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Hybrid Modeling of the Electrocoalescence Process in Water-in-Oil Emulsions Ali Khajehesamedini, Thiago Anzai, Carlos Alberto Castor, Márcio Nele, and José Carlos Pinto Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03602 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 1, 2018

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Hybrid Modeling of the Electrocoalescence Process in Water-in-Oil Emulsions

Ali Khajehesamedini, Thiago K. Anzai1, Carlos Alberto Castor Jr., Márcio Nele2, José Carlos Pinto

Programa de Engenharia Química / COPPE Universidade Federal do Rio de Janeiro Cidade Universitária - CP: 68502 Rio de Janeiro, 21941-972 RJ, Brazil

Abstract A hybrid model based on the population balance approach was developed to represent the electrocoalescence phenomena in water-in-oil emulsions. A semi-empirical aggregation model was used in a population balance equation to simulate the dehydration of two different crude oils. The unknown parameters of the population balance equation were estimated using experimental data. The experiments were performed in a continuous pilot plant used to evaluate the dehydration of crude oil emulsions with initial 4-10wt% of water. Different functional forms for the specific rate of coalescence and sink term of the population balance equation were evaluated. The results of the proposed hybrid model were compared with the experimental data and previous empirical models reported in the literature. The results showed good agreement with the experimental data and values obtained by empirical models.

Keywords Electrocoalescence, dehydration, oil, water-in-oil emulsion, population balance, hybrid model

1

Current address - Petrobras Research and Development Center (CENPES) Av. Horacio Macedo, 950 - Ilha do Fundão, Rio de Janeiro-RJ, Brasil 21941915, + 55 21 38652441 2 Corresponding author, Tel: +55-21-39388337, FAX: +55-21-39388300, [email protected]

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Hybrid Modeling of the Electrocoalescence Process in Water-in-Oil Emulsions

Ali Khajehesamedini, Thiago K. Anzai1, Carlos Alberto Castor Jr., Márcio Nele2, José Carlos Pinto

Programa de Engenharia Química / COPPE Universidade Federal do Rio de Janeiro Cidade Universitária - CP: 68502 Rio de Janeiro, 21941-972 RJ, Brazil

1. Introduction Throughout the useful life of an oil well, water and gas are co-produced along with oil. The mixture passes through the rocky formation of the reservoir, flows up the production column and goes to the stationary production units. Throughout this journey, the mixture is subjected to intense turbulence, which provides sufficient energy for water dispersion in the oil, forming water-in-oil (W/O) emulsions as a consequence [1,2]. The presence of W/O emulsion causes corrosion in the lines, pumps and equipment and extra costs associated with transportation, pumping and heating, among others [3,4]. Various techniques, including demulsifier addition, pH adjustments, gravitational or centrifugal sedimentation, filtration, heating and electrical field application, have been proposed for promoting the breakdown of W/O type emulsions [5]. However, regarding the energy efficiency and equipment volume, electrocoalescence is considered the best technique for breaking W/O emulsions [6]. In order to improve the understanding about desalination/dehydration processes and select the best operational parameters, attempts have been made to model the process. Oliveira et al. [7] proposed an empirical model based on experimental data obtained from a pilot electrostatic

1

Current address - Petrobras Research and Development Center (CENPES) Av. Horacio Macedo, 950 - Ilha do Fundão, Rio de Janeiro-RJ, Brasil 21941915, + 55 21 38652441 2 Corresponding author, Tel: +55-21-39388337, FAX: +55-21-39388300, [email protected]


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treatment plant of PETROBRAS S.A., containing three adjustable parameters that depended on the analyzed oil. The proposed equation had the form:

BS & WO = ( A +

B.K p tR

).Ee C

(1)

where BS &WO is the water content at the outlet of the electrocoalescer and A, B and C are the oil-dependent parameters. In their study, the effects of the inlet volumetric liquid flow ( QI , L ), the cross-sectional area to the flow ( AC ) and the electrodes spacing ( Le ) were grouped into a single term tR (Equation 2), which accounts for the residence time of the flow in the region between the electrodes. Similarly, the electrical field imposed between the electrodes Ee (Equation 3) represents the gradient of potential ( Ve ). The term K p (Equation 4) encompasses the effects of specific mass differences between water and oil and the viscosity of the continuous phase. The following equations show the calculations for these three additional terms.

tR =

AC .Le QL , I

(2)

Ee =

Ve Le

(3)

Kp =

µo

(4)

( ρw − ρ o )

Oliveira et al. [7] evaluated oils in the range of 19.8 to 28.7º API and obtained fits with correlation coefficients above 0.90 in all cases. The authors concluded that the inlet BS&W, in the range between 5wt% to 20wt%, exerted a negligible influence on the treatment performance, which may raise questions regarding the validity of the proposed model. Coutinho [8] expanded the data used by Oliveira [7] from 133 to 220 experimental points and proposed a new empirical model, which also considered the emulsion composition. The effect of the composition on the stability was accounted for by the asphaltene content, according to Equation 5:


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BS & WO = ( A + B.log( K p ) + D.log(t R )).( Ee .Le )

( C0 + C1 .C Asphaltene )

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(5)

where the term CAsphaltenes represents the content of the n-heptane insoluble fraction (asphaltenes) present in the oil. Cunha [9] carried out new experiments in the same pilot plant, adding new 68 experimental points to the data set. The analysis of these results led the author to propose the model presented in Equation 6:

BS & WO = A

µOB .E e E C D ( ρ w − ρ o ) .t R

(6)

The results obtained with the five-parameter model were very close to the experimental ones, capturing well the observed patterns. The obtained correlation coefficient for the new 68 experiments was close to 0.83. Other empirical and semi-empirical models have also been developed to predict the behavior of the desalination process [10,11,12,13]. In spite of that, although empirical modeling has achieved some success in describing the dehydration of water-in-oil emulsions by electrocoalescence, the development of first-principle models is desirable. Two basic phenomenological approaches have been proposed for modeling of particle coalescence, based on physical reasoning: 1. Interface tracking: based on analyses of the interfacial phenomena that take place between the layers placed around the particles and that lead to coalescence; 2. Population balance: based on balances of countable objects that present distributed properties, used to describe how distributions evolve during coalescence. The coalescence of two droplets under the effect of an electrical field is commonly accepted to take place in four steps: (i) droplet approach, (ii) film drainage, (iii) film rupture and (iv) coalescence [14]. The application of an electrical field to an individual droplet, polarizes the uncharged droplet, so that it can be considered as a dipole. The proper alignment of the dipolar interaction between neighboring droplets, experiences attractive forces that move them closer. As two droplets approach together, the medium fluid is squeezed out from between the leading faces, resulting in film thinning. Shape deformation is the instantaneous effect observed on the


