minerals Article
CFD Simulation of Pipeline Transport Properties of Mine Tailings Three-Phase Foam Slurry Backfill Xin Chen
ID
, Jian Zhou
ID
, Qiusong Chen *, Xiuzhi Shi * and Yonggang Gou
ID
School of Resources and Safety Engineering, Central South University, Changsha 410083, China;
[email protected] (X.C.);
[email protected] (J.Z.);
[email protected] (Y.G.) * Correspondence:
[email protected] (Q.C.);
[email protected] (X.S.) Received: 12 July 2017; Accepted: 13 August 2017; Published: 17 August 2017
Abstract: A three-dimensional backfill pipeline transport model is developed using the computational fluid dynamics (CFD) technique, which is applied to study the pipeline transport properties of three-phase foam slurry backfill (TFSB). Based on rheological property tests and CFD simulations, the foam phase, pressure, and velocity in the pipeline system are investigated using the CFD mixture method for different bubble volume fractions and bubble diameters. The simulation results indicate that TFSB can maintain a steady state during pipeline transport, experience a markedly reduced pipeline transport resistance, and exhibit better liquidity than conventional cement slurry. Furthermore, as the bubble volume fraction increases, the resistance of the pipeline decreases and the fluidity improves. By contrast, the bubble diameter has little effect on the transport properties of TFSB. The combined results of CFD simulations, slump tests, and strength tests indicate that, when the bubble volume fraction is 15–20 vol %, TFSB can satisfy the necessary strength requirements and exhibit self-flowing transport. The CFD technique provides an intuitive and accurate basis for pipeline transport research and has the potential for wider application in studies of mine backfill. Keywords: three-phase foam slurry backfill (TFSB); pipeline transportation properties; computational fluid dynamics (CFD) simulation; bubble volume fraction
1. Introduction Paste backfill technology represents an important direction for the development of mine backfill techniques [1–5]. After many years of continuous exploration and practice, paste backfill technology has been accepted and applied in numerous countries throughout the world by virtue of its advantages in terms of environmental protection, emission reduction, safety, and other aspects [6–8]. Backfill pipeline systems have been established in many mines as transportation systems to transport backfill material from the surface to the goaf [9]. As mining depth increased, these backfill pipelines have become much longer and deeper than before, and it has become difficult to achieve self-flowing transport of conventional cement slurry because of its poor fluidity. Although paste pumping technology can solve this problem, the purchase and maintenance of the necessary backfill pump equipment represents an enormous expenditure for a mine. Therefore, an increasing amount of attention has been paid to improve the transport properties of paste slurry while satisfying the transportation and strength requirements of the backfill [10]. Foam concrete is a new type of lightweight concrete material, which is composed of standard foam and cement and possesses a large number of closed pores. With high fluidity and low cement and aggregate usage, foam concrete is applied in sandwich structures, earth-retaining walls, and running tracks or playgrounds [11]. Based on successful experiences with applying foam concrete, Zhang et al. [12] and Chen et al. [13] have studied the application of foam slurry in mine backfill and have concluded that the backfill can meet the requirements.
Minerals 2017, 7, 149; doi:10.3390/min7080149
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For the continuous improvement of foam slurry backfill technology, research on the pipeline transport properties of solid-liquid-gas three-phase foam slurry backfill (TFSB) is necessary. In the past, research on pipeline transportation technology has been performed mostly based on analogy, experience-based formulas, and laboratory experiments to determine the optimal slurry backfill parameters [14,15]. However, such methods cannot be used to investigate the effects of foam factors (bubble volume fraction, bubble diameter, and so on) on the motion characteristics, pipe pressure loss, and changes in velocity of slurry backfill. With the development of computer technology, computational fluid dynamics (CFD) [16,17], which is based on classical fluid mechanics and numerical methods, has begun to be used to study the properties of slurry pipelines for backfill. Eesa and Barigou [18] published a CFD analysis of viscous non-Newtonian flow under the influence of a superimposed rotational vibration. In this paper, the CFD technique is used to build a 3D pipeline transport model, which is applied to simulate the transport properties of TFSB. These simulations are combined with laboratory tests to study the effect of foam on the rheological properties of backfill slurry. 2. Materials and Methods 2.1. Foam Slurry Materials 2.1.1. Constituent Materials TFSB refers to a backfill material that is synthesized from an admixture foam, cement, water, and necessary additives, which are mixed according to certain proportions and hardened by physical and chemical effects. In the case of a high slurry concentration and a low water-to-cement ratio, it also maintains good fluidity [19]. Foam was produced by a high-performance soil foaming agent of the SR-FL-001 [20] (dilution ratio 1:20 by weight). The basic properties of the standard foam are as follows: a density of 40–60 kg/m3 , a foam diameter of 30–100 µm, and segregation-free foam when the temperature is above 0 ◦ C. Cement was P.O 42.5R [21]. The water used in this research was tap water. In this study, mine tailings from a lead–zinc mine in China were used as additives, whose particles are less than 0.074 mm and about 80 wt %, and their mean grain size (d50 ) is 24.2 µm. 2.1.2. Manufacturing Process The preparation of foam slurry is divided into three steps. manufacturing process. 1.
2. 3.
Figure 1 summarizes the
Foam preparation: A special foaming agent is fully mixed with water according to a given dilution ratio to generate foam. Then, the diluted liquid is loaded into a foaming gun along with compressed air at a certain pressure to prepare a standard-density foam. Cement slurry preparation: Cement, tailings, and water are mixed according to given proportions to prepare the cement slurry. TFSB preparation: The premade cement slurry and standard-density foam are mixed in a given proportion to prepare the TFSB.
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Figure 1. Manufacturing processes for foam slurry. Figure 1. Manufacturing processes for foam slurry.
