Experimental and theoretical study of crude oil pretreatment using low-frequency ultrasonic waves

Accepted Manuscript Experimental and theoretical study of crude oil pretreatment using low-frequency ultrasonic waves Ali Khajehesamedini, Ali Sadatshojaie, Payam Parvasi, Mohammad Reza Rahimpour, Mohammad Mehdi Naserimojarad PII: DOI: Reference:

S1350-4177(18)30549-2 https://doi.org/10.1016/j.ultsonch.2018.05.032 ULTSON 4190

To appear in:

Ultrasonics Sonochemistry

Received Date: Revised Date: Accepted Date:

17 April 2018 23 May 2018 26 May 2018

Please cite this article as: A. Khajehesamedini, A. Sadatshojaie, P. Parvasi, M. Reza Rahimpour, M. Mehdi Naserimojarad, Experimental and theoretical study of crude oil pretreatment using low-frequency ultrasonic waves, Ultrasonics Sonochemistry (2018), doi: https://doi.org/10.1016/j.ultsonch.2018.05.032

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Experimental and theoretical study of crude oil pretreatment using low-frequency ultrasonic waves Ali Khajehesamedini1, Ali Sadatshojaie2, Payam Parvasi3,4, Mohammad Reza Rahimpour *4, Mohammad Mehdi Naserimojarad5

1

Programa de Engenharia Química / COPP, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-972, Brazil

2

Chemical and Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran

3

Department of Chemical, Petroleum and Gas Engineering, Shiraz University of Technology, Shiraz, Iran 4

Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran

5

School of Mechatronic Systems Engineering, Simon Fraser University, Vancouver, Canada.

Abstract In this work, an ultrasound experimental setup was designed to investigate the feasibility of using low-frequency ultrasonic waves as a substitute to reduce the consumption of chemical demulsifiers in the pretreatment of crude oil. The experiments were planned to study the effects of irradiation time, ultrasonic field intensity and initial water content on the efficiency of separation. The results of experiments showed that by selecting a proper irradiation time and field intensity, it is possible to decrease the usage of demulsifiers by 50%. Moreover, a population balance model was proposed to explicate the experimental data. A hybrid coalescence model was developed to determine the frequency of aggregation. The parameters of the model were estimated by linear regression. The parameter estimation was performed using a parallel execution of the particle swarm optimization algorithm. The results of the model showed a decent agreement with the experimental data.

*

Corresponding author. Tel.: +987132303071; fax: +987136287294., [email protected]

1

Keywords: W/O Emulsion, Low-Frequency ultrasonic waves, Population Balance Model, Coalescence model, crude oil;

1. Introduction The complex nature of water-in-oil (W/O) emulsions is a principal obstacle to develop a satisfactory separation technique in the petroleum industry [1]. In spite of the recent attempts to develop a reliable demulsification technique, most of the water-in-crude oil emulsions cannot be broken in small timespans [1]. The stability of W/O emulsions originates from the creation of a rigid film at the water-oil interface [2]. The indigenous materials of crude oil such as asphaltenes and resins tend to accumulate at the interface, resulting in a film that performs as a structural barrier to the aggregation of the droplets [2]. The solidity of the film increases by time, as the accretion of the indigenous materials at the interface rises [3]. Electrocoalescence is known as the common industrial process to break the w/o emulsions and separate the disperse water droplets from crude oil [4]. The application of high potential electrical fields to the w/o emulsions polarizes water droplets and accelerates their coalescence [4]. Although the electrocoalescence has proved to be sufficient for breaking the w/o emulsions, a pretreatment process might be necessary for desalination of some crude oils. The high stability of the interfacial film, especially in high viscosity crude oils, demands a pretreatment/destabilization to facilitate the desalination process [5]. Chemical demulsification is known to be the most common method for the pretreatment of crude oil [1]. Due to the high interfacial activity of chemical demulsifiers, they tend to adsorb/displace the indigenous species present in crude oil, which results in weakening of the interfacial film [6]. However, Chemical demulsifiers have shown to have practical problems. The substance is costly and not recyclable after injection. Moreover, a part of the material is added to the wastewater, along with the water separated from the crude oil. Most of the demulsifiers contain synthesized chemical compounds, which enter to effluents and cause environmental problems [7]. Therefore, due to the limitations of thermal and chemical demulsification, new technologies are desired for the pretreatment of crude oil. Over the past few decades, the competency of radiation technologies to manipulate small particles in liquid suspensions has been used as a basis for various filtration and recovery processes [8,9]. Several separation phenomena are observed in the demulsification of emulsions under the influence of ultrasonic field [10]. The molecular transfer of pressure pulses to the material creates a vibrating motion along the direction of wave propagation [11]. 2

