Modeling of Asphaltene Deposition in a Packed Bed Column | Energy

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Cite This: Energy Fuels 2019, 33, 5011−5023

Modeling of Asphaltene Deposition in a Packed Bed Column Narmadha Rajan Babu† and Francisco M. Vargas*,†,‡ †

Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States ENNOVA LLC, Stafford, Texas 77477, United States

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‡

ABSTRACT: Asphaltene deposit buildup in production pipelines and subsea flowlines greatly affects the production rate of oil and, hence, is a major concern for the upstream oil and gas industry. To better understand the behavior of asphaltenes under different production scenarios and operating conditions, the physics of asphaltene deposition and effectively develop mitigation strategies to overcome this problem, experimental techniques, and modeling methods are extremely important. Recently, deposition tests using a packed bed column have been performed to measure and quantify asphaltene deposition in the laboratory. This work focuses on the development of a modeling technique to simulate the process of asphaltene deposition occurring in the packed bed column. A computational fluid dynamics model has been developed to analyze the multi-step process of asphaltene phase separation, aggregation, diffusion, and deposition. Three-dimensional transient flow simulations have been performed using an indigenous in-house finite element solver developed on MATLAB platform. A surface deposition mechanism has been employed to capture asphaltenes deposited on the packed bed spheres. The effects of precipitant, precipitant concentration, and experimental run time on the extent of deposition have been studied in detail. It has been found that the magnitude of asphaltene deposition, the deposition rate, and consequently, the deposition risk increase with an increase in the concentration of phase-separated asphaltene primary particles and the driving force for precipitation and deposition. The model has also been modified to comprehend the effect of chemical dosage on asphaltene deposition. The developed methodology can be applied to analyze the effectiveness of industrially available asphaltene deposition dispersants and solvents and, hence, help us in developing strategies for asphaltene deposition problem mitigation and remediation. This study provides a computationally efficient modeling technique that helps in simulating asphaltene deposition studied in an experimental setup, recognizing the competing phenomena of asphaltene aggregation and deposition that are simultaneously taking place in the system and, hence, providing a better understanding of the asphaltene deposition process.

1. INTRODUCTION Deposition of asphaltenes on the pipeline surface leads to flow assurance problems, which greatly reduce oil production efficiency. Asphaltenes are the heaviest and most polarizable fraction of the crude oil, which are typically soluble in oil under reservoir conditions.1 Asphaltenes phase separate from oil due to changes in the pressure, temperature, and oil composition caused by the addition of a precipitant or miscible gas injection.2 These precipitated asphaltenes can then undergo aggregation and deposition.2,3 With an increase in the offshore deep-water operations and application of enhanced oil recovery (EOR) methods, the concerns of possible plugging of flowlines as a result of asphaltene deposit buildup have also increased.4 Hence, the need to predict and estimate asphaltene deposition risk in a wellbore or a subsea flowline has become extremely important. To perform such a prediction under real field conditions, it is required to analyze the oil sample under laboratory conditions and estimate its deposition tendencies. These laboratory-scale experiments, in turn, facilitate in the development of mathematical modeling techniques and calibration of model parameters. Hence, this would help us to understand the physics of the asphaltene deposition phenomena in flowlines and systematically estimate the risk of plugging at a particular production time and rate for a given oil-producing well. Precipitation of asphaltenes is a thermodynamic process, which is determined by changes in the pressure, temperature, and fluid composition.5 However, deposition of asphaltenes is © 2019 American Chemical Society

a much more complex process, which is controlled by not only the petroleum thermodynamics but also the hydrodynamic conditions, size of the asphaltene primary particles and aggregates, surface roughness, etc.6−9 Over the years, several laboratory-scale deposition experiments and corresponding modeling techniques have been developed. Capillary deposition experiments have been performed to measure the risk of asphaltene deposition under laboratory-scale conditions.10,11 Here, precipitation was induced by the injection of a precipitant to the oil sample. Asphaltene deposition was examined by assessing the increase in pressure drop values across the capillary tube, which are caused due to the formation of the deposits on the tube walls. Vargas et al.2 and Kurup et al.12 used the results from the capillary deposition tests to calibrate their convection−diffusion mass transport model. The estimation of the deposition rate constant from the capillary tube experiments enabled Kurup et al.13 to predict possible deposition in Kuwait’s Marrat oil well and Hassi Messaoud oil field. In these works, perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) was applied to characterize the oil and predict asphaltene precipitation. Zougari et al.14 devised an organic solid deposition and control device (OSDC) to measure deposition caused by Received: March 9, 2019 Revised: May 26, 2019 Published: June 11, 2019 5011

DOI: 10.1021/acs.energyfuels.9b00715 Energy Fuels 2019, 33, 5011−5023

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Energy & Fuels

Figure 1. (a) Schematic diagram of the packed bed column deposition test17 and (b) laboratory setup of the packed bed column and PTFE tubing.

characterized. Even this column can be operated only at ambient conditions. To investigate deposition problems at HPHT conditions, a stainless-steel column was introduced instead of a PTFE column that was used at ambient conditions.16 In these experiments, precipitation of asphaltene is induced by the injection of a precipitant, such as n-alkane. The measurement of the mass of deposited asphaltenes on the surface of the spheres for a particular run time helps in calculating the asphaltene deposition flux for the given driving force and fluid flow rate. Performing deposition tests using a packed bed column requires very less amount of oil sample per run (about 30 mL).16 The deposited material can be obtained and characterized. The multi-section apparatus developed by Kuang et al.16 helps us to study the axial deposition profile and also study the effect of surface properties on asphaltene deposition. The phenomenon of asphaltene deposition taking place in the packed bed column is a very interesting yet complex process. The model implemented to study this process needs to be comprehensive of the mechanisms taking place in the column. This demands a rigorous modeling approach and prediction technique for the simulation of asphaltene deposition in such a geometry. In this work, the development of a computational fluid dynamics (CFD) model to estimate asphaltene deposition in a packed bed column will be discussed. Finite element method (FEM) has been used in this work for solving the equations of the developed mathematical model. The modeling technique will be illustrated in detail, including the construction of the packed bed geometry, generation of the finite element mesh, development of the mathematical model, and the procedure considered for solving the model equations. This work will also show the application of three-dimensional transient simulations in such a geometry. Calibration of the deposition model parameters using such an in-depth procedure would help us to successfully scale from the laboratory to real field conditions. A surface deposition mechanism will be employed to capture the asphaltene deposited on the packed bed spheres. This modeling and analysis facilitate in understanding the deposition tendency and provide more insight into the physics of the asphaltene deposition process.