2.2. Test Methods 2.2. Test Methods 2.2.1. Rheological Test 2.2.1. Rheological Test Rheological properties of TFSB were measured using a rheometer (R/S Plus) from Brookfield Rheological properties of TFSB were measured using a rheometer (R/S Plus) from Brookfield Engineering Laboratories, Inc (Middleboro, MA, USA). According to the proportion ratio, the slurry Engineering Laboratories, Inc (Middleboro, MA, USA). According to the proportion ratio, the slurry was mixed as uniformly as possible for 5 min and subsequently placed in the rheometer. The rotor was mixed as uniformly as possible for 5 min and subsequently placed in the rheometer. The rotor speed of rheometer increased gradually from zero and ran for 120 s. Record shear stress and plastic speed of rheometer increased gradually from zero and ran for 120 s. Record shear stress and plastic viscosity per second. viscosity per second. 2.2.2. 2.2.2. Slump Slump Tests Tests The slumptest testwas wasoriginally originally developed to determine “workability” or “consistency” of The slump developed to determine the the “workability” or “consistency” of fresh fresh concrete, and the standard slump instrument is a tapered cylinder with a height of 30 cm, an concrete, and the standard slump instrument is a tapered cylinder with a height of 30 cm, an upper upper diameter of 10 cm, and a bottom diameter of [22]. 20 cmThe [22]. The was slurry was poured the diameter of 10 cm, and a bottom diameter of 20 cm slurry poured into theinto slump slump instrument and tamped. Then picked up the slump instrument quickly, and the slurry instrument and tamped. Then picked up the slump instrument quickly, and the slurry flowed freely. flowed freely.from Thethe distance the top of top the of slurry to the instrument top of the was slump instrument The distance top of from the slurry to the the slump measured afterwas the measured after the slurry shape is stable; the distance is the slump value. slurry shape is stable; the distance is the slump value. 2.2.3. Strength Tests The slurry slurrywas wasmolded moldedinin dimensions of 70.7 × 70.7 × 70.7 andspecimens the specimens dimensions of 70.7 mmmm × 70.7 mmmm × 70.7 mm,mm, and the were were maintained by a TH10D laboratory humidifier (Texingda, Beijing, China), which was kept maintained by a TH10D laboratory humidifier (Texingda, Beijing, China), which was kept working ◦ working ensure that the temperature was within controlled within a range of 23–26 °Chumidity and that was the to ensure to that the temperature was controlled a range of 23–26 C and that the humidity was controlled within a range of 83%–87%. The compressive strength was tested controlled within a range of 83%–87%. The compressive strength was tested respectively after 7 and respectively after 7 and rigid 28 days by a WDW-2000 rigid hydraulic pressure machine (Ruite, 28 days by a WDW-2000 hydraulic pressure servo machine (Ruite, Guilin,servo China). Guilin, China). 2.3. CFD Simulation 2.3. CFD Simulation As shown in Figure 2, a three-dimensional model was developed for a typical L-shaped backfill pipeline for long-distance which was used here towas study the transport of TFSB. As shown in Figure transport, 2, a three-dimensional model developed for aproperties typical L-shaped The pipe is made of seamless steel, and its detailed geometrical parameters are a vertical height of backfill pipeline for long-distance transport, which was used here to study the transport properties ◦ 100 m, a The horizontal 500 m, a diameter mm, an elbow angle of 90 , and elbow of TFSB. pipe islength made of seamless steel, and of its102 detailed geometrical parameters are an a vertical radius of 1100 m.m, The model can length be usedofto500 analyze the velocity andmm, pressure distribution theand slurry. height a horizontal m, a diameter of 102 an elbow angle ofof90°, an The model was and meshed Gambit, and the accuracy wasdistribution confirmed by elbow radius ofestablished 1 m. The model can be in used to analyze thecalculation velocity and pressure of the mesh number. Six groups different mesh on and the model and compared in terms of slurry. The model was of established and numbers meshed are in tested Gambit, the calculation accuracy was pressure, and volume to ensure a mesh-independent solution. Theon results show that, confirmedvelocities, by the mesh number.fraction Six groups of different mesh numbers are tested the model and compared in terms of pressure, velocities, and volume fraction to ensure a mesh-independent solution. The results show that, when the mesh number exceeds 2.08 × 106, the variations of
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when the mesh number exceeds 2.08 ×are 106so , the variations pressure, velocity and volume fraction pressure, velocity and volume fraction little that theseofcan be negligible generally. We found that 6 are so little that these can be negligible generally. We found that the mesh number of 1.28 × 10 6 the mesh number of 1.28 × 10 gives about a 1% deviation compared to the mesh number of 2.08gives × 106; 6 about a 1% deviation compared to about the mesh of 2.08 × 106 ;tothe the mesh number of 3.24 × 106 gives a 9%number deviation compared themesh meshnumber numberofof3.24 2.08×× 10 106. 6 gives about the a 9%mesh deviation compared the meshfound number of 2.08 × 10 .for Therefore, the mesh number 6 was Therefore, number of 2.08 to × 10 to be sufficient the numerical simulation. 6 was found to be sufficient for the numerical simulation. As an index of the computational of 2.08 × 10 As an index of the computational cost, the model takes approximately 2 h of computing time on a cost, the model takes approximately 2 h of computing time on with(Random-Access two quad-core workstation with two quad-core processors (2.57 GHz) anda workstation 16GB of RAM processors (2.57 GHz) and 16GB of RAM (Random-Access Memory). Memory).
Figure 2. Pipeline transport system for backfill in an underground mine. Figure 2. Pipeline transport system for backfill in an underground mine.
2.3.1. Governing Conservation Equations 2.3.1. Governing Conservation Equations TFSB is composed of a gaseous foam, solid aggregates and cement, and liquid water. In this TFSB is composed of a gaseous foam, solid aggregates and cement, and liquid water. In this work, work, to fully represent the effect of the foam on the transport properties of the backfill slurry, to fully represent the effect of the foam on the transport properties of the backfill slurry, simplified simplified CFD simulations of a two-phase flow are considered, in which the cement slurry is CFD simulations of a two-phase flow are considered, in which the cement slurry is treated as the treated as the first phase and the foam is treated as the second phase. The Fluent CFD tool was used first phase and the foam is treated as the second phase. The Fluent CFD tool was used to perform to perform the simulations, and the interfaces between the slurry and foam were tracked using the the simulations, and the interfaces between the slurry and foam were tracked using the mixture mixture method (MIX). When using MIX for interface tracking, it is customary to use a two-phase method (MIX). When using MIX for interface tracking, it is customary to use a two-phase model, i.e., model, i.e., a model with a mixture pressure field, a mixture velocity field, mixture density, and a a model with a mixture pressure field, a mixture velocity field, mixture density, and a second phase second phase volume fraction [23]. In MIX, the finite volume discretized forms of the equations that volume fraction [23]. In MIX, the finite volume discretized forms of the equations that govern the govern the conservation of mass, momentum and volume fraction (Equations (1)–(3)) are solved conservation of mass, momentum and volume fraction (Equations (1)–(3)) are solved over a collocated over a collocated grid arrangement using a segregated solver approach (the PISO algorithm) for the grid arrangement using a segregated solver approach (the PISO algorithm) for the pressure–velocity pressure–velocity calculations. MIX allows phases to pass through each other; thus, the volume calculations. MIX allows phases to pass through each other; thus, the volume fraction of each phase fraction of each phase can take arbitrary values between 0 and 1. At the same time, the can take arbitrary values between 0 and 1. At the same time, the characteristics of the mixed fluid in characteristics of the mixed fluid in the control region are determined by each phase [23]. The the control region are determined by each phase [23]. The formulas for the viscosity can be written as formulas for the viscosity can be written as shown in Equation (4). shown in Equation (4). * ∂ ρ m + ∇ · ρ v = 0 ( ) ∂ m ∂t * ( ρm m ) + ∇ ⋅*mρ m vmm = 0 v ∂t = n (1) k =1 αk ρk v k /ρm m ∑ n n ρmv m== ∑ α ρα ρ v k ρ (1)
(
)
k
m
k
k =1 k k
k =1 n * * * ρm = α k ρk * *T ∂ + ρm mg+ ρm v m + ∇ · ρm v m v p + ∇ · µm ∇ v m + ∇ v m k =1 m = −∇ ∂t n
*
!
