ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING

Asia-Pac. J. Chem. Eng. (2017)

Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/apj.2122

Research article
Evaluation of wall slip effects on the flow characteristics of
petroleum coke–water slurry flow along pipelines
Xiaobin Zhang,1,2 Meng Liu,3,4* Kagiso Bikane4 and Yanrong Li1
1
College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2
Shanxi Water Conservancy Technical Institute, Yuncheng 044004, China
3
School of Energy and Environment, Southeast University, Nanjing 210096, China
4
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK

Received 19 December 2016; Revised 4 July 2017; Accepted 7 July 2017

ABSTRACT: Flow characteristics of petroleum coke–water slurry (PCWS) were investigated in a slurry transportation
facility. True rheological properties, drag reduction, and flow resistances of PCWS under the influence of wall slip were
studied using the Tikhonov regularization method. Results show that the shear viscosity is insensitive to changes in the shear
rate when the solid loading of PCWS is 59.8 wt%. However, the PCWS of 61.1 wt% exhibits typical dilatant fluid properties.
As the shear rate increases, the PCWS of 63.4 wt% initially exhibits shear thinning, and then, the viscosity increases sharply
when the shear rate exceeds 250 s
1. In addition, the slurry also displays shear thinning at the shear rates exceeding 600 s
1.
Modified friction factor-generalized Reynolds number correlation is established to describe the resistance properties of a
laminar flow of PCWS. When increasing the velocity, the drag reduction produced by the wall slip behavior reduces for
the 59.8 wt% PCWS but increases for the 61.1 wt% PCWS. The drag reduction decreases at the outset followed by an
increase for the 63.4 wt% PCWS. A decrease in the inner diameter of pipeline could enhance the effect of drag reduction
of PCWS flowing in a pipeline. © 2017 Curtin University and John Wiley & Sons, Ltd.

KEYWORDS: petroleum coke–water slurry; wall slip behavior; Tikhonov regularization; drag reduction; generalized
Reynolds number

INTRODUCTION As the flow rate increases, the resistance loss between

the slurry and pipe inner wall is enhanced, especially for
Petroleum coke–water slurry (PCWS) has been widely a slurry flowing in a small pipe diameter. There is a
utilized in numerous industrial applications, and the phenomenon known as drag reduction, which assists
performance of slurry ability of PCWS also has been the slurry transportation. Many factors such as the wall
investigated by several researchers [1–8]. Zhan et al. [1] slip behavior, decreased turbulence production, and
demonstrated that the better rheological properties of rheological characteristics have been proposed to reveal
PCWS were obtained using black liquid instead of the mechanism of drag reduction [9,10]. However, the
water during preparation. Gao et al. [2–4] investigated mechanism of drag reduction in a pipeline has not
the effect of operation parameters on the rheological yet been clarified. According to previous researchers
[11–13]
properties of PCWS and found that the highest solid , the wall slip behavior is one of the main reasons
concentration of 68% can be achieved by optimizing for the drag reduction in a flow of slurry. Additionally,
the particle distribution and the amount of a chemical particle concentration and shear viscosity in the slip
additive. Marchand et al. [5] found that the ideal layer were much lower than other flow regions,
rheological behaviors of PCWS can be obtained using resulting in a reduction of the energy consumption by
polyvinyl alcohol and xanthan gum as chemical the pumping system. Moreover, the viscosity, pressure
additives. However, the flow characteristics of PCWS loss, and friction factor would be underestimated if wall
flowing in a straight pipeline have not been studied slip effects were not considered in the fluid true flow
extensively, particularly the true rheological properties, properties [14]. Zambrano et al. [15] accurately predicted
drag reduction, and resistance properties under the pressure drop and fanning friction factor of heavy oil
influence of wall slip. slurry flowing in a horizontal pipeline using
computational fluid dynamics software combined with
a three-dimensional, algebraic slip mixture model.
*Correspondence to: Meng Liu, School of Energy and
Environment, Southeast University, Nanjing 210096, China. E-mail: Therefore, it is necessary to consider the wall slip
lmubear@seu.edu.cn behavior in the calculation of rheological behavior and
© 2017 Curtin University and John Wiley & Sons, Ltd.
X. ZHANG ET AL. Asia-Pacific Journal of Chemical Engineering

