INTRODUCTION
There is a void in detailed understanding and modeling of the waxingdewaxing
process in the scraped surface exchangers and chillers in unit, in the petroleum
industry. Dewaxing process is one of the most important and most difficult processes
in lubricating oil manufacturing (Gary and Handwerk, 2001).
All lube stocks, except those from a relatively few highly naphthenic crude
oils, must be dewaxed or they will not flow properly at ambient temperatures.
There are two types of processes in use today. One uses is a selective hydrocracking
process to crack the wax molecules to light hydrocarbons. The other uses refrigeration
to crystallize the wax and solvent to dilute the oil portion sufficiently to
permit rapid filtration to separate the wax from the oil. There are two principle
solvents used in solvent dewaxing processes, the first one is the propane with
direct chilling and ketone with indirect chilling. Ketone dewaxing process is
an extractive crystallization process and is the most widely used dewaxing process
in the petroleum industry. The dewaxing process in a series of double pipe scraped
surface exchangers and chillers is shown schematically in Fig.
1 (Worthington, 1984). The waxy feedstock is heated
above the cloud point to dissolve all the wax content. Next, the feed diluted
with a solvent containing toluene as the oil solvent and Methyl Ethyl Ketone
(MEK) as the wax antisolvent.

Fig. 1: 
Double pipe scraped surface exchangers and chillers in solvent
dewaxing unit (Worthington, 1984) 
The exchangers shall perform cooling of the feedstock by means of a counter current flow of filtrate as a cooling agent which is a mixture of dewaxed oil and solvent obtained in the vacuum filtration section.
The chillers shall complete the feedstock cooling bymeans of propane evaporation
in two stages consist of high and low temperatures of the propane. An incremental
dilution in multi injection points used for additional dilution to the solution
to maintain sufficient liquid for easy handling as the temperature is decreased
and the wax crystallizes from solution. Scraped Surface Heat Exchanger (SSHE)
is a specialized piece of heat transfer equipment that handles products that
are viscous, that contain particles and that tends to deposit and form films
on the heat transfer surface (Sequerira, 1994).
It is built as a double pipe element as shown in Fig. 2 (Rao
and Hartel, 2006). The area between the inner pipes contains a rotating
scraper element spaced throughout the length of the pipes which mixes the process
fluid and removes deposit which may form on the tube wall as result of the cooling.
In analyzing particulate system such as SSHE, there is a further need to describe
the kinetics of mass crystallization. Crystallization is a low energy separation
of organic chemicals, is a one way process, the heat is removed, crystals are
formed and the mixture of crystals and solution are then separated (Bloch
and Soares, 1998).
The first step of mass crystallization is the calculation of mass balance from
knowledge of solution concentrations, but in crystallization processes a further
conservation equation is required to account for particles number, crystal size
distribution and quantify processes such as nucleation, crystal growth, agglomeration
and breakage (Jones, 2002).
This is known as population balance, with this mathematical framework introduced a better understanding of the kinetics of the wax crystallization under various operation conditions in scraped surface exchangers and chillers in Ketone Dewaxing Unit.
The major objective of this study is to present an analytical approach to simulate the dewaxing process for different types of lube oil feedstock in double pipe scraped surface as a line production in a typical MEK dewaxing unit. The simulation is based on a mathematical model which links the fluid flow, expressed by NavierStokes equation in cylindrical coordinates, the thermal energy balance, expressed by the energy equation with the kinetics of wax crystallization. The complicated twophase twocomponent flow is expressed by mixture density based on the mass fraction of the phases. The non Newtonian viscosity is expressed by the power law model.
The exact solution is not possible to such complicated flow and the numerical technique by coding the model in MATLAB is the proposed solution method.
PREVIEW OF RELATED WORKS
When introducing automatic control systems in the petroleum refining industry, a mathematical description is required for the processes to be controlled. The development of a mathematical description of the lube oil dewaxing will deliver better understanding of the kinetics of wax crystallization as such process is affected by rate of chilling and the amount of incremental dilution, or on the influence of these factors on the shape and number of crystals. As many parameters are involved in the dewaxing process in the SSHE, a simulation of the process can accomplish the control system of the unit to keep the operation process in the standard design range.
Most of the studies dealing with the processes in SSHE as a crystallizer focused
on mass crystallization from aqueous solution in lab SSHE. A very limited published
analysis works which deals with the kinetics of wax crystallization from waxy
oilsolvent slurry in SSHE. Klimenko et al. (1977)
presents experimental results of the process of crystallization of three samples
of highly purified paraffin wax, dissolved in Methyl Ethyl Ketone solution.
