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Experimental Study on Two-Phase (Solid-Liquid) Flows of Ground Wheat Straw in Inclined Pipes
Kashif Javed1, Vinoj Kurian1, Amit Kumar1,*
Published in Journal of the ASABE 67(1): 69-90 (doi: 10.13031/ja.15730). Copyright 2024 American Society of Agricultural and Biological Engineers.
1Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada.
*Correspondence: amit.kumar@ualberta.ca
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 7 July 2023 as manuscript number ES 15730; approved for publication as a Research Article by Associate Editor Dr. Deepak Kumar and Community Editor Dr. Kasiviswanathan Muthukumarappan of the Energy Systems Community of ASABE on 9 October 2023.
Highlights
Abstract. Long-distance pipeline hydro-transport of lignocellulosic biomass for industrial-scale biofuel production at levels comparable to conventional oil refineries presents an economically and logistically viable alternative to fossil fuels. There is very limited understanding on the behavior of the transportation of agricultural biomass slurries in an inclined pipeline. This research is focused on a laboratory-scale investigation of 6.4 mm nominal particle length (d50 = 4.85 mm) knife-milled wheat straw-water suspensions' uphill and downhill flows for a range of pipe inclination and saturated mass concentrations. The range of pipe inclination and saturated mass concentration was -7° to +21° and 5%-30%, respectively. The inclined test section was 29 m long with a 50 mm inside diameter of a closed pipeline loop. The accuracy of the measurements was verified by calibrating the inclined pipe section with fine sand (d50 = 0.103 mm)-aqueous slurries and comparing the results with established correlations. Most wheat straw-aqueous suspensions in the inclined flows showed the characteristics of the plug flow and the transition flow regions together for saturated mass concentration, Cm = 5%-30% and the entire flow range (0.5-4.7 m s-1), with a clear dependence of both the onset velocity of drag reduction (vOD) and drag reduction (%DR) on the pipe inclination as well as the slurry concentration and the critical concentration of maximum drag reduction (Cm)cr on a specific range of suspension velocity. Because of the accelerating effect of gravity, downhill slurry flows had the lowest vOD and the highest %DR at every Cm and pipe inclination with a maximum drag reduction of 25.53% at vm = 4.5 m s-1 and Cm = 25%. Uphill flows demonstrated some nonmonotonic changes in vOD and %DR, which need more experimental data for us to reach a firm conclusion. The research outcomes could help design and operate a long-distance integrated pipeline network for biomass transportation to produce biofuels on a large scale.
The substantial rise in global energy requirements has increased the transportation sector's dependence on fossil fuels. The global energy demand in the transportation sector is met primarily by fossil fuels. Currently, the transportation sector consumes approximately 50% of global fossil fuel energy (Halder et al., 2019). The significant dependence of transportation and other sectors on fossil fuels results in the emission of greenhouse gases (GHGs), which causes global warming (Goldemberg, 2008; Miller et al., 2012) but is also depleting these reserves (Asomaning et al., 2016; Ritchie and Rosado, 2017; Vohra et al., 2014). One of the most reliable and sustainable ways to reduce global dependence on fossil fuels is to produce renewable biofuels (i.e., bioethanol, biodiesel, etc.) from biomass (i.e., crops and their residues, wood and its wastes, municipal solid wastes, etc.) (Kim and Dale, 2004; Pootakham and Kumar, 2010; Saleem, 2022; US-EIA, 2023). In current practice, biomass conversion facilities rely largely on edible food crops to produce bioethanol (Mohanty and Swain, 2019). That said, lignocellulosic biomass (like agricultural and forest residues) seems more promising and has been gaining attention in bioethanol production because (1) the majority of these feedstocks are currently not used around the globe for liquid fuel production (Balat and Balat, 2009; Banerjee et al., 2010), (2) its low initial cost at agricultural farms (Balat and Balat, 2009), (3) its carbon neutrality with high GHG emission reduction potential when substituting fossil fuels (Banerjee et al., 2010; Halder et al., 2019; Vohra et al., 2014), and (4) the absence of food security issues with respect to the present and future needs of the world’s growing population (Halder et al., 2019).
The high cost of transporting biomass bales from farms to biomass conversion facilities by ground (truck or rail) and the traffic congestion caused by the high frequency of trucks on the road are the main obstacles to commercial bioethanol production from agricultural waste biomass like wheat straw and corn stover (Aden et al., 2002; Kumar et al., 2003, 2005a; Ruth, 1999). A series of studies on the techno-economic and laboratory-scale investigations to address these challenges have been conducted earlier (Kumar et al., 2004, 2005a,b; Luk et al., 2014; Vaezi et al., 2014). The investigations showed that pipeline hydro-transport of chopped agricultural waste biomass from farms to biomass conversion facilities over long distances could be the most cost-effective approach to produce bioethanol commercially on a large-scale. The techno-economic studies, however, were limited to horizontal pipelines (Vaezi et al., 2015). In reality, the long-distance pipeline network would involve horizontal (mostly), inclined (partially), and vertical (mostly in on-site processing) pipe sections. Although the frictional behavior of agricultural residue biomass (ARB) through vertical pipelines have been explored recently (Javed et al., 2022a,b; Javed et al., 2021), to improve their techno-economic assessment, further experimental studies on the frictional behavior of these kinds of slurries through inclined pipe sections are needed.
Many studies are available on the hydraulic transport of conventional solids, i.e., sand, glass beads, etc., through inclined pipelines (Al-Mutahar, 2006; de Vreede, 2018; Matousek et al., 2018; Rai, 1972; Shook et al., 1974; Vlasak et al., 2018; Vlasak et al., 2019b). The flow of solids-water mixtures through inclined pipes is more complex than in horizontal and vertical pipes because in inclined pipes the phases can separate and slip at the same time (Polanský, 2014). Pipe inclination affects the flow characteristics (i.e., pressure drop, concentration distribution across the pipe cross-section, velocity profile, the deposition limit velocity, etc.) of the settling slurries (Kao and Schaefer, 1980; Meng and Lucas, 2017; Vauhkonen et al., 2019; Vlasak et al., 2018; Vlasak et al., 2019a). These characteristics also depend on the mean particle size and density of the solids being conveyed through the pipeline, which may cause the slurries to exhibit different flow regimes, i.e., homogeneous, pseudo-homogeneous, heterogeneous, stratified with a detectable sliding bed, or fully stratified. Each of these regimes has independent empirical correlations for predicting frictional pressure drops (Abulnaga, 2002; Gibert, 1960; Matousek, 2002; Matousek et al., 2018; Miedema et al., 2021; Worster and Denny, 1955). In inclined flows, the frictional pressure drop of the suspension is obtained experimentally by subtracting the hydrostatic head from the measured pressure drop (Doron and Barnea, 1996; Vlasak et al., 2018).
The hydrostatic component is a significant contributor to the pressure drop (both frictional and total) and is determined by the mixture's in situ density, a function of in situ concentration that is typically higher in ascending pipes than in descending ones, and is measured using a suitable concentration measuring device (Vlasak et al., 2017; Vlasak et al., 2019a). The in situ concentration gradient across the pipe cross-section is more pronounced in heterogeneous flows of conventional solids-water slurries through inclined pipes than in pseudo-homogeneous flows. Heterogeneous flows are more difficult to analyze because special techniques are required to measure the in situ concentrations of the suspensions in these regimes. However, under certain flow conditions when the solids are fully suspended, the in situ concentration can be assumed to be equivalent to the delivered concentration for the solids-water suspensions flowing above a specific velocity, known as critical velocity for a pseudo-homogeneous regime (Javed et al., 2022b; Javed et al., 2021). Fine sand-water suspensions with a mean particle diameter of d50 = 0.04-0.2 mm have been found to behave pseudo-homogeneously during flow through horizontal or inclined pipes with slopes < ±25°, exhibiting a weak concentration gradient across the pipe cross-section for suspension velocities above the critical deposition velocity (Matousek et al., 2022; Vlasak et al., 2019a,b).
Natural or synthetic fiber-water suspension flow over inclined pipe sections is rarely studied. Most studies on hole cleaning in inclined wells use small concentrations of fibers (basal seeds, synthetic fibers, etc.) to improve drilling sweep efficiency by introducing a fiber network that hydrodynamically and mechanically affects the suspended and deposited solids particles (Ahmed and Takach, 2009; Elgaddafi and Ahmed, 2020; Movahedi et al., 2017). It is difficult to analyze the fiber suspensions because they form flocs, or intricate networks, when flowing through a pipeline (Duffy, 2006b). One distinctive feature of these kinds of suspensions is the drag reduction (the percent reduction in suspension friction loss relative to water alone at the same bulk velocity) in certain flow conditions. In most of the work carried out to understand the frictional behavior of fibrous suspensions, the primary focus has been understanding the flow regions and phenomena behind the particulate-inertial mechanisms (Bobkowicz and Gauvin, 1965; Kerekes, 1971; Radin et al., 1975; Seely, 1968; Steen, 1989). ARB (wheat straw, corn stover) suspensions act like wood fiber, chemical wood pulp, and semi-chemical pulp suspensions (Vaezi et al., 2014).