The resulting compressions and rarefactions of ultrasonic waves increase the temperature and decrease the viscosity of the fluid which facilitates the separation [12]. Due to the compressibility and density differences between the continuous and disperse phases, a net force is applied to the droplets. When the distance between a pair of droplets is less than the wavelength of the ultrasonic field, the droplets migrate to the node or antinode of the standing waves (droplets approach). Further coalescence of droplets is due to the inter-droplet forces [13]. This is normally the case of low frequency (20−100 kHz) ultrasonic waves, where the droplets coagulation is expected to be the main factor in the separation of phases [14]. In this range of frequency, commonly known as “power ultrasonic”, the waves are able to deliver a high specific energy density (10-1000 W/cm2) to the medium by the phenomena known as acoustic cavitation [15]. The application of intense pressure ultrasonic waves causes the formation of bubbles in the solution that might expand and collapse. Consequently, for the aim of demulsification, the intensity of ultrasonic waves should not exceed the cavitation’s level (threshold) of the emulsion [16]. Further explanations about the demulsification ultrasonic setups and the coalescence of droplets are presented in sections 2.1 and 3.2, respectively. Ultrasonic waves have specifically been used in the demulsification of W/O emulsions. Different kinds of transducers with frequencies between 10 KHz up to 2 MHz and electrical power from 50w to 1000w have been used to facilitate the separation of water from crude oil. Xie [17] studied the utilization of ultrasonic standing waves in a resonant cavity to capture water droplets and improve oil separation. The emphasis of their work was to analyze the influence of ultrasonic irradiation on the properties of w/o emulsion, such as water droplet size, flocculation size of asphaltene, and the shear strength of the oil-water interfacial film. Mohsin [18] designed an experimental setup to investigate the feasibility of using a 20 kHz ultrasonic wave in demulsification of W/O emulsions with different water contents. Their experiments had a proper repeatability and indicated that the emulsion layer with a lower amount of water content (i.e. 10 to 40%) broke significantly faster. Moreover, they performed a finite-element-based simulation using COMSOL Multiphysics software to study the distribution of ultrasonic waves inside the treater and determine the rate of flocculation. Atehortúa [19] designed a chamber of ultrasonic demulsifier system operating in the 1 MHz range. The chamber had a control system which could track the operating frequency and compensate the changes due to temperature variation. They analyzed the effect of ultrasonic waves on the emulsions with different amounts of initial water content and demulsifier. Antes [20] investigated the effect of ultrasound waves on the demulsification of different average 3

droplet size distribution (DSD) w/o emulsions in an ultrasonic bath. They analyzed the influence of different ultrasonic frequencies on the efficiency of separation. In their experiments, when the applied frequency was higher than 45 kHz, no changes could be observed in the characteristics of the crude oil emulsions. Luo [21] studied the effects of irradiation time, acoustic intensity, frequency, oil viscosity, and oil-water interfacial tension on the separation characteristics of the emulsion. They showed that there exists an optimum acoustic intensity, optimal irradiation time and oil-water interfacial tension to achieve the maximum separation efficiency. To improve the understanding about the coalescence of disperse particles under the effect of ultrasonic waves, attempts have been made to model the phenomena. Pangu [22] introduced the microscopic droplet pair model to predict the relative trajectory of binary droplets approaching together in w/o emulsion. They explored the effect of body and interdroplet forces in the droplets approach under the effect of the ultrasonic field. Parvasi [23] extended the droplet pair model for o/w emulsion and added the effect of surfactant agent to the system of equations. Mathew [24] developed a two-dimensional dynamic model to trace the path of microparticles subjected to the ultrasonic field. He found that the trajectory of microparticles which approach together consists of transient and steady phases. Population balance model (PBM) is an appropriate way to model the particulate systems. PBM has been used to simulate a diverse kind of dispersed phase systems, including liquidliquid extraction, dispersed phase reactors, electrocoalescence and many more [25–27]. The precision of the PBM approach relies on the adequacy of the particle-particle interaction models, which are not commonly compatible and depend on adjustable parameters that are determined using experimental data [28]. There exist very few works in the literature which address the application of population balance equation (PBE) to model the demulsification under the effect of ultrasonic waves. Pangu [29] developed a simplified PBM to study the coalescence of oil droplets in o/w emulsion. They used the binary model developed by Pangu [22] to predict the relative motion of two droplets approach together. They implemented the relative velocity of two droplets as a representation of the coalescence model in the PBE. The results of their model to predict the evolution of the droplet size distribution had a good qualitative agreement with the experiments. They attributed the inconsistencies between the modeling and experimental results to the spatial non-uniformities of the acoustic field used in the experiments and the related lateral radiation forces.

4

Most of the above-cited works who used the ultrasonic waves to demulsify the w/o emulsion tried to introduce the ultrasound technology as an alternative to the industrial electrocoalescence process which objectively in practice seems difficult. They didn’t attempt to examine the application of ultrasonic waves as a possible substitute to reduce the consumption of chemical demulsifiers in the pretreatment of crude oil. Additionally, the few population balance based works such as Pangu [29], who tried to model the separation under the effect of ultrasonic waves, were not meant to study the coalescence of water droplets in w/o emulsion. The aim of this paper was to study the utilization of low-frequency ultrasonic waves in enhancing the breakup of water-in-oil emulsions. Due to the limitations that our research group in the Shiraz University (Shiraz/Iran) faced to buy laboratory equipment, it was decided to design an experimental setup to perform the ultrasonic tests. The experiments were planned to investigate the effects of irradiation time, ultrasonic field intensity and initial water content on the efficiency of separation. A PBM was used to explore the evolution of droplets size. A new coalescence model based on the theoretical works of Zhang [30], Pangue [13] and Parvasi [23] was proposed. The work is concluded by making some remarks on the possibility of partially substituting ultrasonic waves with chemical demulsifiers in the pretreatment of crude oil. To the authors’ knowledge, this is the first time where the population balance equation has been used to model the coalescence of water droplets in W/O emulsion under the effect of ultrasonic waves.