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droplet after application of an electrical field [15,16,17]. The deformation of droplets can lead to their contact and coalescence, even when they are initially held stationary [6,18]. Although there are several modeling studies addressing different fundamental aspects of electrocoalescence of two water droplets dispersed in crude oil, there is still a huge gap between experimental and modeling studies [19]. In certain aspects, modeling is still in its very primary steps even when one analyzes the coalescence of two droplets. Besides, the assumptions usually made to allow for tracking of the interfaces are so controversial that overshadow the trustworthy of the problem, when compared to the practical cases of industrial interest [20]. Finally, in order to simulate a practical electrocoalescence process, which is, in fact, the interaction of a whole population of droplets, interface tracking does not seem to be sufficient. A convenient way to model particulate systems is based on population balance equations (PBE), which have been used to model a wide range of dispersed phase systems, such as bioreactors, fluidized bed and dispersed phase reactors, liquid-liquid extraction, solid-liquid leaching [21,22,23,24,25,26,27,28]. The accuracy of the population balance approach relies on the adequacy of the employed particle-particle interaction models, which are not generally applicable and depend on adjustable parameters that usually depend on the characteristics of the multiphase system, which needs be determined with experimental data [29,30,31]. Coalescence is considered as the main particle–particle phenomenon taking place during the electrostatic coalescence of water droplets [32]. Meidanshahi et al. [33] used population balance approach to model a pilot plant of electrostatic desalting drum at steady state condition. The authors considered an arbitrary inlet size distribution for water droplets to calculate the droplet size distribution at the outlet of the drum. In the work of Meidanshahi [33] and in other similar studies [34,35], the aggregation frequency was calculated based on the model proposed by Zhang et al. [36]. However, the parameters of this aggregation frequency are not sufficiently studied for different types of crude oil. For this reason, in the present work, a hybrid approach is considered to determine the aggregation parameters required by the model proposed by Zhang [36]. A second important process that happens simultaneously with coalescence in electrostatic treaters of crude oil is sedimentation of droplets. Sedimentation has not been sufficiently studied in comparison to coalescence in most of the researches related to the modeling of electrocoalescence [37]. The higher density of water droplets, when compared to oil density, drives the sedimentation phenomenon. When a sufficient number of sedimented water droplets


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gather together, a second phase is created in the bottom of the vessel. Gravitational sedimentation is normally limited to relatively large size droplets. The rate of sedimentation for small particles is too low to allow practical separation. Moreover, the Brownian motion of small droplets is too large for effective settling. Very small droplets (< 0.1 µm) do not settle, unless they are extremely dense [38]. Sedimentation under the effect of an electrical field extends the amount of removed water, as many of the small droplets coalesce to form bigger droplets. Meidanshahi [33], Aryafard [34] and Aryafard [35] assumed that sedimentation happens at reasonable rates when droplet sizes are equal to or larger than 20 µm. This way, these authors assumed that the droplets with diameters that are equal to or larger than 20 µm form the segregated phase. However, when one assumes that a certain size defines the sedimentation limit, the model necessarily cannot be applicable to all kinds of crude oil, as this limit certainly depends on the oil properties. The present work is a continuation of the experimental works carried out by Coutinho [8] and Cunha [9] and intends to propose a phenomenological model based on PBE to predict the behavior of electrocoalescence. The unknown parameters of the model were estimated with the experimental data obtained in a pilot plant used to evaluate the electrostatic treatment of real oils. In order to do that, a new approach is also proposed to address for sedimentation in the PBE model.

2. Material and Methods The experiments were conducted in an electrostatic treatment unit (UPTE) located at the Centro de Pesquisas e Desenvolvimento Leopoldo A. Miguez de Mello (CENPES) of PETROBRAS S.A. The schematic drawing of the pilot plant is shown in Figure 1 [9]. The pilot plant essentially consists of two stirred atmospheric storage tank, two external gear rotary pump and an electrostatic alternating current (AC) treater. A brief explanation about the electrostatic cell is provided in Appendix A. All components are interconnected by properly insulated pipelines and heated by electrical resistance. The fluids leaving the treatment vessel are weighed over time in order to obtain the flows of treated oil and separated water.


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Throughout the experiments used as the basis for the simulations, the water-in-oil emulsions were artificially generated and the tests were conducted as follows: 1. The desired volume of distilled water with pH of 6.5 was added to the volume of dead oil at the specified temperature and the mixture was homogenized with help of a pendulum agitator (Ika, RW 20 digital, Biovera, Rio de Janeiro, Brazil); 2. The emulsion was then prepared under vigorous stirring with help of an Ultra-Turrax dispersing system (Polytron PT3100, Biovera, Rio de Janeiro, Brazil). The stirring time and speed varied according to the experimental point; 3. The droplet size distribution (DSD) of the feed emulsion was then determined by light scattering with the Mastersizer 2000 equipment, equipped with the Hydro S dispersion unit (Malvern, Sao Paulo, Brazil); 4. The Dissolvan 961 demulsifier (DISSOLVAN®, Clariant, Rio de Janeiro, Brazil) was added to the mixture at a concentration of 20 ppm, followed by further homogenization; 5. The emulsified system was then poured into the unit tank, as shown in Figure 1, allowing treatment to begin; 6. The treated oil was submitted to the analysis of the residual water contents. The amount of emulsified water in the oil that the electrostatic treatment was not able to remove, was characterized by standard volumetric titration Karl Fischer equipment (Metrohm, KF Titrando 841, Sao Paulo, Brazil). It should be noted that, due to the low concentration of dispersed phase in the outlet oil, it was not possible to measure the size distribution of the droplets in the final emulsion.


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Figure 1: Schematic drawing of the Electrostatic Treatment Pilot plant [9].

These steps were carried out for all experimental points. The more detailed description of the experimental procedures is provided by Coutinho [8] and Cunha [9]. The experiments evaluated the influence of the following variables on the system performance: 1. Electrical field between the electrodes (Ee); 2. Operating temperature (T); 3. Residence time between electrodes (tr).


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The emulsion residence time in the vessel for these experiments is approximately from 8 to 50min. Table 1 shows the half-factorial experimental design used to perform the experiments in terms of the normalized variables [9]. The actual values were varied for each oil, as shown in Table 1 to 4. The characteristics of the two oils used in the present work, here generally referred to as oils A and B, are shown in Table 2. The results of the dehydration process for the evaluated oils are shown in terms of the outlet mass-based water content (BS&WO) in Table 3 and Table 4.