+ ∇ · ∑ αk ρk v dr,k v dr,k T F ∂ ρ m v m + ∇ ⋅ ρ m v m v m = −∇ k =1 p + ∇ ⋅ μ m ∇ v m + ∇ v m + ρ m mg + ∂t * * ∂ n · α ρ v α p ρ p + ∇ · α p ρ p v m = −∇ F + ∇ ⋅ α k ρ k v dr , k v dr , k p p dr,p ∂t k =1 µ = µ 1−α +µ α
(
)
(
*
)
m
q
p
*
(
p p
)
(2)
(2) (3) (4)
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where m is the mixture mass, ρm is the mixture density (kg/m3 ), ρk is the density of phase k (kg/m3 ), * * v m is the mixture average velocity (m/s), v k is the velocity of phase k (m/s), αk is the volume fraction of phase k (%), n is the number of phases, ∇ p is the difference in pressure (Pa), µm is the viscosity of *
the mixture (Pa·s), g is the acceleration of gravity (i.e., 9.8 m/s2 ), and F is the volume force (Pa). 2.3.2. Flow State The flow state of the fluid can be determined based on the Reynolds number. The three-phase flow of foam slurry is non-Newtonian, and the equation for the Reynolds number based on the plastic viscosity can be written as follows [24]: Re = ρvD/µ (5) where Re is the Reynolds number, ρ is the density of the slurry (kg/m3 ), v is the velocity of the slurry (m/s), and µ is the viscosity (Pa·s). When the Reynolds number is less than 2300, the flow state of the fluid in the pipeline is laminar; when the Reynolds number is more than 2300 but less than 4000, the flow is in a transition state between laminar and turbulent flow; when the Reynolds number is greater than 4000, the flow state is turbulent [25,26]. Generally, when the bubble volume fraction is 0–40 vol %, calculated by Equations (2) and (3), their corresponding mixture viscosity is 0.4100–0.2780 Pa·s, and the mixture density is 1750–1070 kg/m3 . Assuming the backfilling ability is 60 m3 /h, the velocity is 2.24 m/s. Therefore, the Reynolds value is 975–879. The maximum Reynolds is 975 when the bubble volume fraction is 0 vol % and less than 2300, the slurry flow state is laminar. 2.3.3. Boundary Conditions The effects of heat exchange, vibration, stress waves, and compression are not considered in the simulations [27]. The applicable boundary conditions are assumed as follows: (1) (2)
At the walls: the wall is stationary and no-slip. At the pipe inlet, the velocity (v) function given below is used at the inlet face [28]: v = k · Q/(900πD2 )
(3) (4)
(6)
where Q is the slurry flow backfilling ability (m3 /h), D is the diameter of the backfill pipe (m), the value of which is 0.102 m, k is a constant, and the value is 1.1. Thus, when the backfilling ability is 60 m3 /h, the slurry velocity is 2.24 m/s. At the pipe outlet, the outflow function is used at the outlet face. In the calculation domain, a gravity field is applied, and the standard atmospheric pressure (1 bar) is used as the reference to atmospheric pressure.
3. Results and Discussion 3.1. Foam Formation Characteristics Foam is a porous membrane dispersion system formed of a mixture of liquid and gas, in which the liquid is in a continuous phase and the gas is in a dispersed phase, and a standard foam flow is the necessary condition and foundation for foam slurry preparation. During the foaming process, surfactant molecules adhere to and orient on the gas–liquid interfaces to form a monolayer [29]. The foam formation process is illustrated in Figure 3. Figure 3a shows the formation of a bubble in the water and the adsorption of a large number of surfactant molecules on its surface. The hydrophilic groups are oriented toward the water, and the hydrophobic groups are oriented toward the air. Figure 3b depicts the bubble rising in the water and the formation of two monolayer films, an inner and an outer layer. Figure 3c shows the surfacing of the bubble, when it finally becomes a free bubble. The surfactant molecules effectively overcome the surface tension of the bubble.
foam foam formation formation process process is is illustrated illustrated in in Figure Figure 3. 3. Figure Figure 3a 3a shows shows the the formation formation of of aa bubble bubble in in the the water and the adsorption of a large number of surfactant molecules on its surface. The hydrophilic water and the adsorption of a large number of surfactant molecules on its surface. The hydrophilic groups groups are are oriented oriented toward toward the the water, water, and and the the hydrophobic hydrophobic groups groups are are oriented oriented toward toward the the air. air. Figure 3b depicts the bubble rising in the water and the formation of two monolayer films, an Figure 3b depicts the bubble rising in the water and the formation of two monolayer films, an inner inner and outer layer. free Minerals 7, 149 19 and an an2017, outer layer. Figure Figure 3c 3c shows shows the the surfacing surfacing of of the the bubble, bubble, when when it it finally finally becomes becomes aa6 of free bubble. The surfactant molecules effectively overcome the surface tension of the bubble. bubble. The surfactant molecules effectively overcome the surface tension of the bubble.
Figure 3. Foam formation process: (a) formation, (b) and rise, and (c) Foamformation formation process: (a) bubble bubble formation, (b) adhesion adhesion andformation. (c) foam foam Figure 3.3.Foam process: (a) bubble formation, (b) adhesion and rise,and and rise, (c) foam formation. formation.
As shown ininFigure 4, when the slurry is mixed with the foam in a mixing tank, under under the action As As shown shown in Figure Figure 4, 4, when when the the slurry slurry is is mixed mixed with with the the foam foam in in aa mixing mixing tank, tank, under the the of external forces, the solid particles and bubblesbubbles collide with and adhere adhere to each other at a certain action action of of external external forces, forces, the the solid solid particles particles and and bubbles collide collide with with and and adhere to to each each other other at at aa speed and angle, ultimately forming TFSB. TFSB. certain certain speed speed and and angle, angle, ultimately ultimately forming forming TFSB.
Figure 4. 4. adhesion and (c) foam foam Figure Formation process process of foam slurry: slurry: (a) (a) mixture, mixture, (b) and (c) 4. Formation Formation process of foam (a) mixture, (b) stirring stirring and and adhesion foam slurry formation. slurry formation. formation.
The stability of the foam is the key to the preparation of TFSB [30]. A greater viscosity leads to The stability stability of of the the foam foam is is the the key key to to the the preparation preparation of of TFSB TFSB [30]. [30]. A A greater greater viscosity viscosity leads leads to to The better stability but poorer foamability. In addition, the bubble size is also an important factor better stability stabilitybut butpoorer poorer foamability. In addition, the bubble is also an important factor better foamability. In addition, the bubble size is size also an important factor affecting affecting the stability of the foam; under normal circumstances, when the bubble size is uniform, affecting the stability of the foam; under normal circumstances, when the bubble size is uniform, the stability of the foam; under normal circumstances, when the bubble size is uniform, the stability of the stability of the the bubbles stability is ofgood. the bubbles bubbles is is good. good. the 3.2. Test Test Results Analyses Test Results Results Analyses Analyses 3.2. 3.2.1. Rheological Properties 3.2.1. Rheological Properties TFSB is is similar similar to to aa paste paste slurry material material because because of of its its high high mass mass fraction, fraction, low TFSB low water water content, content, paste slurry and good integrity. the present work, flow of is aa Bingham [31]. A and work, thethe flow of slurry is modeled as a as Bingham fluid fluid [31]. A fluid and good goodintegrity. integrity.InIn Inthe thepresent present work, the flow of slurry slurry is modeled modeled as Bingham fluid [31]. A τ fluid that behaves as a solid until a minimum yield stress is exceeded, and that exhibits a linear that as a solid minimum yield stress and thatand exhibits a linear relation τ 00 is exceeded, fluidbehaves that behaves as a until solidauntil a minimum yield τ stress that exhibits a linear 0 is exceeded, relation between the shear stress and the share rate of deformation, is referred to as a Bingham between the shear stress and the share rate of deformation, is referred to as a Bingham plastic. The shear relation between the shear stress and the share rate of deformation, is referred to as a Bingham plastic. The shear stress model for a Bingham fluid is [32] stress model for a Bingham fluid is [32] plastic. The shear stress model for a Bingham fluid is [32] ·
