Two industrial case studies in which detailed investigation of the flow behaviour of mineral slurries is used to assess the feasibility of pipeline solid transport are described. The first example deals with the pumping of highly concentrated bauxite tailings to disposal, while the second exam- ple examines the possibility of transporting high-density Victorian brown coal slurries which previously has been thought as uneconomical. It is demonstrated that these typical solid handling problems can be solved by a good understanding of the rheology of suspensions.

Jan 1, 1989

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 Tsunenori Shibata, Kazunori Jimbo, Kaoru Toya, Masafumi Matsumoto, Jinya Mitsui, Toshinori Tsuji

"The Toyama Line is under construction as a natural gas pipeline with a length of 102 km from Itoigawa City to Toyama City. A 2 km-long tunnel section of the pipeline that we are reporting here is being excavated in a mountain area away from an urban area. The geology under which the tunnel is constructed is collapsible fractured breccia slate and Holocene sandy soil. Other tunnels of the Hokuriku Expressway and Hokuriku Shinkansen are in service above the tunnel route. From the starting shaft on Toyama side, conventional tunneling was adopted to facilitate excavating the base rock layer and maintain enough distance from the Hokuriku Expressway tunnel. From the starting shaft on the Itoigawa side, TBM tunneling was adopted to cope with the unconsolidated soft ground for a 200 m-long section from the shaft. We will discuss the issues and countermeasures concerning the selection of a tunnel route and excavation methods, performance of both conventional and TBM tunneling, and underground connecting of these tunnels excavated by conventional (NATM) and TBM methods under a high groundwater pressure up to 1.2 MPa. INTRODUCTION AND BACKGROUND The International Petroleum Exploration Teiseki Co., Ltd. (INPEX) is constructing a high-pressure main pipeline network in the Toyama Prefecture area to promote the use and reliable supply of natural gas as shown in Figure 1. As part of the Toyama line project that has a total length of 102 km, A-1 construction, the nearest section to the tunneling starting point in Itoigawa City, where various tunnel excavation methods have been adopted to install the high-pressure pipeline 20 inches in diameter, a 2 km tunnel in the A-1 construction section discussed here is to be excavated by conventional and TBM methods in a mountain area. Based on environmental studies such as traffic jams due to frequent traffic of heavy vehicles disposing of soil, and the effects of dust, noise and vibration during construction, we selected the route to install the gas pipeline in a mountain area as shown in Figure 2, where the impact on the surrounding environment could be minimized."

Jan 1, 2016

Both as an energy source and as a raw material, natural gas is playing an increasingly important role as a catalyst for the development, continuation and rebirth of mining projects in Australia. Pipelines are the vital link in making natural gas available to a region and to individual mines. This paper will cover the role of pipelines in supplying mining projects in Australia, the development and status of the Ballera to Mount Isa gas pipeline and the future prospects for gas pipelines in the Carpentaria Mineral Province.

Jan 1, 1998

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 James M. Link

The first rule of mineral deposits always seems to be: the deposit is never close to the market. With gems and precious metals, this is not much of a problem. But with most of the mineral commodities used in today&apos;s world, transportation becomes a major part of the cost to the consumer. In Japan, for example, more than 60% of the cost of coal to the consumer may be attributed to transportation. The purpose of this article is to examine pipeline transportation, particularly mineral slurry pipelines, as a means of getting the mineral to market. Pipelines Today Regulated pipelines in the US totaled nearly 724 Mm (450,000 miles) in 1980 according to the Federal Energy Regulatory Commission (FERC). Worldwide, more than 210 Mm (125,000 miles) of new pipelines will start construction in 1982 at an estimated cost of more than $150 billion. According to the Bechtel Corp., the period between 1982 and 2000 will see major growth in pipelines of all kinds. In North America, major movements of crude oil from Alaska and synfuels from the Rocky Mountains will require the construction of nearly 16 Mm (10,000 miles) of new pipelines. Nearly 42 Mm (26,000 miles) of new gas transmission pipelines will be needed to tap both US and Canadian arctic gas fields and move the gas to major markets on both coasts. Other pipelines will be required to move additional quantities of natural gas from the Rocky Mountains to more populous regions. Bechtel says more than 24 Mm (15,000 miles) of slurry pipelines will be needed to transport coal from both eastern and western coal provinces to the Mississippi valley and coastal areas. In 1980, 125 companies delivered more than 1 km3 (6.5 billion bbl) of crude oil and 652 hm3 (4.1 billion bl) of products in the US. At the same time natural gas pipelines transported 498 km3 (17.6 trillion cu ft). The reported investment by these companies was nearly $20 billion at the end of 1980. Advantages of Pipeline Transportation The obvious success and vitality of the oil and gas pipeline industry is based, at least in part, on the fact that pipelines are a very efficient and low-cost method of transportation. This fact, coupled with the need for lower cost trans¬portation, has led to the marriage of oil and gas transmission technology and the bulk mineral solids transportation industry. The off-spring of this marriage is the mineral slurry pipeline. Slurry pipelines have a number of advantages over other transportation methods. One of these is the fact that they are buried-out-of-sight, out-of-mind. Second, they are relatively small users of labor because they lend themselves to automation and remote, or even computer control. Third, they offer an attractive economic alternative to other transportation systems. For example, for a 1000 km (621 miles) distance, rail costs of 1?/ km (1.7?/ton-mile) are about equivalent to slurry pipeline costs. But, as the distance increases, pipeline cost per t-km continues to drop while equivalent rail charges remain essentially insensitive to distance. Where existing rail, barge, or ocean ships are available, the cost of new construction associated with a slurry pipeline probably will render it noncompetitive. However, where new rail or other construction is needed, the cost of a slurry pipeline is very competitive. About three-fourths of the cost of a pipeline is in pipe, fittings, and construction. Nearly a fifth of the investment is in pump stations and the remainder is in right-of-way, surface facilities, utility acquisition, communication facilities, and other support areas. The fact that pipelines are capital intensive is, at the present time, a mixed blessing. For example, the delivered cost of coal in a hypothetical project doubles when the cost of money rises from 9% to 17.5% per year. The largest cost element for delivered coal in this example is in depreciation and finance charges. The next largest cost element is electricity to power the pumps, with labor making up the smallest increment of the delivered cost of coal. World Slurry Pipelines The idea of a slurry pipeline was probably first investigated in the latter 19th century, but the first ones were successfully built and operated in the US in the early 1900s. Today, they are fairly common worldwide. Table 1 shows a number of the world&apos;s slurry pipelines. An examination of these will further emphasize the fact that pipelines provide a cost competitive alternative where new construction of a transportation system is required. In each of the examples, the desired mineral commodity is located in a remote corner of the world, markets are at a great distance, value of the commodity is not great, and no other transport system is available.

Jan 10, 1982

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,