Table 1: Experimental design Experiment BS&WI 1 -1 2 -1 3 -1 4 -1 5 +1 6 +1 7 +1 8 +1 9 0 10 0 11 0

Ee -1 -1 +1 +1 -1 -1 +1 +1 0 0 0

T -1 +1 -1 +1 -1 +1 -1 +1 0 0 0

Tr -1 +1 +1 -1 +1 -1 -1 +1 0 0 0

Table 2: Characteristics of the evaluated oils. Oil Density ºAPI (ASTM D4052) Kinematic viscosity mm2/s 25°C (ASTM D445) Resins %w/w (Sara Analysis) Asphaltenes %w/w (Sara Analysis) Interfacial tension mN/m (Tensiometer DSA100, Kruss) Conductivity nS/m (ASTM D2624)


A 27.8 20.3 20.7 1.1 15.9 15.9

B 26.7 24.7 16.5 1.8 17.5 17.5

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Table 3: Results of dehydration process for oil A [9]. Experiments BS&WI/% Ee/kV.cm-1 1 4 2.16 2 4 2.16 3 4 3.6 4 4 3.6 5 10 2.16 6 10 2.16 7 10 3.6 8 10 3.6 9 7 2.88 10 7 2.88 11 7 2.88

T /ºC 80 120 80 120 80 120 80 120 90 90 90

Q/L.h-1 5.6 0.93 0.93 5.6 0.93 5.6 5.6 0.93 1.6 1.6 1.6

ρ/g.cm-3 0.842 0.813 0.842 0.813 0.842 0.813 0.842 0.813 0.835 0.835 0.835

µ/P 0.05 0.03 0.03 0.05 0.03 0.05 0.05 0.03 0.04 0.04 0.04

BS&WO/% 1.05 0.53 0.53 0.59 0.79 1.06 0.70 0.47 0.60 0.58 0.63

µ/P 0.07 0.03 0.07 0.03 0.07 0.03 0.07 0.03 0.05 0.05 0.05

BS&WO/% 1.10 0.52 0.72 0.81 0.77 1.35 0.80 0.50 0.70 0.66 0.70

Table 4: Results of dehydration process of oil B [9]. Experiments BS&WI/% Ee/kV.cm-1 1 4 2.16 2 4 2.16 3 4 3.6 4 4 3.6 5 10 2.16 6 10 2.16 7 10 3.6 8 10 3.6 9 7 2.88 10 7 2.88 11 7 2.88

T /ºC 80 120 80 120 80 120 80 120 94 94 94

Q/L.h-1 5.6 0.93 0.93 5.6 0.93 5.6 5.6 0.93 1.6 1.6 1.6

ρ/g.cm-3 0.852 0.824 0.852 0.824 0.852 0.824 0.852 0.824 0.842 0.842 0.842

3. Population Balance Modeling The proposed model is built through the application of the balance equation for a population of droplets. The model proposed the discretization of the variable "droplet diameter" in N classes. It is assumed that droplets in a common class "i" present similar physical and chemical properties and size. Figure 2 represents a typical discretization of the droplet size distribution at the inlet of the electrostatic treater. As one can see in Figure 2, the droplet size distribution of the prepared


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emulsion presents bimodal characteristics. In the present study, all emulsions were found to present similar bimodal characteristics for both oils, independent of the initial water content.

3.5 3.0

Volumetric%

2.5 2.0 1.5 1.0 0.5 0.0 0.80 1.25 1.71 2.16 2.62 3.07 3.52 3.98 4.43 4.88 5.34 5.79 6.25 6.70 7.15 7.61 8.06 8.51 8.97 9.42 9.88 10.33 10.78 11.24 11.69

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Diameter of particles(µm) Figure 2: Typical droplet size distribution of the feed water-in-oil emulsion.

The general differential form of the one dimensional PBE is presented in Equation 7 [39]:

−∇[ud n] + ∇[ Dd ∇n] −

∂ ∂n(V , r , t ) [Gn] + S = ∂V ∂t

(7)

The oil’s upward velocity in an industrial electrostatic treater is usually designed to be around 0.2 cm/sec [33]. The distance between the electrodes depends on the characteristics of crude oil and the required electrical field, and it is usually considered to be in the order of 20 cm. Therefore, the flow is laminar and the Peclet number calculated by Equation 8 would be quite higher than one [33].

Pe =

uch Lch Dd

(8)


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In the present work, it was assumed that: - the diffusion is negligible in comparison to the convection, due to the high value of Peclect number; - there is no mass accumulation in the treater; - the electrostatic treater is homogeneous, so the axial gradients were neglected; - particle breakage is negligible [32]. Therefore, the population balance equation can be described in the form: v ∞ ∂n(v, t ) = ni•,I (v, t ) − ni•,O + 12 ∫ n(v − v′, t )n(v′, t )α (v − v′, v′)dv′ − ∫ n(v, t )n(v′, t )α (v, v′)dv′ − Ccap n(v, t ) 0 0 ∂t (9)

That is solved numerically in the form of Equation 13. The term on the left side of Equation 9 represents the accumulation of the droplets in the system. The first term on the right side of the equality is the inlet flow rate of droplets to the electrostatic cell. The second term on the right side corresponds to the outlet flow rate of droplets, which leaves the system with the oil stream after the dehydration process; that is, the amount of untreated residual water. The fourth term on the right side represents the death of droplets due to aggregation. This term takes into account the coalescence between droplets of size "i" with others of size "j", at a specific rate, leading to "consumption" of the population "i" in the system. Here α is the aggregation frequency and represents the probability per unit time of a pair of droplets of specified states to aggregate. The third term on the right side, in turn, is related to the birth of droplets due to aggregation, as droplets of different sizes may coalesce to form droplets in the size range of class "i". Finally, the last term accounts for droplet sedimentation and creation of the segregated water phase. Introduction of this term is, in fact, an improvement of previous works carried out by Meidanshahi [33], Aryafard [34] and Aryafard [35], which assumed the existence of a droplet sedimentation limit. Ccap is a capture sedimentation coefficient, which is a parameter of the model. In this work, the aggregation frequency was calculated by Equation 10 based on the method suggested by Zhang et al. [36]. The equation combines the effects of electrostatic and gravitational forces on drop collision and coalescence.


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α (di , d j ) = α ij = Kπ (di + d j ) 2 uij(0) eij

(10)

where K is a model parameter. This parameter should be determined with experimental data for the oils under study and subsequently used in the model. di is the characteristic diameter of droplets in class "i", and uij(0) is the relative velocity of two widely separated drops given by Equation 11 [40,41]:

(0) ij

u

2( µˆ + 1) ρ w − ρo di 2 (1 − λ 2 ) g = 3(3µˆ + 2) µo

(11)

eij in Equation 10 is the collision efficiency that describes the effects of the applied electrical field, the hydrodynamic interactions between the continuous and disperse phases and the Van der Waals forces on collision and coalescence of two droplets. Several empirical and semi-empirical equations have been proposed to calculate the efficiency of water droplets aggregation in presence of electrical field [42,36]. The proposed approaches are based on some controversial assumptions that might not be applicable for the real industrial electrostatic treaters. Therefore, the term αij (Equation 10) in the present work is named as the coefficient of aggregation frequency (Ke) and was considered as a parameter to be estimated. The coefficient of aggregation frequency (Ke) and capture sedimentation coefficient ( Ccap ) were both estimated using experimental data. The concentration of dispersed phase in the outlet oil was very low, then it was not feasible to measure the size distribution of the outlet droplets. Therefore, the objective of the parameter estimation procedure was to find the best values for Ke and Ccap that fit the experimental values of outlet BS&W (Table 3 and Table 4) using Equation 9.