One of the basic factors influencing the dewaxing process is the initial chilling
rate of solution. The experimental data shows that an increasing in chilling
rate produces extensive nucleation so that the average crystal is smaller and
the number of crystals per unit volume of solution is greater. Bessarabov
et al. (1996) introduced a mathematical model of the kinetics of
wax crystallization from a raffinatesolvent solution in scraped crystallizer.
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, 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.
Chi (2001) investigated the performance of an industrial
scraped surface ice generator from brine solution in steady state operation
in both experimentally and numerically. The prediction of heat transfer rate
in scraped surface channel is characterized in two regions with and without
ice crystals. He has used the empirical approach involving dimensional analysis.
In ice crystallization region, heat and mass balance performed at each axial
segment were the ice fraction distribution formulated as a function of heat
transfer rate and initial salinity of the brine. The predicted results from
the simulation model such as salt concentration, bulk temperature and ice fraction
along the axial distance of scraper channel shows a good agreement with the
measurements results.
Tahti (2004) conducted an experimental work on the SSHE
using aqueous solution. The kinetics of crystallization process described two
factors; nucleation and crystal growth rates which are predicted simultaneously
in steady state operation by using Mixed Suspension Mixed Product Removal (MSMPR)
population balance developed by Randolph and Larson (1988).
The main variables investigated during the experiments were the rotational speed
of the scraper blades, the concentration of the feed solution, the temperature
of cooling media and the residence time. The experimental results showed that
it is possible to control the size and the shape of the product crystals by
adjusting the scraper parameters. An empirical equation was used to describe
the heat transfer coefficient in the scraper side. A major limitation of the
MSMPR model is that the interplay of fluid flow, heat transfer and crystallization
kinetics is not modeled. Lakhdar et al. (2005)
have carried out an experimental study on a SSHE which was used for freezing
of waterethanol mixture and aqueous sucrose solution. The influence of various
parameters on heat transfer intensity was investigated on such product type
and composition, flow rate, blade rotation speed and the distance between the
blade edge and tube wall. The results show that the internal heat transfer coefficient
depends mainly on rotation speed. Lakhdar et al.
(2005) carried out an experimental study for ice crystallization from sucrose
aqueous solution in SSHE. The study focused on the experimental measurements
of heat transfer and power consumption of the drive shaft ith and without phase
change. For freezing stage (ice crystals formation), a coupling of heat and
mass transfer done by assuming that the measured bulk temperature is the same
freezing point temperature of sucrose solution where a correlation exists. The
experimental results showed that the overall heat transfer coefficient having
a step functional jump at the onset time of phase change and the magnitude of
heat transfer gain with phase change greater than that without phase change.
Qin et al. (2006) presented a computer modeling
of combined CFDPopulation Balance (PB) for sucrose solution in SSHE. The modeling
consist of coupling of steady state fluid flow that was adopted for the simulation
of the transient heat transfer and ice crystallization, where different time
is corresponded to different location of the transverse plane along the axial
direction of the exchanger. Only the ice crystal nucleation and growth rates
have been described by discrete population balance equation rather than the
moment transformation. Another development of numerical modeling of sucrose
solution freezing in SSHE is presented by Benkhlifa et
al. (2008) where two approaches have been used. The first one is a 2D
transient approach considering thermodynamical equilibrium between solid and
liquid phases. Assumption lead to consider the two phase mixture as an equivalent
single phase fluid for which the mass ice fraction depends only on local temperature
for a given initial solutes mass fraction. The second approach is a 1D radial
transient model where a suggestion to replace the geometrical description of
scraping blades by an effective radial diffusivity. The model coupled the discrete
population balance equation with CFD modeling in such case the evolution of
the population density, temperature, ice fraction and mean crystal size in the
exchanger were obtained. It can be realized that the literature suffers a lack
of published studies dealing with the analyses of dewaxing process in SSHE.
The reason behind that, that those processes are very confidential to the petroleum
industry companies. The design of SSHE's has been in the hands of companies
manufacturing commercial heat exchangers and as a result, is largely kept secret’.