Several laboratory-scale investigations have been conducted earlier to explore the frictional behavior of wheat straw and corn stover suspension flows in horizontal and vertical pipe sections and found that these suspensions exhibit three flow regions: plug flow, transition flow, and turbulent flow. Four nominal particle sizes were used: 19.2, 6.4, 3.2, and < 3.2 mm at saturated mass concentrations ranging from 5%-25%, 5%-30%, 5%-35%, and 5%-40%, respectively, for both the wheat straw and corn stover suspensions. It was further discovered through longitudinal frictional pressure drop measurements of the biomass suspensions that, for a fixed pipe diameter, the development of these regions depended on multiple factors, including pipe orientation, type of feedstock, the aspect ratio of fibers, suspension velocity, suspension concentration, suspension apparent viscosity, and fiber-carrier fluid density ratio. The suspensions exhibited drag reduction in both horizontal and vertical upward flows after specific slurry velocities, which increased with increases in saturated concentration, slurry velocity, and particle aspect ratio (Javed et al., 2022a,b, 2021; Vaezi et al., 2014). Although water-based slurries of ARB (i.e., wheat straw and corn stover) have been extensively studied by measuring their longitudinal frictional pressure drops flowing through horizontal and vertical pipelines for various mass concentrations, to the best of our knowledge, no work has been done to understand the frictional behavior of wheat straw-aqueous slurry flows through inclined pipes.
The present study conducts an experimental investigation of the hydro-transport of wheat straw slurries through inclined pipe sections of varying slopes with the aim of understanding the fundamental parameters impacting the slurry's rheological characteristics during the flow. The specific objectives are to:
- Calibrate and commission the inclined pipe section using fine sand-aqueous slurries by comparing their experimental frictional pressure drops at various concentrations and flow rates with pre-established empirical correlations of pressure drops of conventional slurries.
- Examine the frictional behavior and flow regions of uphill and downhill flows of wheat straw-aqueous slurries through inclined pipes at different concentrations and flow rates.
- Investigate the conditions of drag reduction for wheat straw-aqueous slurries in both uphill and downhill flows.
- Explore the effect of inclination on the onset velocity of drag reduction of wheat straw-water slurries in both uphill and downhill flows.
Material and Methods
Experimental Setup
Figure 1 shows the schematic of the experimental setup used in this study.
The lab-scale setup comprises a 29 m long closed pipeline loop with a 50 mm inside diameter (i.d.) and Schedule 40 PVC transparent and carbon steel pipe sections, an open-impeller centrifugal pump (CD80M; Godwin Pumps Ltd., Bridgeport, NJ, USA) with a capacity of 38.52 m3 h-1 for 157 kPa at 1765 rpm and a ˜43% efficiency (for water) driven by a 7.45 kW electric motor (CC 068A; Madison Industrial Equipment, Vancouver, BC, Canada) to pump the desired fluid (i.e., water or conventional solids-water or biomass-water slurries), a glycol chiller (KEZA030H8; KeepRite Refrigeration Corp., ON, Canada) to maintain the fluid temperature, a 0.64 m long flow visualization section, a magnetic flow meter (FMG-424; Omega Eng., Stamford, CT, USA) set at 200D (D is the i.d. of the pipeline) downstream of the slurry pump to measure the bulk velocity of the fluid, a temperature sensor (RTD-E; Omega Eng., Stamford, CT, USA) to monitor the fluid temperature, a large semi-circular pipe bend (with a curvature radius [Rc] of 14.5D) upstream of a 7.6 m long inclined pipe section, two flush diaphragm pressure transducers (PTs) (PX42G7; Omega Eng., Stamford, CT, USA), each with a range of 0-104 kPa and accuracy of ±0.25% to measure fluid pressures upstream and downstream of the inclined pipe, a digital inclinometer (2170-1; Insize Co. Ltd., Suzhou, Jiangsu, China) with a magnetic base and a range of 0-360° with 0.1° resolution and accuracy of ±0.2° to measure the angle of inclination of the inclined pipe section, a differential pressure transmitter (DPT) (FKCT22V55; Fuji Electric Ltd, France) with a range of 0-6 kPa and accuracy of ±0.04% (of the adjusted span) to measure the fluid pressure drop across the inclined test section, a conical mixing tank (0.8 m diameter and 455 l capacity) connected to a centrally placed heavy-duty gear-driven vertical mixer (EV6P50M; Lightning Inc., Rochester, NY, USA) with a double impeller powered by a 0.37 kW electric motor (3336P; Baldor reliance, ABB Motors and Mechanical Inc., Fort Smith, AR, USA) to agitate the solids-water slurry in the tank, a watt transducer (PC5; Flex-Core, Columbus, OH, USA) to measure the power consumed by the induction motor of the centrifugal pump for any specific velocity of fluid, and a 14.91 kW variable frequency drive (VFD) controller (MA7200-2020-N1, TECO-Westinghouse Co., Round Rock, TX, US) to change the rotation of the induction motor of the centrifugal pump to obtain the required fluid velocity. Further details on the type of mixer impeller and the heat exchanger used in the experimental setup are given in our earlier studies (Javed et al., 2022b; Vaezi and Kumar, 2014).
The DPT was connected to the inclined pipe at high- and low-pressure ports with a span (dL) of 10D through PVC tubes/impulse lines, each with an inner diameter and length of 9.5 mm and 0.89 m, respectively. The specifications of the impulse lines were selected based on best practice (Reader-Harris and McNaught, 2005). The impulse lines contained water that served as a pressure-sensing medium between the fluid flowing inside the inclined pipe and the diaphragm of the DPT. The pressure drop of the fluid flowing inside the inclined pipeline sensed by the DPT was converted to electrical output signals of 4-20 mA. The output signals obtained from all the instruments except the mixer and heat exchanger (i.e., watt transducer, magnetic flow meter, temperature sensor, the DPT, and PTs) connected to the closed pipeline loop were recorded at a frequency of 100 data s-1 on a customized data-acquisition system. The data-acquisition system was equipped with a resistance temperature detector (RTD) input module (NI9217; National Instrument Corp., Austin, TX, USA), the current excitation module (NI9219; National Instrument Corp., Austin, TX, USA) with four channels each dedicated to different types of measurements, and a data-acquisition program (LabView V.9.0.1f2; National Instrument Corp., Austin, TX, USA).
Physical Arrangement for Various Pipe Inclinations
The physical arrangement of the inclined pipe section built in the large-scale fluids lab at several inclination angles is shown in figure 2.
The heights of the centerlines of the horizontal pipe sections of the closed pipeline loop and the lab ceiling above the ground were 1.1 m and 3.3 m, respectively. At a height of 1.1 m above ground level, there was a limitation in the existing experimental setup for the inclined pipe section (7.6 m long) to attain an inclination angle (?) > 7° in the descending position and > 14° in the ascending position with respect to the x-axis (fig. 2a). To reach the maximum possible angle of inclination for the inclined pipe section in the ascending position, the pivot point of the inclined pipe section was shifted downward from an existing position of 1.1 m to 0.43 m above the ground. With this arrangement, the increase in ? to 21° was possible for the ascending pipe position (figs. 2b and 2d). However, this arrangement did not affect the pressure drop measurements of water or slurries in the horizontal position of the inclined pipe with a pivot point placed at any of these heights (fig. A, supplementary section). The inclined pipe was attached at its bottom to a support beam made from hollow carbon steel pipe with a rectangular cross-section (76 mm x 38 mm). This support beam was strong enough to minimize the chances of vibrations that could be created during slurry flow through a 7.6 m long inclined pipe section. The beam was pivoted at one end (i.e., near the large semicircular pipe bend) connected to a wire rope of an electrical winch (SKU-8880429, 1500 lb. 120V AC; Pro. Point Automotive, ON, Canada) at the other end (i.e., near the downstream end of the pipe) for a quick and automatic movement of the inclined pipe section in an upward or downward direction to a desired angle (fig. 2a).
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| Figure 1. Schematic of the experimental setup: (1) centrifugal slurry pump, (2) drain valve-1, (3) drain tub, (4) counter-flow heat exchanger, (5) glycol chiller, (6) thermocouple, (7) flow visualization section, (8) magnetic flow meter, (9) temperature sensor, (10) semicircular pipe bend, (11) inclined pipe section, (12) pressure transducer, (13) inclinometer, (14) differential pressure transmitter, (15) lifting mechanism for inclined pipe, (16) drain valve-2, (17) return pipe, (18) mixer with double impeller, (19) mixing tank, (20) water supply tank, (21) data logger, (22) watt transducer, and (23) variable frequency drive. |
To avoid the chances of transmitting vibrations from the inclined pipe section to the DPT during pressure measurements, an independent vertical support was used to hold the DPT in the desired position. This vertical support was isolated from the entire support structure of the inclined pipe section (figs. 2a and 2c). The DPT was provided with a smartly operated moveable base with a locking and unlocking mechanism to move it to a desired position on the vertical support. For any pipe inclination, the position of the DPT was always located at a sufficient distance below the pipe centerline, as recommended by the manufacturer (Fuji Electric, 2014). The primary reason for installing the moveable base with the DPT was to keep the lengths of the impulse lines as small as possible while changing the ? for the inclined pipe section; this could help reduce errors in pressure drop measurements (ISO, 2007).
Locations of Pressure Ports
The downstream and upstream distances of the high- and low-pressure ports of the DPT and PTs with respect to the nearest flow disturbances in the loop were carefully selected to ensure proper flow field recovery and the elimination of the end effect on the pressure measurements. The nearest flow disturbance on the upstream of the high-pressure ports was a semicircular bend, and on the downstream of the low-pressure ports was a flexible hose connecting the exit end of the inclined pipe section to drain valve-2 (shown in figs. 1 and 2a). The maximum permissible distance reported in the literature downstream of the semicircular bend to dissipate the secondary flows is 35D (Anwer et al., 1989; Azzola et al., 1986; Rowe, 1970; Vaezi et al., 2014). In our earlier work, the downstream distances of the low-pressure ports of the DPT and PTs were selected with respect to the corresponding pipe section exits as 5D and 12D, respectively (Javed et al., 2021; Vaezi et al., 2014). Therefore, for the inclined pipe section, the upstream and downstream distances
of high- and-low-pressure ports for both the DPT and PTs with respect to the corresponding nearest flow disturbance were taken to be equal to or greater than the maximum distance reported in the literature (Javed et al., 2021; Vaezi et al., 2014). These distances are shown in table 1.
