Effect of operating conditions on crude oil fouling through CFD simulations

Crude oil comprises of different components such as saturates, aromatics, resins and asphaltenes. Crude oil fouling is attributed to various factors but asphaltenes are generally considered as the main precursors of fouling on heat transfer surfaces. Asphaltenes are partly in dissolved state and partly in colloidal dispersion form in crude oil [1]. Asphaltenes tend to precipitate upon changes in temperature and pressure conditions; and agglomerate and deposit on the heat transfer surfaces in the processing equipment causing fouling [2]. Fouling reduces the heat transfer between fluids, affecting the delicate balance of heat integration in crude preheat trains in refineries [3-6]. Fouling also leads to the reduction in cross sectional area for fluid-flow due to the increase in the thickness of the fouling layer requiring additional pumping power [7].

A generalized fouling mechanism is perceived to happen in a three-step process [8]. In the first step, suspended asphaltenes particles from crude oil form as aggregates and undergo chemical reactions in the bulk and/or on the wall and form as soluble precursors. The soluble precursors react to form insoluble foulant species in the second step. Due to the higher surface temperatures, insoluble foulant species undergo physical and chemical changes to form coke deposits on the wall.

Coke formations from asphaltenes cracking are associated with thermal or catalytic reactions [2, 9, 10]. During the process of thermal cracking, asphaltenes become more aromatic and undergo phase separation by breaking of colloidal equilibrium of crude oil which leads to the occurrence of chemical reactions to form as coke [11].  The reactions associated with coke formation due to the thermal/catalytic cracking of asphaltenes are described by poly-condensation reactions. The following reactions represent the simplest form of the reactions associated with asphaltenes cracking [12]:  

As + As $\rightarrow$ coke + gas

As + n. Ar $\rightarrow$coke + gas

As + n. olefins $\rightarrow$coke + gas

The rate of coke formation with asphaltenes and/or any other unsaturated hydrocarbons cracking is more intense compared with saturated hydrocarbons [13-15]. This is due to the fact that the saturated hydrocarbons undergo various other reactions before reacting into coke. A wide variety of other reactions might occur with various components of the crude oil. However, the formation of coke is associated mainly through asphaltenes cracking [13].

Coke formation starts near the wall and then propagates towards the center of the pipeline or heat exchanger tube. The coke near the wall was found to be hard and difficult to be removed [16]. As the fouling deposit layer builds up, the thermal efficiency drops and pressure drop increases significantly, the heat exchanger must be shut down and mechanical or chemical cleaning is required to recover unit performance [10]. Frequent cleaning of heat exchangers results in huge economic losses in terms of loss in production, cleaning costs and associated issues. The concerns of fouling can be avoided only through preventing coke from being formed on the heat transfer surfaces.

Over the last decade, the petroleum industries have moved from treating fouling as a chronic problem to one which should be treated and, where possible, eliminated. A general solution adopted to mitigate fouling in the heat exchangers is to increase tube side velocities, thus, wall shear stress increases [17] and hence, decreases the accumulated fouling material [18, 19]. Wall shear stress depends on the velocity gradient near the wall and it is acknowledged that by increasing the fluid-flow velocity, the shear stress increases. Mechanically, wall shear stress can be enhanced by increasing the flow inclination angle. The flow inclination relative to the tube axis of 20 degree or more is equivalent to the increase of flow velocities up-to 2.5 times near the wall [20]. Also, the rotating or swirling flow at the pipe entrance increases the velocity near the wall and consequently the shear stress which reduces the fouling rate on heat transfer surfaces [21]. Studies also reported that, imposing small amplitude sound waves on a turbulent boundary-layer flow will create oscillations and increase the wall shear stress [22]. While the fluids with high tendency of fouling are processed in the heat exchangers, wall shear stress of 50 Pa or above is required to mitigate the fouling [23]. Thus, the effect of wall shear stress needs to be investigated for a better understanding of fouling mitigation efforts.