τ = τ0 + µγ (7) (7) ττ == ττ 0 ++ μ γγ (7) μ 0 · where τ is the shear stress (Pa), τ0 is the yield stress (Pa), µ is the plastic viscosity (Pa·s), and γ is the share rate (1/s). Figure 5a,b show the evolutions of the shear stress and the plastic viscosity with the share rate for the cement slurry and the standard foam. Figure 5a shows that the relationship between the shear stress and the shear rate is linearly increasing. The yield stresses of the cement slurry and the standard foam are 68.23 and 15.54 Pa, respectively. Figure 5b shows that the relationship between the plastic
shear stress and the shear rate is linearly increasing. The yield stresses of the cement slurry and the standard foam are 68.23 and 15.54 Pa, respectively. Figure 5b shows that the relationship between the plastic viscosity and the shear rate is exponentially decreasing. The plastic viscosity tends to reach a stable value for shear rates higher than 60 r/s, and these stable values of the plastic viscosity for the cement slurry and the standard foam are 0.41 and 0.08 Pa·s, respectively. In the present CFD Minerals 2017, 7, 149 7 of 19 simulations, these values are used as the average values for the rheological properties of the materials. However, in reality, slurry is not a homogeneous fluid. Therefore, in the simulations, viscosity andisthe shearas rate is exponentially decreasing. The plastic viscosity tends to the reach a stable each phase treated a homogeneous body, and all phases are mixed in motion; rheological value for shear rates higher than and 60 r/s, and these stable values of in theTable plastic properties of the cement slurry standard foam are as shown 1. viscosity for the cement slurry and the standard foam are 0.41 and 0.08 Pa·s, respectively. In the present CFD simulations, Tableas 1. the Theaverage rheological properties of rheological the cement slurry and standard foam. these values are used values for the properties of the materials. However, in reality, slurry is not aFluid homogeneous fluid. Therefore, in the simulations, each phase is treated as Type Yield Stress τ0 (Pa) Plastic Viscosity μ (Pa·s) a homogeneous body, Cement and allslurry phases are mixed properties of the cement 68.23in motion; the rheological 0.41 slurry and standard foam are as shown in Table 1. Standard foam 15.54 0.08
Figure properties of the cement slurry and standard foam:foam: (a) evolution of shearofstress Figure5.5.Rheological Rheological properties of the cement slurry and standard (a) evolution shear with share andrate (b) and evolution of plastic with share rate. stress withrate share (b) evolution ofviscosity plastic viscosity with share rate. Table 1. The rheological properties of the cement slurry and standard foam. Fluid Type
Yield Stress τ 0 (Pa)
Plastic Viscosity µ (Pa·s)
Cement slurry Standard foam
68.23 15.54
0.41 0.08
3.2.2. Slump The method used to perform the laboratory experiments conducted in this study is depicted in Figure 6a. Using this device, the slump behaviors of TFSB materials with different bubble volume fractions were detected, and the results are shown in Figure 6b. As shown in Figure 6b, the slump increases with the increasing of bubble volume fraction, which shows that the lubrication of bubbles is
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3.2.2. Slump The method used to perform the laboratory experiments conducted in this study is depicted in Figure 6a. Using Minerals 2017, 7, 149 this device, the slump behaviors of TFSB materials with different bubble volume 8 of 19 fractions were detected, and the results are shown in Figure 6b. As shown in Figure 6b, the slump increases with the increasing of bubble volume fraction, which shows that the lubrication of helpful to theimprove fluidity the of slurry. Generally, slump of the paste is from 15 to 25 bubbles is improve helpful to fluidity of slurry.the Generally, slump of paste is cm. fromWhen 15 tothe 25 slump is between 15 and 22 cm, the slurry is a small slump paste; in such a case, the dehydration cm. When the slump is between 15 and 22 cm, the slurry is a small slump paste; in such a case, the equipment and pumpingand equipment necessary. isEspecially the slump lessslump than 20 cm, dehydration equipment pumpingisequipment necessary.when Especially whenisthe is less industrial applications are not easily made. Thus, the paste where the slump was between 22 and than 20 cm, industrial applications are not easily made. Thus, the paste where the slump was 25 cm was andwidely was called Figure 6b shows that, when the between 22widely and 25 used cm was used the and“big was slump called paste” the “big[33]. slump paste” [33]. Figure 6b shows bubble volume fraction is 15, 20, and 25 vol20, %, and the 25 slump is 23.4, 23.8, and 24.923.8, cm, and respectively. that, when the bubble volume fraction is 15, vol %, the slump is 23.4, 24.9 cm, The slurry has good fluidity and meets the requirements of the big slump paste. respectively. The slurry has good fluidity and meets the requirements of the big slump paste.
Figure Figure 6. 6. Slump Slump tests: tests: (a) (a) method method and and (b) (b) results. results.
3.2.3. 3.2.3. Strength Strength The The strength strength of of specimens specimens was was tested tested with with bubble bubble volume volume fractions fractions from from 00 to to 40 40 vol vol %, %, and and the the results after 7 and 28 days are shown in Figure 7. As shown in this figure, the strength decreases results after 7 and 28 days are shown in Figure 7. As shown in this figure, the strength decreases with increase of of the the bubble bubble volume volume fraction, fraction, which no advantage advantage with the the increase which shows shows that that the the bubbles bubbles are are of of no in terms of improving the strength. The trend lines of strength with the bubble volume fraction in terms of improving the strength. The trend lines of strength with the bubble volume fraction are are illustrated in Figure 7, and there is a linear relationship between the strength of 7 days and the illustrated in Figure 7, and there is a linear relationship between the strength of 7 days and the bubble bubble However, the strength of 28there days,isthere is adecrease rapid decrease when the volumevolume fraction.fraction. However, for the for strength of 28 days, a rapid when the bubble volume fraction exceeds 20 vol %. The strength of backfill is an important factor to ensure the safety of stopes [34].
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Minerals 2017, 7, 149fraction exceeds 20 vol %. The strength of backfill is an important factor to ensure 9 of 19 bubble volume the safety of stopes [34].
Figure Figure 7. 7. Results Results of of strength strength tests: tests: (a) (a) method method and and (b) (b) results. results.
The foam can improve the fluidity of slurry, but the excessive foam is harmful to ensure the The foam can improve the fluidity of slurry, but the excessive foam is harmful to ensure the strength of backfill. Therefore, the bubble volume fraction from 15 to 20 vol % is a better choice. strength of backfill. Therefore, the bubble volume fraction from 15 to 20 vol % is a better choice. 3.3. Effect of Bubble Volume Fraction 3.3. Effect of Bubble Volume Fraction During the process of preparing TFSB, the quantity of the standard foam is measured based on During the process of preparing TFSB, the quantity of the standard foam is measured based on the bubble volume fraction, which indicates the volume fraction of the standard foam. In this work, the bubble volume fraction, which indicates the volume fraction of the standard foam. In this work, the influences of different bubble volume fractions and different average bubble diameters on the the influences of different bubble volume fractions and different average bubble diameters on the pipeline performance of foam slurry are simulated and studied. The basic properties of the cement pipeline performance of foam slurry are simulated and studied. The basic properties of the cement slurry and the standard foam are shown in Table 2. slurry and the standard foam are shown in Table 2. Table 2. The basic properties of the cement slurry and the standard foam. Table 2. The basic properties of the cement slurry and the standard foam. Cement-to-Sand Mass Fraction Mass Cement-to-Sand Ratio (wt %) Fraction Ratio (wt %) Cement slurry 1:5 70 Cement slurry 70 Standard foam * 1:5 * Standard foam * * Fluid Type Fluid Type
Density Density (kg/m3) (kg/m3 ) 1750 1750 50 50
Bubble Volume Bubble Volume Fraction (vol %) Fraction (vol %) * * 0–40 0–40
Plastic Yield Bubble Bubble Yield Plastic Viscosity μ Stress Diameter Diameter(μm)Stress Viscosity 0 (Pa·s) τ0τ(Pa) (µm) (Pa) µ (Pa·s) * 68.23 0.41 * 68.23 0.410.08 30–100 15.54 30–100 15.54 0.08
* Represent no corresponding parameters. * Represent no corresponding parameters.