organic solids (asphaltene and wax) in live oil samples under real field high-pressure and high-temperature (HPHT) conditions. It functions based on Taylor−Couette flow principles.7 The pressure is progressively reduced to induce asphaltene precipitation and, thus, mimic the pressure reduction scenario, similar to that of a field case. The high rotation speed of the inner cylinder facilitates in achieving a turbulent fluid flow in the annular space, and it can be operated in both batch and flow-through modes. Eskin et al.3 developed a detailed analysis for the applicability of this Taylor−Couette device to study and measure asphaltene deposition in the wellbore and pipelines. Their work accounts for Brownian and turbulent diffusions, turbophoresis mechanisms to model particle transport to the wall, and deposition in turbulent flow fluid is modeled using particle flux mass transfer expressions in such a flow condition. Although several works have been performed using capillary and OSDC deposition tests, capillary flow loop tests consume a lot of the oil sample (of the order of liters), experiments on OSDC are very expensive, and very few experimental data are available for tuning the model parameters.7,11 OSDC flowthrough experiments also consume liters of expensive live oil sample to generate a single data point. Thus, this has created the necessity for developing new laboratory experiments to study asphaltene deposition, which consume less amount of the expensive oil sample, comparatively. More recently, asphaltene deposition was measured using a packed bed apparatus by Vilas Bôas Fávero et al.15 The apparatus consisted of stainless-steel beads in a glass column. Experiments were run for a particular run time at ambient temperature by introducing an oil−precipitant mixture into the column. The amount of asphaltene deposited and specific deposition rate were obtained for each deposition test. A mass-transfer-limited model was introduced to estimate deposition in a packed bed.15 The model did not have any parameters to be tuned with the experimental data, but the mass transfer coefficient was calculated using a simplified correlation. A multi-section deposition system to assess asphaltene deposition on metal surfaces was developed by Kuang et al.16 This apparatus used a polytetrafluoroethylene (PTFE) column stacked with carbon steel spheres. Inspired by the system used by Vilas Bôas Fávero et al.,15 this device has been modified such that it separates into two sections and the asphaltenes deposited in each section can be individually quantified and 5012


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where u is the velocity field, p is the pressure, μ is the viscosity of the fluid, ρ is the density of the fluid, and gz is the acceleration due to gravity. Initial condition: u(t = 0) = 0, ∀ x, y, z. Boundary conditions: for all t > 0

2. EXPERIMENTAL PROCEDURE In this work, the experimental technique developed by Kuang et al.16,17 will be used for deposition model development. A 316 stainless-steel column is packed with about 975−985 carbon steel spheres, which have a diameter of 3/32 in. The HPHT packed bed column setup is shown schematically in Figure 1. The operating temperature (70−570 °F) can be controlled inside an explosion-proof oven, and the downstream pressure (0−3000 psi) can be manipulated by a back-pressure regulator connected to the column outlet. The oil sample and precipitant are injected using highperformance liquid chromatography (HPLC) separately at constant flow rates and mixed at a T junction, which is kept inside an ultrasonic bath. The mixture then inlets into the packed column at its bottom section through a PTFE tubing. The column is maintained at the required temperature inside an oven. Two pressure transducers, as shown in Figure 1, are used to record the pressure drop. The concentration of the precipitant, flow rate of the oil−precipitant mixture, and run time have been maintained in such a way that there is no quantifiable deposition in the PTFE tubing. This is checked by continuously monitoring the pressure drop across PTFE tubing. After the deposition test, the packed bed is drained by gravity. The mixed liquid remaining inside the column is slowly displaced with nitrogen. The spheres with deposits are collected and heated to 248 °F to ensure that the deposited materials are completely dried.16 The occluded oil is removed by pre-rinsing the deposited materials with a neutral solvent (cyclohexane) and filtering it. Then, the actual mass of deposited asphaltene is obtained by washing the remaining deposits in a Soxhlet extractor, a second wash using toluene, and evaporating the toluene at 248 °F until a constant weight is achieved.17 The deposition tests performed using the packed bed column help in analyzing the deposition tendencies at high-temperature conditions. The experimental results obtained under various operating conditions further help in the development of a deposition model for such a geometry and, hence, checking its validity. Rajan Babu et al.18 described the methodology to investigate the asphaltene precipitation and aggregation kinetics using a near-infrared region (NIR) spectroscopy method. In this method, the light transmittance values of oil−precipitant mixtures were recorded over time using a spectrophotometer to obtain a measure of the weight fraction of the precipitated and aggregated asphaltenes at different aging times. The packed bed column deposition test results, along with the precipitation and aggregation experiments, are used to calibrate our developed mathematical model and estimate the asphaltene aggregation and deposition rates.

\(on metal surfaces) = 0 \(z = 0) = uin , ∀ x , y U ·σ(z = L) = 0, ∀ x , y

where n is the unit normal vector, L is the length of the packed column, and σ is the shear stress. These boundary conditions are shown in Figure 2.

Figure 2. Boundary conditions to solve eqs 1 and 3 in packed bed column geometry.

On the addition of a precipitant to the oil sample, asphaltenes are phase-separated from the oil phase and, hence, precipitated. In this work, precipitation of asphaltenes is assumed to be instantaneous as the precipitant is injected into the crude oil. The phase-separated precipitated asphaltenes are referred to as primary particles in this work, which further aggregate with each other. Two primary particles come together and form an aggregate. Then, two aggregates with n number of primary particles each can come together and form another aggregate (such as A + B → C). Hence, by considering aggregation as a two-body phenomenon, it is modeled using a second-order kinetic process.13,18,19 All asphaltenes (ranging from primary particles to aggregated asphaltenes), which are of size less than the critical particle size, are assumed to diffuse toward the boundary layer by Brownian diffusion and, hence, undergo deposition.2,3,18 In the literature, authors have used the first-order reaction mechanism to model asphaltene deposition.2,12,13,15 In this work, instead, a surface deposition mechanism is implemented.18 This stems from the idea of incorporating the effects of wall shear stress (velocity gradient) in the near wall region to the deposition term. It helps us to capture the near wall region effects by including an additional term in the deposition kinetics when compared to the first-order reaction mechanism used in earlier works. The surface deposition mechanism has been included in the material balance equation to mimic the

3. MODEL DEVELOPMENT In this section, the model developed to simulate asphaltene deposition in a packed bed column will be discussed. The transport of asphaltenes in this HPHT packed bed column is modeled using a multi-step mechanism, which includes precipitation, advection, diffusion, aggregation, and deposition.18 The fluid flow in the packed bed column is first computed based on its three-dimensional geometry (x, y, and z coordinates). The fluid flow simulations help in evaluating the effect of hydrodynamics. It will help in understanding the velocity profiles in the system and further facilitate in modeling asphaltene deposition in such a geometry. Because the fluid flow in the packed bed is laminar, three-dimensional Navier− Stokes equations are used to perform the fluid flow simulation and the corresponding initial and boundary conditions are shown in eqs 1 and 2 ρ

∂\ + ρ(\∇)\ = ∇·( −pI + μ∇\) + ρgz ∂t

(2)

(1) 5013


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Figure 3. Flowchart describing the methodology used for modeling deposition of asphaltenes in a packed bed.