2. Materials and methods 2.1. Basis of the experimental setup design As expressed in the introduction, the idea of this work is to study the influence of the ultrasonic field on the separation of disperse water from oil phase in w/o emulsions. This imposes several constraints on the design of the experimental setup. First, the ultrasonic setup should be able to produce a proper distribution of ultrasonic filed. The ultrasonic setups that have been proposed for the desalination of crude oil are generally based on ultrasonic bath [20] and ultrasonic horn system [19]. An ultrasonic bath has large transducer areas that produce a high-powered ultrasonic intensity throughout the entire vessel. An ultrasonic horn is a dwindling bar of metal which is usually used to enlarge 5

the amplitude of oscillation displacement. Although both techniques apply ultrasound to the samples, there are significant differences in their effectiveness, efficiency and process capabilities [31]. The experimental analysis performed by Dhanalakshmi [32] showed that the sonication produced by the ultrasonic probe-type device is stronger and more uniform than the one produced by the ultrasonic bath. While there is still no ultimate verification to the preference of probe-type sonication over bath sonication, the horn type seems to be preferred in most of the demulsification works [16]. Second, the acoustic intensity should be less than the maximum threshold of the desired crude oil. The application of high intensities of ultrasonic waves can decompose the structure of crude oil and form bubbles that expand and collapse. Finally, the frequency of ultrasonic waves should be appropriate for the aim of demulsification. Although the frequency of the ultrasonic field is still being debated in the literature, most of the works have shown that low-frequency waves are more competent in the demulsification of crude oil and high-frequency waves are more suitable for emulsification purposes.

2.2. Experimental setup In this work, we intended to design an ultrasonic batch setup which is also capable of being employed in the continuous process of crude oil desalination. Therefore, it was resolved that a cylindrical container similar to the crude oil pipeline can be appropriate for the geometry of ultrasonic setup. Figure 1 shows the ultrasonic systems that were designed to perform the experiments. The setups were made of stainless steel and glass containers. Due to the better reflection of ultrasonic waves inside the metal vessel, the metal container has a better efficiency in comparison to the glass one. Whereas, the glass container can be utilized to observe and shot the separation process. The length and diameter of the vessels are 25cm and 4.8cm, respectively.

As shown in Figure 1, the transducers were aligned/coordinated at the two ends of vessels to create ultrasonic standing waves inside the container. The application of an ultrasonic field to the w/o emulsion makes the water droplets to accumulate at the node or antinode of standing 6

waves which accelerates the separation and precipitation of disperse phase. To prevent any leakage from the two ends of containers, two especial Teflon gaskets were employed to cover the space between the transducers and the container. Therefore, the transducers could easily be clamped or removed from the container without any further welding or screwing. The inlet and outlet gates on the upper and lower sides of the vessel were considered to allow the employment of ultrasonic setup in the continuous desalination process. The vessels were fastened by two polyethylene holders to a wooden plate to neutralize the possible vibration of containers during the transmission of ultrasonic waves. The HNT-8AE-2520(5X4) model transducers (Hainertec) which are able to produce 20KHz and 100w ultrasonic waves were utilized in the experimental setup. The main component of the HNT-8AE-2520(5X4) transducer is shown in Figure 2.

Since there were no pre-constructed electrical circuits to provide the necessary electrical potential for the transducers, two electrical circuits were designed for each transducer. A computer application using LabVIEW software (National Instruments) was programmed and installed on the ICs to control the function of transducers. Therefore, it was possible to alter the power of transducer to 25w, 50w and 75w in addition to 100w and observe the effect of ultrasonic intensity on the emulsification of crude oil.

2.3. Experimental procedure The crude oil that was used in the experiments was supplied from Gachsaran (Ilam /Iran) and Cheshmeh Khosh (Kohgiluyeh and Boyer-Ahmad /Iran) oilfields. The characteristics of the three oils used in this work, here named as Cheshmeh Khosh, Gachsaran1 and Gachsaran2 are shown in Table 4.

Table 4 shows that the crude oils of the Gachsaran reservoirs are lighter than the one from Cheshmeh Khosh field. Moreover, the Gachsaran crude oils have a lower concentration of Asphaltenes and Resins. Therefore, it was expected that the demulsification of Cheshmeh Khosh crude oil to be more difficult in comparison to the samples from Gachsaran oilfield.