3.3.1. Foam Phase 3.3.1. Foam Phase To study the effects of different amounts of foam addition on the slurry properties, nine To study the effects of different amounts of foam addition on the slurry properties, nine simulated simulated cases are considered in this work, with bubble volume fractions of 0, 5, 10, 15, 20, 25, 30, cases are considered in this work, with bubble volume fractions of 0, 5, 10, 15, 20, 25, 30, 35, and 40 vol %. 35, and 40 vol %. Let us assume that the cement slurry and standard foam maintain a constant Let us assume that the cement slurry and standard foam maintain a constant viscosity before mixing.
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viscosity The values of theviaplastic viscosity obtained via theoretical calculation The valuesbefore of the mixing. plastic viscosity obtained theoretical calculation (Equation (4)) and simulation (Equation and 3.simulation are shown in simulated Table 3. Analysis the simulated viscosity are shown (4)) in Table Analysis shows that the viscosityshows valuesthat are close to the theoretically values are close to the theoretically calculated values, with a relative error between them of noevenly more calculated values, with a relative error between them of no more than 0.4%. Thus, the mixture is than 0.4%. Thus, the mixture is evenly mixed during pipeline transport. mixed during pipeline transport. Table 3. The The value value of of plastic plastic viscosity viscosity by by theoretical theoretical calculation calculation and and simulation. simulation. Table 3. Plastic Viscosity μ (Pa·s) Studied Bubble Volume Relative Error (%) Plastic Viscosity µ (Pa·s) Bubble Volume Case Fraction (vol %) Theoretical Calculation Simulation Relative Error (%) Studied Case Fraction Theoretical Simulation 1 0 (vol %) 0.4100 Calculation 0.4116 0.39 5 0 0.3935 0.3902 0.190.39 12 0.4100 0.4116 10 5 0.3770 0.3690 0.240.19 23 0.3935 0.3902 34 0.3770 0.3690 15 10 0.3605 0.3491 0.170.24 45 0.3605 0.3491 20 15 0.3440 0.3287 0.210.17 56 0.3440 0.3287 25 20 0.3275 0.3080 0.140.21 67 25 0.3275 0.3080 30 0.3110 0.2878 0.250.14 7 30 0.3110 0.2878 0.25 8 35 0.2945 0.2667 0.05 8 35 0.2945 0.2667 0.05 9 40 0.2780 0.2462 0.05 9 40 0.2780 0.2462 0.05
The foam phase in TFSB exists in the form of bubbles. The simulations show that the bubbles The foam phase distribution in TFSB exists thepipeline. form of In bubbles. The simulations that the the bubbles maintain a uniform in in the the vertical section of show the pipe, TFSB is maintain a uniform distribution in the pipeline. In the vertical section of the pipe, the TFSB is mainly mainly affected by gravity and the wall viscosity. Because of the low air density, the bubbles are affected by gravity and the wall viscosity. Because of the low air density, the bubbles are easily pushed easily pushed toward the wall of the pipe, which causes the bubble volume fraction to be small in toward the wall of the pipe,At which bubble to be small the center of the the center of the pipe. the causes elbow,the the foamvolume slurry fraction is influenced by in centrifugal force; pipe. At the elbow, the foam slurryfraction is influenced by centrifugal consequently, the bubble volume consequently, the bubble volume distribution presentsforce; an overall decreasing trend from the fraction distribution presents an overall decreasing trend from the inside to the outside of the inside to the outside of the elbow, and the bubble volume fraction distribution is not stableelbow, with and the bubble fraction is not stable variations in the slurry flow. In the variations in thevolume slurry flow. In distribution the horizontal section of with the pipe, the TFSB is mainly affected by horizontal section of the pipe, the TFSB is mainly affected by buoyancy. After long-distance transport, buoyancy. After long-distance transport, the slurry maintains a stable flow, and the bubble volume the slurrydistribution maintains ashows stable aflow, and the trend bubblefrom volume distribution a decreasing fraction decreasing the fraction top to the bottom ofshows the pipe, but the trend from is thetoo topsmall. to the bottom thebubble pipe, but the difference small.constant, Hence, the bubble volume difference Hence, of the volume fraction isistoo almost and the pipeline fraction is almost and the pipeline transport of the foam slurry is feasible. The bubble transport of the constant, foam slurry is feasible. The bubble volume fraction distribution for a volume bubble fraction distribution for a bubble volume fraction of 15 vol %, which follows the identified bubble volume fraction of 15 vol %, which follows the identified bubble volume fraction distribution law, volume fraction distribution law, is shown in Figure 8. is shown in Figure 8.
Figure 8. Cont.
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Figure 8. Bubble Bubblevolume volumefraction fraction (unit in vol %) distribution thefor pipe for a volume bubble fraction volume Figure 8. (unit in vol %) distribution in theinpipe a bubble fraction vol %: (a) (b)and elbow, and (c) outlet. of 15 volof %:15(a) inlet, (b)inlet, elbow, (c) outlet.
3.3.2. Pressure 3.3.2. Pressure To realize self-flowing transport of a backfill material through a pipeline, the gravitational To realize self-flowing transport of a backfill material through a pipeline, the gravitational potential potential energy must be greater than the resistance loss of the pipeline, which is defined as the energy must be greater than the resistance loss of the pipeline, which is defined as the total pressure total pressure difference between the inlet and outlet of the pipeline. The equations for the difference between the inlet and outlet of the pipeline. The equations for the gravitational potential gravitational potential energy and resistance loss are as follows [35]: energy and resistance loss are as follows [35]: p = ρ gh (8) p = ρgh (8) h f = p y = pin − pout (9) h f = py = pin − pout (9) where p is the gravitational potential energy (Pa), g is the acceleration of gravity (i.e., 9.82m/s2), where p is the gravitational potential energy (Pa), g is the acceleration of gravity (i.e., 9.8 m/s ), h is h is the height difference (m), hf is the resistance loss (Pa), py is the total pressure difference (Pa), the height difference (m), h f is the resistance loss (Pa), py is the total pressure difference (Pa), pin is the pout ispressure is the total pressure at the inlet the totalatpressure at (Pa). the outlet (Pa). p total pressure at the inlet (Pa), and (Pa), pout isand the total the outlet in Sixty points points along alongthe themiddle middleline lineofof pipe were chosen to investigate the evolution the thethe pipe were chosen to investigate the evolution of theoftotal total pressure. As shown in Figure 9, the total pressure in the pipeline fromtothe to pressure. As shown in Figure 9, the total pressure in the pipeline decreasesdecreases from the inlet theinlet outlet, the and the total pressure value at aincreases given point with an bubble increase in thefraction. bubble and outlet, the total pressure value at a given point with increases an increase in the volume volume fraction. simulations, thetoinlet is supposed to atmosphere, be connectedand to the atmosphere,pressure and an In simulations, theIninlet is supposed be connected to the an atmospheric atmospheric the inlet is set as the with reference pressure. with the isdecrease of at the inlet is pressure set as theat reference pressure. Thus, the decrease of Thus, pressure, there a negative pressure,atthere is a negative part Table and the outlet theand pipeline. 4 lists pressure the latter part andpressure the outletatofthe thelatter pipeline. 4 lists theof inlet outlet Table pressures in the inlet andfor outlet pressures the pipeline forand different fractions and showsresistance that the pipeline different bubbleinvolume fractions shows bubble that thevolume total resistance and average total and average resistance of thefraction pipe decrease as the bubble fraction fraction increases. of theresistance pipe decrease as the bubble volume increases. When the volume bubble volume is When volume fraction is greater than compared 15 vol %,with thethe total reduction in resistance greater the thanbubble 15 vol %, the total reduction in resistance cement slurry alone exceeds compared with the cement slurry alone exceeds 0.22 MPa, which to a the proportional 0.22 MPa, which corresponds to a proportional reduction of more thancorresponds 12%. In addition, reduction reduction of more than 12%. In addition, the also reduction in the average resistance exceeds 0.36 in the average resistance exceeds 0.36 kPa/m, corresponding to a proportional reduction of kPa/m, also12%. corresponding a proportional of more than 12%. Thethe results thus indicate more than The results to thus indicate thatreduction the addition of foam can reduce resistance during that thetransport additionand of foam can reduce the resistance during slurry transport improve the fraction fluidity slurry improve the fluidity of the slurry. Moreover, when theand bubble volume of the slurry. when the bubble exceeds 15 vol %, thepotential total resistance exceeds 15 volMoreover, %, the total resistance of thevolume pipelinefraction is less than the gravitational energy of the pipeline is lessthe than the gravitational potential energyAsofshown 1.72 MPa, allowing the is realization of 1.72 MPa, allowing realization of self-flowing transport. in Figure 10, there a non-linear self-flowing transport. shown in Figure 10, bubble there isvolume a non-linear relationship between the total relationship between theAs total resistance and the fraction, according to the polynomial, resistance the volume bubble volume according to the polynomial, the critical bubble volume the critical and bubble fraction fraction, is 12 vol %. fraction is 12 vol %.