resistance properties of PCWS flowing in the pipelines. stainless steel pipelines, water cooling system, and a
It is well known that different fluids show different wall slurry tank (1 m3). PCWS was prepared and sealed in
slip characteristics when flowing in pipes, and the wall a slurry tank, and the flow characteristics of PCWS
slip effect is related to many factors, including particle were conducted using different internal diameters (10,
size, test geometry, concentration, and surface 14, 16, and 20 mm) of stainless steel pipelines with
properties [11,16]. Numerical methods have been absolute surface roughness 0.015 mm. The flow rate
developed to investigate the wall slip characteristics of Q and pressure drop ΔP of PCWS flowing in the
slurry flowing in a pipeline [17–21]. The most important pipeline were measured using the electromagnetic flow
and the most widely used numerical method is the meter and a differential pressure sensor, respectively, in
classical Mooney method [17]. However, the classical which the data were recorded online. The slurry was
Mooney method cannot be used in the non-Newtonian pumped through the test section straight pipe (1.8 m)
solid–liquid fluid with a significant immigration of by a 2 m3/h screw pump with a frequency converter
particles. A modified Mooney method was developed to regulate the flow rate. The water cooling system
by Jastrzebski et al. [18] for the generalized Newtonian was installed in the pipeline to control the slurry
fluids, and it built the relationship of slip velocity and temperature. All the experiments were operated at
flow dimension [19]. Tikhonov regularization method 25 ± 1°C. Before each experiment, the slurry was
developed by Yeow et al. [20,21] has been widely used stirred and pumped for more than 0.5 h to allow it to
to analyze the experimental data to calculate the slip homogenize the slurry. In addition, each test was
characteristics of a fluid relating to phase separation, repeated twice to ensure the accuracy of the
i.e. particle immigration and sedimentation, and experimental data.
changes in local solid concentration [11,12,22]. This
method is modified from classical Mooney method,
and the results of slip characterization do not depend Materials
on the assumed rheological constitutive equation and
data extrapolation. Petroleum coke–water slurry was prepared by blending
In this study, the true rheological characteristics, pulverized petroleum coke (obtained from Jinling
drag reduction behavior, and resistance properties of Petro-Chemistry Company, Nanjing, China), tap water,
PCWS flowing in straight pipelines under different and chemical additives (stabilizer and anionic surface
flow conditions (solid loading, velocity, and pipe inner active agents, obtained from Nanjing University) in a
diameter) were investigated using the Tikhonov slurry tank. Weighed tap water was first added into
regularization method. Additionally, the prediction of the tank, and then, the speed of agitator was set to
the friction factor in straight pipeline by applying 100 rpm/min. Subsequently, the petroleum coke
generalized Reynolds number for non-Newtonian particles and a chemical additive were placed into the
fluids was developed. tank. The ratio of additive was kept at 3 wt‰ based
on the mass of petroleum coke for all PCWS. The
mixture was stirred using an agitator at 100 rpm for
EXPERIMENTAL 1 h. Flow behaviors of PCWS were investigated at
three solid loading at 59.8, 61.1, and 63.4 wt%,
Experimental setup respectively. The particle size distribution of petroleum
coke is shown in Fig. 2. Petroleum coke particles
The schematic of the closed-loop pipeline is shown in exhibit a typical bimodal distribution, and more than
Fig. 1. The experiment setup consists of a screw pump, 80% of the particles are less than 200 μm.

Figure 1. Schematic diagram of slurry transportation test facility.

© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering WALL SLIP ON THE FLOW PROPERTIES OF PCWS

THEORETICAL slip velocity function and shear rate function at the

discrete shear stress point is minimized. When the
Determinations of wall slip behavior in pipeline linear combination of S1 and S2 is smallest, the value
of us(τ w) and γ(τ) is the solution of the Tikhonov
The flow structure of slurry in a pipeline consists of a regularization method [11,12,20,21,24–27].
plug flow region, deforming region, and slip layer and
is described in Fig. 3. The thickness of the slip layer Method for determination of friction factor
is very thin compared with the pipe diameter, and the
shear viscosity of the fluid in the slip layer is much For the non-Newtonian fluids, the generalized
lower than that of the other two regions [23]. From Reynolds number is often used to establish the relation
Fig. 3, the velocity in the laminar flow regime consists with friction factor and is given by Eqn (2).
of wall slip velocity us and bulk slurry velocity Vc.
Based on the classical Mooney method [17], the τw 16 τ w =μe 16 16
velocity equation can be described by Eqn (1). f ¼
¼ ¼ ¼ (2)
ρV 2
ρVD=μe 8V=D Reμe =M Reg
2

8V 8us ðτ w Þ 4 τw 2
¼ þ 3 ∫τ¼0 τ γðτ Þdτ (1) where Reμe is the Reynolds number calculated by the
D D τw
effective viscosity μe which is defined as the ratio of
wall shear stress and apparent shear rate 8Vc/D [28].
where V is the mean velocity, D is pipe internal
diameter, and 8V/D is apparent shear rate; 8usDðτw Þ is the
τw τ 4w
contribution of wall slip behavior; us(τ w) is the wall slip μe ¼ 8V c  ¼ τw 2 (3)
velocity and function of wall shear stress τ w; D 4∫τ¼0 τ γðτ Þdτ
4 τw 2
τ 3w ∫τ¼0 τ γðτ Þdτ is ascribed to the shear flow and only
function of local wall shear stress. The Tikhonov
regularization method was applied to solve Eqn (1)
using many sets of data from different internal τ w =μe 8V c =D
M¼ ¼ ¼ 1
us =V (4)
diameters. The solution of the Tikhonov regularization 8V=D 8V=D
method is to discretize the right two terms of Eqn (1) in
the range of wall shear stress and calculate the apparent Therefore, the generalized Reynolds number for non-
shear rate using the data of Q and ΔP under different Newtonian fluids exhibiting wall slip phenomenon is
internal diameter. In addition, the calculation should determined by Eqn (5).
meet the following two conditions: (1) minimum
overall relative error S1 of apparent shear rate between Reμe ρVD
the calculated value and the experimental value and (2) Reg ¼  
us ¼
  (5)
the sum of the square S2 of the second derivative of the 1
V μe 1
uVs

Figure 2. Particle size distribution of pulverized petroleum

coke.
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
X. ZHANG ET AL. Asia-Pacific Journal of Chemical Engineering

Figure 3. Flow structure of petroleum coke–water slurry.

Method for determination of drag reduction overlap, particularly for the 61.1 and 63.4 wt% PCWS.
For the 63.4 wt% PCWS, the larger the diameter of the
During the transportation of PCWS in the pipelines, pipe diameter, the greater the wall stress at the same
drag reduction phenomenon takes place due to the apparent shear rates. The rheological properties of
existence of slip phenomenon near the pipe wall. slurry should be intrinsic features of the slurry, and the
Drag reduction is defined as the ratio of pressure flow behavior curves should be independent of the
drop reduction caused by wall slip behavior and geometry size [14,19]. Yilmazer et al. [30] and Kalyon [31]
pressure drop of PCWS flowing in the pipelines demonstrated that the rheological flow curves for
without wall slip [29]. different pipe diameters exhibited a deviation and did

2τ w
fs ¼ (6)
ρV 2

2τ w
fc ¼ (7)
ρV 2c

 2
ΔPc
ΔPs fs Vc
DR ¼ ¼1
¼1

ΔPc fc V

us 2
¼1
1
(8)
V

where ΔPc and fc are the pressure drop and friction

factor of PCWS flowing in the pipelines without wall
slip and ΔPs and fs are the pressure drop and friction
factor of PCWS flowing in the pipelines exhibiting wall
slip phenomenon.