boundary conditions are shown in Figure 2. Transient simulations are executed to evaluate the total mass of deposited asphaltenes and also to analyze the effect of time. The introduction of the deposition term in eq 3 helps in satisfying the material balance of asphaltenes in a given control volume of the packed bed column and also helps in capturing surface deposition (facilitated by the introduction of the velocity gradient Gu in the deposition term). The strategy described above helps in modeling asphaltene deposition in the given geometry and computationally capturing the deposited asphaltenes on the curved surfaces of the spheres. The finite element method implemented helps in calculating the variation of the velocity, velocity gradients, and concentration of the deposited asphaltenes at different points of the flow domain in the column.

collision and adherence of the particles on the surface of the packed bed spheres. A three-dimensional mathematical model has been developed for convection, diffusion, aggregation, and deposition of asphaltenes in the system under consideration. The mass conservation of asphaltene primary particles in a given volume of the packed bed column in the transient state is given as ∂C + (\·∇)C = De∇2 C − K agC 2 − (kd)pb (Gu)pb C ∂t

(3)

where C is the asphaltene primary particle concentration. The concentrations are normalized with respect to Co, which is the total concentration of asphaltenes in the oil phase before the addition of the precipitant. De is the diffusion coefficient, and the transport of the particles toward the boundary layer is governed by Brownian diffusion, evaluated using the Stokes− Einstein relation.20 The fluid flow simulations performed using eq 1 yield the velocity field u. Kag = kagCo is the aggregation kinetic parameter, which helps in capturing the rate of aggregation. It is obtained using the methodology and equations illustrated in Rajan Babu et al.18 for modeling the kinetics of asphaltene precipitation and aggregation. It should be noted that, in the concentration boundary layer around the surface of a sphere, two competing phenomena occur. One of them is the mass transfer of the asphaltene primary particles and aggregates toward the boundary layer, and the other is the depletion of the particles by deposition kinetics. There is a concentration gradient of the primary particles as we proceed from the bulk to the surface boundary layer. The rate of deposition is given as Rd = (kd)pb(Gu)pbC. For the packed bed column, (Gu)pb = (nnT:∇u)pb, where n refers to a unit normal vector. (nnT:∇u)pb merely reduces to the summation of the velocity gradient terms.18 (kd)pb is the packed bed deposition kinetic parameter and gives a measure of the asphaltene deposition rate and deposition flux. The variation in the values of the deposition kinetic parameter between different experiments helps in evaluating the extent of asphaltene deposition that can be caused, under different driving forces, by different fluid flow rates, etc. (kd)pb is tuned to reduce the difference between the experimental and modeling results obtained for the total mass of asphaltene deposited in the packed bed column. Equation 3 is solved by applying the following conditions: Initial condition: C(t = 0) = 0, ∀ x, y, z. Boundary conditions: for all t > 0

4. SOLUTION TECHNIQUE CFD enables the simulation of a packed bed in a completely explicit manner, taking into account the position of each sphere and its relative influence on the flow distribution and pressure profiles in a packed bed. Various authors have used CFD simulation to model flow distribution in packed beds. Nijemeisland and Dixon,21 Calis et al.,22 and Romkes et al.23 simulated the flow distribution through structured sphere packings. Atmakidis and Kenig24 simulated the flow distribution through random sphere packings. From the literature, it is evident that the increase in computational performance in recent years has steadily pushed the boundaries and limitations in the simulation of packed beds using CFD codes. The various key modeling issues that require attention include building the three-dimensional geometry, contact points between the spheres, and mesh generation. An indigenous in-house solver based on the FEM has been established on MATLAB platform to solve the partial differential equations (PDEs), shown in section 3, for momentum and mass transport. CFD modeling has been implemented in this work. CFD modeling employs several spatial discretization methods for solving the PDEs. FEM is used in this work for the spatial discretization of the PDEs. The FEM offers higher accuracy, better convergence analysis, and mesh adaptation for complex geometry compared to finite difference and finite volume methods. In this section, the construction of the packed bed column geometry and the finite element mesh generation for the built geometry will be discussed. Hence, the FEM solution technique applied by discretizing the partial differential equations using the generated mesh will help us in calculating the amount of asphaltene deposited in the packed bed column computationally. Figure 3 shows the sequence of steps adopted to model deposition of asphaltenes in a packed bed. The techniques implemented in each of these steps are described in detail in the following paragraphs of this section.

U ·∇C(at metal surfaces) = 0 C(z = 0) = Cin , ∀ x , y −U ·De ∇C(z = L) = 0, ∀ x , y

(4)

where Cin is the asphaltene primary particle concentration at inlet conditions and L is the length of the packed column. The 5014


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pressure drop. Figure 4 shows the variation of the sphere size and its corresponding impact on the pressure drop for different

The specifications of the stainless-steel packed bed column geometry, operated at HPHT conditions, are shown in Table 1. First, a geometric model is constructed, and then, a finite Table 1. Geometric Specifications of the Packed Bed Column specification

value

diameter of the column (in.) height of the column (in.) diameter of the spheres (in.) number of spheres void fraction

0.5 5.1 3/32 981 0.5773

element mesh is generated for the numerical simulation. In this work, mesh generation has been performed using “Gmsh: a three-dimensional finite element mesh generator”.25 The FEM is used for spatial discretization of the partial differential equations shown in eqs 1 and 3. In FEM, the spatial domain is divided into several elements (facilitated by the generation of finite element mesh), the solution is approximated using basis functions, and the problem is solved on individual elements. First, weighted functions are introduced to derive the weak form of the partial differential equations. The weak formulation is then approximated using the Galerkin FEM of weighted residuals, which is the most common method of solving PDEs using FEM. The three-dimensional simulation performed in this work demands the implementation of tetrahedron elements with the application of a Lagrangian shape function for the unknown parameter (velocity or concentration). For time integration, the secondorder backward differentiation formula (BDF) is applied. This technique is chosen because BDF is an implicit technique, which offers better accuracy and convergence compared to an explicit method. The system of equations that is obtained as a result of the complete discretization of the PDEs needs to be solved to compute the unknowns. At every iteration and time step of the implicit method, the coupled equation system needs to be solved, which is of the form, Ax = b. This system is too large to be solved using a direct method. Hence, it is solved iteratively. The biconjugate gradient stabilized method (BiCGSTAB) has been used in this work to perform the computation.26 BiCGSTAB is a Krylov subspace method, which is a projection method used to solve a problem iteratively. The simulation is considered complete when the residual values of all of the solvers show no variation and a residual value below 10−4 and a steady-state solution are achieved. Once the partial differential equations are solved, the velocity profile and asphaltene deposit profile in the packed bed are obtained. The finite element mesh generated for the constructed geometry needs to be fine in restricted flow areas. It should also be made sure that, for the numerical fluid flow simulation, these elements have a finite dimension and the volume of each element is non-zero. However, this is not the case where the spheres are in contact with each other or when they are in contact with the wall. While this geometry is meshed, the continuity of the meshes is disrupted, because the spheres are in contact with each other. Thus, a very small gap needs to be introduced at these contact points. The radius of each of the spheres can be reduced to achieve this. Hence, a sensitivity study has been performed to understand the effect of the reduction of the sphere size on the fluid flow and column

Figure 4. Sensitivity analyses to analyze the effect of sphere size reduction on the pressure drop.