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4. Numerical Procedure In order to estimate the parameters of Equation 9, first, the population balance equation should be solved. Among the several numerical procedures that have been developed to solve the population balance equation, this work used the method of classes proposed by Kumar [43]. The method enforces the conservation of number and volume of the particle population, and allows the direct usage of particle size classes defined by the particle size analyzer in the inlet. The sectional moment of the ith class, Ni , including all particles with a volume between vi and vi +1 is defined as:

Ni = ∫

vi +1

vi

n(v)dv

(12)

This class is denoted by the pivot xi = 0.5(vi + vi +1 ) . Based on the experimental data reported by the particle size analyzer (Malvern® Mastersizer 2000), the water droplets had diameters in the

0.1 − 100µ m range. Therefore, the classes vi were determined by a geometric grid defined by

vi+1 / vi = 1.514 , k = 0,..., n , v0 = 5.24 ×10−7 µ m3 (d0 = 0.01µm) considering the droplets as perfect spheres with n=100. Following the procedure proposed by Kumar [43] to Equation 9, leads to the subsequent set of ordinary differential equation:

dN i (t ) = N i•, I − N i•,O + dt

j ≥k

∑

j ,k xi−1 ≤ ( x j + xk ) ≤ xi +1

M 1 (1 − δ j , k )η j ,k ,iα j ,k N j (t ) N k (t ) − N i (t )∑ α i ,k N k (t ) − Ccap N i (t ) 2 k =1

(13) where η j ,k ,i is defined as:

η j , k ,i

 xi +1 − ( x j + xk )  xi +1 − xi  =  ( x j + xk ) − xi −1  xi − xi −1

xi ≤ ( x j + xk ) ≤ xi +1 xi −1 ≤ ( x j + xk ) ≤ xi

(14)


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The first term on the right side of Equation 13 is calculated according to Equation 15:

Ni•, I =

QW , I V%i

(15)

Vi

The volumetric percentage of class "i", V%i , is the proper result of the droplet size distribution (Figure 2). The volumetric flow rate of water is obtained as the ratio between the mass flow and the specific mass of the water, according to Equation 16:

QW , I =

WW , I

(16)

ρW

The corrected water density ρW (in kg/L) at the analyzed treatment temperature T (in K) was calculated according to Equation 17 [44]:

ρW =1− 2.04×10−4 (T − 275.15) − 6.17×10−5 (T − 275.15)1.5

(17)

Similarly, the oil specific mass ρO (in kg/L), measured at 20 °C, was also corrected as [44]:

ρO = ( ρO ,20

2 o

C

− 0.00012(T − 293.15))

(18)

The water mass flow rate WW , I , in turn, was obtained as the product of the inlet water content BS&WI and the mass flow rate of liquid entering the system WW , I :

WW ,I = WL, I .BS &WI

(19)

and Vi represents the volume of the droplets of class "i".


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The second term on the right-hand side of Equation 13 can be calculated as follows:

N i•, O =

Q L ,O N i

(20)

V

where V is the volume of the electrostatic cell (0.785 liter) and QL , S is the volumetric flow rate of liquid exiting the oil line. For this calculation, it is accepted that all oil entering the system leaves the system in the oil stream; meaning that the amount of oil carried by the outlet water stream is negligible. This constitutes a reasonable hypothesis, since the amount of residual oil in the water stream is usually measured in ppm (parts per million) and, given an efficient control of the interface level, is usually fairly small. In the present work, Fortran was used to write the computer codes. The IVPAG routine, contained in the IMSL FORTRAN library, was utilized to solve the system of ODEs of Equation 13. This routine solves the initial value problem based on a multiple step method for integration [45]. In order to evaluate the outlet BS&W calculated by the model, the size distribution must be converted into mass distribution. The droplet mass distribution can be obtained as the product of the volume distribution from the DSD and the specific mass. Therefore, the total mass of water leaving the system from the bottom of the treater can be calculated as:

N

WW ,O, Bottom = Ccap ρw ∑ Nivi

(21)

i =1

According to Equation 21, it can be said that the mass of water leaving the system from the bottom is proportional to the mass of water which is carried out of the system by the oil phase, as calculated with Equation 22:

N

WW ,O ,Oilphase = ρ w ∑ N i vi

(22)

i =1

Subsequently, the mass flow rate of liquid (oil phase) leaving the treater can be calculated as:


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Energy & Fuels

WL,O = WL,I −WW,O,Bottom

(23)

Consequently, the outlet water content in the oil phase (BS&WO), can be calculated as:

BS & WO =

WL , I BS & WI − WW ,O

(24)

WL ,O

4.1. Estimation of Model Parameters The goal was to estimate the coefficient of aggregation frequency (Ke) and capture sedimentation coefficient ( Ccap ) in Equation 9. The objective function used for parameter estimation was the minimization of the quadratic mean of the differences between the experimental and calculated outlet BS&W values, according to Equation 25:

FF =

NE

1

∑N p =1

( BS & WO ,exp, p − BS & WO ,cal , p ) 2

(25)

E

where NE is the number of experimental points and the subscript p indicates the points of the experimental matrix. The ModeFRONTIER® 4.3.0 software of ESTECO Company [46] was used to estimate the parameters contained in the aggregation and sink terms of Equation 9. ModeFRONTIER® is a multi-purpose optimization program developed to facilitate the integration with various CAE (Computer Aided Engineering) tools [46]. In addition, the software comprises numerous algorithms for statistical analyses and post-processing evaluations, which adds greater flexibility to simulations. In the present work, each optimization process was preceded by an initial exploration of the sample space using a Design of Experiments (DOE) strategy. The goal of the DOE is to train the optimization algorithm, that is, to identify the main trends, so that the algorithm can evolve


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 45

smoothly to the desired problem solution [46]. In this study, in particular, the Uniform Latin Hypercube (ULH) method was used for DOE. With this algorithm, 50 points were generated and distributed in the analyzed RNP space, where NP is the number of model parameters, according to a uniform distribution for each variable. The use of the ULH algorithm allows for the definition of an initial population of equally spaced uncorrelated guesses for the estimated coefficients [47]. The genetic algorithm (GA) with surface responses (FMOGA II) was utilized for optimization. The advantage of using GA, which is a stochastic algorithm, over deterministic procedures is its insensitivity to modification of the model structure and of the objective function formulation [48], simplicity for computational implementation [49] and applicability to non-derivable and non-continuous functions. The decisions made in most steps of the genetic algorithm are based on the generation of random numbers. These steps, in a conventional GA, encompass reproduction of the initial population, recombination or crossover, and mutation of individuals [50]. The great advantage in choosing the FMOGA-II algorithm lies on the use of response surfaces to extrapolate the system response, depending on the evaluated variables in a virtual optimization process without the use of the executable program [47]. Hence, it is expected that the search process can become faster, since the number of real simulations tends to decrease [46]. Table 5 summarizes the parameters prescribed for the genetic algorithm model.