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0.28 0.27 0.25 0.24 0.22 0.21 0.19 0.18
-1.56 -1.51 -1.39 -1.33 -1.23 -1.14 -1.07 -1.04
1.84 1.78 1.64 1.57 1.45 1.35 1.26 1.22
3.06 2.96 2.73 2.60 2.42 2.25 2.09 2.02
1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72
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Table 4. The resistances in the various studied cases. Studied Case
Bubble Volume Fraction (vol %)
Inlet Pressure (MPa)
Outlet Pressure (MPa)
Resistance (MPa)
1 2 3 4 5 6 7 8 9
0 5 10 15 20 25 30 35 40
0.0044 0.28 0.27 0.25 0.24 0.22 0.21 0.19 0.18
-1.86 -1.56 -1.51 -1.39 -1.33 -1.23 -1.14 -1.07 -1.04
1.86 1.84 1.78 1.64 1.57 1.45 1.35 1.26 1.22
Average Resistance (kPa/m) 3.09 3.06 2.96 2.73 2.60 2.42 2.25 2.09 2.02
Gravitational Potential Energy (MPa) 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72
Self-Flowing Transport No No No Yes Yes Yes Yes Yes Yes
Figure 9. Total pressure profiles for various bubble volume fractions. Figure 9. Total pressure profiles for various bubble volume fractions. Table 4. The resistances in the various studied cases. Studied Case
Bubble Volume Fraction (vol %)
Inlet Pressure (MPa)
Outlet Pressure (MPa)
Resistance (MPa)
Average Resistance (kPa/m)
Gravitational Potential Energy (MPa)
Self-Flowing Transport
1 2 3 4 5 6 7 8 9
0 5 10 15 20 25 30 35 40
0.0044 0.28 0.27 0.25 0.24 0.22 0.21 0.19 0.18
−1.86 −1.56 −1.51 −1.39 −1.33 −1.23 −1.14 −1.07 −1.04
1.86 1.84 1.78 1.64 1.57 1.45 1.35 1.26 1.22
3.09 3.06 2.96 2.73 2.60 2.42 2.25 2.09 2.02
1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72
No No No Yes Yes Yes Yes Yes Yes
Figure 9. Total pressure profiles for various bubble volume fractions.
Figure 10. Relationship between total resistance and bubble volume fraction.
Table 5 compares the pressures in the pipeline and the elbow for the various bubble volume fractions. As shown in Table 5, the total and average resistances of the elbow also decrease as the bubble volume fraction increases. Moreover, when the bubble volume fraction is greater than 15 vol %, the total resistance reduction at the elbow compared with the cement slurry alone exceeds 0.0012 MPa, corresponding to a proportional reduction of more than 14%, whereas the reduction in
Figure 10. Relationship between total resistance and bubble volume fraction.
Figure 10. Relationship between total resistance and bubble volume fraction.
Table 5 compares the pressures in the pipeline and the elbow for the various bubble volume
Table 5 compares pressures theand pipeline the elbow forelbow the various bubble fractions. As shownthe in Table 5, the in total averageand resistances of the also decrease as volume the bubbleAsvolume increases. Moreover, when the bubble volume fractionalso is greater than fractions. shownfraction in Table 5, the total and average resistances of the elbow decrease as the 15volume vol %, the total resistance reduction at the elbow with thefraction cement slurry alone exceeds bubble fraction increases. Moreover, when thecompared bubble volume is greater than 15 vol %, 0.0012 MPa, corresponding a proportional reduction more than 14%, whereas the reduction inMPa, the total resistance reduction attothe elbow compared withofthe cement slurry alone exceeds 0.0012
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corresponding to a proportional reduction of more than 14%, whereas the reduction in the average resistance exceeds 0.72 kPa/m, corresponding to a proportional reduction of more than 13%. The results indicate that, although the total resistance of the pipe elbow is less than 1% of that of the pipeline, Minerals 2017, 7, 149 13 of 19 the average resistance of the elbow is 2 to 3 times that of the pipeline as a whole. This leads to a rapid increase in the local resistance, in increased resistance at the elbow. the average resistance exceedsresulting 0.72 kPa/m, corresponding to a proportional reduction of more than 13%. The results indicate that, although the total resistance of the pipe elbow is less than 1% of that Table 5. Comparison between theelbow pressures in the pipeline the pipeline elbow. as a whole. of the pipeline, the average resistance of the is 2 to 3 times thatand of the This leads to a rapid increase in the local resistance, resulting in increased resistance at the elbow. Studied Case
Elbow Pipe Bubble Volume Table 5. Comparison between the pressures in the pipeline and the elbow. Resistance Average Resistance Average Resistance Fraction (vol %) (MPa) Resistance kPa/m) (MPa) (kPa/m)
1Studied Case 2 3 1 4 2 5 3 6 4 7 5 8 6 9 7 8 9
3.3.3. Velocity
Elbow Pipe 0.0086 5.46 1.86 3.09 Resistance Average Resistance Resistance Average Resistance 5 0.0083 5.30 1.84 3.06 (MPa) kPa/m) (MPa) (kPa/m) 100 0.0077 4.88 1.78 0.0086 5.46 1.86 3.092.96 0.0083 5.30 1.84 3.062.73 155 0.0074 4.74 1.64 0.0077 4.88 1.78 2.962.60 2010 0.0070 4.46 1.57 0.0074 4.74 1.64 2.732.42 2515 0.0066 4.19 1.45 0.0070 4.46 1.57 2.602.25 3020 0.0062 3.94 1.35 0.0066 4.19 1.45 2.422.09 3525 0.0056 3.59 1.26 0.0062 3.94 1.35 2.252.02 4030 0.0051 3.24 1.22 35 0.0056 3.59 1.26 2.09 W represents the percentage of pipe average resistance in1.22 elbow average resistance. 40 0.0051 3.24 2.02
Bubble Volume 0 Fraction (vol %)
W (%) 43.41 W (%) 42.26 43.4139.34 42.2642.41 39.3441.70 42.4142.24 41.7042.89 42.2441.78 42.8937.65 41.78 37.65
W represents the percentage of pipe average resistance in elbow average resistance.