7

Throughout the experiments, the W/O emulsions were artificially generated. The procedure to prepare the samples and run the experiments was as follows: 1. Different volume percent of distilled water with pH = 6.5 was added to the dead (dehydrated) crude oils to prepare 100cc samples; 2. The mixture was homogenized with the help of a pendulum agitator (Ika, RW 20 digital); 3. The emulsions were then prepared under vigorous stirring of an Ultra-Turrax dispersing system (Polytron PT3100, Biovera); 4. The initial droplet size distribution (DSD) of the emulsion was measured by light scattering with the Mastersizer 2000 equipment, equipped with the Hydro S dispersion unit (Malvern); 5. The RP-6348 demulsifier (Parslian/Tehran/Iran) for Cheshmeh Khosh oil and V-4654 demulsifier (Pars HalalShimi/Tehran/Iran) for Gachsaran1 oils were added to the mixtures at the concentration of 50ppm, followed by further homogenization; 6. The 100cc samples of emulsions were poured into the ultrasonic container, allowing the ultrasonic treatment to begin; 7. The treated samples were analyzed to study the effect of ultrasonic field on the emulsions. These steps were carried out for all experimental points. The samples were prepared and put under the effect of different ultrasonic intensities in the container. The objective of the experiments was to evaluate the influence of the following variables on the demulsification of emulsion: a) Ultrasonic intensity b) Initial water content c) Irradiation time In this study, as a result of the low concentration and unclarity of dispersed phase in the treated emulsion, it was not possible to measure the DSD and observe the coalescence of droplets. Therefore, another method should have been used to investigate the influence of ultrasonic waves on the demulsification of W/O emulsion. Bottle test [33] is a renowned technique in the chemical industry to evaluate the capability of demulsifiers in the separation of water from crude oil. The procedure of bottle test is to place the treated samples in an oven at 60°C for 12 hours and measure the separation/segregation of aqueous and oil phases [6]. The difference between the amount of separation/segregation in the cases when the agent is added and not added shows the 8

performance/influence of demulsifier. The amount of separation in bottle test, which is desired in the Cheshmeh Khosh and Gachsaran desalinization units is in the range of 75%85% volume [6]. Since in this work, the ultrasonic waves were introduced as an alternative to the demulsifiers in the pretreatment of crude oil, the bottle test was employed to examine the influence of ultrasonic field on the demulsification of W/O emulsion. The treated samples of ultrasonic experiments were poured into graduated cylinders for conducting the bottle test. Similarly, the difference between the amount of separation in the cases when the ultrasonic waves are applied and not applied to the emulsion shows the performance/influence of ultrasound field. This technique was utilized to study the effects of ultrasonic intensity, initial water content and irradiation time on the efficiency of separation by ultrasonication. The efficiency of separation was evaluated by dehydration rate ηd, which is the ratio of the removed water volume in bottle test Volsep to the initial volume of the distilled water Voltot added to the crude oil:

d 

Volsep Voltot

100%

(1)

2.3.1. Electrocoalescence in series with ultrasonication In this section, a set of experiments were performed to compare the performance of demulsifiers and ultrasonic waves in the pretreatment of crude oil prior to the electrocoalescence. For this purpose, the control sample was prepared by adding 100ppm of V-4654 demulsifier (Pars HalalShimi/Tehran/Iran) to a 100cc emulsion of Gachsaran1 crude oil with 15% initial water content. The reason for choosing the Volw,init % = 15 is that it is the most probable composition in the oilfields of Gachsaran (Ilam /Iran). Moreover, the demulsifier and its concentration are the ones employed in the Gachsaran desalinization unit for the pretreatment of the crude oil. In a separate experiment, the 100cc emulsion was prepared by injecting 50 ppm of V-4654 demulsifier and then poured into the ultrasound container for a 5minute 1.0 kw.cm-3 ultrasonication. In both cases, a 3000ppm of salt (NaCl) was added in the preparation of the two emulsions to examine the ability of the treatments to desalt the samples. Next, the two pretreated samples were poured into a batch electrostatic vessel and put under the effect of a 4 KV electrical field and 60°C for 20minutes. The electrostatic cell and its electrical source are shown in Figure 3.

9

The electrostatic vessel consists of two grid electrodes. The upper electrode is the ground and the lower one is connected to a high voltage electrical source. During the experiments, the distance between the electrodes was set to 4cm and the voltage of the lower electrode was provided by a sinusoidal 4 KV AC current. Therefore, the average electrical field between the electrodes ( E  V delectrodes ) was equal to 10e5V/m which is in the range of industrial value. The height of the electrostatic vessel is 11.2 cm and its inside diameter is 4.5 cm. The elevations of the lower and upper electrodes from the bottom of the vessel were maintained 4.7 cm and 8.7 cm during the experiments, respectively. To compare the effects of demulsifier and ultrasonic waves, the water and salt content of the initial emulsion and the desalted samples were measured. In this work, the ASTM D400702 and IP 77-72 standards were used to determine the water and salts content, respectively.

3. Population balance modeling The average number of droplets per unit volume of droplet state space is the droplet number density function, n . To predict the evolution of the number density function, the population balance equation (PBE) should be solved. The general differential form of the onedimensional PBE is presented in Equation (2) [34]. In this representation, the number density: n , is a function of v which characterizes the size of droplets and the spatial position of

droplets: z.