Table 5: Parameters of the genetic algorithm. Number of generations

50

Probability of crossover

0.9

Probability of mutation

Automatic

Random number generation seed

0

As one can observe in Table 5, the crossover probability (that is, the recombination of genetic information between two individuals in order to generate a better solution) was equal to 90% during the simulations. The mutation probability can guarantee the diversification of the population, allowing for analyses of new individuals and more efficient sweep of the sample space. In this study, simulations were conducted on an Intel® Core ™ i5-3210M 2.50GHz machine with 4GB of RAM.


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Energy & Fuels

5. Results and Discussions In this study, the experiments were based on a half-factorial experimental design with two levels and three replicates at the central point for the estimation of experimental error (Table 1). An important advantage of using the half-factorial designs is the orthogonality of plans, which makes the independent estimation of variable effects on the response variables possible [51]. Prior to model fitting and parameter estimation, it is important to evaluate the error associated with the experiments. This error was assumed to be uniform and proportional to the standard deviation of triplicates in the central point of the experimental region. Table 6 and 7 show the results of the replicates for oil A and B, respectively, with the sample means and standard deviations of BS&WO. Table 6: Results of replicates of dehydration process for oil A. Experiment BS&WI/% Ee/kV.cm-1 T/ºC 9 7 2.88 90 10 7 2.88 90 11 7 2.88 90

Q/L.h-1 BS&WO/% 1.6 0.60 1.6 0.58 1.6 0.64 0.606 Average 0.0265 Standard deviation

Table 7: Results of replicates of dehydration process for oil B. Experiment BS&WI/% Ee/kV.cm-1 T/ºC 9 7 2.88 90 10 7 2.88 90 11 7 2.88 90

Q/L.h-1 BS&WO/% 1.6 0.69 1.6 0.67 1.6 0.71 0.69 Average 0.0202 Standard deviation

The experimental error associated with the outlet values of BS&W is ± 0.053% w/w for oil A and ± 0.040% w/w for oil B, admitting normal distributed error and 95% of the confidence


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Page 20 of 45

interval, which are both fairly small values. This shows the good quality of the proposed experimental procedures for both oils. Preliminary estimation of the coefficient of aggregation frequency (Ke) and capture sedimentation coefficient ( Ccap ) showed that these parameters are highly correlated. For this reason, due to the mathematical interaction between Ke and Ccap , the capture sedimentation coefficient was assumed to be proportional to the coefficient of aggregation frequency, enclosing various combined effects, such as of viscosity, specific mass of the dispersed and continuous phases, among others: C cap = Cφ .K e

(26)

where Cφ is the new parameter named constant of capture coefficient to be estimated. Several mathematical forms were considered for both Ke and Cφ . It was assumed that Ke and Cφ are functions of the electrical field between the electrodes Ee , operating temperature T and the volumetric flow rate of liquid entering to the treater QL , E , which is proportional to the residence time between the electrodes te . The validity of the models based on different mathematical forms were examined by comparing the calculated and experimental results for Oil A. The best model was then tested to predict the behavior of dehydration process of Oil B. Finally, the performances of model for both oils were compared to those calculated with other empirical ones already discussed in this literature. Table 8 shows the equations used for the coefficient of aggregation frequency (Ke), where "Par" represents the estimation parameters. The model parameters were estimated as exponents to a power in order to avoid negative values for Ke and Cφ . The representation I has only one parameter which is independent of process variables and varies only from oil to oil. The representation II has three parameters (Par1, Par2 and Par3). According to this representation, the aggregation frequency coefficient is considered proportional to the electrical field imposed on the system and inversely proportional to the temperature. The representation III consists of four parameters (Par1, Par2, Par3 and Par4) which include the effects of electrical field, temperature


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and residence time. Similarly, Table 9 shows the representations used for the constant of capture coefficient.

Table 8: Mathematical forms evaluated for the coefficient of aggregation frequency. Representation Coefficient of aggregation frequency (Ke) 10Par1 I 10(Par1 + Par2.Ee + Par3/T) II 10(Par1 + Par2.Ee + Par3/T + Par4/QL,I) III

Table 9: Mathematical forms evaluated for the constant of capture coefficient. Representation Constant of capture coefficient (Cϕ) 10(Par0) I 10(Par5).T II

The representation I for the constant of capture coefficient provides the same constant of proportionality for all the experiments of a given oil. The representation II, however, inserts a behavior that is inversely proportional to the viscosity or, in other words, a behavior proportional to the temperature in the term of capture coefficient. In addition, it is important to note that preliminary tests have shown difficulty in parameter estimation due to the wide range of different orders of magnitude among the parameters. The forms presented in Table 8 and Table 9 are, therefore, an artifice of parameterization of the model to minimize computational difficulties. Moreover, it should be noted that due to the small number of experiments, all of the 11 experimental points were used for regression and no validation with external data was carried out. Several scenarios were tested for parameter estimation. Table 10 shows the matrix of case studies for parameter estimation which address the combination of the different equations for coefficient of aggregation frequency (Ke) and constant of capture coefficient (Cϕ), along with the total number of parameters to be estimated by the model.


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Page 22 of 45

Table 10: Matrix of case studies for parameter estimation of oil A. Case 1 2 3 4

Ke representation I II II III

Cϕ representation I I II II

Number of parameters 2 4 4 5

5.1. Parameter Estimation for Oil A Case 1 considered two constants for the coefficient of aggregation frequency (Ke) and constant of capture coefficient (Cϕ). The main objective of this case was to perform the preliminary analysis of the model and of the numerical implementation, besides the performance of the optimization algorithm. For this purpose, three simulations were performed, changing only the 50 points that configured the initial population of guesses in the sample parameter space. The initial points were scattered in the two-dimensional space in order to retain as much information as possible, with the minimum number of points. This distribution, as already mentioned, was obtained with the ULH algorithm, available in the ModeFRONTIER® program. The first 50 generations of these 50 points were then evaluated, using the FMOGA-II algorithm, totaling 2500 iterations per simulation. Table 11 shows, for three different estimation runs (Estimation 1, 2 and 3), the values of the estimated parameters, with the error defined as the mean square of the difference between and the values of BS&WO estimated by the model and experiments and the confidence interval for the parameters, setting a value of 95% confidence interval in each of the three simulations. As it can be observed, the confidence interval shows a good convergence of the simulation towards the optimal parameter values.


