INTRODUCTION
Solvent dewaxing is the most difficult and most important step for the base
lube oil production. Wax is the most troublesome product in the manufacture
of lubricating oil. Its presence in lubricating oils prevents free movement
at lower temperatures (Sequerira, 1994). One of the separation
technique of the wax components is done by solvent dewaxing which selectively
removes higher carbon number nparaffins due to the highest crystallization
temperature where the dewaxed oil dominated by non normal paraffins and contains
also lower carbon number of normal paraffins (Thomas, 2008).
The waxy lube oilsolvent mixture was chilled at a specified cooling rate in
a series of hairpin double pipe Scraped Surface Heat Exchangers (SSHE) and chillers.
This method is one of the most popular for dewaxing oils and deoiling waxes
because it allows variation in the dilution ratio of the feedstock with solvent
in optimum range without affecting the cooling rate and degree of supersaturated
concentrations of the flow. Solvent dewaxing is a chemical separation process
in which no chemical reactions occur. The composition of the dewaxed oil is
completely dependent on the waxy feed and it represents the subtraction of the
wax composition. An experimental study was conducted to compare the normal paraffin
distribution between solvent and catalytic lube oil dewaxing by analyzing the
feedstocks and products from processes (Taylor and McCormack,
1992). The chemical analysis of the carbon number distribution for three
paraffinic wax samples were conducted using high temperature Gas Chromatography
(GC) methods. The results showed that the distribution of normal and nonnormal
hydrocarbons remaining in the oils after dewaxing process was clearly different
and this suggested that the two processes have different ways in removing the
higher paraffin. There are limited literatures dealing with crystallization
process in the SSHE, These studies introduced a numerical simulation of the
fluid flow and heat transfer combined with the population balance to represent
the kinetics of ice particles crystallization using commercial CFD software
such the works that conducted by Lian et al. (2006)
and Benkhlifa et al. (2008).
The publication of the modeling analysis in the dewaxing lube oil feedstock
in SSHE for the previous studies was found to be very limited. Bessarabov
et al. (1996) proposed an analytical model (1D) transient of the
dewaxing process from a raffinatesolvent solution, the authors suggested that
the temperature distribution of accumulated wax layer on pipe wall between two
adjacent rotational scrape blades actions can be solved combined with wax crystallization
kinetics. The kinetics of crystallization processes is described by using jth
moment transformation of population density function. A suggestion that the
wax crystallized on the inside tube wall in scraped channel has the form of
a hollow cylinder layer, so in order to solve the kinetic problem of wax crystallization
in such a way that the temperature distribution in a wax layer crystallized
on the tube wall at any moment of time must be determined. Li
et al. (2008) conducted a one dimensional parallel flow direction in
steady state condition. The authors used a pilot plant for his model, consists
of four single elements of SSHEs with multi solvent dilution points after each
exchanger. The operation condition including the temperature distributions,
solvent composition, wax compound and the crystallizer dimensions were examined.
The results discussed the effect of operational condition on the wax crystal
size distribution in the waxoilsolvent solution. The previous literatures
suffer a lack of the studies that deals with the analysis of the combination
between the heat exchangers rating mode and wax crystallization kinetics of
real solvent dewaxing in the SSHEs and chillers. The reason behind this that
those processes are confidential to the petroleum industry companies beside
that the design data for the plant depended on the physical properties that
predicted experimentally for each lube oils feedstock. The major objective of
this study is to develop a general numerical model to characterize the wax crystallization
process for waxy paraffin oils in double pipe SSHEs and chillers in a typical
MEK dewaxing unit. This model consists of combination of the kinetics of wax
crystallization with heat transfer.
Mokhlif and AlKayiem (2011) presented analytical model
and analysis for the periodic deposition and removal of the wax in a solvent
dewaxing process in a lubricating oil manufacturing.
The main aim of the present study is to present a mathematical procedure to
predict the wax crystallization in the solvent dewaxing process. The procedure
involves experimental and numerical analysis. The experimental part consists
of measuring the dissolved temperature, onset crystallization temperature and
the wax content. The Differential Scanning Calorimeter (DSC) has been used as
the main equipment for the thermal properties measurement and analysis.
MATHEMATICAL MODEL
Heat transfer model: The SSHE’s
performed as a counter current system, hence, in order to simulate the double
pipe SSHEs numerically; the model equations for heat transfer balance for a
segment for both fluids in steady state condition are as follows:
where m_{h}, C_{ph}, T_{h} and T_{c }are the
hot fluid mass flow rate, heat capacity, hot fluid temperature and cold fluid
temperature, respectively.
The differential equation for the cold fluid (filtrate) side is as follows:
where, m_{C}, C_{ph}, are the cold fluid mass flow rate and
heat capacity, respectively.
The equations above can be solved with the boundary conditions as follows:
The two ordinary differential equations above are of the kind of two boundary
value problems and can be solved using RungeKutta combined with the shooting
method (root finding) (Muralidhar and Sundararajan, 2003).
Solving Eq. 1 and 2 depending on using the
suitable empirical correlations for heat transfer coefficients in both sides
of the heat exchanger beside the available methods to identified the physical
properties of the fluids. The overall heat transfer coefficient U in the equations
mention above can be calculated based on the outer surface of the heat exchange
tube as follow:
where, h_{i} and h_{o} are the heat transfer coefficients for
inner pipe (scraper channel) and the outer tube, respectively. The fouling factor
h_{fo} represent the deposit thermal resistance just for the outer pipe
where inside pipe is clean surface due to scraping effect.
The heat transfer coefficient h_{i} can be predicted using the correlation
below for crystallization process (Lakhdar et al.,
2005):
where, Re_{r} is the rotational Reynolds number and w_{0 }is
global mass fraction.
For forced convection in turbulent flow where Reynolds number >2300 we can
use Gnielinski correlation as follow (Incropera, 2007):
where, f is the Darcy friction factor that can either be obtained from the
Moody chart or for smooth tubes from correlation developed by Incropera
(2007):
The Gnielinski Correlation is valid for:
(0.5≤Pr≤2000) and (3000≤Re≤5x10^{6}) 
The corrected Nussle number for the concentric annular ducts with heat transfer
at the inner wall and the outer wall is insulated we can use the Petukhov and
Roizen correlation as follows (Incropera, 2007):
In the evaluation of the overall heat transfer coefficient, the surrounding
temperature, i.e., the chiller temperature is assumed constant along the pipe,
where the fluid in the annulus is working as a flooded refrigerant system.
Kinetics of wax crystallization: Particles conservation in any system
is governed by the particle number continuity equation, essentially a Population
Balance (PB) to identify particle numbers in each and every size range and account
for any changes due to particle formation. The PB equation of nucleation and
crystal growth is expressed as follows:
where, n = dN/dL is the crystal population density, (number of crystal per
unit size per unit volume of system), G = dL/dt is the crystal growth rate and
B = dN/dt is the nucleation rate, V is the mean velocity and δ is the Dirac
function meaning that nucleation creates crystals with a size equal to critical
size L_{c}.
Most recent studies employed ‘moment method’ to solve the PB. The
jth moment M_{j} of the population density function is defined as (Mullin,
2001):
The moment equation above can be rearranged for steady flow as follows:
The first four moments represent the total crystal number, total crystal length,
total surface area and crystal mass (phase volume of the dispersed particles).
The initial boundary conditions to solve Eq. 15 depend on
assumption that the number of crystals at the inlet of the heat exchangers is
zero.
The overall nucleation rate can be predicted from the empirical form Mullin
(2001):
where, k_{b} is the nucleation constant, b is the nucleation reaction
order and ΔC is the difference in concentration (supersaturation).
The growth rate may be expressed as Mullin (2001):
where, k_{g }and g are the crystal growth constant and index, respectively.
In crystallization work the exponent g which applied to a concentration difference,
has no fundamental significance and cannot give any indication of the number
of elementary species involved in the growth process. Depends on this assumption
the first order (g = 1) will take in this study.
To calculate ΔC, the solubility for the wax dissolved in oilsolvent solution
is required. The nparaffins in wax content extended from C_{19} or
C_{20} to C_{40} or even C_{53} (Dirand
et al., 1998) and this depended on the chemical analysis of the feedstock
to predict the nalkanes distribution in wax content.
As the solubility of such multicomponent solution is much complex, in such
a case the wax (solute) and the oil portion can be treated as single component.
This treatment is much dependent on two major parameters, (i) the mass fraction
of the wax in the lube oil feedstock and (ii) the dissolved temperature of this
wax and this can be proved from the chemical analysis of the feedstock.
The correlation model for the solubility of nalkanes dissolved in organic
solvents is as follows by HaulaitPirson et al.
(1987):
where, the subscript, i represent the solvent portion which refer to Toluene,
Methyl Ethyl Ketone (MEK) and the liquid oil in the solution. The mass fraction
of the wax w_{w,i} can be predicted with the equation (HaulaitPirson
et al., 1987):
Equation 13 and 14 are solved numerically
by Root Finding iteration method.
In order to calculate the particle size distribution, the lognormal function
is adopted by Li et al. (2008):
where, L_{g} and β are the geometrical standard size and standard
variance of the distribution and the formulated description for there are as
follow by Li et al. (2008):
To accomplish the mathematical model many data are required, including the
dimensions of exchangers, operation condition, physical properties of oil and
wax, kinetics constants of the wax components and carbon distribution of nparaffins
in each feedstock. The model is written in MATLAB computer language.
EXPERIMENTAL MEASUREMENT
All the experiments were performed on SN150 lube oil feedstock obtained from
distillation of Kirkuk crude in Baiji Refinery, Iraq. The lube oils feedstock
charged to the dewaxing unit were treated in a deasphalting process to remove
the asphalt and resin while the solvent extraction unit was used to reduce the
aromatics components. The following experiments were carried out:
Differential scanning calorimetry test: Differential Scanning Calorimetry
DSC is a method used to analyze the melting and crystallization regions of materials.
It is capable of evaluating a great amount of data which are collected simultaneously
with quality and stability. The major parameters which can be predicated from
the thermal analysis of the DSC are the onset crystallization temperature, dissolution
temperature and the wax content (Chen et al., 2004).
The thermal analyses were performed using Pyris 1DSC apparatus consisted of
a measurement unit for setting and measuring the sample and a base unit for
processing signals sent from the measurement unit. The acquired data are sent
to the data acquisition software for analysis. The two measurement chambers
of the DSC are designed to measure the heat flux. To predict the wax content
by using the thermal analysis of the DSC scan. The procedure is developed by
Chen et al. (2004) which depended on computing
the total thermal heat released of wax crystallization. This can be done by
integrating the area under the deflection curve between the onset and endset
intersection temperatures points of base line.
An empirical formula is suggested by Chen et al.
(2004), connecting the heat released and the wax content also allows the
prediction of the wax content from the measure of the total heat (Q_{oil}/Q_{wax})
as follows:
For Acetone method the empirical equation is:
where, w_{w} (wt. %) wax content and Q is the total heat in (J/g).
RESULTS AND DISCUSSION
The predicted wax content from the DSC thermal analysis of the sample using
the empirical correlations are illustrated in Table 1.
Figure 1 and 2 illustrate the DSC thermal
analysis of the SN150 feed sample mention above, before and after dewaxing process,
respectively.
Figure 3 illustrates the comparison of wax content of the
SN150 lube oil feedstock with the predicted solubility of the closest higher
carbon number of the nparaffin that represent the solid wax dissolved in Decane
nC_{10} or Undecane nC_{11} as light liquid portion of the
feed solution.
The feedstock pumped to the SSHEs at initial temperature of 322 K for the sample
SN150 above each desired cloud point. The kinetics constants of the wax crystallization,
in special case the crystal growth constant (kg) which is difficult to find
publishing works of the nalkanes that extended from nC_{22} to nC_{32}
in this study. However, the fitting of the k_{g} can be predicted from
the wax mass fraction removal which depended on the experimental thermal analysis
of DSC tests of the feed before and after dewaxing.
Table 1: 
Predicted wax content of lube oils samples 