Computational Fluid Dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze various problems that involve fluid flow and heat transfer. CFD is an emerging simulation tool for predicting the fluid flow and heat transfer behavior in various industries such as automotive, aerospace, power generation, process industries, etc. [24-27]. Several CFD studies have been performed on the thermal cracking using kinetic modeling of asphaltenes and coke deposition [2, 9, 10, 28-31]. The effects of shear stress, fluid velocity and surface temperature were predicted [10] based on the kinetic model presented by Koseoglu and Phillips [32]. The coke formation in a petrochemical preheater tube due to the thermal cracking process using two-phase gas–liquid flow models has been investigated and reported high concentrations of coke near higher surface temperature regions [30]. A multi-phase CFD model has been developed to predict the phase change and coke deposition by varying the inlet velocities in a straight pipe and reported less coke formation rate for higher velocities [33]. Discrete phase CFD model has been developed to predict the asphaltenes mass depostion from crude oil in a shell and tube heat exchanger [34] and heat exchanger tube [35]. Various parameters such as fluid velocity, shear stress and surface roughness were varied and reported that the asphaltenes mass deposition decreases with an increase in fluid velocity, shear stress and surface roughness.     

Being time-dependent in nature, fouling is a process that should be monitored continuously. As such, fouling experiment are time-consuming and often difficult to perform. In view of the above, CFD has been used as one of the predominant approaches to investigate crude oil fouling phenomena. The crude oil fouling process involves momentum transfer, mass transfer, heat transfer, flow turbulence and chemical reactions. The effects of various operating conditions on fouling resistance with crude oil fouling through CFD simulations have not been well explored till date. The present work develops an elaborate CFD methodology to predict the coke deposition rate and fouling resistance in a heat exchanger tube. The effects of shear stress and surface roughness on fouling resistance and rate of coke deposition at different flow velocities have been investigated.

The present paper is divided into five sections. Section two presents the description of the fouling mechanism. Section three presents the CFD methodology to investigate the effects of various operating conditions on fouling resistance and coke deposition rate. The results obtained from the CFD simulations are discussed in section four. The conclusions drawn from this study are summarized in section five.

A single horizontal tube in a typical shell and tube heat exchanger is considered in this study, the geometry of which is shown in Figure 3. A three-dimensional model of the heat exchanger tube is developed in CFD to investigate the effect of various operating conditions on crude oil fouling. The basic equations which together form the model of the heat exchanger tube are explained below. The fluid-flow in the heat exchanger domain is governed by incompressible Navier-Stokes equations for mass, momentum and energy. All the governing equations (1) – (9) together form a complete mathematical model of the heat exchanger tube undergoing chemical reaction fouling. The equations are then solved on each node to obtain a numerical solution.  

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Figure 3. Heat exchanger tube

The basic CFD equations are as follows:

Continuity equation:

$\frac{\partial \rho}{\partial t}+\nabla \cdot \overline{(\rho v)}=0$     (1)

Momentum equation:

$\frac{\partial(\overline{\rho v )}}{\partial t}+\nabla \cdot(\overline{\rho v v )}=-\nabla p+\nabla \cdot(\overline{\tau})+\rho \overline{g}$     (2)

Energy equation:

$\frac{\partial\left(\rho C_{P} T\right)}{\partial t}+\nabla \cdot\left(\rho C_{P} \vec{u} T\right) )=\nabla \cdot(k \Delta T)+H$     (3)

Turbulence model:

In order to analyze the flow fields involving turbulence, a set of Reynolds-Averaged Navier-Stokes (RANS) equations, which are developed by adapting suitable time-averaging techniques on Navier-Stokes equations, are assembled. Several turbulence models such as k-ɛ, k-ω, Reynolds Stress Model (RSM), etc., are available within the RANS equations to approximate the influence of turbulent fluctuations in the flow domain. In k-ɛ turbulence model, the energy in the turbulence is computed from the turbulent kinetic energy (k) and the rate of dissipation of the turbulent kinetic energy is computed from the turbulent dissipation (ɛ). The k-ω turbulence model predicts the turbulence with turbulent kinetic energy (k) with a specific rate of dissipation (ω). RSM is a higher-level turbulence model which is considered for predicting the complex interactions in the turbulence flow fields. The most common turbulence model considered in the field of crude oil fouling is k-ɛ model [9, 28, 31, 33] which assumes that the turbulence is isotropic and requires less computational time for simulation. Therefore, in the present work, the RANS k-ɛ turbulence model is used to analyze the fluid-flow in the heat exchanger tube.  