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Energy & Fuels

Table 11: Values of the estimated parameters, error and confidence interval for the repetitions of Case 1. Case Estimation 1 Confidence -95 % Confidence +95 % Par0 33.30 33.21 33.36 Par1 -30.61 -30.67 -30.52 1 Error 0.27 Estimation 2 Confidence -95 % Confidence +95 % Par0 33.55 33.48 33.60 Par1 -30.87 -30.88 -30.70 1 Error 0.27 Estimation 3 Confidence -95 % Confidence +95 % Par0 29.50 29.52 29.59 Par1 -26.63 -26.67 -26.54 1 Error 0.27

A small variation can be observed in the values obtained for the parameters. However, this small difference was expected since the utilized optimization algorithm is stochastic in nature, which means that the numerous decisions made by it, based on random numbers, can lead to slightly different results between one simulation and another [50]. Despite this feature, the results for case 1 showed the good robustness of the selected optimization algorithm and the capacity of the hybrid model to predict the experimental BS&WO values with excellent accuracy. The results of parameter estimation for case 1 along with the experimental values are shown in Figure 3.


Energy & Fuels

Oil A 1.300 Experimental Proposed Model

1.100

Outlet BS&W % w/w

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 45

0.900

0.700

0.500

0.300

0.100 1

2

3

4

5

6

7

8

9

10

11

Experimental Condition

Figure 3: Prediction of the proposed model against experimental data for Case 1

As one can see in Figure 3, the calculated results are fairly close to the experimental data, except for the first four experimental conditions. This indicates that average values of Ke and Cϕ can to some extent represent the behavior of oil dehydration in a continuous pilot plant treater. Furthermore, as one can see in Table 11 the value of capture coefficient is much larger than the aggregation frequency. This indicates that the sink term dominates the calculations, or in fact, the sedimentation is more important than the aggregation in the oil dehydration process. A closer look at the experimental results shows that the water content of the treated oil varies from 1.1 to 0.5%w/w, a very narrow range. Therefore, one can speculate that such a narrow range of dehydration is not suitable for precise parameter estimation, so that deeper investigation of the phenomena is needed to fairly describe the dehydration performance. It is important to observe that the observed model deviations come from the simplified form of the aggregation parameter. For example, the equation proposed for Ke in Case 1 predicts the same value of the aggregation frequency coefficient for experiments with the electrical fields of 3.6 and 2.16


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Energy & Fuels

kV.cm-1, which is not valid. Nevertheless, given the cited limitations, the model fitting obtained were surprisingly good. It is expected that a complete model of the rate and sink terms, which is able to vary according to the imposed experimental conditions, will provide better representativeness of the phenomenon. Case 2 utilizes a three-parameter mathematical form for the coefficient of aggregation frequency corresponding to representation II in Table 8. The first term is an independent constant, the second term is associated with the applied electric field and the third term addresses the process temperature. For the constant of capture coefficient (Cϕ), the same mathematical form as case 1 was used. Table 12 shows the values of estimated parameters, error and confidence intervals for case 2.

Table 12: Values of the estimated parameters, error and confidence interval for Case 2. Case

2

Par0 Par1 Par2 Par3 Error

14.01 -3.42 8.81E-6 15.21 0.280

Confidence -95 % Confidence +95 % 13.83 14.20 -3.52 -3.45 8.58E-6 9.05E-6 15.14 15.99 -

The comparison between the calculated and experimental data for case 2 is shown in Figure 4. It is interesting to notice that, despite the larger number of parameters in the model, the fitting and the error of case 1 and case 2 were comparable. Observing Figure 4, it can be noted that while in case 2 the model deviations from the experimental points decreased in the regions with BS&WI equal to 10% (experiments 5-8) and for the central point (experiments 9-11), the deviations remained high for BS&WI equal to for 4% (experiments 1-4) and they were even slightly higher than those obtained in case 1.


Energy & Fuels


1.100

Outlet BS&W % w/w

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 45

0.900

0.700

0.500

0.300

0.100 1

2

3

4

5

6

7

8

9

10

11


Figure 4: Prediction of the proposed model against experimental data for Case 2.

In case 3, a modification in the form of the capture coefficient was devised to improve the model performance at low water content in the feed. This case uses the same mathematical form of aggregation frequency coefficient proposed in case 2, but modifies the constant of capture coefficient (Cϕ) to include the effect of temperature. Considering the Stokes equation for sedimentation velocity [52] ( Vs = 2( ρw − ρo ) gd 2 9µo ) and its inverse relation with viscosity, the Cϕ is assumed to be a linear function of the operating temperature. The results of parameter estimation, associated error and confidence intervals for case 3 are presented in Table 13.


Page 27 of 45

Table 13: Values of the estimated parameters, error and confidence interval for Case 3 Case

3

Confidence -95 % Confidence +95 % 11.94 12.52

Par5

12.39

Par1

-4.98

-5.11

-5.02

Par2

2.15E-4

2.1E-4

2.06E-4

Par3

-165.67

-167.02

-159.51

Error

0.280

-

-

Comparing case 3 with cases 1 and 2, it can be seen that the mean square error has remained practically constant. Moreover, no significant gains were observed in relation to the case evaluated with only two parameters, as shown in Figure 5.


1.100

Outlet BS&W % w/w

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.900

0.700

0.500

0.300

0.100 1

2

3

4

5

6

7

8

9

10




11

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Similar to cases 1 and 2, the largest differences between the calculated and experimental data were observed at points with the lowest values of BS&WI, as shown in the highlighted region of Figure 5. In fact, in all of the cases, the model has predicted a greater amount of dehydration than what it was observed. In other words, the simulation has overestimated the efficiency of dehydration process for experimental point with low values of BS&WI. The low inlet water content refers to a sparse population of droplets with large average distance in between, which can hamper the frequency of collision and consequently the coalescence. It is possible to speculate that different phenomena are relevant for low and high water content electrocoalescence treatment, and a more detailed model should be used in this case. According to Alves [53], a minimum value of 5% for BS&WI should be adopted in practice for high-speed AC type treaters in order to avoid the reduction of equipment efficiency, as observed in experiments with low values of inlet water content. The other point which is observed in Figure 5 is the difference between the experimental and predicted values for point 6. Therefore, it seems valuable to study the trends between the experimental points of 5 and 6, and 5 and 7. The increase of flow rate from 0.93 L/h to 5.6 L/h was not handled by the increase of temperature from 80 °C to 120 °C between the experiments 5 and 6 which led to an increase in BS&WO from 0.794% to 1.058%. However, the increase of electrical field between the electrodes was compensated by the increase of flow rate between points 5 and 7 which resulted in a small reduction in BS&WO. This comparison shows the effect of residence time on the model parameters. Consequently, due to the importance of residence time for electrocoalescence and since the spacing between electrodes remained constant (1inch) during the experiments, it was decided to include the effect of feed rate on the coefficient of aggregation frequency. In case 4, a new term was added to the mathematical equation of aggregation frequency coefficient to consider the effect of feed rate (QL,E) and the same equation as in case 3 was considered for capture coefficient constant. The objective of this case was to evaluate whether a larger number of parameters would be able to capture the effects of all operating variables particularly in low values of BS&WI. Table 14 shows the results of parameter estimation for case 4.