Fig. 1: 
DSC thermal analysis for Feedstock SN150 before dewaxing 

Fig. 2: 
DSC thermal analysis for Base SN150 after dewaxing 

Fig. 3: 
Solubility model for C_{26} in C_{11} and
C_{28} in C_{10} compare with mass fraction of SN150 feedstock 
The predicted moments from the model will give the characteristics for the
wax crystals in exit of the pipe before filtration. The mass yield of the wax
or the removable solid can be predicted from the third moment, in order to support
the nucleation constant with available experiments. Figure 4
illustrate the predicted wax mass fraction along the pipe line after prediction
the moment which represents the solid fraction and the assumption of spherical
shape of the crystal the volume and the mass fraction can be predicted. The
distribution along the pipeline shows rapid increased after onset crystallization
due to releasing of heat of fusion of nuclei particles and mention that this
region demonstrated by nucleation process.
The Crystal Size Distribution (CSD) of the wax crystallization at the exit
of the heat exchangers is shown in Fig. 5.

Fig. 4: 
Solid mass fraction distribution along SSHEs and chillers 

Fig. 5: 
Predicted crystal size distribution of the removed wax at
the exit 
The results taken into account the liquid portion of the oil in the mixture
represented by C10 and C11 which shows no big difference between the two components.
Study of the effect of the operation conditions on the CSD are illustrated in
Fig. 6 and 7, respectively. In Fig.
6 shows the wax CSD after each position of the solvent injection points.
The injection point for solvent should not effect on the linearity of the wax
crystallization in the suspension system and this need controlling of the temperature
of the solvent injected in the solution.
Figure 7 shows the effect of the ratio of the MEK in solvent
mixture where the high content of MEK in solvent dewaxing process is beneficial
to produce a large number of the crystal with large sizes.

Fig. 6: 
Predicted crystal size distribution at different solvent injection
point 

Fig. 7: 
Predicted crystal size distribution at different MEK percentage
ratio 
CONCLUSION
The developed model specifies the crystals characteristic in the SSHEs and
chillers in solvent dewaxing unit. The nalkanes solubility model give a suitable
choice for the carbon number existed in the solid wax which attaches the wax
weight fraction and dissolving temperature of the feedstock, this assumption
allowed to represent the physical properties of the waxoilsolvent mixture
in both the dissolution region and the crystallization region. Knowing the global
wax mass fraction and the dissolved temperature of the feedstock are very important
parameters to handle with crystallization kinetics of the solution system. The
flow behavior is much dependent on the controlling of the solvent ratio in order
to keep the flow diluted and suspension. The predicted simulation results implemented
on real operation data collected from the field. The predicted wax crystal size
distribution at exit of the chillers was fitted with removal wax that predicted
from the DSC thermal analysis. The established model can be applied for different
arrangement and different feedstock for solvent dewaxing, but it is important
to have the system exact compositions for all the processing material.
ACKNOWLEDGMENTS
The first author acknowledges Universiti Teknologi PETRONAS for sponsoring
the work under GA scheme and the financial support to publish the paper. Also,
appreciations are due to the staff of the ionic liquid center for allowing the
experimental DSC tests.