The turbuent kinetic energy, k is described as:

$\frac{\partial k}{\partial t}+\left(u_{i} \cdot \nabla\right) k-\nabla \cdot\left(\frac{\mu_{t}}{\sigma_{k}} \nabla \cdot k\right)=P^{k}-\varepsilon+S_{k}$     (4)

and dissipation rate, ɛ is given by

$\frac{\partial \varepsilon}{\partial t}+\left(u_{i} \cdot \nabla\right) \varepsilon-\nabla \cdot\left(\frac{\mu_{t}}{\sigma_{\varepsilon}} \nabla \varepsilon\right)=\frac{\varepsilon}{k}\left(C_{1} P^{k}-C_{2} \varepsilon\right)+S_{\varepsilon}$     (5)

Species-transport equation:

Petroleum, asphaltenes, non-asphaltenes and coke are considered as species in the crude oil and the transport mechanism is studied through species-transport mathematical tool available in the commercial CFD software Ansys FLUENT version 16.2. Gravitational force is enabled for all the species, which is the main reason for the species to transport from the bulk to the heat transfer surface.   

Species transport equation for species j is given as:

$\frac{\partial}{\partial t}\left(\rho \Upsilon_{i}\right)+\nabla \cdot\left(\rho \Upsilon_{i} \overline{u}\right)=-\nabla \cdot \overline{j_{i}}+R_{i}+S_{i}$     (6)  

Reaction kinetics equations:

The reaction of C, the foulant particles, to form D, coke is considered in this study. The foulant particles are assumed to be made of precipitated asphaltenes particles and the coking reaction is given by:

2C→D     (7)

Further, the coking reaction is assumed to take place on the heat transfer surface only. The reaction rate is given by:

$-r_{3}=k_{1}[a s]$     (8)

the reaction rate constant, k, is given by:

$k_{1}=A \exp \left(\frac{-E}{R T}\right)$     (9)

where, frequency factor (A) is 9.12 x 10¹¹ (s^-1) and activation energy (E) is 1.6 x 10⁵ (J/mol).

All the governing equations of the fluid flow are then solved numerically by discretizing all the above equations of the model. The discretization process is commonly performed through three methods, namely: (1) finite difference method, (2) finite element method and (3) finite volume method. The most popular is finite volume method and is considered in the present study. The discretized governing equations are solved on a structured mesh generated for the heat exchanger tube as shown in Figure 4.

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Figure 4. Heat exchanger tube mesh

The final mesh after the mesh dependence study consists of 0.198 million quadrilateral cells. The choice of very fine mesh near the heat exchanger tube surface was aimed at considering the capability to capture the thin coke deposition layers. The number of mesh elements required to obtain mesh independent simulation results has been determined by performing steady-state simulations on different grids.

Table 1. Operating conditions

Table 2. Crude oil species properties  

The governing equations together with the turbulence model and species-transport equations of the fluid flow will result in a solution with the precise boundary and operating conditions. The common boundary conditions are usually observed in the fluid flow probems are inlets, solid walls, symmetric boundaries, pressure boundary conditions and outflow. At the inlet, fluid enter the heat exchanger domain and therefore, inlet suface is specied with velocity inlet boudanry condition. The outlet surface is specified with outflow boundary condition. The inlet and outlet boundary conditions are specified from the boundary conditions panel available in the commercial CFD software Ansys FLUENT version 16.2. Initially, the wall boundary condition is specified as no-slip and smooth surface wall. Once the coke deposition rate and fouling resistance were calculated, the effects of wall shear and surface roughness on coke deposition rate and fouling resistance are investigated by varying the wall boundary conditions. The operating and boundary conditions of flow through the heat exchanger tube are detailed in Table 1. The properties of crude oil species are given in Table 2.