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| Figure 2. (a) Supporting structure and lifting mechanism for the inclined pipe section, (b) The inclined pipe section in ascending position for an inclination angle (?) = 21°, (c) DPT with independent vertical support, and (d) The inclined pipe section in horizontal position at a height of 0.43 m above the ground level. |
| Table 1. The locations of the high- and low-pressure ports of the DPT and PTs on the inclined pipe section in the closed pipeline loop. | |||
| Instrument | Span (dL) | Distance of High- Pressure Port from the Semicircular Bend | Distance of Low-Pressure Port from the Inclined Pipe’s Exit |
| DPT | 10D | 95D | 38D |
| PT | 91D | 40D | 12D |
Feedstock Preparation and Particle Size Analysis
The wheat straw bales of dry stalks were obtained with some initial moisture content (MC) directly from farms in Northern Alberta, Canada, and used a commercially available knife mill (SM 100; Retsch Inc., Surrey, BC, Canada) to grind the bales into various particle sizes. The ground straw particles obtained from knife milling were classified by a commercial classifier (BM&M Inc., Surrey, BC, Canada) into four different groups with nominal particle sizes of 19.2, 6.4, 3.2, and < 3.2 mm. The nominal sizes were chosen based on the classifier sieve opening sizes. The classifier had seven sieves. The particles obtained in the top three sieves were discarded. The nominal sizes obtained in the bottom four sieves are the four different groups of particles with specific particle lengths given in the paper. Further details on the nominal sizes and their significance are given in our earlier work (Vaezi et al., 2013). The grinding and classification of wheat straw bales were performed in the laboratory. The current study focuses on the hydro-transport of wheat straw particles of a nominal size of 6.4 mm through an inclined pipe section. Because the duration of the inclined pipe experiments with ARB (see slurry pressure drop measurement section) was almost twice the duration of the vertical and horizontal pipe experiments, the chance of particle degradation is higher in inclined pipes. Particle degradation occurs due to (1) particle-particle interactions or (2) the multiple passing of slurry through the centrifugal pump in the closed pipeline loop. Based on our previous experience with the degradation of wheat straw particles (Vaezi et al., 2013) and the limitations on achieving higher slurry velocities during the hydro-transport of different nominal particle sizes of wheat straw through vertical pipes (Javed et al., 2022a,b), we selected the nominal size of 6.4 mm for the initial phase of our experiments with the inclined pipe section to get the highest achievable slurry bulk velocity and the lowest effect of particle degradation. We recently performed particle size distribution (PSD) and shape analysis of knife-milled wheat straw particles through dynamic image processing in the Camsizer (Javed et al., 2022a). Table 2 shows the particle morphology of wheat straw particles of a nominal size of 6.4 mm obtained from the Camsizer.
| Table 2. Particle morphology for knife-milled wheat straw particles of the 6.4 mm nominal size using the Camsizer (Javed et al., 2022a). | |||||||
| D90 | D50 | D10 | Xig[a]± ??ig[b] | Max. | Min. | Aspect Ratio (fp) | |
| dFE_max (mm) | 6.04 | 4.85 | 3.58 | 4.84±0.93 | 11.44 | 3.35 | 8.70 |
| dc_min (mm) | 2.87 | 1.52 | 0.59 | 1.37±0.87 | 6.14 | 0.28 | |
[a]Xig = [(D16 +D50 + D84) / 3], Graphic mean (Vaezi et al., 2013) [b]??ig = [{(D84 – D16 ) / 4} + {(D95 – D5 ) / 6.6}], Graphic standard deviation(Vaezi et al., 2013) | |||||||
Here, dFE_max is the Feret diameter (the longest distance between two parallel tangents of a particle projection), or particle length, and dc_min is the short chord diameter (the smallest of the longest chords of a particle projection), or particle width. The characteristics’ dimensions D10, D50, and D90 shown in table 2 for both dFE_max and dc_min are the 10th, 50th, and 90th percentiles derived from the cumulative distributions of the corresponding parameters. Xig and sig represent the graphic mean and standard deviations for both dFE_max and dc_min. The complete procedure of the dynamic image processing of ARB using the Camsizer is given in detail in our recent work (Javed et al., 2022a). Figure 3a shows the microscopic image of wheat straw particles of a nominal size of 6.4 mm captured by the high-speed Camsizer cameras.
Knife-milled wheat straw particles are mostly composed of rectangular rib-like particles and are fibrous (i.e., their aspect ratio > 3.3) in nature with a length range of 3.35-11.44 mm (see table 2) for the 6.4 mm nominal particle size. Further, wheat straw particles have fewer irregularities, and their surfaces are repetitive and less random in nature (fig. 3b) than corn stover. More details on the surface features of wheat straw particles can be seen in our previous work (Vaezi et al., 2013).
Slurry Preparation
Once the pipeline loop was thoroughly cleaned with water or an occasionally circulating sand-water slurry, clear water was added to the loop to the required level in the mixing tank. The clean water was circulated by the centrifugal pump running at full speed for a few minutes to deaerate the system. To ensure reliable pressure drop measurements, the impulse lines of the DPT were cleaned and filled with clear water while the pipeline loop was running. This removed contaminants (if any) and air bubbles from the impulse lines. Then the pressure drop measurements for clear water were recorded for velocity ranges of 0.5-4.7 m s-1 at a controlled temperature maintained by the chiller. The mixer was then turned on gradually to prevent adding air to the system (resulting from cone formation on the water surface inside the tank). To prepare an aqueous slurry of the nominal 6.4 mm particle size of wheat straw with the desired solid mass concentration of 30%, the pre-measured mass of straw with some initial moisture content was slowly added to the mixing tank. This was the highest mass concentration that could be tested in the slurry loop for this particle size because the i.d. of the pipeline was small (i.e., the i.d. = 50 mm) and for Cm > 30%, the loop clogged at low velocities.
Depending on the initial moisture content of the wheat straw particles and the water temperature inside the loop, the wheat straw-water slurry was continually circulated through the loop for roughly 12 to 14 hours until it became stable (i.e., fully saturated) at the highest attainable Cm. ARB has a propensity to absorb moisture when water is introduced to it; as a result, the slurry’s rheology changes throughout pumping until it stabilizes at a saturated MC of almost 82% for the suspended biomass particles (Javed et al., 2022b). After every hour of the slurry's circulation through the pipeline loop, the slurry stability was examined by observing its pressure drop and velocity changes. When these variations in both the pressure drop and velocity fell to about 1.0%-2.0% h-1, the wheat straw slurry was deemed stable.
Slurry Pressure Drop Measurements
Once the wheat straw-water slurry was fully saturated or stable at the highest mass concentration, i.e., Cm = 30%, its pressure drop measurements were recorded for the entire range of bulk velocities (0.5-4.7 m s-1) with mutual velocity intervals of 0.5 m s-1 and an angle of inclination (?) of 0° (i.e., horizontal position) for the inclined pipe section with respect to the x-axis. The ? of the inclined pipe was then changed with the help of an electric winch to the desired angle (i.e., a 7° descending pipe position), and the pressure drop measurements were recorded for the complete range of slurry bulk velocities. A similar procedure was repeated for the ascending position of the inclined pipe section of ?= 7°. All the pressure drop measurements were thus recorded for the wheat straw-water slurry flows at inclined pipe positions of 0°, 7° (ascending), and 7° (descending) and Cm = 30%. For each of the angular positions of the inclined pipe section at Cm = 30%, the pressure drop measurements were recorded after 5 minutes of acquiring the desired pipe angle to avoid any errors in measurements. The slurry was then diluted to Cm = 25% by adding the required volume of water from the water supply tank to the mixing tank to the desired slurry level, as shown in table A in the supplementary information section.
  | ||||
| (a) | (b) | |||
| Figure 3. Microscopic images for the 6.4 mm nominal size of wheat straw particles taken by (a) high-speed Camsizer digital cameras (not to scale) and (b) light microscope (Zeiss Stemi 508). | ||||
The slurry was drained using drain valve-1 (fig. 1) to a fixed level of 60 gallons (imperial) in the mixing tank after at least 5 minutes of slurry dilution to reach Cm = 25%. The same procedure was then followed for the pressure drop measurements of the wheat straw-water slurry flows at Cm = 25% and the three positions (0°, 7° ascending, and 7° descending) of the inclined pipe section as described earlier for a slurry of Cm = 30%. Table A in the supplementary information section shows the levels of wheat straw-water slurry required in the mixing tank to obtain the saturated mass concentrations of 25% to 5% by diluting the slurry from the highest to the lowest concentration at equal intervals of 5%. Every time the wheat straw-water slurry was diluted from Cm of 25% to 5%, the pressure drops of the corresponding slurry concentrations were recorded at the three angular positions (0°, 7° ascending, and 7° descending) of the inclined pipe section in a similar way as described for Cm = 30% and 25%. All the pressure drop measurements of the biomass slurry for the range of Cm’s from 30% to 5% were recorded during a single trial of the experimental run. The pressure drop experiments for ARB-water slurries in the inclined pipe were longer in duration (approx. 42-45 h) than those in the vertical and horizontal pipe sections (approx. 22-26 h). Therefore, instead of taking pressure drop measurements at ? = 14° of the inclined pipe section with the pivot point’s position of 1.1 m above ground level, this angle was included for the second trial for the second position of the pivot point at 0.43 m above the ground (fig. 2a). To obtain the slurry pressure drops for ? of 0°, 14°, and 21° in the ascending positions of the inclined pipe section, the pivot point of the supporting beam (fig. 2a and 2c) was shifted from 1.1 m to 0.43 m before starting the experiment. The procedure for the rest of the experiment is the same as described for three angular positions of 0°, 7° ascending, and 7° descending of the inclined pipe section.
