Analysis of minimum specific energy consumption and optimal transport concentration of slurry pipeline transport systems
Graphical abstract
Introduction
Pipeline transportation is extremely popular because of its advantages of low power consumption, environmental protection, and easy optimisation control. It has been widely used for transporting energy, food, and minerals as well as several other industries. Furthermore, pipeline transportation is regarded as the most ideal transportation method for deep sea mining in the future. However, to utilise the economic and other efficiency advantages of the pipeline transportation system fully, it must be designed scientifically and operated properly; determining the optimum working conditions is an important issue in pipeline design and operation.
The pipeline transportation system is extensive and complicated, includes driving equipment, centrifugal pumps, pipelines, and other mechanical equipment, and involves several academic fields such as fluids, machinery, and electricity. The economy of this complicated system can not only significantly reduce because of the limitation of a single factor but also fluctuate with the changing working conditions (such as the distance of transmission, diameter of pipeline, and characteristics of the material being transported). Therefore, equipment performance and working conditions must be considered at the beginning of the design of the conveying system and the engineering construction process, especially the matching between the characteristics of the particulate material (such as particle size, particle gradation, and transport concentration). To realise all these objectives, a prerequisite is to clarify the energy consumption of the pipeline under the specific soil conditions of the construction site.
In the pipeline transportation of granular materials, especially medium and coarse sand pipelines in a heterogeneous regime, a lowest resistance point (P) exists within the working velocity range of the slurry with a specific concentration (Fig. 1).
Fig. 1 shows that P has the least resistance in the entire flow rate range when the transport concentration in the pipeline is fixed. This indicates that the energy required to transport a unit mass of solids over a unit pipeline length (named specific energy consumption (SEC) by Wilson et al. (2006)) is minimum with a certain concentration when working near point P. Therefore, an in-depth study of the working parameters of point P of the granular material conveying system, especially the flow rate (referred to as the key flow velocity) can provide important guidance and is economically significant for the construction. In recent years, many scholars have devised various methods for finding the key flow velocity. The key flow-velocity calculation methods include those proposed by (1) Zandi & Govatos (1967), Larsen (1968), and several others, based on the particle-resistance coefficient; (2) Göğüş & Kökpınar (1993) and Kökpınar & Göğüş (2001), based on the particle-sedimentation velocity; (3) Wilson et al. (2006), which directly uses the particle size, pipeline diameter, and slurry concentration as variables; and (4) Schiller & Herbich (1991), for non-uniform particle groups. These algorithms satisfy the engineering calculation requirements to a certain extent.
Because the slurry concentration changes, its resistance characteristics and energy consumption change as well (Fig. 1). Different concentrations of slurry composed of the same particles correspond to different values of key flow velocity, and different key flow velocities correspond to different transport-particle-volume production and specific power consumption (SPC). For any type of granular slurry, a transport concentration exists and is defined as the optimal transport concentration (OTC) with the smallest SPC.
Wilson et al. (2006), Wang (1998), and especially Hashemi et al. (2014), among others, made outstanding contributions to the study of the minimum SEC of particulate material pipeline transportation. Wilson et al. (2006) defined SEC to calculate the energy consumption. It can be expressed aswhere im and Cv represent the hydraulic gradient and transport concentration, respectively, and Ss represents the specific gravity of the solid, i.e., the ratio of particle density to water density.
Wang (1998) provided an energy consumption equation that is more suitable for an economic calculation of coal transportation: energy consumption per tonne-kilometre (kW h/(t km)), which represents the energy consumption required to transport a unit weight (per tonne) of granular materials over a unit length (per kilometre) of the pipeline:where Qm and Qs represent the slurry and solid flow rates (m3/h), respectively; ρs, ρm, and ρf represent the solid, slurry, and water densities (kg/m3), respectively; im,F represents the hydraulic gradient of slurry; L represents the pipe length (km); ΔH represents the difference between transportation heights (i.e., the difference between the end and starting points considered positive when the starting point lies below the end point and vice versa (km)); η represents the pump efficiency; and K represents an additional coefficient of friction loss and local resistance. The author recommends K values of 1.15 and 1.1 for long- and short-distance pipeline transportation systems.