particle Reynolds numbers. The particle Reynolds number for a packed bed column is calculated as Rep =

ρUd p μ(1 − ϕ)

(5)

where dp is the diameter of the spheres, ϕ is the void fraction, and U is the superficial fluid flow velocity. To evaluate the pressure drop for the case when the spheres are in contact with each other, the Ergun equation is used, which is given as ψ=

(1 − ϕ) 150 (1 − ϕ) + 1.75 3 Rep ϕ ϕ3

(6)

where ψ is the dimensionless pressure drop, and hence, the dimensional pressure drop is given as ΔP = ψL(ρU2/dp). These calculations have been performed for the geometry specifications shown in Table 1, when a fluid (corresponding to test 1 in Table 3), which has a viscosity of 5.1 cP and a density of 771.1 kg/m3, flows through the column. On the basis of the results from Figure 4, the diameter of the spheres was reduced by 1% for this work, so that we have a reasonable match with the pressure drop values when the spheres are in contact with each other (solid black line) without exponentially increasing the number of mesh elements, which would increase the computational time and computer memory. The void fraction, as a result, increases by 2%. The geometry constructed is shown in Figure 5. It is constructed in such a way that lattices with 12 spheres each are stacked one over the other. Each lattice is displaced by an angle of 45° along the centerline and then placed over the previous lattice. The mesh used in this work is a tetrahedral mesh. Surface and domain (refers to fluid flow domain) mesh generation has been performed. The surface mesh generated is also shown in Figure 5. Owing to the intricacies in the packed bed column geometry, it was made sure that there is no mesh distortion in the areas where very fine mesh was generated and optimum mesh resolution was used to avoid any numerical instability. As 5015


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the CFD modeling technique, the packed bed column operating conditions, corresponding to test 1, shown in Table 3, are considered. Table 3. Experiments Performed in the Packed Bed Column Using Crude Oil C2 property

test 1

test 2

type of precipitant amount of precipitant (vol %) flow rate of oil (mL/h) flow rate of precipitant (mL/h) run time (h)

n-pentane 60 3.6 5.4 6

n-heptane 60 3.6 5.4 6

Velocity profiles are simulated by solving eq 1 using the initial and boundary conditions shown in eq 2 for the operating conditions shown in Table 3 as per the solution technique illustrated in section 4. Laminar flow simulations have been performed. The velocity profiles along different lengths of the packed bed column are shown in Figure 6.

Figure 5. Constructed geometry of the packed bed column and surface mesh generation shown for a section of the column (along the x−z plane).

a result, the complete mesh consists of 7 778 396 domain elements. Correct simulation of mesh density ensures efficient and accurate simulation of flow phenomena and asphaltene deposition, using eqs 1 and 3, with the boundary and initial conditions specified in eqs 2 and 4, respectively.

5. RESULTS AND DISCUSSION Deposition experiments were performed using crude oil C2 in a HPHT stainless-steel packed bed column. The pressure− volume−temperature (PVT) properties of crude oil C217 are shown in Table 2. Table 2. PVT Properties for Crude Oil C2 property

value

density at 60 °F and 14.7 psi (g/cm3) molecular weight (g/mol) saturates (wt %) aromatics (wt %) resins (wt %) C5 asphaltenes (wt %) C7 asphaltenes (wt %)

0.91 290 50.0 19.8 20.1 11.1 10.1

Figure 6. Velocity profiles (x−y plane) across different lengths of the packed bed column (test 1).

It can be seen from the results shown in Figure 6 that the fluid velocity is greatest in the narrow spaces that occur in between spheres stacked together in a lattice. This happens because the fluid is forced to flow through a relatively constricted space, compelling it to accelerate. This results in areas of local maximum velocity in this type of geometry. If we proceed from the center of the column, along the radius, the magnitude of velocity peaks at two points. The first peak is seen along the centerline of the column, because it is surrounded by three spheres of a lattice, rendering an extremely constricted flow. The second peak occurs at the contact occurring between the spheres closer the centerline and its neighboring sphere. The velocity profiles show the variation of the fluid flow along the x−y plane. It can be seen

Using the geometry built and mesh generated, as shown in section 4, CFD simulation based on FEM is performed. The packed bed deposition kinetic parameter is calibrated based on the experimental results for the given operating conditions. All experiments considered in this work are performed using crude oil C2 in the packed bed column as per the specifications in Table 1, at a temperature of 176 °F and back pressure of 100 psi. The value of the aggregation parameter for crude oil C2 was evaluated by Rajan Babu et al.18 as Kag = 5 × 10−6 s−1. 5.1. Fluid Flow Simulation. To illustrate the fluid flow simulation and deposition simulation by the implementation of 5016


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Energy & Fuels that these are in fact the two areas where local maximum velocities occur. It is also seen that, at varying heights, the velocity profiles are different. This has to do with the bed geometry and the fact that the slices are across different cross sections along the length of the column. Also, from Figure 6, it can be seen that areas with the highest maximum velocity are occurring along the centerline at column heights of 3.5 and 4 in. These areas are caused because, at these bed heights, the distance between spheres around the centerline, along that cross section, is the smallest. It should be noted that a no-slip boundary condition has been applied on the surface of the stainless-steel spheres and walls of the column. The packed bed column is operated only in the laminar region, where Rep < 10 for this work. 5.2. Asphaltene Deposition Simulation. Deposition simulations are performed by solving eq 3 using the initial and boundary conditions in eq 4 and operating conditions in Table 3 for test 1. The hydrodynamics evaluated using the fluid flow simulation, shown in section 5.1, facilitate in further solving the mass transfer equations. The experimental results obtained by performing deposition tests using the HPHT packed column are shown in Table 4. For test 1, 60 vol % pentane has been

Figure 7. Cumulative mass of deposited asphaltenes with respect to the packed bed column length (test 1).

Table 4. Packed Bed Column Experimental Results for Deposition Tests Performed Using Crude Oil C2 mass of deposited asphaltenes (mg) column section

test 1

test 2

deposits in the top section deposits in the bottom section total

15.4 662.7 678.1

14.2 217.2 231.4

used to precipitate asphaltenes, and on the other hand, for test 2, 60 vol % n-heptane has been used. To illustrate the deposition simulations, test 1 is considered first. Therefore, (kd)pb is tuned such that the simulation results match the experimental results, shown in Table 4 for crude oil C2 (test 1), corresponding to the mass of deposited asphaltenes quantified in the bottom and top sections of the column. The calibration is performed with respect to the mass of asphaltenes only and not the mass of the total deposited material, because (kd)pb is reflective of the deposition rate of only asphaltenes. Figure 7 shows the variation of the amount of deposited asphaltenes as we proceed from the bottom to the top section of the column. For this case, (kd)pb = 1.5 × 10−4 yielded the best result, where the percentage error with respect to the experimental values was a minimum. Deposition profiles across the x−y plane at different column heights are shown in Figure 8. It can be seen from Figures 7 and 8 that asphaltene deposition is significant in the column bottom section compared to the top section for the considered operating conditions. This indicates that deposition will most likely occur when the driving force toward asphaltene precipitation and deposition is a maximum, which is in the bottom section of the column, closer to the inlet. This is seen in the modeling results as well. As the oil−precipitant mixture enters the packed bed column, there is an influx of precipitated asphaltene nanoaggregates (asphaltene primary particles) into the column. They further aggregate and deposit on the packed bed spheres. The aggregation of asphaltene nanoaggregates and its diffusion toward the boundary layer of the spheres, hence, its deposition,