Page 28 of 45

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Energy & Fuels

Table 14: Values of the estimated parameters, error and confidence interval for Case 4.

Case

4

Par5 Par1 Par2 Par3 Par4 Error

17.24 -15.97 7.29E-5 -849.486 2.68 0. 176

Confidence -95 % Confidence +95 % 17.19 17.32 -16.07 -15.92 6.88E-5 7.56E-5 -856.25 -848.61 2.60 2.67 -

As one can observe in Table 14, the simulation presented an evident improvement in comparison to the previous models. Also, the trends of the experiments were well captured by the model as shown in Figure 6. In fact, by adding the effect of flow rate to aggregation frequency coefficient, the model was able to predict the greater influence of flow rate increase over the temperature rise between points 5 and 6, as well as the influence of the electrical field increase on the flow rate rise between points 5 and 7 in the experiments matrix.


Energy & Fuels


1.300

Outlet BS&W % w/w

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 45

1.100

0.900

0.700

0.500

0.300

0.100 1

2

3

4

5

6

7

8

9

10

11



The biggest associated errors were once again concentrated on the first four points, where the BS&WI has the lowest value. Although the model managed to capture the behavior of the experimental points with good precision, it is remarkable that the model was found to be overestimating the efficiency of dehydration in these four points. In all cases, the distance between the calculated and experimental data suggests the need for an additional term to account for the behavior of diluted water-in-oil emulsions. However, the general evaluation of the model to predict the values of BS&WO and capture patterns of experimental data can be considered to be good. Given the good performance of this representation for the coefficient of aggregation frequency and constant of sink term using five parameters, these mathematical forms were adopted to predict the behavior of dehydration process of oil B.


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Energy & Fuels

5.2. Parameter Estimation for Oil B The five-parameter model used in case 4 was evaluated for oil B. As one can observe in Table 2, oil B is heavier and more viscous than oil A, with a slightly higher content of asphaltenes in addition to a lower amount of resins in its composition. The effect of these characteristics is evidenced by the amount of the oil’s dehydration. At the same operating conditions, the BS&WO of oil B was usually higher than that of oil A. It is also worth to mention, that the trends of experimental data between points 5 and 6, and between points 5 and 7 which were fundamental for the development of the hybrid model, is also present for oil B. Analogous to case 4, case 5 corresponds to the parameter estimation using all of the available experimental points for oil B. Table 15 shows the values of estimated parameters, error and parameter confidence intervals for this case.

Table 15: Values of the estimated parameters, error and confidence interval for Case 5. Case

5

Confidence -95 % Confidence +95 % 17.78 17.84

Par0

18.01

Par1

-17.98

-18.10

-17.61

Par2

1.29E-3

1.33E-3

1.37E-3

Par3

-390.36

-435.39

-402.73

Par4

1.38

1.28

1.41

Error

0.289

-

-

As shown in Figure 7, which portrays the comparison between calculated and experimental data for case 5, the model was able to predict the trend of experimental points. However, in this case, the deviation of calculated points from the experimental ones was more evident than the equivalent case for oil A.


Energy & Fuels

Oil B 1.3 Experimental Proposed Model

1.1

Outlet BS&W % w/w

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 45

0.9

0.7

0.5

0.3

0.1 1

2

3

4

5

6

7

8

9

10

11



In addition to the performance analysis of the proposed model to predict the trends of experiments, hybrid modeling also provides the possibility of better understanding of the phenomena associated with the dehydration process. Table 16 shows the pooled results of Tables 14 and 15 for comparison of the estimated parameters of oils A and B. Table 17 shows the range/value of composing terms of the mathematical form of the aggregation frequency coefficient (representation III in Table 8) in the eleven experimental points.


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Energy & Fuels

Table 16: Comparative results between the estimated parameters for oils A and B for Case 4. Oil Case

Par0

Par1

Par2

Par3

Par4

Error

A

4

17.24 -15.97 7.29E-5 -849.486

2.68

0. 176

B

5

18.01 -17.98 1.29E-3

1.384

0.291

-390.36

Table 17: Terms of mathematical form of aggregation frequency coefficient (Ke) for oils A and B in Cases 4. Oil

Independent term (Par1)

A

-15.97

Electrical field term (Par2×Ee) 0.158 to 0.262

B

-17.98

2.783 to 4.634

Temperature term (Par3/T)

Flow rate term (Par4/QL,E)

-2.407 to -2.162

0.479 to 2.883

-0.993 to -1.105

0.247 to 1.488

As it can be expected from the first estimation, where a single parameter was able to capture a significant part of the experimental trend, the terms of independent, temperature and flow rate remained in the same order of magnitude between oils A and B, nevertheless the independent term has the largest value. Furthermore, the term relative to the electrical field has undergone a substantial modification between oils A and B. This factor shows the greater influence of this variable on the coalescence rate of droplets for oil B than oil A, although both oils have similar electrical conductivity. The relative importance of electrical field on the two oils may suggest that the oil properties exert a pronounced effect on its response to the modifications of the field, which is not systematically well studied in the literature.

5.3. Comparison to Empirical Models Using the results obtained for oils A and B, an analysis was performed to compare the performance of the proposed hybrid model with the empirical models of Oliveira [7], Coutinho [8] and Cunha [9] to predict the efficiency of the dehydration process. It is important to state that the developed model in this work was based, approximately, on the same variables’ domain of the other empirical models. Table 18 and Table 19 show the values of BS&WO obtained by the


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

empirical models and by the proposed hybrid model with the experimental data for oils A and B, respectively.

Table 18: Calculated and experimental values of BS&WO for oil A Oil Experiment Experimental

A

1 2 3 4 5 6 7 8 9 10 11

1.05 0.53 0.53 0.60 0.79 1.06 0.70 0.47 0.60 0.58 0.64

Error Maximum deviation

Oliveira Coutinho Cunha Proposed [7] [8] [9] Model 1.31 0.87 1.38 0.69 0.28 0.45 0.58 0.30 0.21 0.31 0.38 0.30 0.93 0.58 0.88 0.46 0.28 0.46 0.58 0.79 1.27 0.87 1.37 1.33 0.96 0.59 0.89 0.76 0.20 0.30 0.37 0.47 0.37 0.51 0.60 0.57 0.37 0.51 0.60 0.56 0.37 0.51 0.60 0.57 0.295 0.169 0.191 0.18 -0.51 -0.34 0.32 -0.38


Page 34 of 45

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Energy & Fuels

Table 19: Calculated and experimental values of BS&WO for oil B Oil Experiment Experimental 1 2 3 4 5 6 7 8 9 10 11