[ud n]  [ Dd n] 

 n(v, z, t ) [Gn]  S  V t

(2)

The first and second terms on the left-hand side of the equation represent the convection and diffusion of droplets, respectively. The third term on the left-hand side of the equation is related to the growth of the droplets. The term S denotes the nucleation, breakage, and aggregation of the droplets. The right-hand side of Equation (2) indicates the accumulation of droplets in the system. Based on the characteristics of the phenomena happening in a specific particulate system, the appropriate terms of population balance equation are considered in the formulation of a PBM.

10

3.1. Simplified model for experimental analysis A PBM was proposed for the ultrasonic setup explained in Section 2.2, to predict the coalescence of water droplets in w/o emulsions under the effect of ultrasonic field. Based on the characteristics of the particulate system of the ultrasonic setup, the following assumptions were made to derive the PBM: - The diffusion and convection of droplets are insignificant in comparison to their coalescence. - The ultrasonic treater is homogeneous; thus, the axial and radial gradients inside the vessel were not considered. - Due to the low frequency (20KHz) and intensity (100w) of the applied ultrasonic fields in the experiments, the droplet breakage is negligible [14]. Therefore, the general PBE (Equation (2)) will be reduced to Equation (3) for the ultrasonic setup.

dn(v, t )  B(v, t )  D(v, t ) dt

(3)

In this equation, the B(v, t ) and D(v, t ) terms are the birth and death aggregation of the droplets, respectively. When two droplets coalesce together, they form a bigger droplet. The birth aggregation term addresses the creation of the big droplet; while, the death aggregation denotes the loss of the two initial droplets. The mathematical representations of birth aggregation and death aggregation are given by Ramkrishna [34]:

B(t , v) 

1 v C (u, v  u )nv (v  u, t )nv (u, t )du (4) 2 0 

D(t , v)  nv (v, t )  C (v, u )nv (u, t )du 0

(5)

where B(v, t ) represents the birth of a droplet with the size of ‘ v ’ through the coalescence of droplets with the size of ‘ u ’ and ‘ v  u ’. Also, D(t , v) signify the death of a droplet with the size of ‘ v ’ to another droplet with the size of ‘ u ’ while the coalescence of droplet ‘ v ’ to other droplets. C (t , u, v  u) is the coalescence frequency which indicates the number of 11

collisions that result in the coalescence of the droplets ‘u’ and ‘v-u’. The functionality of this coefficient is dependent on the characteristics of the particulate system. In the following section, an effort has been made to develop a coalescence frequency for the ultrasonic system.

3.2. The coalescence model An attempt was made to develop a coalescence frequency that can be applied to the range of droplet sizes witnessed in the ultrasonic experiments. In this work, the method suggested by Zhang [30] was used for the determination of coalescence frequency. Thus, the term C (t , v, u) in Equations (4) and (5) can be calculated by

C (ai , a j )     ai  a j  uij 2

(6)

where ai and a j are the diameters of two droplets coalescing together. In this equation, uij is the relative velocity of two droplets coalescing together and  is an adjustable parameter which is dependent on the characteristics of the crude oil. Here, the data extracted from the ultrasonic experiments were used to estimate the  parameter. The procedure of parameter estimation is explained in Section 4.3. In this work, the droplet pair model developed by Pangu [35] and Parvasi [23] was used to calculate the relative velocity of two droplets. The model considers the application of a one-dimensional standing ultrasonic waves to a low concentration emulsion. Due to the small size of droplets, the inertial forces can be neglected. Therefore, every collision which is a result of a binary droplet interaction leads to an irreversible coalescence of the droplets. The model is limited to large Peclet numbers, where the Brownian diffusion can be disregarded compared to other effective forces of the system [35]. The formulation of the droplet pair model is based on the balance of forces that apply to the droplets while coalescing together [36]. The forces are subcategorized to body forces and interdroplet forces. The body forces are the ones that act on droplets as individuals; while, interdroplet forces are the ones that act on a droplet because of its close vicinity to another. In the particulate system of ultrasonic setup, the body forces are the gravity, buoyancy, drag and primary acoustic force. The velocity of an individual droplet can be calculated by solving the 12

balance equation of the body forces. The Equation (7) is proposed by Pangu [22] for the calculation of this velocity:

  1 k 1 Y 2 2 2  u  1  Y sec      W 1  P2   

  1 Y 2 t   W 

   

(7)

where:

 1  3ˆ 2  3 o 1  ˆ   W 2 aˆ   w  o  g

(8)

Y

3kEac F   w  o  g

(9)

F

ˆ  2 3ˆ  1 1  1  2ˆ  3 2 ˆ

 k 1 Y 2 P  1  Y 2 tan     W 

(10)

 t  Y  

(11)

 tan  kx0   Y    tan 1   1 Y 2  

(12)

and x0 is the initial distance of the droplet from the pressure antinode [22]. The relative velocity of two individual droplets ( uij  u i  u j ) should be corrected by adding the influence of interdroplet forces. The interdroplet forces are conceptually different from the body forces as their strength increases when the droplets approach together. The primary acoustic force makes the droplets move to the closest pressure antinode. Throughout this motion, the droplets approach each other and the interdroplet forces become important. The interdroplets forces acting on droplets are the Van der Waals [37,38] and the attractive secondary acoustic [22,39,40] forces. The corrected relative velocity of the droplets uij is presented as [41]:

13

 rr rr   Dij  uij  uij   2 L  s    I  2  M  s   r   r  kT

 rr rr     r 2 G  s    I  r 2  H  s  (ij )    

(13)

In this equation s  2r / (a1  a2 ) is the dimensionless droplet separation, r is the droplets’ center-to-center distance and I is the second-order unit tensor. The first two terms on the right side of Equation (13) describe the contributions of body forces to the relative velocity, while the last two terms indicate the interdroplet effects. Also, Dij is the relative diffusivity of two widely separated droplets due to the Brownian motion:

Dij 

KT  ˆ  1 1  aˆ 1 

(14)

2o  3ˆ  2  ai

The relative mobility functions for the motion along the center of two droplets center: Ls  ,

Gs  , and normal to the droplets centerline: M s  , H s  denote the influences of hydrodynamic interactions between the two droplets [41]. A detailed explanation of the droplet pair model can be found in the original references [23,35].

4. Numerical Procedure 4.1. Solution of the population balance model To estimate the parameters of Equation (6), first, the population balance equation should be solved. Among the several numerical procedures that have been suggested to solve the PBE, this work used the method of classes developed by Kumar [42]. The method enforces the conservation of volume and number of the droplet population and permits the direct use of initial droplet size classes defined by the particle size analyzer. 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

(15)

n(v)dv

This class is represented by the pivot xi  0.5(vi  vi 1 ) . Based on the experimental data reported by the particle size analyzer (Malvern® Mastersizer 2000), the diameter of water droplets in the initial emulsion was in the range of 0.1  100 m . Therefore, the classes vi 14

were

determined

by

a

geometric

grid

defined

by

vi 1 / vi  1.514 ,

k  0,..., n ,

v0  5.24 107  m3 (d0  0.01 m) with n=100.

Applying the procedure proposed by Kumar [42] to Equation (3) leads to the subsequent set of ordinary differential equation (ODE): j k

dNi (t )  dt



j ,k xi1  ( x j  xk )  xi 1

M 1 (1   j ,k ) j ,k ,i C j ,k N j (t ) N k (t )  Ni (t ) Ci ,k N k (t ) 2 k 1

(16)

where  j ,k ,i is defined as:

 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

(17)

4.2. Determination of the final amount of separated water using the population balance model In this work, as a result of the low concentration and unclarity of disperse phase in the treated emulsion, it was not possible to measure the distribution of water droplets. Therefore, the volume of separated water in the bottle test could be the only experimental data to evaluate the PBM. Here, a criterion in the PBM should have been considered to denote the volume of separated water. According to the study of Meidanshahi [43], it was assumed that the population of water droplets which are larger than 20μm represents the volume of separated water from oil phase in the bottle test. The first moment of the number function (N) in the PBE (Equation 16) represents the total volume of the droplets (Kumar, 1996): 

Voltotal   N (v)dv

(18)

0

Therefore, the volume of the separated water phase can be calculated by

VolSep  



20 

N (v)dv

(19)

15

and similar to Equation (1), the dehydration rate can be calculated as the ratio of separated water volume to the total water volume: 

d

 N (v)dv    N (v)dv 20 

(20)

0

The following section explains the estimation of the β parameter by comparing the value calculated by Equation (20) and the experimental amount.

4.3. Estimation of model parameter The aim of this section is to use the experimental data to estimate the parameter of PBM (β). The objective function used for parameter estimation was the minimization of the quadratic mean of the differences between the experimental and calculated values of the dehydration rate, according to Equation (21): FF 

NE

1

p 1

exp

N

(d ,exp, p  d ,cal , p )2

(21)

where NE is the number of experimental points and the subscript p indicates the points of the experimental matrix. In this work, the Asynchronous and Immediate Update Parallel Particle Swarm Optimization (AIU-PPSO) algorithm developed by Moraes [44] was employed to determine the parameter of the PBM (β). In this work, the computer programs were written using Matlab 2017a (Mathworks) software.

5. Results and discussion 5.1. Analysis of the ultrasonic experiments In this section, the results of the ultrasonic experiments performed for the samples of the three crude oils described in Table 4 are presented. Primarily test showed that it is not possible to have any demulsification/separation without the injection of demulsifiers. That is

16

the reason, it was necessary to add some demulsifier in the preparation of emulsions to create an initial driving force to start the demulsification. The RP-6348 and V-4654 demulsifiers are the ones used in the desalination units of Cheshmeh Khosh (Kohgiluyeh and Boyer-Ahmad /Iran) and Gachsaran (Ilam/Iran), respectively. The amount of demulsifier which is added to the crude oils in the desalination units of Gachsaran and Cheshmeh Khosh is 100ppm. However, in this work, to investigate whether the demulsifiers can partially be substituted with ultrasonication, the amount of injected demulsifier was 50ppm. The experiments analyzed the effects of ultrasonic intensity, initial water content and irradiation time on the amount of separation in the bottle test. The samples were prepared in 10%, 15%, 20% and 25% of water content at 60°C. The emulsions were put under the effect of 0.25, 0.5, 0.75 and 1w.cm-3 ultrasonication for 1, 2 and 5 minutes. The experiments were conducted in triplicates and the reported values of the results showed that the experimental errors were less than 5%. The effects of variables are discussed in the following sections. The complete data of ultrasonic experiments are provided in Appendix A.