Based on the pipeline transportation resistance calculation model given by Wilson et al. (2006), Hashemi et al. (2014) concluded that the minimum energy consumption of particulate material pipeline transportation generally occurs at a transmission concentration of approximately 30%, which provides a valuable reference for the pipeline transportation industry.
However, the aforementioned energy consumption models have several limitations. It is difficult for the construction personnel to use the SEC given by Wilson et al. (2006) to assess the construction efficiency. Moreover, it is difficult for engineers to obtain the fuel consumption curve of the pump driver to calculate the energy consumption proposed by Wang (1998). Many experimental studies have established that the foundation of the Hashemi et al. (2014) model, i.e. the resistance calculation equation given by Wilson et al. (2006), is used to calculate the hydraulic gradient. However, for broad-graded slurry, especially high-concentration broad-graded slurry, the pipeline resistance calculated using this formula is greater than the experimental measurements. Therefore, the conclusion that the optimal concentration is 30% is applicable only to pipeline transportation systems with a certain particle unevenness and slurry concentration range. In this study, based on the Shanghai Jiao Tong University high-concentration multi-sized slurry pressure drop (SJTU-HMSPD) model by Li et al. (2018), a calculation model of slurry pipeline transportation power consumption called SJTU-SPC, which is capable of accurately calculating the SPC of high-concentration complex slurry pipeline transportation, corresponding to the parameters available in actual production, is established. Based on this calculation model, the influence of slurry transport concentration, particle size, particle unevenness, and pipeline diameter on the smallest SPC and the corresponding OTC is studied.
The remainder of this paper is organised as follows. Section “Proposed SJTU-SPC model” establishes the SJTU-SPC model and introduces its basis—the pipeline-resistance-calculation model SJTU-HMSPD. Section “Calculations” describes the utilisation of the experimental data obtained by Sundqvist et al. (1996) to verify and analyse the calculation accuracy of the SJTU-SPC model. Section “Results and analysis” presents the analysis of the effects of parameters such as particle uniformity coefficient, pipe diameter, particle size on the minimum SPC and the corresponding OTC and its results. Finally, the conclusions of this study are summarised in Section “Conclusions”.
Section snippets
Proposed SJTU-SPC model
This study uses the amount of electricity consumed for transporting a unit volume of particles over a unit length of the pipeline to describe the energy consumption level of the pipeline system. Thus, the calculation results can be directly predicted based on the fuel consumption curve of the generator and the efficiency curve of the pump; additionally, the changing trend of pipeline power consumption under different transportation conditions can be directly displayed. Furthermore, it is
Model verification
To demonstrate the accuracy of the calculation model, in this study, the SPCs under the working conditions corresponding to the experiment data published by Sundqvist et al. (1996) are calculated, compared, and analysed. The experimental pipe diameters are 0.203 m and 0.305 m. Three grades of sand with a median diameter of approximately 0.65 mm and uniformity coefficients of 1.26, 3.14, and 7.98 were used in the experiment. The experimental particles gradation curve is shown in Fig. 2.
The
Results and analysis
This research evaluates the SPC only at the condition in which the flow velocity is greater than the key flow velocity, i.e. there is no stable deposition bed of particles.
Conclusions
Based on the SJTU-HMSPD pipeline-resistance-calculation model, we established the SJTU-SPC calculation model for a slurry transport system with the uniformity coefficient of 1.26–7.98, median particle size of 0.075–4.000 mm, transport concentration of 10–60%, and pipeline diameter of 0.203–0.800 m. The influence of working conditions, such as particle gradation and pipe diameter, on the minimum SPC were studied, and the calculation results of the SJTU-SPC model were verified against the
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Declaration of Competing Interest
The authors report no declarations of interest.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (Grant No. 51779143) and the Cultivation of Scientific Research Ability of Young Talents of Shanghai Jiao Tong University (Grant No. 19×100040072).
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