RESULTS AND DISCUSSION

True rheological characteristics of petroleum

coke–water slurry

The flow behaviors of PCWS in the pipeline based on

the assumption that there is no wall slip phenomenon
are displayed in Fig. 4. The flow behavior curves of Figure 4. Apparent flow curves of petroleum coke–water
PCWS flowing in different diameter pipes did not slurry.
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering WALL SLIP ON THE FLOW PROPERTIES OF PCWS

not overlap at constant apparent shear rate, indicating the center) when the slurry was flowing, resulting in a
effect of the presence of the apparent wall slip. Barnes generally relatively thin layer of water near to the pipe
[32]
also found that the most obvious evidence of the wall and produced the wall slip phenomenon [35–37]. As
presence of wall slip is obtaining different rheological the solid loading of PCWS increases, velocity gradients
properties in different-sized geometries. This suggests increase in the slip layer and the wall slip phenomenon
that there is the wall slip behavior in the PCWS flowing. gets enhanced. Flow behavior curves obtained based on
For the concentrated suspensions, the ‘slip layer’ the assumption that the PCWS flowing in the pipelines
adjacent to the wall is generated by the migration of the does not have wall slip phenomenon deviate from the
solid particles. It will decrease the viscosity of slurry true flow behaviors. The stronger the wall slip is, the
and friction loss and has strong influence on the deviation is more apparent.
rheological properties. In addition, the factors affecting The experimental data were analyzed using a
wall slip include [24,33,34] particle size, concentration of numerical method based on Tikhonov regularization
slurry, dimensions of the measuring geometries, to solve Eqn (1), and the true rheological characteristics
temperature, and shear stress. From Fig. 4, the flow of PCWS are shown in Fig. 5(a). The flow curves of
behavior curves diverged more significantly for PCWS three solid loading PCWS obtained from different
at high solid loading than that for PCWS at low solid diameter overlap closely, suggesting that the effect of
loading, suggesting that the wall slip behavior became wall slip on the flow curves was modified. In addition,
more significant on the PCWS with the higher solid the plot of viscosity and shear rate is also displayed in
loading. The particles in the high shear rate region (near Fig. 5(b). The shear viscosity of PCWS is influenced
the pipe wall) were migrated to low shear rate region (the by solid loading and shear rates. At a PCWS solid
loading of 59.8 wt%, the shear viscosity is insensitive
to the shear rates and has the similar shear properties
as Newtonian fluids. When the solid loading of PCWS
is 61.1 wt%, PCWS becomes a dilatant fluid, and its
shear viscosity increases significantly with shear rates.
PCWS changes from a dilatant fluid to a pseudo-plastic
fluid when the shear rates increase for a solid loading of
63.4 wt%. Galindo-Rosales et al. [38] also found that
some shear thickening non-Newtonian fluids exhibited
complex rheological properties. Slurry first exhibits
shear thinning at low shear rate, followed by shear
thickening when shear rate exceeds a critical value,
and a subsequent shear thinning at high shear rates.
The variation trend of shear viscosity vs. shear rates
for slurry flowing in the pipe is controlled by two
forces: repulsion and hydrodynamic forces [39]. When
the interactions between particles are dominated by
repulsion forces, the forces keep particles as far away
as possible from each other. In addition, the slurry flow
arises in the form of particles moving into adjacent
vacancies, resulting in an extremely high but finite
viscosity of slurry. As the hydrodynamic forces
dominate the interactions, the particles with small
space in the direction of shear are forced into layers.
However, the space between the layers is larger, which
brings about a lower viscosity than the ordered three-
dimensional situation. In a flow of slurry, different
forces control the different shear rate regions. The main
parameters that control the variation trends are particle
size distribution, solid loading, particle shape, and
interaction between particles [40].
The rheological properties of PCWS is very
complicated and controlled by the two forces: repulsion
and hydrodynamic forces in the pipe flow. When the
Figure 5. True rheological of petroleum coke–water slurry solid loading of PCWS is 59.8 wt%, the particle
flowing in pipline. (a) Shear rate vs. shear stress. (b) Shear spacing is large, and the interactions between the
rate vs. true shear viscosity. particles are weak as observed in Fig. 5. Hydrodynamic
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
X. ZHANG ET AL. Asia-Pacific Journal of Chemical Engineering