Figure 8. Deposition profiles (x−y planes) across different lengths of the packed bed column (test 1).

are competing phenomena. The deposition model in this work is developed in such a way that deposition profiles are simulated for the available primary particles, surface area, flow rate, and residence time. Based on the aggregation and surface deposition rates, the precipitated asphaltenes adhere to the sphere surfaces in the bottom section as soon as they get in contact with their metallic surfaces, where the driving force toward asphaltene deposition is a maximum. This work focuses on the process of deposition taking place in the packed bed column that is not dominated by the effect of gravitational settlement. The flow rate of the oil−precipitant mixture, the concentration of the precipitant in the oil− precipitant mixture, and the experiment run time have been chosen in such a way that there is no measurable sedimentation in the column. For the considered operating conditions, the diffusion coefficient was estimated as ∼2 × 10−12 m2/s. Hence, accordingly, the particle size diameter of the unstable phase-separated asphaltene primary particles in the fluid flow domain during the deposition test 1 is assessed as 50.6 nm. Hence, the dominating factor is the driving force for deposition, which effectively drives the nanometer-sized 5017


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Energy & Fuels particles toward the surface boundary layer by Brownian diffusion and causes deposition. Figure 8 is obtained as a result of the CFD simulation based on the FEM. The asphaltene deposit profiles can be seen around the surface of the spheres. The mass of the asphaltene deposited on the packed bed spheres is evaluated by constructing a concentration boundary layer over the surface of each of the spheres and adding the values of the deposited asphaltene mass in each finite element in those boundary layers. The concentration boundary layer develops when there is a difference in concentration of a component between the free stream and the surface. The thickness of the concentration boundary layer is defined as that point at which the difference in concentration between the fluid and the surface is 99% of the difference in concentration between the free stream fluid and the surface. The concentration of deposited asphaltene is 0 in the free stream of the fluid. Hence, the concentration boundary layer thickness, in this work, simplifies to the distance from the sphere−fluid interface where the concentration of deposited asphaltene in the fluid is 1% of the concentration of deposited asphaltene on the surface of the sphere, and hence, this forms our thickness of the deposited asphaltene. Once the rate of asphaltene deposition, Rd = (kd)pb(nnT:∇u)pbC is calculated after solving eq 4), the corresponding concentration of deposited asphaltenes (Cd) and the mass of deposited asphaltenes in the system can be calculated (md). Figure 8 precisely shows how the mass of deposited asphaltene decreases as we move from the surface of the sphere toward the bulk of the system. This feature is captured by the model using the surface deposition mechanism implemented for the asphaltene deposition calculations and simulations. These calculations are feasible because of the finite element mesh generated to perform the CFD simulation. It has been made sure that the current mesh is fine enough and the change in cumulative mass of asphaltene deposited is negligible with an increase in mesh resolution (much finer mesh). In other words, CFD simulations and deposition kinetic parameter calibrations have been performed only after achieving mesh independency. 5.3. Effect of the Driving Force on Asphaltene Deposition. The most common approach to phase separate asphaltenes from the given oil sample in laboratory-scale experiments is by the injection of a precipitant, such as nalkane. The effect of the driving force for deposition can be analyzed on the basis of the type and concentration of the precipitant used in the packed bed column deposition tests. This will have a possible effect on the amount of asphaltene deposited, rate of deposition, and deposition flux. In this work, the effects of two precipitants, n-pentane and n-heptane, are studied in detail. Deposition tests on crude oil C2 were performed using each of them as precipitants at 176 °F. The operating conditions and experimental results of the deposition tests are shown in Tables 3 and 4, respectively as tests 1 and 2. CFD modeling, as illustrated in sections 5.1 and 5.2, has been performed for test 2 as well. The deposition kinetic parameter, (kd)pb, is tuned in each case to match the experimental data. The cumulative mass of asphaltene deposited in the packed bed for both of the cases is shown in Figure 9. A comparison between the results obtained from the experiments and simulations and their corresponding deposition kinetic parameter values are shown in Table 5. The absolute percentage deviation (APD) of the modeling results from the

Figure 9. Comparison of the cumulative mass of asphaltene deposited with respect to the packed bed column length when 60 vol % npentane and 60 vol % n-heptane are used as a precipitant.

Table 5. Comparison of the Overall Asphaltene Deposition and Deposition Kinetic Parameter between Tests 1 and 2 total asphaltene deposition on spheres test

experiment (mg)

CFD model (mg)

APD (%)

deposition kinetic parameter, kd)pb

1 2

678.1 231.4

678.1 223.2

0 3.5

1.5 × 10−4 7.6 × 10−5

experimental results are also shown. The amount of asphaltene deposited, when n-heptane is used as a precipitant, is much lower than that deposited when n-pentane is used, for the same run time and flow rate. Hence, the deposition rate is higher when n-pentane is used as a precipitant, and this is seen in the values of the deposition kinetic parameter, (kd)pb. The fluid properties used to perform the CFD simulation are shown in Table 6. The indirect method, developed by Tavakkoli et al.,27 can be implemented to determine the onset of precipitation and precipitation amounts. If the solubility parameter of the oil− precipitant mixture is known at its onset of precipitation (δonset), then the difference between the solubility parameters of the mixture at any instant (δmix) and that at its onset of precipitation gives a factor to measure the stability of the asphaltenes in the mixture. The higher the difference between the solubility parameters, Δδ = (δonset − δmix), the lower the stability of the asphaltenes, the higher the driving force, and hence, the higher the concentration of the unstable precipitated asphaltenes. The solubility parameters of pure components is obtained from their respective refractive index values.28 The solubility parameter of a mixture is given by the Vargas et al.29 mixing rule. The equations used to perform these calculations are shown as follows: FRI =

(N 2 − 1) (N 2 + 2)

δ = 52.042FRI + 2.904 δmix 2 = 5018

∑ viδi 2

(7) DOI: 10.1021/acs.energyfuels.9b00715 Energy Fuels 2019, 33, 5011−5023

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Energy & Fuels Table 6. Fluid Properties at 176 °F for Tests 1 and 2 test

precipitant

density of precipitant (g/cm3)

viscosity of precipitant (cP)

density of oil−precipitant mixture (g/cm3)

viscosity of oil−precipitant mixture (cP)