The simulation methodology followed in this study is shown in flow chart in Figure 5:

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Figure 5. Flow chart – simulation methodology

The governing equations for fluid flow, turbulence, heat transfer and chemical reactions are solved through finite volume method. Often times, the governing equations solved with low-order discretization schemes can impair the quality of CFD simulations. Accuracy of the results can be a major problem with first-order schemes particularly for complex naure of fluid flows. As the simulation involves complex crude oil fouling phenomena, the discretization of convective transport terms was performed through a high-order differencing scheme i.e. Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and second-order upwind scheme for momentum, turbulent kinetic energy and dissipation rate. The Second-order upwind schemes are one of the most stable discretization schemes and highly used for CFD simulations involving chemical reactions [9].

Once the heat exchanger tube geometry and mesh are developed, the operating and boundary conditions are specified for mesh dependence study. The chosen mesh was used to perform the non-reacting flow simulation with crude oil species except asphaltenes. The simulation is iterated till the desired convergence criteria of tolerance 1x10-6 is achieved. Then, the species-transport is activated and the petroleum species are introduced into the bulk-fluid and surface reactions are activated. The reacting flow is simulated for 190 h of flow-time.

The coke particles stick to the heat transfer surface and grow in thickness over a period of time. As the thickness of the coke layer increases, the resistance to heat transfer increases. The fouling resistance is calculated by:  

$R_{f}=\frac{1}{U_{d}}-\frac{1}{U_{c}}$     (10)

The process of crude oil fouling through coking reactions is simulated at different wall boundary conditions (shear stress and surface roughness). The simulations were repeated at 0.14, 0.31 and 0.47 m/s flow velocities for Cases 2 – 5 in Table 3 in which the matrix of wall boundary conditions is given.

Table 3. Matrix of wall conditions

All the governing equations are numerically computed at thousands of discrete points (computational mesh) in the heat exchanger tube. In this context, the validation of the developed CFD model and the methodology is highly necessary to predict the accuracy of the results with realistic models. Validation of the CFD model provides evidence that the conceptual computational model is computed accurately compared to the reality. The validation of the CFD model is performed by predicting the heat transfer coefficients with crude oil as fluid medium in the heat exchanger tube. Steady state CFD simulations are performed and heat transfer coefficients are evaluated at different flow velocities. The calculated HTC’s from CFD simulations are compared with the existing theoretical heat transfer correlations. The graphical representation of heat transfer coefficients at various crude oil velocities calculated through the CFD simulations and following empirical correlations are shown in Figure 6.  

Dittus and Boelter correlation [39]:

$N u=0.023 R e^{0.8} \operatorname{Pr}^{0.3}$        (11)

Colburn correlation [40]:

$N u=0.023 R e^{0.8} P r^{0.4}\left(\frac{\mu}{\mu_{w}}\right)^{0.14}$       (12)

The HTC’s calculated from the simulation results were impressively correlated with the Colburn correlation with maximum 9.81 % deviation. Therefore, the CFD code and the mathematical model can be considered validated.

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Figure 6. Heat transfer coefficients vs flow velocity

A three-dimensional Computational Fluid Dynamics study was performed to investigate the effect of flow velocity, shear stress and surface roughness on coke deposition rate and fouling resistance in a heat exchanger tube. The fouling resistance and coke deposition rate at various operating conditions are studied through species-transport CFD approach at different time-steps. Flow velocity, wall shear stress and surface roughness are found to have a high impact on mitigation of fouling. The thermal efficiency of the heat exchanger tube is enhanced though increasing the fluid velocity, wall shear and surface roughness, which minimizes the fouling resistance. Further, the developed CFD methodology can be employed to understand the coke mass deposition in an industrial shell and tube heat exchanger.