forces dominate the structure of PCWS, resulting in a

lower viscosity of the slurry. Additionally, the lower
viscosity is insensitive to the shear rate. When the solid
loading is increased to 61.1 wt%, the particle spacing
decreases and the dominant forces change from
hydrodynamic forces to repulsion forces. That is to
say, PCWS transforms from a layer structure to a
three-dimensional spacing structure. Moreover, its
shear viscosity increases accordingly [37]. As the solid
loading reaches 63.4 wt%, the three-dimensional
spacing structure formed from the transformation of
PCWS in a low shear rate zone is destroyed gradually
when the shear rate surpasses a critical shear rate. As
a result, the shear viscosity of PCWS increases with
shear rate in the low shear rate zone and decreases with
shear rate in high shear rate zone. This indicates that Figure 7. Relationship between f and Reg of petroleum
the PCWS transforms from a dilatant fluid to a coke–water slurry in pipe flow.
pseudo-plastic fluid.
linearly with velocity in the dual-logarithm coordinate
Friction factor of petroleum coke–water slurry system. When the solid loading is increased from
in pipe flow 59.8 to 61.1 wt%, the friction factor increased
significantly. However, a further increase in the solid
Solid loading and shear rate have an important impact loading from 61.1 to 63.4 wt.% led to a smaller growth
on the wall slip phenomenon, rheological of the friction factor. This is because the PCWS
characteristics, and flow pattern of PCWS in the pipe exhibits a significant wall slip phenomenon at high
flow and thus have a considerable influence on the solid loading and produces a drag reduction
flowing resistance of PCWS. In the study, friction phenomenon that reduces the influence of the viscosity
factor was employed to investigate the flowing difference [12,24]. Moreover, PCWS at 61.1 wt% is a
resistance properties of PCWS. Average values of dilatant fluid and has a high shear viscosity at high
measured parameters were used to calculate the friction shear rate. Consequently, the viscosity difference was
factor and the generalized Reynolds number according weakened, and the differences between the friction
to Eqns (2) and (5), respectively. Figures 6 and 7 factors decreased as observed from Fig. 6.
present the data for the friction factor of PCWS flowing The generalized Reynolds number is employed to
in the pipelines. From Fig. 6, it can be observed that the replace the Reynolds number for Newtonian fluids.
friction factor of PCWS with different solid loadings This number was calculated according to Eqn (5) using
decreases rapidly with an increase in velocity at a low true rheological characteristics. The wall slip velocity
velocity region and at a smaller velocity in a high was obtained by solving Eqn (1) based on Tikhonov
velocity region. Additionally, the friction factor varies regularization. Figure 7 displays the relation between
the friction factor and the generalized Reynolds
number. It indicates that the friction factor for PCWS
with different solid loading falls on the same line. The
power law equation was employed to fit these curves.
The fitting result is expressed in Eqn (9). Results show
that it has a similar form with Newtonian fluids.

f ¼ 16=Reg (9)

Drag reduction of petroleum coke–water slurry

in pipe flow

The friction factor is dependent on the wall slip

behavior and rheological characteristics as analyzed in
the preceding texts. Therefore, the drag reduction is
employed to investigate the resistance properties. The
Figure 6. Resistance coefficient of petroleum coke–water drag reduction could reveal the flow pattern of PCWS
slurry in pipe flow. in pipe flows and demonstrate the variation trends of
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering WALL SLIP ON THE FLOW PROPERTIES OF PCWS

the rheological characteristics and the wall slip [12].