3.3.3. Velocity
Control of the transport velocity of the slurry is also an important factor in pipeline transport [36]. of is thetoo transport velocity of is also anwill important factor in pipeline When theControl velocity low, settlement of the the slurry solid particles occur. By contrast, whentransport the velocity [36]. When velocity is too settlement of the will occur. By frequency contrast, when is too high, the the stress induced bylow, the slurry on the pipesolid wallparticles is enhanced, and the withthe which velocity is too high, the stress induced by the slurry onwhich the pipe is enhanced, andwall the frequency the solid particles impinge on the pipe wall increases, canwall easily to cause the of the pipe to with solid particles impingeof onthe theslurry pipe wall which can easily fractions to cause the wear andwhich eventhe deform. The velocities for increases, various bubble volume arewall shown of the pipe to wear and even deform. The velocities of the slurry for various bubble volume in Figure 11. As shown in this figure, the maximum velocity among all considered cases is 4.68 m/s fractions are shown in Figure 11. As shown in this figure, the maximum velocity among all for a bubble volume fraction of 30 vol %, and the minimum velocity is 3.91 m/s for a bubble volume considered cases is 4.68 m/s for a bubble volume fraction of 30 vol %, and the minimum velocity is fraction of 35forvol %. These velocities doof not monotonically with volume fraction 3.91 m/s a bubble volume fraction 35vary vol %. These velocities do the not bubble vary monotonically with but satisfy the requirements for pipeline transport. the bubble volume fraction but satisfy the requirements for pipeline transport.
Figure11. 11.Maximum Maximum velocities Figure velocitiesininthe thesimulations. simulations.
The velocity distribution for a bubble volume fraction of 15 vol % is shown in Figure 12, which The velocity distribution for ainbubble volume fraction of 15 volof%theispipe. shown in elbow, Figure 12, shows an obvious flow core zone the vertical and horizontal sections In the which shows the an obvious core zone inbecomes the vertical and and horizontal the pipe. the elbow, however, flow coreflow zone gradually smaller moves sections from the of center of theInpipe to however, the flow core zoneLet gradually becomes smaller from thesection center(yof= the pipethe to the the outside of the elbow. us consider the inlet sectionand (y = moves 1 m), the elbow x), and outletofsection (x = 1 Let m) separately to study the section change in the vertical the the outside the elbow. us consider the inlet (y the = 1velocity m), the on elbow sectionsurface (y = x),atand elbow in Case in Figure 13, the corein zone shifted on toward the outside of the outlet section (x =4.1 As m) shown separately to study theflow change the is velocity the vertical surface at the elbow, and the shape of the flow core zone changes from an “O” shape to a “U” shape. Moreover,
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elbow in Case 4. As shown in Figure 13, the flow core zone is shifted toward the outside of the elbow, thereMinerals is a high-velocity area concentrated at the outside of the elbow, and the shear stress on19 the 2017, 7, 149 14 of and the shape of the flow core zone changes from an “O” shape to a “U” shape. Moreover, there is wall increases, which can easily cause wear. a high-velocity area concentrated at the outside of the elbow, and the shear stress on the wall increases, there is a high-velocity area concentrated at the outside of the elbow, and the shear stress on the which can easily cause wall increases, whichwear. can easily cause wear.
Figure 12. Velocity distributions in the pipe for a bubble volume fraction of 15 vol %: (a) inlet, Figure 12. Velocity distributions inin thethe pipe for afor bubble volume fraction of 15 vol (b) elbow, Figure Velocity pipe a bubble volume fraction of %: 15 (a) volinlet, %: (a) inlet, (b) 12. elbow, and (c)distributions outlet. and (c) outlet. (b) elbow, and (c) outlet.
Figure 13. Cont.
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Figure 13. Velocity contours at the elbow for a bubble volume fraction of 15 vol %: (a) the 3D total Figure 13.contours Velocity contours at the forsection a bubble fraction of 15 section vol %: (a) pressure the elbow, (b) elbow the inlet (y volume = 1 m), (c) the elbow (y =the x), 3D andtotal (d) Figure 13. Velocityatcontours at the elbow for a bubble volume fraction of 15 vol %: (a) the 3D total pressure contours at the elbow, (b) the inlet section (y = 1 m), (c) the elbow section (y = x), and (d) the the outlet section (x = 1 m). pressure contours at the elbow, (b) the inlet section (y = 1 m), (c) the elbow section (y = x), and (d) outlet section (x = 1 m). the outlet section (x = 1 m).
3.4. Effect of Bubble Diameter 3.4. Effect of Bubble Diameter 3.4. Effect of Bubble Diameter The bubble diameter is an important parameter affecting the performance of a foam [37]. When The bubble diameter is an important parameter affecting the performance of a foam [37]. When the the diameter is too small, isthe cannot effectively adsorb solid particles. contrast, when The bubble diameter anbubbles important parameter affecting the performance of By a foam [37]. When diameter is too small, the bubbles cannot effectively adsorb solid particles. By contrast, when the the defoaming phenomenon can easily Therefore,By it is necessary to the diameter diameter is is too too large, small, athe bubbles cannot effectively adsorboccur. solid particles. contrast, when diameter is tooperformance large, a defoaming phenomenon can easily occur. for Therefore, it bubble is necessary to simulate simulate the of foam slurry pipeline transport various diameters. The the diameter is too large, a defoaming phenomenon can easily occur. Therefore, it is necessary to the performance ofisfoam slurry pipeline transport forlevels various bubble diameters. The diameter 30, of foam diameter 30–100 μm; thus, slurry five different were selected for the simulations: simulate of thefoam performance of foam pipeline transport for various bubble diameters. 47.5, The is 30–100 µm; thus, five different levels were selected for the simulations: 30, 47.5, 65, 82.5, and 100 µm. 65, 82.5, and 100 μm. diameter of foam is 30–100 μm; thus, five different levels were selected for the simulations: 30, 47.5, The resistance and velocity results are shown in Figure 14. As shown in this figure, the diameter The resistance 65, 82.5, and 100 μm.and velocity results are shown in Figure 14. As shown in this figure, the has little influence on the resistance inresistance the pipe. in The impact on theimpact velocity slightly larger, but the diameter has little influence on the the pipe. The onisthe velocity is slightly The resistance and velocity results are shown in Figure 14. As shown in this figure, the velocity still generally remains between 4 andbetween 5 m/s, which is within the acceptable range. Thus, larger, but the velocity still generally remains 4 andThe 5 m/s, which within the acceptable diameter has little influence on the resistance in the pipe. impact onisthe velocity is slightly the bubble diameter has diameter little effect onlittle the transport properties of properties TFSB. range. thevelocity bubble has effectbetween on the transport TFSB. the acceptable larger, Thus, but the still generally remains 4 and 5 m/s, which of is within range. Thus, the bubble diameter has little effect on the transport properties of TFSB.
Figure 14. Cont.
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Figure Figure 14. 14. Resistance Resistanceand andvelocity velocityresults resultsfor forvarious variousbubble bubblediameters: diameters:(a) (a)resistance resistanceand and(b) (b)velocity. velocity.