1 2

n-pentane n-heptane

0.5628 0.6314

0.14 0.23

0.7711 0.7986

5.1 6.1

Table 7. Refractive Index and Solubility Parameter Calculations Corresponding to Tests 1 and 2 solubility parameter of precipitant, δprecip (MPa0.5)

test

precipitant

refractive index, n

1 2

n-pentane n-heptane

1.3578 1.3878

at 68 °F

at 176 °F

onset of precipitation (vol % of precipitant)

solubility parameter at onset, δonset (MPa0.5)

solubility parameter of 60 vol % precipitant and 40 vol % oil, δmix (MPa0.5)

Δδ = δonset− δmix (MPa0.5)

14.33 15.18

13.12 13.91

31 34

16.72 16.92

15.3 15.72

1.42 1.19

where N is the refractive index of a component, vi is the volume fraction, and δi is the solubility parameter of component i. The refractive index of crude oil C2 at 68 °F is 1.51, and the refractive index of crude oil C2 at 176 °F is 1.49. The solubility parameters of n-pentane and n-heptane at higher temperatures are evaluated using PC-SAFT EOS. Calculations are performed using this procedure, and the resultant values of Δδ for tests 1 and 2 are shown in Table 7. When 60 vol % of the precipitant is added to crude oil C2, it is seen from Table 7 that Δδ is higher when n-pentane is used as a precipitant in comparison to n-heptane. Hence, using npentane in the experiments to precipitate asphaltenes results in a comparatively higher driving force. This is consistent with the results obtained from CFD simulations. The mass of asphaltene deposited and the deposition kinetic parameter are higher when Δδ = (δonset − δmix) is higher. Table 8 shows the different values of the unstable asphaltene concentrations on the addition of different precipitants. Even

the oil phase and cause effective deposition to play a crucial role in the laboratory-scale asphaltene deposition studies. Performing such experiments helps in providing a better understanding of the potential deposition risk that can be caused under different operating conditions and driving forces. 5.4. Effect of the Run Time on Asphaltene Deposition. Based on the simulations performed in section 5.3, the effect of the run time on the mass of asphaltene deposited can be investigated. Although the experimental results are available only for a run time of 6 h, the CFD simulation results can be used to analyze the effect of time. This is possible because (kd)pb has been tuned to match the deposited asphaltene mass at both sections of the column, obtained from the experiments. Figure 10 shows the variation of the total mass of asphaltene

Table 8. Comparison of Unstable Asphaltene Concentrations for Tests 1 and 2

test

precipitant

percentage of asphaltene precipitated with 60 vol % precipitant (with respect to total asphaltenes) (%)

1 2

n-pentane n-heptane

69.22 54.38

unstable asphaltene concentration (weight of asphaltenes precipitated/ weight of total asphaltenes) 0.0768 0.0549

though the pressure, temperature, flow rates, and run time are the same in both of these cases, the driving force for precipitation and concentration of the unstable asphaltenes formed as a result of the precipitation are very different, because these values correspond to the precipitant used in each test. These relationships prove to be useful, because they can be extended to study the effect of the concentration of the precipitant added to the oil sample. As the volume percent of precipitant increases, Δδ increases, the driving force toward deposition increases, and hence, the concentration of available asphaltene primary particle increases. This, in turn, has a corresponding effect on the rate at which these asphaltenes further aggregate with each other and deposit. It can accordingly be inferred that, with an increase in the concentration of the precipitant, (kd)pb and the deposition rate correspondingly increase. Hence, the type of precipitant and precipitant/oil ratio used to destabilize the asphaltenes in

Figure 10. Cumulative mass of deposited asphaltenes in the packed bed with respect to run time for tests 1 and 2.

deposited in the packed bed column with respect to time. The cumulative mass of deposited asphaltenes increases with run time because there is a continuous influx of asphaltene primary particles as the oil−precipitant mixture flows into the column, which are available for further aggregation and deposition. It should also be noted that the rate of asphaltene deposition, Rd = (kd)pb(nnT:∇u)pbC, is given by the surface deposition mechanism. It depends upon the deposition kinetic parameter, the velocity gradients, and the asphaltene 5019


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Energy & Fuels concentration in the fluid. Therefore, the mass of asphaltene deposited over each period of time can be different. The rate of deposition also depends upon other competing phenomena taking place in the column, which include the aggregation of asphaltenes, their consequent diffusion toward the spheres, and fluid flow rate. Asphaltene deposition slowly increases initially, and after a certain period, it becomes almost linear with respect to time. Asphaltene primary particles participate in deposition, by diffusing toward the boundary layer by Brownian diffusion and depositing on sphere surfaces by a surface deposition mechanism, for a given residence time. The primary particles can also aggregate with each other. The nanoaggregates that have an average particle size diameter lower than the diameter corresponding to the critical particle size can also undergo deposition. At the same time, there is an influx of fresh primary particles at regular intervals of time. The deposition is further governed by the rates of aggregation and surface deposition, which are occurring simultaneously. The multi-step deposition model introduced in this work facilitates this concept. 5.5. Extension of the Current Deposition Model To Study the Effect of Chemical Dosage. One of the extensively used methods to mitigate asphaltene deposition is chemical injection. Chemicals injected into the oil usually act as chemical dispersants by delaying asphaltene aggregation.30 As asphaltenes represent the most polarizable fraction of crude oil, dispersants are developed to peptize and stabilize these compounds in solution.31 The injection of asphaltene dispersants is expected to prevent the aggregation and deposition of asphaltenes.32 A problem with using chemical dispersants is that the reduction in the sizes of asphaltene aggregates has not been shown to always reduce the overall asphaltene deposition.17 This concern arises because smaller sized particles and aggregates effectively diffuse to the boundary layer and deposit on wall surfaces, increasing the deposition tendency. Nevertheless, the effect of such chemicals on asphaltene deposition has been studied using packed bed column experiments.17 Hence, it is of prime interest to investigate the changes in the values of aggregation and deposition kinetic parameters as a result of the addition of a chemical. This will facilitate in analyzing the effect of chemicals on the deposition mechanism at the laboratory scale and thereby predict its impact on asphaltene deposition taking place in the wellbore. Therefore, extending the current deposition model to study the effect of chemical addition will provide valuable information on how the aggregation and deposition processes are altered. Based on the rates of aggregation and deposition obtained, it will become easier to infer if a given chemical will act just as a dispersant, delaying the aggregation process, or act as an asphaltene inhibitor, reducing further deposition buildup. The current deposition model, introduced in section 3, does not have the feasibility to capture the effect of a chemical dosage on asphaltene deposition but possesses the capability to be extended. The chemical injected into an oil sample may affect two processes: (1) Aggregation: The addition of the chemical may slow the process of aggregation. The average particle size of asphaltene aggregates may increase at a slower rate in the presence of a chemical compared to the aggregation process in the absence of the same chemical with the same dosage. The slower the aggregation rate, the smaller the size of the asphaltene aggregates for an extended time period. This further enhances the rate of diffusion of the asphaltenes toward the surface

boundary layer and results in more asphaltene deposition. The chemical, in this case, would act merely as a dispersant and would not do a good job as an inhibitor. On the other hand, the chemical could increase the rate of aggregation, which results in larger sized aggregates much faster that become easily carried along with the flow as a result of inertia. Here, it could effectively reduce the amount of deposition. (2) Deposition: The injected chemical could interfere with the surface deposition of asphaltenes. It can alter surface− asphaltene interactions, asphaltene−asphaltene interactions, or both. When the chemical interrupts the surface−asphaltene interactions, the rate at which the first asphaltene monolayer is formed on the metallic surface will be affected. Alternatively, if it hinders the interactions between the asphaltenes, then the rate at which further deposition occurs on the deposited asphaltene monolayer will be affected. On the basis of the above discussion, the developed deposition model for the packed bed can be modified to account for the effect of chemical addition and can thus be written as ∂C + (\ ·;∇)C = De∇2 C − K agC 2 − R d ∂t