5.1.1. The effect of irradiation time The effect of irradiation time on dehydration rate of the emulsion is shown in Figure 4. The dehydration rate of the emulsion without ultrasonic irradiation at tr=0 is due to the effect of chemical demulsifier. Based on the findings of Razi [6], the relation between the dehydration rate and the amount of injected demulsifier is normally not linear. Therefore, it can be expected that for example, to increase the efficiency of separation from 70 to 80%, the amount of demulsifier needs to be doubled [6].

As shown in Figure 4, the dehydration rate increased with the increase of irradiation time. However, the dehydration rate decreased slightly (e.x. Figure 4 (b)) and was basically unchanged (e.x. Figure 4 (a)) with the further increase of irradiation time. It took a long time for the droplets that are far from the pressure node to migrate to the banding zone due to the primary acoustic force [22]. Therefore, the extended irradiation time is advantageous to the aggregation of the droplets. Moreover, the secondary acoustic force increases as the droplets get closer together and aggregate [22], which enhances the dehydration efficiency. Nevertheless, the dehydration rate of emulsion decreased slightly for a long irradiation time. 17

Excessive long irradiation time would raise the temperature of the emulsion, which reduces the acoustic cavitation threshold [16]. Acoustic cavitation would disperse the aggregating droplets and reduce the separation efficiency. Therefore, an optimal irradiation time can be reached, when the separation efficiency has its highest value and further irradiation would have little effect on improving the dehydration. This is more apparent in higher acoustic intensities as the temperature can rise in a smaller period of time (e.x. Figure 4 (b)). Furthermore, our tests showed that the emulsion might evaporate in a longer period of irradiation. That is the reason, we were not able to perform the experiments for longer than 5minutes. The difference between the dehydration rates of the three samples can be mainly attributed to the difference of viscosity and interfacial tension of the crude oils. The higher viscosity of Cheshmeh Khosh crude oil applies a higher drag force on the droplets in comparison to the samples of Gachsaran crude oils. Consequently, it is expected that the droplet migration velocity is smaller for the Cheshmeh Khosh emulsions. The other reason is the higher interfacial tension of Cheshmeh Khosh crude oil in comparison to the samples of Gachsaran. The high amount of interfacial tension hinders the segregation of water droplets from the oil phase and their migration to the banding zone. Figure 4 portrays the dehydration rate of emulsions at Ir = 0.5w.cm-3 & Volw,init % = 20 and Ir = 1.0w.cm-3 & Volw,init % = 25. However, the profile of separation efficiency versus irradiation time had similar trends in other ultrasonic intensities and initial water contents (Appendix A).

5.1.2. The effect of acoustic intensity Acoustic intensity is an important factor in ultrasonic demulsification. The effect of acoustic intensity on dehydration rate of the emulsions is the portrayed in Figure 5. Similarly, the dehydration rate of the emulsion without no ultrasonication (Ir = 0 W.cm-3), which represents the initial segregation of phases is due to the effect of chemical demulsifier.

As shown in Figure 5, the increase of acoustic intensity (i.e. increase of primary and secondary acoustic forces), decreases the time required for the droplets to migrate to the banding zone. Therefore, the dehydration rate increases with an increase of acoustic intensity. 18

However, there exists an optimal acoustic intensity where the separation efficiency achieves its maximum value [17,45]. If acoustic intensity exceeds the cavitation threshold, local turbulence and shear forces would be created which implode and break the dispersed droplets [16]. The acoustic cavitation threshold is influenced by factors such as viscosity, interfacial tension and saturated vapor pressure [16]. As Figure 5 expresses, an optimal acoustic intensity was obtained for Gachsaran crude oil samples. While, the Cheshmeh Khosh samples had more monotonic change with the increase of ultrasonication as the acoustic cavitation threshold increases with the increase of liquid viscosity in the same condition. The point which can be inferred by comparing Figure 4 and Figure 5 is that the acoustic cavitation threshold is more sensitive to the increase of irradiation time which is consistent with the previous findings [21]. Figure 5 depicts the dehydration rate of emulsions at tr = 5mins & Volw,init % = 15 and tr = 2mins & Volw,init % = 25. Nevertheless, the profile of separation efficiency versus ultrasonic intensity had similar trends in other irradiation times and initial water contents (Appendix A).

5.1.3. The effect of initial water content The effect of initial water content on dehydration rate of the emulsion is the depicted in Figure 6. The increase of initial water content increases the load on the ultrasonic waves to make a higher number of droplets to migrate to the bonding zone. On the other hand, the increase of initial water content, increase the number/size of the droplets which boost their collision and coalescence. Therefore, it is expected that the amount of separated water increases with the increase of initial water content while the dehydration rate decreases.