1.10 0.52 0.72 0.81 0.77 1.35 0.80 0.50 0.69 0.67 0.71

Error Maximum deviation

Oliveira Coutinho Cunha Proposed [7] [8] [9] Model 1.26 0.93 1.52 0.42 0.52 0.50 0.63 0.40 0.44 0.45 0.46 0.40 0.61 0.52 0.87 0.41 0.59 0.67 0.71 1.07 0.82 0.77 1.35 1.07 0.94 0.63 0.98 0.94 0.39 0.34 0.41 0.43 0.52 0.54 0.66 0.73 0.52 0.54 0.66 0.73 0.52 0.54 0.66 0.73 0.23 0.25 0.17 0.29 -0.53 -0.58 0.42 -0.68

As one can see, the empirical models were able to appropriately predict the experimental data and capture the experimental trends, with the exception of some points with low values of BS&WI where the highest deviations of empirical models from the experimental data were found. The proposed hybrid model had similar performance in predicting the experimental results; however, unlike the empirical approach [7,8,9], where the estimated parameters are only fitting terms, in the hybrid model they effectively represent the rate at which the coalescence of the droplets occurs. It is also interesting to note the discrepancy at point 6 for oil A, where the calculated values of BS&WO by the empirical models were well below the experimental one and the behavior was not captured by any of the equations, unlike the proposed hybrid model, where the effects were consistent with the experiments (Figure 6). For oil B, among the empirical models, the correlation of Cunha [9] was able to predict the outlet water content in oil phase marginally better. As shown in Table 19, the hybrid model was able to provide a good representation of the dehydration of oil B, comparable to the empirical models. The differences between the values calculated by the model and the experimental data were more accentuated for oil B. This difficulty in capturing the behavior of dehydration of oil B can be associated with the composition of the oil. It gives the idea that there exists a systematic


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difference between the behaviors of different oils in dehydration. This difference results from the interactions of physical, chemical and electrical properties of oil which are not yet captured by existing models. For example, the influence of electrical field on the natural demulsifiers present in crude oil and the interdroplet forces between the droplets coalescing together is still not clear. Also, it seems that the effect of water contents must be explicitly considered in the models. Different values of BS&WI may cause different fluid flow regimes [9], which can influence the efficiency of electrocoalescence. In the proposed hybrid model, the effect of water content is implicit, as it results in the number of aqueous particles suspended in the treating medium. However, it appears fundamental to mention that the rate of coalescence also depends on the BS&WI, particularly when the water content is low.

6. Conclusion This work presented an experimental and theoretical study on the dehydration of crude oils by electrocoalescence. A hybrid model based on population balance equation coupled with a semiempirical aggregation frequency equation was developed to fit the experimental data. The proposed model, in addition to capturing the effects of electrocoalescence, also accounted for the sedimentation of droplets. Several mathematical forms were proposed for the aggregation frequency and sink terms. The parameters of the population balance equation were estimated using the experimental data. The first model tested had only two adjustable parameters and, surprisingly, it was able to account for the trend of the experimental data. The used experimental conditions were based on the operation of full-scale units that led to high dehydration efficiency in all cases, so that parameters that represent the average behavior of the parameters in the experimental conditions were able to fit fairly well the experimental data. The final model contained five adjusted parameters and was able to account for the effect of the electrical field, temperature and flow rate in electrocoalescence process. The relative effect of the experimental variables on the model parameters depended on the oil and on experimental condition. The largest deviations of calculated values from the experimental data were concentrated on points with low BS&WI, indicating that the water content of the emulsion can significantly affect the rates of droplet coalescence and sedimentation. A model that explicitly includes the reduced interdroplet


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interactions under low water concentration may be able to capture the electrocoalescence behavior for diluted emulsions.

7. Acknowledgment The authors thank PETROBRAS, CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), FAPERJ (Fundação Carlos Chagas Filho de Apoio à Pesquisa do Estado do Rio de Janeiro), ANP (Agência Nacional do Petróleo), SINOCHEM and STATOIL for providing scholarships and financial support.

Appendix A: In this section, a brief description of the electrostatic cell shown in Figure 8 is presented.

Figure 8: Electrocoalescer cell

The electrostatic cell manufactured by INTERAV S/A (model DC-250) is composed of a stainless steel body, with the length and internal diameter of 40cm and 5cm, respectively. The


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pressure threshold and maximum operating temperature of the cell are 34.5 bar and 150 ºC. At the bottom of the cell, there is an adjustable distributor which allows the fluid to enter at any desired level below the cell electrodes. The feeder is horizontally oriented with 12 holes of 2mm internal diameter (Figure 9).

Figure 9: Emulsion feeder

At the upper side of the cell, the circular horizontal electrode plates are located (Figure 10). The upper electrode is the ground and the upper one is connected to the AC electrical source. The distance between the electrodes can be changed from 1 to 4 inches. Although, for the experiments performed in this study, the distance between the electrodes was set to 1inch.


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Figure 10: Electrodes of electrocoalescer cell a) side view b) frontal view

The precipitated water is drained from a needle valve in the lower side of the cell and the treated oil exits from the upper side of the cell. During the experiments, the interface between oil and water is manually controlled in batch steps. The valves are connected to coil condensers to cool down the fluids and prevent their evaporation. Besides, pressure relief valves are considered to adjust the outlet pressure.

8. Nomenclature α (d i , d j )

aggregation frequency of the particles with the characteristic diameter of di and dj

AC

cross-sectional area of treater to the flow

CAsphaltene

concentration of Asphaltene

d

droplet’s diameter

Dd

diffusion coefficient of dispersed phase (water)

Ee

electrical field between the electrodes

Le

electrodes spacing in the treater

n

number density of particles


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n•

number density of particles that enters to the treater

Ni

number of drops with size "i" at a given instant of time

Ni•,I

flow rate of drops with size "i" that enters to the treater

QL , I

volumetric flow of liquid entering the treater by the oil stream

QL,O

volumetric flow of liquid leaving the treater by the oil stream

QW , I

volumetric flow of water entering the treater

T

temperature

t

time

tR

residence time

V

electrostatic cell volume

Ve

voltage imposed on the electrodes of treater

V%i

percentage, in terms of volume of class "i"

vi

particle volume of class "i"

u

velocity

ud

droplet velocity

WL , I

mass flow of liquid entering the treater

WW ,O

water mass flowing out of the treater through the water stream

WL ,O

Mass flow of liquid exiting the treater through the oil stream

xi

pivot of class i

Greek symbols

µ

viscosity

µˆ

ratio of the viscosity of dispersed phase (water) to that of continuous phase (oil)

ρ

density

ρˆ

ratio of water density to oil density

λ

ratio of the radius of the small drop to that of the large drop


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Subscripts cal

calculated by model

e

electrode

ch

characteristics

exp

experimental value

I

at the inlet of treater

L

liquid

o

oil phase

O

at the outlet of treater

w

water phase

Abbreviations

AC

alternative current

BS & W

basic sediment and water (water content)

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