(8)

R d = (kad)pb (Gu)pb C ,

∀ x , y , z on sphere surface

(9a)

R d = (k bd)pb (Gu)pb C ,

∀ x , y , z elsewhere

(9b)

where Rd is the rate of asphaltene deposition and (kad)pb is the kinetic parameter corresponding to the rate of formation of the first monolayer on the surface of the spheres. We will refer to this adsorption kinetic parameter in this work. (kbd)pb is the kinetic parameter corresponding to the rate of deposition buildup after the first monolayer on the surface of the spheres. If the chemical affects the surface−asphaltene interaction, then the value of (kad)pb will be affected, whereas if the chemical affects the interactions between the asphaltenes, the value of (kbd)pb will be affected. Irrespective of how the chemical affects (kad)pb and (kbd)pb, it might affect Kag, which is the aggregation kinetic parameter. This extension of the original model illustrated in section 3 does not increase the number of degrees of freedom. The rate of asphaltene deposition shown in eq 9 is not a boundary condition, rather eq 9a is used for all of the finite element mesh points on the sphere surfaces. This forms a representative of the first monolayer of asphaltenes adsorbed on the sphere surfaces. Equation 9b is used for all finite element mesh points that are elsewhere in the fluid domain, where the asphaltene deposit could further build up on the asphaltene monolayer. This simulation has only been made possible due to the implementation of the CFD simulation based on FEM to study such systems. This is a unique contribution of this work to study the mechanism of asphaltene deposition. Equation 8 will be solved using the boundary conditions in eq 4 after the fluid flow simulation is performed using eqs 1 and 2. The solution technique discussed in section 4 will be employed. (kad)pb and (kbd)pb will be calibrated with respect to the cumulative mass of deposited asphaltenes, obtained from the deposition experiments. It will also be made sure during the CFD simulation that the mass of deposited asphaltene with respect to run time passes through the deposition lag time, tΔP.17 In this work, it is defined as the time at which any first visible pressure drop is measured using the pressure transducers in the experimental setup. This adds another constraint 5020


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asphaltene−asphaltene interactions and lowers the risk of further asphaltene deposition buildup. Case 3: Here, the value of Kag is lower than the baseline case, and hence, there is a decrease in the rate of aggregation. The chemical acts as a dispersant and delays the aggregation process, resulting in more diffusion of asphaltenes toward the boundary layer of the spheres and deposition on their surfaces. This is seen in increased values of (kad)pb and (kbd)pb compared to the baseline case, which has resulted in an increased amount of asphaltene deposition, and this can be seen in Figure 11. (kad)pb = (kbd)pb; therefore, the chemical is not affecting the surface−asphaltene interactions or further asphaltene deposition. Case 4: Similar to case 3, the value of Kag is lower than the baseline case, resulting in slowing the aggregation rate. The expected result would be an increase in the amount of deposition due to the presence of smaller aggregates initially, which would diffuse toward the surface boundary layer and participate in the deposition process. However, it is seen that (kad)pb is much lower here compared to the baseline case, indicating that the chemical is affecting the surface−asphaltene interactions. However, (kbd)pb > (kad)pb, indicating an increased deposit buildup later. The nature in which the interactions between the asphaltenes are affected and that with the surface are not the same. The chemical, in this case, does act as a dispersant but does not increase the total amount of deposition to an extent as seen in case 3. As more experimental data become available, the asphaltene deposition process in the presence of a chemical can be modeled using eq 8 shown in this work and the corresponding effect can be investigated. Once, the kinetic parameters are calibrated with respect to the experimental results, the sensitivity analysis shown can be used to analyze the effectiveness of the chemical injected and understand its wholesome effect on asphaltene deposition.

to the calibration technique, when we tune the (kad)pb and (kd)pb kinetic parameters with respect to experimental data. To illustrate the application of eq 8 to study the effect of chemical dosage on asphaltene deposition, the operating conditions and results for test 1, shown in Tables 3, 4, 6, and 8, will be used. Different values of the kinetic parameters will be assumed, and sensitivity analysis will be performed. Such a sensitivity study would help in obtaining a better understanding of the modified deposition model. The scenarios considered for this analysis are shown in Table 9. The CFD simulation results for all of the cases considered in Table 9 are shown in Figure 11 for comparison. Table 9. Scenarios Considered To Illustrate the Applicability of the Extended Deposition Model To Analyze the Effect of Chemical Addition case

tΔP (h)

1 2 3 4

2.3 4 1.5 3

aggregation kinetic parameter, Kag (s−1) 5.0 6.5 5.0 1.0

× × × ×

10−6 10−5 10−7 10−6

adsorption kinetic parameter, (kad)pb 1.5 8.0 7.5 6.0

× × × ×

10−4 10−5 10−4 10−5

deposition kinetic parameter, (kbd)pb 1.5 6.0 7.5 4.5

× × × ×

10−4 10−5 10−4 10−4

6. CONCLUSION A CFD model to simulate asphaltene deposition in a packed bed column setup has been introduced in this work. The mass of asphaltene deposited due to the injection of a precipitant into an oil sample has been successfully calculated by employing a multi-step mechanism that includes convection, diffusion, aggregation, and deposition. Three-dimensional transient CFD simulations based on the FEM have been performed to explore the asphaltene deposition profiles at different cross sections and column heights. To perform FEM calculations, the methodology adopted for the construction of required geometry, mesh generation, fluid flow, and deposition simulation has been discussed in detail. The effects of the type of precipitant, precipitant concentration, driving force toward deposition, and run time have been extensively investigated. Calibrations performed with respect to experimental data and, hence, the value of the obtained deposition kinetic parameter provide useful information about the rate of deposition process taking place. It is seen that the higher the concentration of unstable asphaltene primary particles, the higher the driving force for deposition, the value of the deposition kinetic parameter, and the consequent rate of deposition. The overall mass of deposited asphaltene in the column increases with an increase in run time for a given flow rate. The current deposition model has also been extended to study the effect of chemical dosage on asphaltene deposition. A change in the values of new kinetic

Figure 11. CFD simulation results showing the variation of cumulative mass of asphaltene deposited in a packed bed column with respect to run time for the cases shown in Table 9, to illustrate the effect of chemical addition.