Moisture Content and Density Measurements
ASABE S358.3 standards were used to estimate the wet basis or initial MC of the nominal 6.4 mm ground wheat straw particles (ASABE Standards, 2012). To measure the MC, five samples with a net weight of at least 25 g each were collected from the required nominal size of chopped wheat straw particles. They were then oven-dried at 105 °C for 24 hours. The saturated density of the particles was determined by following ASTM C127 standards (ASTM, 2015). The saturated wheat straw particle samples were collected during the dilution phase of the slurry as it ran through the pipeline loop. The samples were spread on a thick paper towel to absorb their surface moisture. A perforated cylinder with a diameter and height of 150 mm was loosely filled with the saturated wheat straw particles and weighed in both air and water. The difference between these weights is the buoyant force acting on the wheat straw particles; from this force, the saturated density of the material was evaluated. On average, the initial MC and the saturated particle density of wheat straw particles were found to be 6.492%±0.5 and 1061.03 ±6.62 kg m-3, respectively. Table 3 shows the approximate values of the saturated densities for several volumes and mass percentages of saturated and dry solids of aqueous-based wheat straw slurries, considering a density of water to be 1000 kg m-3.
| Table 3. Volume and mass percentages of saturated and dry solids of wheat straw-water mixtures. | ||||
| Mass Percentage of Saturated Solids (%) | Volume Percentage of Saturated Solids[a] (%) | Mass Percentage of Dry Solids (%) | Volume Percentage of Dry Solids (%) | Saturated Slurry Density (kg m-3) |
| 30 | 28.76 | 5.4 | 5.35 | 1014.49 |
| 25 | 23.89 | 4.5 | 4.45 | 1012.05 |
| 20 | 19.06 | 3.6 | 3.55 | 1009.62 |
| 15 | 14.25 | 2.7 | 2.65 | 1007.19 |
| 10 | 9.47 | 1.8 | 1.76 | 1004.79 |
| 5 | 4.72 | 0.9 | 0.88 | 1002.39 |
[a]The volume percentages of dry and saturated solids were evaluated by dividing the volumes of the dry or saturated solids with the total volume of slurry loop. | ||||
Calibration of Inclined Pipe
In the current investigation, the inclined test section (the horizontal, ascending, and descending positions) was calibrated by measuring the frictional pressure drops of clear water and aqueous slurries of fine sand (d50 = 0.103 mm) (at known volumetric concentrations, i.e., CV = 1%-5%) passing through the pipe sections at different velocities and comparing our results to those of corresponding models (Churchill, 1977; Durand, 1953; Durand and Condolios, 1952; Gibert, 1960; Worster and Denny, 1955). Fine sand (d50 = 0.103 mm) was selected for the calibration of the experimental setup because (1) the slurries of fine sand with a mean particle diameter (d50) range of 0.04-0.20 mm behave pseudo-homogeneously, that is, the particles remain dispersed because of their interaction with the turbulent eddies of the carrier fluid (Matousek et al., 2022), (2) the limit deposition velocity for the fine sand (d50 = 0.103 mm) is small (see table 4) and the variation in the deposition velocity for these particles with respect to the pipe inclination is usually not very significant (Spelay et al., 2016), thus providing a wide range of slurry bulk velocities for the pressure drop analysis, (3) the local slip is negligible and the related velocity distribution would be slightly uneven (Matousek, 2002), (4) the delivered and in situ concentrations are almost the same for the fine sand particles because of the very small terminal settling velocity (Javed et al., 2021), thus these particles are suitable given that the experimental setup did not have a concentration measuring device, and (5) the concentration gradient across the pipe cross-section would be very small for fine sand particles with no contact bed for velocities higher than the critical deposition velocity (Matousek, 2000, 2002). The reasons for the lack of concentration measuring device in our experimental setup are explained in one of our earlier studies (Javed et al., 2021).
The physical properties of fine sand used in the present study are given in table 4.
| Table 4. Physical properties of the fine sand solids used in the calibration of the inclined pipe section. | |||||
|---|---|---|---|---|---|
| Material | Particle Density (?s) (kg m-3) | Mean Particle Diameter (d50) (mm) | Terminal Settling Velocity (vt) (mm s-1) | Critical Deposition Velocity (m s-1) | Critical Velocity for Pseudo- Homogenous Regime (m s-1) |
| Fine sand[a] | 2500 | 0.103 | 10.06 (Newitt et al., 1961) | 0.52–0.76 (Wasp and Aude, 1970; Wasp et al., 1977) | 0.895 (Newitt et al., 1961) |
[a]Target Products, AB, Canada; Material Grade: LM–125. | |||||
The experimental frictional pressure drop of the mixture in the inclined test section (fig. 1) was obtained by subtracting the static head caused by the pipe elevation from the pressure drop measured by the DPT connected to the pressure taps of the inclined test section through impulse lines filled with water. Equation 1 provides a general expression for the experimental frictional pressure drops of slurry flow through the inclined pipe section.
(1)
The indexes m, w, f, and ? represent the slurry (mixture), water (carrier fluid), friction, and pipe inclination with respect to the x-axis, respectively. The terms 
and 
are the experimental frictional pressure and the measured pressure drops of the mixture flowing through an inclined test section of span dL; ?m and ?w are the mixture and water (carrier fluid) densities, respectively. The mixture density (?m) was calculated using equation 2:
(2)
where
CV = mixture’s volumetric concentration for fine sand-water slurries,
Cm = mixture’s saturated mass concentration for wheat straw-water slurries, and
?s = density of the fine sand (table 4) or saturated density (i.e., 1061.03±6.62 kg m-3) of wheat straw particles.
The inclination angle (?) was taken as positive for the ascending position and negative for the descending position of the inclined pipe section, which is common practice for the inclined flows (Kao and Schaefer , 1980; Vlasak et al., 2018). For the horizontal position of the inclined pipe section (i.e., ? = 0°), the gravity effect would be zero because the static head term in equation 1 will be diminished, and the pressure drop measured by the DPT will directly give the frictional pressure drop of the slurry. Further, the static component of equation 1 will be eliminated in the situation of water flowing through an inclined pipe section and water present in the impulse lines of the DPT, and we will obtain the frictional pressure drop directly from the DPT. However, to obtain the total pressure drop of the fluid (mixture or water) in the inclined pipe section, the following expression was used:
(3)
The general relationship to define the theoretical frictional pressure drop (dPf /dL)wof water flowing with a bulk velocity (vw) through a test section of the span (dL) with an inner diameter of D is given in equation 4:
(4)
where g, (fD)w, and (hf)w are the acceleration due to gravity, the Darcy-Weisbach friction factor, and the loss of head due to friction for water, respectively. The values of (fD)w for the entire range of vw were evaluated using Churchill’s model (Churchill, 1977), which can be applied to all the flow regimes (laminar, transitional, and turbulent) of water through pipes with both smooth and rough surfaces (see table B in the supplementary information section). Because the inclination of the pipe has no impact on the frictional pressure drop of water (Matousek et al., 2018), for all the inclinations (-7° = ? = +21°) of the test section in the present work, Churchill’s model was used to evaluate the theoretical frictional pressure drops of water. The theoretical frictional pressure drops for fine sand-water slurry flows were evaluated through the inclined pipe section using two semi-empirical models for heterogeneous flows in inclined pipes (Gibert, 1960; Worster and Denny, 1955). For the horizontal pipe section, the famous correlation proposed by Durand and Condolios (Durand, 1953; Durand and Condolios, 1952) was used to evaluate the theoretical frictional pressure drops for fine sand-aqueous slurries. The supplementary information section (table B) shows these semi-empirical models for horizontal and inclined flows. The plots of the frictional pressure drop and bulk velocity of water at specific volumetric concentrations of aqueous fine sand slurries for inclined pipes at different inclinations with respect to the horizontal pipe position are shown in fig. 4. Excellent agreement was found between the experimental values and the corresponding models, validating the reliable design of the experimental setup used in the present work.
 |  |
| (a) | (b) |
| Figure 4. Calibration of the inclined pipe section at (a) ? = -7° to +21° using clear water and (b) ? = +14° and 0° using fine sand-water slurries of d50 = 0.103 mm for solid particles at volumetric concentrations of 5% and 1%, respectively. | |
In the case of water flowing through the inclined test section, the percentage error between the experimental frictional pressure drops and those obtained using Churchill’s model was found to be 1.2%-5.5% for the entire range of pipe inclinations and water flow rates (fig. 4a). For the fine sand-water slurries (fig. 4b; fig. B in the supplementary information section), Worster and Denny’s model showed the best fit for all the inclined flows exhibiting the pseudo-homogeneous regime (i.e., for vm > 1.0 m s-1) with a percentage error of 0.16%-8.61%. One reason for good agreement between our experimental results with Worster and Denny’s model is that their model was developed considering the negligible effect of the slip velocity. For the largest inclination angle (i.e., +21°) and CV = 3%, the experimental results deviated from Worster and Denny’s model at low slurry velocities, i.e., vm = 1.5 m s-1 (fig. B, supplementary information section). The maximum percentage error for the horizontal flows using Durand’s model is 7.87% (fig. 4b; fig. B, supplementary information section).
Experimental Results and Discussion
Frictional Behavior of Various Solids-Water Mixtures in Inclined Flows
Classical Solids
Figure 5 illustrates the frictional pressure drops of fine sand-water slurries flowing at various volumetric concentrations (CV = 1%-5%) and velocities = 1.0 m s-1 through the inclined pipe section at a ? of +14° and +21° relative to the x-axis.