Besides, the drag reduction could indicate effects of
the rheological characteristics and the wall slip on the
variation trends of resistance properties of PCWS in
pipe flow. Figures 8 and 9 present the variations of
the drag reduction of PCWS in the pipe flow with an
increase in the velocity. From Fig. 8, it was observed
that the drag reduction of PCWS with solid loading at
59.8 wt% decreases with velocity. As the solid loading
is increased to 61.1 wt%, the drag reduction of PCWS
in pipe flow increases with velocity. However, there
is a critical velocity at which the drag reduction
transforms from a downward trend to an upward trend
at a solid loading of 63.4 wt%. This was a result of the
PCWS flow in the pipelines consisting of the slip layer,
deforming zone, and plug flow region [11,13,14]. An Figure 9. Effects of diameter on the drag reduction of
increase in the velocity led to an increase in the velocity petroleum coke–water slurry in pipe flow.
gradients and a gradual expansion of the deforming
zone. However, the shear viscosity of PCWS at viscosity at a low shear rate situation, and the viscosity
59.8 wt% was insensitive to the shear rate and velocity. decreases for a short shear zone. The viscosity then
Therefore, an increase in velocity has a greater impact increases with the shear rate. As the shear rate
on the deforming zone and contributes less to the surpasses 600 s
1, the shear viscosity begins to
velocity gradients in the slip layer. This suggests that decrease. Reduction of viscosity would accelerate the
the mean velocity in the bulk slurry region increases expansion of the deforming zone, and the mean
rapidly than the wall slip velocity in the slip layer. velocity in the bulk slurries increases quickly. An
Furthermore, the drag reduction is mainly dependent increase in viscosity would play an opposite role.
on the wall slip velocity and the mean velocity However, when the curve of shear viscosity has an
according to Eqn (8). Therefore, the drag reduction of extreme point, the growth rate of the wall slip and the
PCWS in a pipe flow decreases with an increase in mean velocity in the bulk slurries need to go through
velocity. When the solid loading is increased to a process of change to match the variation of the shear
61.1 wt%, the PCWS becomes a dilatant fluid, and viscosity of the PCWS [11,13,14,24]. Therefore, when the
the shear viscosity of PCWS increases with the shear shear rate surpasses the critical point, the viscosity
rate. As a result, the deforming zone expands slowly, changes in the opposite trend. However, the drag
and the velocity gradients in the slip layer increase reduction still varies in the original trend at a smaller
rapidly [13]. Consequently, the wall slip velocity greatly shear rate. As such, unlike viscosity, the variation of
impacts the PCWS flow and causes the drag reduction the drag reduction has a delaying phenomenon.
to rise with an increase in velocity. At a solid loading Consequently, the drag reduction of PCWS with
of 63.4 wt%, the shear viscosity of PCWS has a high 63.4 wt% only has two opposite variation trends, while
the viscosity of PCWS has two critical shear rates, and
its variation trends change twice.
Figure 9 demonstrates the effects of pipe inner
diameter on the drag reduction. It can be seen from
Fig. 9 that the drag reduction of PCWS in pipe flow
increases with a decrease in pipe inner diameter.
According to Eqn (8), the drag reduction of PCWS
flowing in the pipelines can be expressed as shown in
the following equation.

us 2
DR ¼ 1
1

V !2
us
¼1
1
   (10)
us þ 4VR c R4

From Eqn (1), us is a function of wall shear stress and

Figure 8. Effects of concentration on the drag reduction of does not change with pipe inner diameter. Besides, 4Vc/R
petroleum coke–water slurry in pipe flow. is the second term in Eqn (1).
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
X. ZHANG ET AL. Asia-Pacific Journal of Chemical Engineering