SIMULATION MODEL OUTLINES
The present study consists of a model that describes the kinetics of wax crystallization from waxy oilsolvent mixture in SSHE. This model couples mathematical models for energy (heat transfer), fluid flow (mass, momentum) and the constriction distribution in the flow. The coupling between the kinetic and the heat transfer models will be done by a correlation equation to connect the periodic concentration of process fluid and the heat transfer rate to complete prediction of the wax crystallization.
Kinetics of wax crystallization: The general mathematical model of the kinetics of wax crystallizes from the waxoilsolvent solution is described by using the moment transformations of population balance and consideration of the processes of nucleation and crystal growth rates is as follows:
where, Mj are the moment transformation function, B is the nucleation, G is the crystal growth and t is the time. The equation above can be rearranged as follows:
The first four moments (M0, M1, M2, M3) represent the total crystal number, total crystal length, total surface area and crystal mass (phase volume).
The nucleation and growth rates can be expressed in the following forms:
where, C and C* are solute and equilibrium concentrations, k_{b} and k_{g }are nucleation and growth rate constant and b and g are power indices.
The heat transfer modeling: The energy equation of the scraped surface channel will be solved to predict the temperature distribution in 2D transient state as follow:
where, α is the thermal diffusivity, T is temperature, t is time, r is radial direction and z is the axial flow direction.
The fluid flow modeling: The fluid flow can be further simplified to
the equivalent single phase of the mixed phases (Lakhdar
et al., 2005; Lian et al., 2006),
incompressible and steady flow in scraper channel. Accordingly, the mass conservation
equation becomes:
and momentum represented in NavierStokes equation:
rcomponent:
zcomponent:
A very important assumption is the local thermodynamic equilibrium within the chilling zone, to predict the thermal and physical properties by knowing the wax mass fraction in the slurry. The slurry density of the mixture could be obtained from:
where, ρ, ρs and ρ l are the densities of the mixture slurry, solid wax and liquid solution. Φ_{m} is the wax mass fraction. The volume fraction of the wax in the slurry is:
For engineering applications, the PowerLaw or OstwaldDeWaele model is the most frequently used twoparameter generalized non Newtonian fluid model. It is given by:
where, K is the consistency index, n is the power law index and is the shear rate. For the powerlaw fluids, the apparent viscosity, γ_{a} decreases as the increases for n < 1. If n<1; the fluid is said to be pseudoplastic or shearthinning fluid.
RESULTS AND DISCUSSION
The simulation model results compare first with standard operation conditions of two types of feedstock (Spindle oil and Intermediate oil) depending on the standard manual design of the unit. The main comparison is the bulk temperatures and pressure distribution of the feedstock in axial direction of the pipeline with the measurements of temperature and pressure as shown in Fig. 3 and 4.
This comparison will ensure that the model has a good agreement or not. The
good agreement of bulk temperature of the solution will enable to predict the
wax mass fraction in segment distance beside the characteristic of wax crystal
as this unit is designed for uniform and moderate size.

Fig. 3: 
Temperature distribution in scraped surface exchangers and
chillers in line train Worthington (1984) Data Book 

Fig. 4: 
Pressure distribution in scraped surface exchangers and chillers
in line train Worthington (1984) Data Book 
As the chilling rate is the main factor to control the cooling of the dewaxing
process in the scraped surface exchangers and chillers, so the simulation model
will enable to inspect the chilling rate incrementally along the axial distance,
as this unit is designed at uniformly slow rates, of e.g., 1 to 8° F. min^{1},
(0.56 to 4.4°C min^{1}) (Harrison et al.,
1989)
CONCLUSION
The outline of simulation model describes the dewaxing process performance in double pipe scraped surface heat exchanger. The simulation deals with non Newtonian multiphase multicomponents fluid flow. Hence suitable expressions for the fluid properties are presented and involved in the model to permit prediction of the waxing rate on the internal surface of the outer pipe. The incremental mass fraction along the axial location of the pipe is evaluated by prediction of the removed wax in a scraped segment surface. The model will also specify the chilling rate, cloud point location, the pressure distribution, the overall heat transfer coefficient and the crystals characteristic. This model presents the capability of the effect of the solvent injection point for each feedstock. The simulation results will be compared with the real data from the field work. The feature work will be develop a simulation model can be accomplish the control system of the unit, in order to inspect the processing of the lubricant oil dewaxing before the each solvent injection point.
ACKNOWLEDGMENT
The authors would like to acknowledge Universiti Teknologi PETRONAS for sponsoring the presented work under the GA scheme.