Case 1: This is corresponding to test 1 discussed in sections 5.1 and 5.2. This does not contain any chemical, and here, (kad)pb = (kbd)pb. The interactions between the asphaltenes and with the surface are not affected. This case will be considered as the baseline for this sensitivity study. Case 2: Here, the value of Kag is higher than the baseline case, and hence, there is an increase in the rate of aggregation. This causes the formation of larger asphaltene aggregates sooner and reduces its diffusion toward the boundary layer of the spheres. A consequent decline in the amount of deposition is seen in Figure 11. The values of (kad)pb and (kbd)pb are also lower compared to the baseline case, indicating the reduction in the rate of deposition. Hence, the chemical here acts as an inhibitor. From the values of the kinetic parameters, it is also seen that (kbd)pb < (kad)pb. The inhibitor disturbs the 5021


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parameters introduced in the modified deposition model, on the addition of a chemical to an oil sample, translates to the effect of the chemical on the aggregation rate, formation of the first monolayer, and further rate of deposition. The model developed to study the process of deposition in a packed bed can be extended to predict deposition in pipelines and flowlines under real field conditions. The model parameters, calibrated with respect to experimental data, can be scaled to simulate deposition in the wellbore by establishing a correlation such that the deposition taking place in the boundary layer of the wellbore is similar to that in the packed bed column. Using the deposition model outlined in this work, precipitation, aggregation, and deposition of asphaltenes can be simulated simultaneously by employing a multi-compartment approximation of the flow field.

■

μ = viscosity of the mixture δmix = solubility parameter of the fluid mixture δonset = solubility parameter of the oil−precipitant mixture at its onset of precipitation ρ = density of the mixture σ = shear stress ϕ = void fraction ψ = dimensionless pressure drop Acronyms

APD = absolute percentage deviation BDF = backward differentiation formula BiCGSTAB = biconjugate gradient stabilized method CFD = computational fluid dynamics EOR = enhanced oil recovery EOS = equation of state FEM = finite element method HPHT = high pressure and high temperature HPLC = high-performance liquid chromatography OSDC = organic solid deposition and control device PBM = population balance modeling PC-SAFT = perturbed chain statistical associating fluid theory PTFE = polytetrafluoroethylene PVT = pressure−volume−temperature

AUTHOR INFORMATION

Corresponding Author

*Telephone: +1-713-348-2384. E-mail: [email protected]. ORCID

Narmadha Rajan Babu: 0000-0002-1289-4617 Francisco M. Vargas: 0000-0001-5686-5140 Notes

The authors declare no competing financial interest.

■

■

ACKNOWLEDGMENTS The authors acknowledge Chevron Energy Technology Company for the generous financial support.

■

REFERENCES

(1) Panuganti, S. R.; Vargas, F. M.; Gonzalez, D. L.; Kurup, A. S.; Chapman, W. G. PC-SAFT Characterization of Crude Oils and Modeling of Asphaltene Phase Behavior. Fuel 2012, 93, 658−669. (2) Vargas, F. M.; Creek, J. L.; Chapman, W. G. On the Development of an Asphaltene Deposition Simulator. Energy Fuels 2010, 24 (4), 2294−2299. (3) Eskin, D.; Ratulowski, J.; Akbarzadeh, K.; Pan, S. Modelling Asphaltene Deposition in Turbulent Pipeline Flows. Can. J. Chem. Eng. 2011, 89 (3), 421−441. (4) Gonzalez, D. L.; Ting, P. D.; Hirasaki, G. J.; Chapman, W. G. Prediction of Asphaltene Instability under Gas Injection with the PCSAFT Equation of State. Energy Fuels 2005, 19 (4), 1230−1234. (5) Vargas, F. M.; Gonzalez, D. L.; Hirasaki, G. J.; Chapman, W. G. Modeling Asphaltene Phase Behavior in Crude Oil Systems Using the Perturbed Chain Form of the Statistical Associating Fluid Theory (PC-SAFT) Equation of State. Energy Fuels 2009, 23 (3), 1140−1146. (6) Akbarzadeh, K.; Hammami, A.; Kharrat, A.; Zhang, D.; Allenson, S.; Creek, J. L.; Kabir, C. S.; Jamaluddin, A. K. M.; Marshall, A. G.; Rodgers, R. P.; Mullins, O. C.; Solbakken, T. Asphaltenes Problematic but Rich in Potential. Oilfield Rev. 2007, 19 (2), 22−43. (7) Akbarzadeh, K.; Eskin, D.; Ratulowski, J.; Taylor, S. Asphaltene Deposition Measurement and Modeling for Flow Assurance of Tubings and Flow Lines. Energy Fuels 2012, 26 (1), 495−510. (8) Juyal, P.; McKenna, A. M.; Fan, T.; Cao, T.; Rueda-Velásquez, R. I.; Fitzsimmons, J. E.; Yen, A.; Rodgers, R. P.; Wang, J.; Buckley, J. S.; Gray, M. R.; Allenson, S. J.; Creek, J. Joint Industrial Case Study for Asphaltene Deposition. Energy Fuels 2013, 27 (4), 1899−1908. (9) Ghahfarokhi, A. K.; Kor, P.; Kharrat, R.; Soulgani, B. S. Characterization of Asphaltene Deposition Process in Flow Loop Apparatus; An Experimental Investigation and Modeling Approach. J. Pet. Sci. Eng. 2017, 151, 330−340. (10) Broseta, D.; Robin, M.; Savvidis, T.; Féjean, C.; Durandeau, M.; Zhou, H. Detection of Asphaltene Deposition by Capillary Flow Measurements. Proceedings of the SPE/DOE Improved Oil Recovery Symposium: Tulsa, OK, April 3−5, 2000; DOI: 10.2118/59294-MS. (11) Wang, J.; Buckley, J. S.; Creek, J. L. Asphaltene Deposition on Metallic Surfaces. J. Dispersion Sci. Technol. 2004, 25 (3), 287−298. (12) Kurup, A. S.; Vargas, F. M.; Wang, J.; Buckley, J. S.; Creek, J. L.; Subramani, J.; Chapman, W. G. Development and Application of an

NOMENCLATURE

Symbols

Co = total concentration of asphaltenes in the oil sample C = dimensionless concentration of the asphaltene primary particle Cin = dimensionless concentration of asphaltene primary particles at the packed bed column inlet De = asphaltene particle diffusivity/diffusion coefficient dp = sphere size gz = acceleration due to gravity Kag = kagCo = aggregation kinetic parameter (kd)pb = packed bed deposition kinetic parameter (kad)pb = kinetic parameter corresponding to the rate of formation of the first monolayer (kbd)pb = kinetic parameter corresponding to the rate of deposition after the first monolayer L = axial length of the packed bed column md = mass of the deposited asphaltene N = refractive index of a component n = unit normal vector nT = transpose of the unit normal vector p = pressure ΔP = pressure drop across the column U = superficial velocity of the fluid u = velocity field uin = inlet velocity vi = volume fraction Rd = rate of asphaltene deposition Rep = particle Reynolds number for the packed bed column [ρUdp/μ(1 − ϕ)] t = time (or run time) 5022


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Modeling of Asphaltene Deposition in a Packed Bed Column | Energy

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