4V c 4 τw [5] Marchand DJ, Abrams A, Heisera BR, Kim YK, Kim J, Kim
¼ 3 ∫τ¼0 τ 2 γðτ Þdτ (11) SH. Rheological modifiers for petroleum coke-water slurry.
R τw Fuel Process. Technol. 2016; 144: 290–298.
[6] Wang RK, Zhao ZH, Liu JZ, Lv YK, Ye XM. Enhancing the
storage stability of petroleum coke slurry by producing
Equation (11) was transformed into Eqn (12) after biogas from sludge fermentation. Energy 2016; 113:
integration using the power law rheological model. 319–327.
[7] Liu M, Duan YF, Ma XY. Effect of surface chemistry and
structure of sludge particles on their co-slurrying ability
4V c
τ w 1n 4n
with petroleum coke. Int. J. Chem. React. Eng. 2014; 12:
429–439.
¼ (12)
R k 3n þ 1 [8] Liu M, Duan YF, Li HF. Effect of modified sludge on the
rheological properties and co-slurry mechanism of petroleum
coke-sludge slurry. Powder Technol. 2013; 243: 18–26.
Therefore, 4Vc/R also does not change with pipe [9] Gallego F, Shah SN. Friction pressure correlations for
inner diameter. Therefore, the drag reduction increases turbulent flow of drag reducing polymer solutions in straight
and coiled tubing. J. Petrol. Sci. & Eng. 2009; 65: 147–161.
with an increase in the pipe diameter basing on [10] Kostic M. On turbulent drag and heat transfer reduction
Eqn (10). phenomena and laminar heat transfer enhancement in non-
circular duct flow of certain non-Newtonian fluids. Int. J.
Heat & Mass Transfer 1994; 37: 133–147.
[11] Chen LY, Duan YF, Zhao CS, Yang LG. Rheological
CONCLUSIONS behavior and wall slip of concentrated coal water slurry in
pipe flows. Chem. Eng. Process. 2009; 48: 1241–1248.
[12] Ma XY, Duan YF, Li HF. Wall slip and rheological behavior
The rheological properties of PCWS 59.8 and of petroleum-coke sludge slurries flowing in pipelines.
61.1 wt% exhibit a nearly Newtonian fluid and shear Powder Technol. 2012; 230: 127–133.
thickening fluid property, respectively. As the shear [13] Chen LY, Duan YF, Pu WH, Zhao CS. CFD simulation of
coal-water slurry flowing in horizontal pipelines. Korean J.
rate increases, PCWS of 63.4 wt% initially displays a Chem. Eng. 2009; 26: 1144–1154.
little shear thinning fluid, followed by a shear [14] Rahman NAA. Wall slip in pipe rheometry of multiphase
thickening fluid, and a subsequent shear thinning fluid. fluids. Ph.D thesis, 2013, University of Manchester, UK.
[15] Zambrano H, Sigalotti LDG, Klapp J, Peña-Polo F, Bencomo
The friction factor increases with an increase of the A. Heavy oil slurry transportation through horizontal
solid loading and decreases when the velocity is pipelines: experiments and CFD simulations. Int. J
increased. The friction factor Reynolds number Multiphas. Flow 2017; 91: 130–141.
[16] Ozkan S, Gillece TW, Senak L, Moore DJ. Characterization
correlation is established for the laminar pipe flows of of yield stress and slip behaviour of skin/hair care gels using
PCWS. When increasing the velocity, the drag steady flow and LAOS measurements and their correlation
reduction produced by the wall slip decreases for with sensorial attributes. Int. J. Cosmet. Sci. 2012; 34:
193–201.
59.8 wt% PCWS and increases for 61.1 wt%. [17] Mooney M. Explicit formulas for slip and fluidity. J. Rheol.
However, for 63.4 wt% PCWS, there is an observed 1931; 2: 210–222.
initial reduction of the drag reduction and an increase [18] Jastrzebski ZD. Entrance effects and wall effects in an
extrusion rheometer during flow of concentrated suspensions.
thereafter. A reduction of the pipe inner diameter could Ind. Eng. Chem. Fundamen. 1967; 6: 445–454.
enhance the drag reduction of PCWS. [19] Crawford B, Watterson JK, Spedding PL, Raghunathan S,
Herron W, Proctor M. Wall slippage with siloxane gum and
silicon rubbers. J. Non-Newtonian Fluid Mech. 2005; 129:
38–45.
Acknowledgements [20] Yeow YL, Ko WC, Tang PPP. Solving the inverse problem
of Couette viscometry by Tikhonov regularization. J. Rheol.
2000; 44: 1335–1351.
The research is supported by National Nature Science [21] Yeow YL, Lee HL, Melvani AR, Mifsud GC. A new method
Foundation of China (51206028) and China of processing capillary viscometry data in the presence of