Figure 5 shows that for any pipe inclination, the frictional pressure drop of fine sand-water slurries increases with solid volume concentration and was always greater than that of clear water for similar bulk velocities. The conventional solids-water slurries, which have mean particle diameters of 0.04-0.2 mm, actually show pseudo-homogeneous flow, that is, the solids are evenly distributed across the pipe's cross-section (Matousek et al., 2022). In pseudo-homogeneous flows of settling slurries, the frictional pressure drop increases with velocity throughout the entire velocity flow range. This increase in frictional pressure drop with respect to slurry velocity follows the shape of a curve similar to that of the carrier fluid alone but at a certain offset from the carrier fluid’s curve (fig. 5a and 5b), indicating that solid particles contribute to flow friction through their interaction with the carrier fluid instead of through their interaction with each other and the pipe wall.
Flow Visualization
For the fine sand used in our current investigation, the critical deposition velocity and the critical velocity for pseudo-homogeneous flow were evaluated using standard correlations from several sources (Newitt et al., 1961; Wasp and Aude, 1970; Wasp et al., 1977). These values are shown in table 4 and were reconfirmed by capturing the images of the flow patterns of fine sand-water slurries flowing at bulk velocities of 0.5 m s-1 and 1.0 m s-1 and various concentrations (CV = 1%-5%) through the inclined and horizontal pipe positions (shown in table C in the supplementary information section). It was found through visual observations that for all the slurry concentrations of fine sand at slurry bulk velocities of 0.5 m s-1, stationary bed or dunes formed at the pipe invert at all the slopes. However, as the slurry velocities increased to 1.0 m s-1 for any of the pipe inclinations (-7° = ? = +21°), no bed formation was observed; instead, for most of the pipe slopes, the fine sand particles seemed to be fully dispersed across the pipe cross-section with a minimal concentration gradient at higher angles in the uphill flows. Vlasak et al. (2018) made a similar observation and determined that the influence of pipe inclination on local concentration distribution was insignificant for aqueous slurries of fine sand (d50 = 0.18 mm) running at CV = 11%-36% through an inclined pipe section at low inclination angles (< ± 25°) (Vlasak et al., 2018). Although Vlasak et al. used fine sand, the d50 was almost double the size of the particles we used in our present work.
 |  |
| (a) | (b) |
| Figure 5. Frictional pressure drops for fine sand-water mixtures for velocities = 1.0 m s-1 and volumetric concentrations of CV = 1%-5% flowing through a 50 mm diameter inclined pipe section of (a) ? = +14° and (b) ? = +21°. | |
Based on visual observations, findings from the literature, and calculations of specific parameters for the fine sand from pre-established correlations (shown in table 4), it can be deduced that fine sand-water slurries in inclined flows exhibited a pseudo-homogeneous flow for vm = 1.0 m s-1 and, at lower velocities, i.e., = 1.0 m s-1, these slurries either showed heterogeneous flow with a weak concentration gradient across the pipe cross-section or exhibited a stationary bed for vm = 0.5 m s-1. For the fine sand-water suspensions flowing through inclined pipe sections for all the inclinations at vm = 1.0 m s-1, we evaluated the corresponding frictional pressure drops using the prepared volumetric concentrations (i.e., CV = 1%-5%) because of the absence of slip.
Wheat Straw Particles
Figure 6 shows the frictional pressure drops of 6.4 mm particle size wheat straw-water suspensions flowing at different saturated mass concentrations (Cm = 5%-30%) and velocities of 0.5 m s-1 through pipe section with inclinations of +14° and +21° relative to the x-axis.
In inclined flows of wheat straw-water slurries (fig. 6; fig. C, supplementary information section), the frictional pressure drops increased in proportion to the increase in the slurry's velocity for any concentration. This is the behavior of any solids-water suspensions in pipe flows, regardless of the type of solids (i.e., classical solids or fibers) and pipe inclination (Javed et al., 2021; Matousek, 2009; Rai, 1972; Steen, 1989). Because the frictional pressure drop has a quadratic relationship with the suspension velocity, it increases with an increase in velocity (eq. 4). Equation 4 is a general equation for evaluating the frictional pressure drop of water or any suspension. In the case of a suspension, the subscript w (water) is replaced by m (mixture). Further, it was observed that for low velocities and all the concentrations of wheat straw-aqueous slurries (fig. 6; fig. C, supplementary information), except for the suspensions of low concentrations, i.e., Cm = 5%-10% flowing through the ascending pipe position with an inclination angle of -7°, the pressure drops were always above the water curve; however, after specific slurry velocities, they were consistently below the corresponding pressure drops of clear water. This unique characteristic differentiates the wheat straw-water suspensions from the conventional solids-water suspensions in pipe flows where the pressure drop curve is always above the water curve (see fig. 5) for the entire range of slurry velocities and mass concentrations.
Wheat straw particles are fibrous and behave like other natural or synthetic fiber suspensions (Bobkowicz and Gauvin, 1965; Javed et al., 2021; Kerekes, 1971; Radin et al., 1975). In the fiber-water suspension flow through pipes, the fibers interact with each other mechanically, hydrodynamically, or both, forming networks within the carrier fluid and significantly impacting the suspension’s rheological characteristics. The presence of fibers in the carrier fluid offers exceptional resistance to the fluid flowing over the fibers. Eventually, it suppresses the fluid’s turbulence intensity by damping hydrodynamic instabilities. After a specific suspension velocity, it decreases the frictional pressure drop of fiber-based suspensions with respect to the carrier fluid (Steen, 1989; Vaseleski and Metzner, 1974).
One distinctive feature of knife-milled wheat straw particles over natural or synthetic fibers is the wide range of particle lengths with a low aspect ratio, which increases the probability of the hydrodynamic interaction of these particles with the surrounding fluid (because to prepare a specific solid mass concentration with a required amount of dry mass, the number of particles with a wide range of sizes would be higher than the number with narrow size distribution, which is typical of synthetic fibers), as well as the interactions among the particles themselves at even low suspension concentrations. For instance, in the present study, a 6.4 mm nominal particle size of wheat straw was used with an aspect ratio of 8.7 (table 2). In contrast, the aspect ratios of nylon fibers used by Kerekes and Douglas were 12-74 (Kerekes and Douglas, 1972). Wheat straw particles tend to reduce turbulence intensity at even low suspension concentrations, reducing the frictional pressure drops of the suspensions relative to the water (or carrier fluid) beyond specific suspension velocities. This behavior can be observed in fig. 6 for wheat straw-water suspensions at Cm = 5%-10%.
 |  |
| (a) | (b) |
| Figure 6. Frictional pressure drops for aqueous slurries of a 6.4 mm particle size of wheat straw for velocities = 0.5 m s-1 and Cm = 5%-30% flowing through a 50 mm diameter inclined pipe section at (a) ? = +14° and (b) ? = +21°. | |
Further, it is evident from figure 6 that with increases in the slurry concentration, the pressure drops of wheat straw-water suspensions decreased after certain velocities for each concentration of the suspension. This is attributed to the increase in the particle-particle and particle-fluid (hydrodynamic) interactions, which increases the apparent suspension viscosity (Djalili-Moghaddam and Toll, 2006), the strength of the fiber network, and, ultimately, the ability of large flocs to grow at higher fiber concentrations and low suspension velocities (Duffy, 2006a; Javed et al., 2022a). Hence, a further increase in the concentration of wheat straw suspension beyond Cm = 10% flowing through any of the pipe inclinations (-7° to +21°) causes more significant suppression of the longitudinal turbulence intensities and, consequently, a further decrease in the frictional pressure drop compared to the water curve. At higher concentrations (i.e., Cm = 25%-30%) of wheat straw-water suspensions for all pipe inclinations, because of extensive increases in the mutual interactions of the wheat straw particles and the strength of their networks, larger flocs will be developed, particularly at low flow rates. Therefore, a decrease in the frictional pressure drops of highly concentrated wheat straw suspensions (i.e., Cm = 25%-30%) was observed relative to water at higher velocities. The
reasons for this behavior have been elaborated in a section on onset velocity of drag reduction. Visual observations (despite the dark brown background, which made the analysis challenging) showed no bed formation for 6.4 mm particle size wheat straw-water slurries across the whole range of mass concentrations (Cm = 5%-30%) running down the inclined pipe section of any of the slopes (-7° to +21°) used in the current investigation, even at the minimal slurry velocity of 0.5 m s-1. This outcome was on par with an earlier study on the deposition velocity of biomass particles, in which it was discovered that this velocity was 0.21-0.28 m s-1 for slurries of wheat straw particles with d50 = 4.81 mm for Cm = 5%-20% in horizontal flows (Vaezi et al., 2018). Further, in the earlier work, the terminal settling velocity (vt) of several particle lengths (5-30 mm) of wheat straw was evaluated as 13-17 mm s-1 in a quiescent medium and it was found that these particles were buoyant (i.e., (vm / vt) = 0.021), specifically for vm = 0.5 m s-1 and particle sizes of 5-10 mm (Javed et al., 2022a). This means that for vm = 0.5 m s-1, it was reasonable to assume that there was no slip between the liquid and solid phases of the 6.4 mm nominal size of wheat straw particles with d50 = 4.85 mm and that the in situ concentration of the suspension was almost equal to the delivered concentration for the minimum slurry velocity used in the current study. Therefore, it was concluded that the biomass-water suspensions were flowing as a heterogeneous mixture with some concentration gradient across the pipe cross-section for all the pipe inclinations at the minimum slurry velocity (i.e., 0.5 m s-1). Since the delivered concentration of the 6.4 mm nominal particle size of wheat straw suspension was found to be almost equal to the prepared concentration with a maximum difference of 7% (Javed et al., 2022b), the prepared mass concentrations were used (i.e., Cm = 5%-30%) and the saturated slurry densities shown in table 3 to evaluate the frictional pressure drops of these suspensions in a similar fashion as we did for the fine sand-water slurries.