3.5. 3.5. Industrial Industrial Applications Applications According the CFD CFD simulations, simulations, the According to to the the analysis analysis of of the the rheological rheological properties properties of of TFSB TFSB are are predominantly affected by the bubble volume fraction. Using TFSB can effectively reduce the predominantly affected by the bubble volume fraction. Using TFSB can effectively reduce the resistance resistance during slurry pipelineand transport andonthe theself-flowing pipe, and self-flowing transport can during slurry pipeline transport the wear thewear pipe,onand transport can be realized be realized when the bubble volume fraction is higher than 15 vol %. when the bubble volume fraction is higher than 15 vol %. Based the CFD CFD simulations simulations and and the the laboratory laboratory tests, tests, the the optimal optimal material material parameters parameters can Based on on the can finally bedetermined determinedasasfollows: follows: a cement-to-sand ratio of 1:5, a bubble volume fraction of vol 15–20 finally be a cement-to-sand ratio of 1:5, a bubble volume fraction of 15–20 %, 3/h, and a backfill ability of 50–60 m3/h. The number S01, N02, and vol %, aflow foamrate flow 3 /h, m a foam of rate 8–12ofm8–12 and a backfill ability of 50–60 m3 /h. The number S01, N02, and S05 S05 0 m in level in were mine chosen were chosen as the industrial tests area. theof backfill of and the goafsgoafs at theat0the m level mine as the industrial tests area. After theAfter backfill the goaf goaf and the achievement of condensation the pit roof was support was larger than the achievement of condensation stability, stability, the rate of pitrate roofofsupport larger than 90%. The90%. test The test results in Table 6 show that the 7 and 28-day strengths greater than 1.2 and 2.3 results in Table 6 show that the 7 and 28-day strengths greater than 1.2 and 2.3 MPa, respectively. MPa, Thus, respectively. Thus,a the TFSB showed a good backfill effect. the TFSB showed good backfill effect. A comparative analysis of the economic indicators for the conventional cement slurry and TFSB shows that, although the Table use of TFSB incurs an additional 6. The results of industrial tests. cost for the foaming agent, it simultaneously reduces the amount of cement consumed. As shown in Table 7, for a cement unit price of 0.05 $/kg and a foaming agent unit price of 6 $/kg, the use of TFSBStrength saves $1.56 (MPa)per cubic Bubble Volume Fraction (vol %) Density (kg/m3 ) Goaf Number meter of the backfill. For mine “A”, which mines 1 million 800 thousand tons of stone annually 7 days 28 days and has an annual backfill volume of 600 thousand cubic meters, under the assumption of a direct S01 1496 16 1.21 2.33 savings in material cost of 1.56 $/m3, the mine would save of cement per N02 1402 19 220 thousand tons1.20 2.17year and would consequently reduce 1533 the annual backfill cost by an S05 12936 thousand dollars, 1.38which represents 2.38 enormous economic benefit. A comparative analysis of the economic indicators for the conventional cement slurry and TFSB Table 6. The results of industrial tests. shows that, although the use of TFSB incurs an additional cost for the foaming agent, it simultaneously Strengthunit (MPa) Bubble Volume reduces the amount of cement consumed. As shown in Table 7, for a cement price of 0.05 $/kg Goaf Number Density (kg/m3) Fraction (vol %) 7 days 28 and a foaming agent unit price of 6 $/kg, the use of TFSB saves $1.56 per cubic meterdays of the backfill. S01which mines 1 1496 1.21 For mine “A”, million 800 thousand16tons of stone annually and has an2.33 annual backfill N02thousand cubic 1402 1.20 savings in2.17 volume of 600 meters, under the 19 assumption of a direct material cost of S05 1533 12 1.38 2.38 3 1.56 $/m , the mine would save 220 thousand tons of cement per year and would consequently reduce the annual backfill cost by 936 thousand dollars, which represents an enormous economic benefit. Table 7. The economic indicators for conventional backfill material and three-phase foam slurry backfill (TFSB). Project Specifications Cement consumption (kg/m3) Foam agent consumption (kg/m3) Unit cost ($/m3) Cost savings ($/m3)
Conventional Cement Slurry 288 0 14.4 1.56
TFSB 240 0.14 12.84
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Table 7. The economic indicators for conventional backfill material and three-phase foam slurry backfill (TFSB). Project Specifications
Conventional Cement Slurry
TFSB
288 0 14.4
240 0.14 12.84
(kg/m3 )
Cement consumption Foam agent consumption (kg/m3 ) Unit cost ($/m3 ) Cost savings ($/m3 )
1.56
4. Conclusions This paper develops a three-dimensional CFD transport model of a backfill pipeline, which is used to study the pipeline transport properties of TFSB. Simulated results indicate that TFSB can maintain a steady state during pipeline transport, experiences a markedly reduced pipeline transport resistance and exhibits better liquidity than conventional cement slurry. Furthermore, a multiphase flow model is established using the mixture method in FLUENT to study the evolutions of the foam phase, pressure, and velocity in the pipeline system for different bubble volume fractions and bubble diameters. The results show that, as the bubble volume fraction increases, the resistance of the pipeline decreases and the fluidity improves. By contrast, the bubble diameter has little effect on the transport properties of TFSB. The combined results of the CFD simulations, slump tests, and strength tests indicate that, when the bubble volume fraction is 15–20 vol %, TFSB can satisfy the necessary strength requirements, good fluidity, and exhibit self-flowing transport. Furthermore, TFSB represents an enormous economic benefit. Finally, although the CFD technique provides an intuitive and accurate basis for pipeline transport research with regard to TFSB, several factors were not addressed in the design of this study, including temperature, free fall, and the solid particle phase. Therefore, a more comprehensive study of the problem will be conducted in future work. Acknowledgments: The authors would like to acknowledge the financial support from the National Key R & D Program of China (Grant No. 2017YFC0602902), the Innovation-Driven Plan of Central South University of China (Grant No. 2015CX005), and the Fundamental Research Funds for the Central Universities of Central South University (No. 2016zztx096) for their financial support. Author Contributions: X.C., Q.C. and X.S. conceived and designed the experiments; X.C. and Y.G. performed the experiments; X.C. and J.Z. performed the simulations; X.C., J.Z. and Q.C. analyzed the data; X.C. and X.S. contributed reagents/materials/analysis tools; X.C. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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Li, S.; Wang, X.M. Fly-ash-based magnetic coagulant for rapid sedimentation of electronegative slimes and ultrafine tailings. Powder Technol. 2016, 303, 20–26. [CrossRef] Liang, C.; Fall, M. Multiphysics modeling of arching effects in fill mass. Comput Geotech. 2017, 83, 114–131. Wu, D.; Yang, B.G.; Liu, Y.C. Transportability and pressure drop of fresh cemented coal gangue-fly ash backfill (CGFB) slurry in pipe loop. Powder Technol. 2015, 284, 218–224. [CrossRef] Chen, Q.S.; Zhang, Q.L.; Wang, X.M.; Xiao, C.C.; Hu, Q. A hydraulic gradient model of paste-like crude tailings backfill slurry transported by a pipeline system. Environ. Earth Sci. 2016, 75. [CrossRef] Zhang, Q.L.; Chen, Q.S.; Wang, X.M. Cemented Backfilling Technology of Paste-Like Based on Aeolian Sand and Tailings. Minerals 2016, 6, 132. [CrossRef] Belem, T.; Fourie, A.B.; Fahey, M. Time-dependent failure criterion for cemented paste backfills. Richard Jewell and Andy Fourie. In Proceedings of the 13th International Seminar on Paste and Thickened Tailings, Perth: Australian Centre for Geomechanics, Australian, 3–6 May 2010; pp. 147–162.
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7. 8. 9. 10. 11. 12. 13. 14. 15.
16.
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