Postdoctoral Science Foundation and Special wall slip. J. Rheol. 2003; 47: 337–348.
[22] Martin PJ, Wilson DI. A critical assessment of the
Foundation (2012M520971 and 2013T60491). Jastrzebski interface condition for the capillary flow of
pastes, foams and polymers. Chem. Eng. Sci. 2005; 60:
493–502.
[23] Hatzikiriakos SG. Slip mechanisms in complex fluid flows.
REFERENCES Soft Matter 2015; 11: 7851–7856.
[24] Chen LY, Duan YF, Liu M, Zhao CS. Slip flow of coal water
[1] Zhan XL, Zhou ZJ, Kang WZ, Wang FC. Promoted slurries in pipelines. Fuel 2010; 89: 1119–1126.
slurryability of petroleum coke-water slurry by using black [25] Yeow YL, Choon B, Karniawan L, Santoso L. Obtaining the
liquor as an additive. Fuel Process. Technol. 2010; 91: shear rate function and the slip velocity function from
1256–1260. Couette viscometry data. J. Non-Newtonian Fluid Mech.
[2] Gao FY, Liu JZ, Zhou JH, Cen KF. Preparation and 2004; 124: 43–49.
improving stability of bubble petroleum coke water slurry. [26] Yeow YL, Leong YK, Khan A. Non-Newtonian flow in
Fuel 2014; 128: 404–409. parallel-disk viscometers in the presence of wall slip.
[3] Gao FY, Liu JZ, Wang CC, Zhou JH, Cen KF. Effects of the J. Non-Newtonian Fluid Mech. 2006; 139: 85–92.
physical and chemical properties of petroleum coke on its [27] Zahirovic S, Lubansky AS, Yeow YL, Boger DV. Obtaining
slurryability. Pet. Sci. 2012; 2: 251–256. the steady shear rheological properties and apparent wall slip
[4] Gao FY, Hu EJ. Effects of pH on rheological characteristics velocity data of a water-in-oil emulsion from gap-dependent
and stability of petroleum coke water slurry. Pet. Sci. 2016; parallel plate viscometry data. Rheol. Acta 2009; 48:
13: 782–786. 221–229.
© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering WALL SLIP ON THE FLOW PROPERTIES OF PCWS
[28] Hua H, Larson RG, Magda JJ. Measurement of wall-slip- [35] Wang ZY, Lam YC, Chen X, Joshi SC. Viscosity corrections
layer rheology in shear-thickening wormy micelle solutions. for concentrated suspension in capillary flow with wall slip.
J. Rheol. 2002; 46: 1001–1021. AlChE J. 2010; 56: 1447–1455.
[29] Yanuar, Ridwan, Budiarso, Koestoer RA. Hydraulics [36] Allende M, Kalyon DM. Assessment of particle-migration
conveyances of mud slurry by a spiral pipe. J. Mech. Sci. effects in pressure-driven viscometric flows. J. Rheol. 2000;
Technol. 2009; 23: 1835–1839. 44: 79–90.
[30] Yilmazer U, Kalyon DM. Slip effects in capillary and parallel [37] Howard AB. A review of the slip (wall depletion) of polymer
disk torsional flows of highly filled suspensions. J. Rheol. solutions, emulsions and particle suspensions in viscometers:
1989; 33: 1197–1212. its cause, character, and cure. J. Non-Newtonian Fluid Mech.
[31] Kalyon DM. Apparent slip and viscoplasticity of 1995; 56: 221–251.
concentrated suspensions. J. Rheol. 2005; 49: 621–640. [38] Galindo-Rosales FJ, Rubio-Hernández FJ, Sevilla A. An
[32] Barnes HA. A review of the slip (wall depletion) of polymer apparent viscosity function for shear thickening fluids.
solutions, emulsions and particle suspensions in viscometers: J. Non-Newtonian Fluid Mech. 2011; 166: 321–325.
its cause, character and cure. J. Non-Newtonian Fluid Mech. [39] Barnes HA. Shear-thickening (“dilatancy”) in suspensions of
1995; 56: 221–251. nonaggregating solid particles dispersed in newtonian liquids.
[33] Sofou S, Muliawan EB, Hatzikiriakos SG, Mitsoulis E. J. Rheol. 1989; 33: 329–366.
Rheological characterization and constitutive modeling of [40] Chang L, Friedrich K, Schlarb AK, Tanner R, Ye L. Shear-
bread dough. Rheol. Acta 2008; 47: 369–381. thickening behaviour of concentrated polymer dispersions
[34] Liu M, Duan YF, Ma XY. Effects of the types and addition under steady and oscillatory shear. J. Mater. Sci. 2011; 46:
amounts of sludge on the true rheological properties of 339–346.
petroleum-coke slurry flowing in pipelines. Int. J. Chem.
React. Eng. 2015; 13: 311–322.

© 2017 Curtin University and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. (2017)
DOI: 10.1002/apj