Effect of Inclination on Frictional Behavior of Wheat Straw-Water Slurries
Flow Regions
Figure 7 shows the friction factor measurements for the 6.4 mm particle size of wheat straw-water slurry flow through a 50 mm diameter inclined pipe section at various slopes (-7° to +21°) for slurry bulk velocities = 0.5 m s-1 and a mass concentration range of 5%-30%.
 |
| (a) |
 |
| (b) |
| Figure 7. Friction factor versus generalized Reynolds number for velocities = 0.5 m s-1 of the 6.4 mm particle size of wheat straw-water slurry flows through a 50 mm inside diameter pipe section with inclination angles of (a) ? = 0°, (b) ? = -7°, (c) ? = +7°, (d) ? = +14°, (e) ? = +21° relative to the x-axis. |
The experimental values of friction factors (fD) for the wheat straw slurries (fig. 7) were determined by substituting index m for w in equation 4 for wheat straw-water mixtures. The corresponding values of slurry frictional pressure drops in equation 4 were calculated using equation 1, and the slurry densities (pm) were determined using equation 2. The generalized Reynolds number (Reg) (the generalized Reynolds number can be obtained using the relation Reg = ?mvmD / ??f, where ??f is the carrier fluid viscosity in Pascal-sec) was used to express the suspension velocities (fig. 7). The ARB-water slurries, during their flow through a horizontal pipe, behave somewhat similarly to wood fiber slurries (Mih, 1967; Robertson, 1957; Sumida and Fujimoto, 2015), chemical wood pulp suspensions (Duffy and Lee, 1978), and semi-chemical pulp suspensions (Duffy et al., 1976). In earlier studies, three fairly distinct zones: plug flow, transition flow, and turbulent flow were observed that characterizes the flow behavior of ARB-water suspensions in horizontal pipelines (Javed et al., 2021; Vaezi et al., 2014).
 |
| (c) |
 |
| (d) |
| Figure 7 (continued). Friction factor versus generalized Reynolds number for velocities = 0.5 m s-1 of the 6.4 mm particle size of wheat straw-water slurry flows through a 50 mm inside diameter pipe section with inclination angles of (a) ? = 0°, (b) ? = -7°, (c) ? = +7°, (d) ? = +14°, (e) ? = +21° relative to the x-axis. |
In the first zone, the plug flow region, which appears at a low Reynolds number, a plug of flocculated fibers moves along the central core of the pipe. In this region, the flow appears without any plug-wall interaction, with a progressive increase in annulus size and a rapid fall in the friction factor. The plug is always encompassed by a carrier fluid annulus free of fibers in this region (Mih, 1967; Wiklund et al., 2001; Wiklund et al., 2006), and the suspension's friction factor is always greater than water's at the same flow rate because a flatter velocity profile develops in the core (because of the fiber’s plug), which causes a steeper profile near the boundary. This results in an increase in wall shear stress and hence the friction factor (Vaseleski and Metzner, 1974). The size of the annulus is influenced mainly by the Reynolds number of the fiber suspension; it grows larger as the flow rate of the suspension rises, leading to an abrupt decrease in the friction factor of the suspension and, finally, to a transition point (D in fig. 7, identified in our earlier study (Vaezi et al., 2014)), where the friction factors of the fiber suspensions and the water are equal (Duffy et al., 1976).
The transition or mixed flow region shows up after the transition point, where an increase in slurry velocity decreases the friction factor at a comparatively lower rate than in the plug flow region. The compressed fibers in the plug prevent the water annulus around it from growing with the suspension velocity. This phenomenon causes the start of the high shear zone in the annulus, where a further increase in the suspension velocity causes the fiber plug to disintegrate at the junction of the annulus and the plug’s periphery, and the velocity profile in the core starts changing its shape to be less blunt than what appeared in the plug flow region (Cotas, 2016; Mih, 1967; Vaseleski and Metzner, 1974). The fiber plug’s disintegration continues with an increase in the suspension velocity, and the fragmented fibers continue to mingle with the surrounding annulus until a maximum drop (E in fig. 7c, from an earlier study (Vaezi et al., 2014)) in the slurry friction factor is achieved with respect to that of the clear water curve. The fiber plug diameter is reduced in the transition flow region until a turbulent flow region appears and the fiber plug completely disappears. The individual fibers in the suspension are fully dispersed in the turbulent flow region across the pipe’s cross-section; however, the friction factor curve remains below and parallel to the water curve with an almost constant friction factor at all the subsequent flow rates (Cotas, 2016; Duffy, 1989).
 |
| (e) |
| Figure 7 (continued). Friction factor versus generalized Reynolds number for velocities = 0.5 m s-1 of the 6.4 mm particle size of wheat straw-water slurry flows through a 50 mm inside diameter pipe section with inclination angles of (a) ? = 0°, (b) ? = -7°, (c) ? = +7°, (d) ? = +14°, (e) ? = +21° relative to the x-axis. |
In the present study, an effort was made to understand these regions (or zones) based on the friction factor measurements for the range of mass concentrations and bulk velocities of 6.4 mm particle size wheat straw-water suspensions flowing through an inclined pipe section with different slopes (fig. 7). In general, all the wheat straw-aqueous suspensions in an inclined pipe of any degree (-7° to +21°) demonstrated the characteristics of the plug flow (Region 1) and the transition flow (Region 2) regions together for Cm = 5%-30% in the entire flow range (0.5-4.7 m s-1). No suspension for any pipe inclination exhibited the turbulent flow region under the flow conditions; however, this region is expected to appear at higher flow rates than the maximum suspension velocities achieved in this study.
For any specific mass concentration of wheat straw-water slurry and slope of the inclined pipe section, the friction factor decreased with increasing the Reynolds number. This decrement in the friction factor was more pronounced in higher concentrations of the slurries for Reynolds number beyond the transition point (D) because of the increase in the particle-particle interaction at higher concentrations that suppresses the turbulence intensities more than the suspensions at low concentration, as discussed in earlier studies on other fiber suspensions (Steen, 1989; Vaseleski and Metzner, 1974). For the flow conditions investigated here, the minimal friction factor was obtained at the maximum feasible slurry Reynolds number for Cm = 25% and any given pipe inclination (fig. 7). For the highest mass concentration (i.e., Cm = 30%) of wheat straw suspensions and every pipe inclination, it was possible to decrease the friction factor further, but at high turbulent flows of the suspensions with velocities beyond a specific range of 4.15-4.7 m s-1, depending on the range of pipe inclinations (-7° to +21°) used in the present study.
From the friction factor curves of wheat straw-water slurries shown in figure 7, a monotonic change in the transition point (D) was found with respect to certain saturated mass concentrations and pipe inclinations. The axial component of gravity influences the location of the transition point (D) for suspensions with equal mass concentrations in relation to the pipe's angle, as stated in the following section (i.e., onset velocity of drag reduction). It was also observed that point E, associated with the minimum friction factor (fig. 7c) (or the point of maximum drop in the slurry's friction factor relative to the water curve), was almost recognizable on the friction factor curves for most pipe inclinations and wheat straw-water slurry concentrations until Cm = 25%, after which a further increase in suspension velocity will increase the friction factor instead of decreasing it, as stated in other studies (Duffy, 1989; Vaezi et al., 2014). For Cm = 30% and any of the pipe inclinations (-7° to +21°), it was still possible to achieve a further drop in the friction factor at higher flow rates until point E (not depicted on the graphs); however, all of these possibilities were typically associated with the pump characteristics (feedstock preparation and particle size analysis section highlights the pump limitations) used in the current investigation. Further, the wheat straw-water suspensions at Cm = 5%-10% flowing through an inclined pipe of ? = +7° were found to exhibit plug flow region (i.e., Region 1) only for the entire range of the suspension velocity. More research on the frictional behavior of different particle sizes of wheat straw-aqueous slurries through inclined pipes at ? = ±7° and higher inclination angles (?) for uphill and downhill flows (e.g., ±14° and ±21°) is required to determine the root cause of this anomaly.
Onset Velocity of Drag Reduction (vOD)
The onset velocity of drag reduction (vOD) is the velocity at which a suspension’s flow zone changes from plug flow to transition flow. This velocity corresponds to the transition point (D) (shown in fig. 7) of any suspension. By creating a code in RStudio (4.0.5) to get the coordinates of each transition point, the values of vOD (table D in the supplementary information section) were determined. Figure 8 depicts the vOD in inclined (both uphill and downhill) flows of wheat straw-aqueous suspensions with a 6.4 mm particle size at Cm = 5%.
In general, the vOD for wheat straw-water suspension flowing through any of the slopes of the inclined pipe section (except 7° ascending) reduced with increasing slurry mass concentration up to a particular threshold, as depicted by each curve's lowest value in figure 8. Similar behavior for different particle sizes of corn stover-water slurries in upward flows through a vertical pipe section was observed in a recent study (Javed et al., 2022a). The average inter-fiber distance (hav) (Doi and Edwards, 1978a,b) in the wheat straw suspension is greater at low fiber concentration (i.e., Cm = 5%) than at higher concentrations of similar-sized particles (see table 5).
 |
| Figure 8. Onset velocity of drag reduction (vOD) for the 6.4 mm particle size wheat straw-water slurries of several mass concentrations flowing through an inclined pipe section of varying inclinations (i.e., ? = -7° to +21°) relative to the x-axis. |
The hav was evaluated using the relation hav = (nXig)–1/2 (where n (n = [(4 / p)CV(1 / XigXig,w2)]), Xig, and Xig,w are the fiber number fraction, graphic mean length, and the graphic mean width of the wheat straw particles, respectively; see table 2 for the values of Xig and Xig,w) originally proposed by Doi and Edwards (1978). The lower the value of hav, the more the adhesive forces and hence flocculation. Further, in an earlier study, a hypothesis was proposed that at low fiber concentrations, when there are more void spaces among the fibers, hav decreases with an increase in the suspension velocity (Javed et al., 2022a). Therefore, for the suspension at Cm = 5%, the hav decreases as the flow rate increases, bringing the fibers closer together. On the other hand, the fiber-free annulus grows until the suspension, which is still in the plug flow region, reaches a high flow rate where the fibers are so close together that there are very few empty spaces between them and strong connections form between the fibers. This is where the fiber-fiber interactions are most noticeable. A further increase in suspension velocity at this stage at high flow rate will cause the plug to disrupt from its outer periphery (which is intact with the annulus) and results in the onset of drag reduction at a high value of vOD for a low concentration (Cm = 5%) of the suspension (fig. 8). The fiber number fraction (n) increases and the hav decreases as the slurry concentration is increased further beyond Cm = 5% (table 5) until the suspension reaches the threshold point, so relatively low flow rates of the suspensions are required to form a plug with a minimum amount of void spaces and a strong inter-fiber connection. As a result, compared to the suspension at a Cm = 5%, the commencement of drag reduction occurs at somewhat lower slurry velocities at the concentration related to the threshold. An earlier study on vertical upward flows showed a similar trend for corn stover-water suspensions (Javed et al., 2022a).
| Table 5. Mechanistic properties to comprehend the flow behavior of the 6.4 mm nominal particle size wheat straw-water suspension. | ||||||
| Parameters | Saturated Mass Concentration (Cm) (%) | |||||
| 5 | 10 | 15 | 20 | 25 | 30 | |
| Average inter-fiber distance (hav) | 5.59 | 3.93 | 3.20 | 2.77 | 2.47 | 2.25 |
| Fiber number fraction (n) | 0.0067 | 0.0134 | 0.0202 | 0.0269 | 0.0338 | 0.0406 |
| Contact number (nc) | 0.83 | 1.66 | 2.50 | 3.34 | 4.19 | 5.04 |
| Crowding number (N) | 2.40 | 4.82 | 7.25 | 9.69 | 12.15 | 14.61 |
| Suspension behavior regime | Dilute | Semi- conc. | Semi- conc. | Conc. | Conc. | Conc. |
After the threshold, for every pipe inclination, the vOD increased with increasing saturated mass concentrations of the wheat straw-water suspension (fig. 8). Kazi et al. (1999) and Duffy and Lee (1978) linked this increase in vOD to fiber network strength. The strength of the fiber network in a suspension depends on the number of contacts (nc) of each fiber with the adjacent ones, which is defined as nc = 2CV(fp)2 (where CV and fp are the saturated solid volumetric concentration and the particle aspect ratio, respectively). The fiber suspension is categorized as being in the concentrated regime when nc = 3.0, whereas it is in the dilute regime for nc < 1.0 (Dodson, 1996; Kerekes, 2006). Another way to distinguish between a fiber suspension’s dilute and concentrated regimes is the crowding number (N), defined as N = (2 / 3)CV(fp)2. The suspension is in the concentrated regime if N > fp. The fiber network strength significantly increases in the concentrated regime where the fibers develop coherent networks (Dodson, 1996). In the present study, the wheat straw-water suspension was close to the concentrated regime (i.e., nc ˜ 3.0 and N > fp) at the threshold limit; hence, because of increased adhesion forces and flocculation, the suspension had sufficiently high inter-fiber connections at its threshold limit to strengthen the fiber network, which progressively increased in strength for the subsequent increase in concentration above the threshold limit. Consequently, this suspension needs larger flow rates for concentrations beyond the threshold point (see fig. 8) to disrupt the fiber plug boundaries, which increases the vOD with concentration. Wheat straw suspensions at 5%-10% mass concentration were observed to be in the plug flow region for upflow at a 7°inclination of the pipe(fig. 7c), so their drag reduction onset points are not shown in figure 8.
The change in the inclination angle of the pipe typically results in a change in the deposition velocity of conventional solids-water slurries that is highly dependent on the mean particle size, particle density, and particle size distribution, keeping the pipe diameter constant (Al-Mutahar, 2006; Durand, 1953; Kesely et al., 2019; Wasp and Aude, 1970; Wasp et al., 1977). In the present study, no bed formation was observed for the wheat straw-water slurries of the 6.4 mm particle size at any of the pipe inclinations, even at the minimum velocity of 0.5 m s-1 (shown in table C in the supplementary information section). However, the effect of inclination on the vOD for the wheat straw-aqueous suspension can be observed in figure 8, where it was found that at any given concentration, the vOD increased with an increase in the inclination of the inclined pipe for ? = -7°, 0°, and +7° and Cm = 10% (except for Cm = 10% and ? = +7°, where there was plug flow). For this range of angles and concentrations, at any specific value of Cm of the suspension, vOD was lowest for ? = -7° and highest for ? = +7°. For the uphill flows, the axial component of the gravity (i.e., gsin?) being opposite to the flow direction of the suspension (fig. 2a) decelerates the flow, and hence the suspension moves with low velocity compared to the downhill flows, where the axial component of the gravity is in the suspension’s flow direction, which in turn accelerates the flow, causing the suspension to move faster (de Vreede, 2018; Vlasak et al., 2017).
In the present work, the ranges of the highest achievable velocities of wheat straw-water suspension flows for Cm = 5%-10% as 4.53-4.69 m s-1 and 4.43-4.61 m s-1 were obtained at inclinations of -7° (downhill) and +7° (uphill), respectively. A similar decrease in the suspension velocity for other inclinations (i.e., +14° and +21°) was observed, which are not reported here. As the inter-fiber distance hav also depends upon slurry velocity and decreases with an increase in slurry velocity, especially when the suspension is in the plug flow region (Javed et al., 2022a), in the downhill flow of a wheat straw-aqueous suspension at ? = -7°, the axial component of the gravity facilitated the flow more than similar conditions for horizontal or uphill flow at ? = +7°, causing the hav to decrease faster for any specific concentration. Ultimately, the fiber plug starts to disintegrate at the plug-annulus interface at a comparatively lower magnitude of vOD than the corresponding vOD for horizontal or uphill flows of similar suspensions. For conventional solids-water slurries flowing in inclined pipes, the in situ concentration is lower in the downflow direction, and the likelihood of particle slip is lower in the upflow direction, resulting in a higher frictional pressure drop for the upward flows. However, the wheat straw-water suspensions behave entirely differently than the conventional solids-water slurries (as shown in figs. 5 and 6). As these suspensions have low density, are fibrous, and form networks and flocs, the axial component of gravity has a different effect on these suspensions flowing in inclined pipes.
While comparing the vOD for higher slopes of the inclined pipe, i.e., +14° and +21°, a similar pattern (i.e., vOD increased when the pipe inclination was increased) was found across the entire range of Cm’s, as observed for lower inclination angles. However, these results were inconsistent with respect to the lower inclination angles (i.e., 0° and +7°). Nonmonotonic onset velocity variation at ascending angles of 14° and 21° compared to lower inclination angles (i.e., +7° uphill or horizontal pipe position) needs further investigation. It is challenging to interpret the results at this stage because of the need for more information for fiber suspension flows in inclined pipes. Therefore, more data needs to be collected for the present research for different particle sizes and pipe inclination angles (i.e., 7°-21°, both uphill and downhill).
Drag Reduction (%DR)
Figure 9 shows the percentage drag reduction (%DR) by 6.4 mm particle size of wheat straw-water suspensions flowing at various mass concentrations (Cm = 5%-30%) and different bulk velocities through an inclined pipe section of various slopes (i.e., -7° to +21°).
Here, the %DR for slurry bulk velocities of 4.5 and 2.0 m s-1 is presented. The complete results are given in figure D of the supplementary information section. For all the pipe inclinations and specific ranges of slurry bulk velocities = vOD, %DR increased with an increase in the saturated mass concentration of wheat straw-water suspensions until a specific concentration at which the %DR for each suspension was highest. This concentration is known as a critical concentration of maximum drag reduction (Cm)cr. With an increase in Cm, the particle-particle interaction, hence the fiber contact number (nc), increases, which increases the fiber network strength and the tendency of the suspension to reduce the turbulence intensity and the turbulent momentum transfer, giving rise to an increase in the drag reduction (Javed et al., 2021; Vaezi et al., 2014). The increase in the fiber network with Cm also causes the fiber flocs to grow, hence the apparent suspension viscosity, which has a linear relationship with lower values of Cm and a cubic relationship with higher Cm (Djalili-Moghaddam and Toll, 2006). This increase in the viscous nature of the suspension and floc size with Cm affects the drag reduction capabilities of the suspension beyond (Cm)cr because of an increase in the viscous momentum transfer (Xu and Aidun, 2005). Therefore, a maximum %DR at (Cm)cr is observed in this study for wheat straw-water suspensions flowing through inclined pipe sections. After the critical concentration (Cm)cr, a decrease in %DR occurred instead of an increase (shown in fig. 9). A similar phenomenon in vertical upward flows of various particle sizes of wheat straw- and corn stover-water suspensions was observed in the recent work (Javed et al., 2022a).
For suspensions flowing at vm = 2.5 m s-1 through an inclined pipe section, the (Cm)cr was 25% for all the slopes, whereas for suspensions flowing at comparatively lower velocities (i.e., < 2.5 m s-1), the (Cm)cr was 20% for all the pipe inclinations (fig. 9). The flow characteristics of the fiber suspensions greatly depend upon the regimes of the fiber suspension (i.e., dilute, semi-dilute, or concentrated) and the suspension velocity (Bobkowicz and Gauvin, 1965; Javed et al., 2022a; Kerekes, 2006; Kerekes, 1971; Li et al., 1994; Xu and Aidun, 2005). Kerekes found that the (Cm)cr for inelastic fiber suspensions increased with suspension velocity (for any fiber length) and fiber aspect ratio (Kerekes, 1971). In an earlier study, the (Cm)cr for any specific particle size was found to be a strong function of feedstock and suspension velocity, which increased with an increase in vm (Javed et al., 2022a). At Cm = 25%, the wheat straw-water suspension was in the concentrated regime (see table 5), so the viscous nature of the fiber suspension (due to high apparent viscosity) dominated the drag reduction characteristics for vm < 2.5 m s-1, and we observed the maximum %DR at Cm = 20% instead of 25% regardless of pipe inclination (fig. 9b). In general, it was determined that for most of the suspensions, the (Cm)cr appeared to be a strong function of suspension velocity and was independent of the pipe inclination.
  | ||||
| (a) | (b) | |||
| Figure 9. Drag reduction of the 6.4 mm particle size of wheat straw-water slurries for Cm = 5%-30% flowing through an inclined pipe section of various inclinations (i.e., -7° to +21°) and slurry bulk velocities of (a) 4.5 m s-1, and (b) 2.0 m s-1. | ||||
Over the entire range of slopes (-7° to +21°) of the inclined pipe section and any of the saturated mass concentrations (Cm = 5%-30%), the %DR was highest for downflows of the suspension at a -7° inclination and lowest for upflows at a +7° inclination. A maximum %DR of 25.53% was achieved with a suspension of Cm = 25% running at the highest attainable bulk velocity of vm = 4.5 m s-1 through an inclined pipe of -7° (i.e., downflow). In downhill flows, the axial component of gravity facilitates the flow, giving the suspension the lowest value of vOD for any specific Cm (fig. 8), resulting in a higher %DR compared to the uphill flows of similar flow conditions. The upward inclined flows of the wheat straw suspension at all mass concentrations (Cm = 5%-30%) and slurry velocities (1.5-4.5 m s-1) through an inclined pipe section at slopes of +7° to +21° showed an intriguing characteristic. For this range of conditions in uphill flows and any specific mass concentration and velocity, it was found that the %DR first increased when the pipe inclination increased from +7° to +14° and then decreased when the pipe inclination further increased to +21°.
A specific trend of variation in the %DR was not observed with a slope for specific mass concentrations in uphill flows. The reason for this anomaly is still an open issue in the research. Extensive experimental data is needed for us to come to a concrete conclusion, as explained in the previous section. The highest %DR at any concentration and velocity in uphill flows of the wheat straw-water slurry was found at the pipe inclination of +14°. With a suspension of Cm = 25% running at the highest attainable bulk velocity of vm = 4.5 m s-1 in uphill flows of wheat straw-water slurry through an inclined pipe of +14° inclination, the maximum %DR of 24.64% was achieved. We further observed that suspensions with low vOD’s (see fig. 8) in uphill flows (i.e., +7° to +21°) exhibited more drag reduction than suspensions with high vOD’s for similar mass concentrations. This was obvious because the sooner the onset of drag reduction occurs, the sooner the suspensions can attain high velocities for similar flow conditions to reach a higher %DR.
Uncertainty Analysis
To evaluate the level of uncertainty and repeatability in the pressure drop measurements of the 6.4 mm nominal particle size of wheat straw-aqueous slurries for each pipe inclination, at least two sets of tests (i.e., independent trials) were run for the same range of Cm’s (i.e., 5%-30%) and bulk velocity (0.5-4.7 m s-1). A typical uncertainty analysis was used to determine the precision uncertainty (Px) of differential pressure drop measurements and the biased uncertainty (Bx) of the DPT to estimate the overall uncertainty (Ux) (the total uncertainty (Ux) can be evaluated from the precision uncertainty (Px) and biased uncertainty (Bx) as 
) (Javed et al., 2022b; MECE 301, 2018; Moffat, 1988). Broadly speaking, an overall uncertainty of ±0.00497 kPa m-1 to ±0.1793 kPa m-1 was found in the entire pressure drop measurements of wheat straw-aqueous slurries. Figure 10 demonstrates the repeatability of the experimental measurements of the 6.4 mm particle size of wheat straw-aqueous slurries for various Cm’s and angles of inclination of the pipe.
The range in the repeated measurements for the complete series of experiments on wheat straw-aqueous slurries was observed to be ±5.0%.
 |
| Figure 10. The repeatability of the experimental measurements for various mass concentrations of the 6.4 mm nominal particle size of wheat straw-water slurry flow through a 50 mm inside diameter pipe section at different angles of inclination. |
Conclusion
The frictional behavior of aqueous-based wheat straw suspensions of 6.4 mm particle sizes through pipe sections (i.d. = 50.8 mm) of different inclinations was experimentally studied. While commissioning the pipeline loop, we found that Worster and Denny’s model exhibited the best fit to all the experimental pressure drops of aqueous slurries of fine sand (d50 = 0.103 mm) in the pseudo-homogeneous regime (i.e., for vm > 1.0 m s-1) for all the inclined flows (uphill or downhill) with an error range of 0.16%–8.61%. Wheat straw-aqueous suspensions of the 6.4 mm particle size exhibited the plug flow and transition flow regions together for Cm = 5%-30% and the entire flow rate range (0.5-4.7 m s-1) in an inclined pipe with different slopes (-7° to +21°), except for suspensions at low mass concentrations (Cm = 5%-10%) for the lowest slope (i.e., +7°) in uphill flows, where only the plug flow region existed. For the particle size of wheat straw used in this investigation, both the onset velocity of drag reduction (vOD) and percentage drag reduction (%DR) seem to be a function of concentration (Cm) and pipe inclination (?). The vOD achieves its lowest value (threshold) for any pipe inclination at a Cm close to the condition, i.e., nc = 3.0 and N > fp (where the suspension just entered the concentrated regime), beyond which the slurry behavior reverses (i.e., vOD rises with Cm) because of a progressive increase in the strength of the fiber network. Drag reduction, on the other hand, increased with Cm for all the inclinations (?) at vm > vOD up to a specific mass concentration (Cm)cr, where the %DR reaches a plateau and then starts to decline again because of the increase in the apparent suspension viscosity. The (Cm)cr depends solely on a certain range of vm (i.e., it was 25% for vm > 2.5 m s-1 and 20% for vm < 2.5 m s-1) and is unaffected by the pipe inclination.
In certain aspects, wheat straw-water slurries behave differently in downhill flows than in uphill flows. The downhill flows of slurries showed a minimum vOD and maximum %DR compared to uphill flows at all Cm because of the accelerating effect of gravity. For uphill flows with larger angles, i.e., ? > +7°, and the entire range of Cm, vOD increased and %DR decreased with pipe inclination. In contrast, for uphill flows at ? = +7°, the vOD was the highest and the %DR the lowest of all the inclinations. In general, given similar flow conditions, wheat straw-aqueous suspensions proved to be more effective in lowering drag in downhill flows than in uphill flows. The nonmonotonic variations in vOD and %DR, specifically in uphill flows, suggest it is worth looking at the corresponding results for different feedstocks and particle sizes of ARB-water slurry flows through inclined pipes (both uphill and downhill) of various inclinations and diameters and determining the optimum flow conditions and the empirical pressure drop correlation of ARB-water slurries through pipes at different slopes. Finally, the optimum flow conditions and empirical correlations of ARB-water slurries through horizontal, vertical, and inclined pipe sections can assist in designing and operating a long-distance integrated pipeline network for a commercial biorefinery.
Acknowledgments
The authors are thankful to the Natural Sciences and Engineering Research Council of Canada (NSERC) and Alberta Innovates for financial support. As a part of the University of Alberta’s Future Energy Systems research initiative, this research was made possible in part thanks to funding from the Canada First Research Excellence Fund. Special thanks to Astrid Blodgett for editing this paper.
Supplemental Material
The supplemental materials mentioned in this article are available for download from the ASABE Figshare repository at: https://doi.org/10.13031/24431068
Nomenclature
D = Inner diameter of the pipe (m)
dL = Span of inclined test section (m)
fD = Darcy Weisbach friction factor (m)
?Pf L-1 = Frictional pressure drop in a pipe (kPa m-1)
??w = Dynamic viscosity of fluid (Pa s)
?w = Density of water (kg m-3)
CVp = Prepared concentration (% volume)
v = Bulk velocity of fluid (m s-1)
Cmd = Delivered concentration (% mass)
Cm = Saturated mass concentration (%)
vt = Terminal settling velocity (m s-1)
vm = Bulk velocity of the mixture (m s-1)
= Experimental frictional pressure drops of the mixture flowing through an inclined test section
= Total pressure drops of the mixture flowing through an inclined test section
Xig = Graphic mean length (mm)
Xig,w = Graphic mean width (mm)
GHG = Greenhouse gas
MC = Moisture content (% mass)
dFE_max = Feret diameter (mm)
asc = Ascending position of the inclined pipe with respect to the x-axis
? = Angle of inclination of the pipe with respect to the x-axis
?m = Density of mixture (kg m-3)
?s = Density of solid particles (kg m-3)
fp = Particle aspect ratio
vt = Bulk velocity of mixture (slurry) (m s-1)
g = Acceleration due to gravity (m s-2)
Reg = Generalized Reynolds number, (?mVmD / ??f)
PVC = Polyvinylchloride
vOD = Onset velocity of drag reduction (m s-1)
CVd = Delivered concentration (% volume)
(Cm)cr = Critical concentration of maximum drag reduction (%)
Cmp = Prepared concentration(% mass)
i.d. = Inside diameter of the pipe (m)
= Measured/manometric pressure drops of the mixture flowing through an inclined test section
DXX = Feret or shortest cord diameter in mm at respective XXth percentiles of the cumulative distributions of particles
S = Specific gravity or relative density (?s /?w)
sig = Graphic standard deviation (mm)
DPT = Differential pressure transmitter
PSD = Particle size distribution
dc_min = Shortest cord (mm)
desc = Descending position of the inclined pipe with respect to the x-axis
horiz = Horizontal position of the inclined pipe section with respect to the x-axis
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