The point that should be mentioned in Figure 6 (b) is the sharp decrease of dehydration rate between the initial water contents of 20 and 25%. As the water content of the emulsions increases, the saturation vapor pressure increases [16]. This case is particularly evident at high irradiation time and/or ultrasonic intensity (Figure 6 (b)) as the temperature of the emulsion increases quickly. Therefore, the acoustic cavitation threshold decreases which disperse the aggregated droplets and reduce the separation efficiency. Figure 6 represents the dehydration rate of emulsions at Ir = 0.25 W.cm-3 & tr = 2mins and Ir = 0.75 W.cm-3 & tr = 5mins. Nonetheless, the profile of separation efficiency versus initial 19

water content had similar trends in other irradiation times and ultrasonic intensities (Appendix A). To summarize the results of section 5.1, for a constant initial water content, the dehydration rate is more responsive to the irradiation time in comparison to acoustic intensity. This can be justified as the increase of acoustic intensity is dominant over the increase of irradiation time to make the W/O emulsion reach the threshold temperature and acoustic cavitation. By increasing the initial water content, the responsiveness of dehydration rate to both irradiation time and ultrasonic intensity increases as the saturation vapor pressure increases. Therefore, considering the energy consumption, the optimum dehydration rate was seen at Ir = 0.25-0.5 W.cm-3 & tr = 2mins for the three crude oil samples at a constant initial water content.

5.2. Analysis of the ultrasonic experiments in series with electrostatic tests In this section, the results of the electrostatic tests after chemical and ultrasonic pretreatments are presented. As stated in section 2.3.1, the objective of this section was to compare the performance of ultrasonic wave and in the pretreatment of the Gachsaran1 crude oil. However, since it was not possible to have any demulsification with pure ultrasonication, it was necessary to add some demulsifier in the preparation of samples. The preparation and experimental conditions of the control and ultrasonic samples are presented in . Specifically, the experiments examined whether the ultrasonication can compensate the 50% reduction in demulsifier injection. It should be mentioned that the procedures that have been used to measure the water/salt content after the ultrasonic/chemical pretreatments and electrostatic separation were different. The reason is that there was no clear separation between the phases immediately after the ultrasonic/chemical pretreatments. Therefore, in order to evaluate the efficiency of pretreatment, the bottle test procedure was used which lasts 12 hours. As presented in Appendix A, the dehydration rate of Volw,init % = 15 Gachsaran1 crude oil after 5 min, 1 W/cm3 ultrasonic is 92.27%; and based on the work of Razi [6], the amount of dehydration rate after the pure chemical is in the range of 87-90%. Besides, it is expected that the salt shouldn’t have any significant change after the pretreatment as a distinct phase separation is not observed after the pretreatments. However, the electrostatic tests were performed 20

immediately after the pretreatment and there is a segregation between the aqueous and oil phases after the electrostatic treatment. Therefore, it would be possible to immediately measure the water/salt contents using the ASTM D 4007-02 and IP 77-72 standards. The results of the analysis are shown in Figure 7.

As shown in Figure 7, the water and salt contents of the two desalted samples had comparable values. Moreover, the results were in the range of desired values of in the industry. Therefore, it can be deduced that the ultrasonic waves have the potential to partly substitute with chemical demulsifiers pretreatment of crude oil prior to electrostatic desalinization.

5.3. Parameter estimation The parameter estimation procedure described in section 4.3 was applied to determine the parameter  of the coalescence frequency Equation (6). The initial discrete droplet volume distribution (Nv,k) and the dehydration rate were utilized as the independent and dependent variables, respectively. Since in this the work, demulsifier was added in the preparation of emulsions, the separation of phases after ultrasonication cannot be only ascribed to the effect of ultrasonic waves. Therefore, it was assumed that effect of the 50ppm demulsifier which can be associated with the characteristics of the emulsions is encompassed in the  parameter. The coalescence frequency parameter of the PBE is an empirical/semi-empirical term to address the effect of variables that have not been implicitly or explicitly considered in the modeling [34]. In the PBE of Equation (3), the initial water content is seen through the distribution of droplets. However, the effect of initial water content on the flow pattern is not reflected in the PBM. Different initial water contents create dissimilar flow regimes which influence the rate of aggregation [1]. Besides, the ultrasonic intensity is considered through the primary and secondary forces in the relative velocity of two droplets (Equation (13)) in the PBE. The relative velocity of two droplets is a function of disparity of droplets which is absolutely stochastic. Therefore, in this work, we assumed that the  parameter is a function of initial water content (Volw,init) and ultrasonic intensity (Ir). for this reason, an empirical equation was considered for the parameter of aggregation frequency as: 21

  A  (Volw,init %) B

(22)

where A  A1  I r  A2

(23)

B  B1  I r  B2

(24)

The idea of choosing this form of equation was to investigate the sensitivity/functionality of the  parameter to the initial water content (Volw,init) and ultrasonic intensity (Ir). To perform the parameter estimation, 75% of the experimental data for each crude oil sample (i.e. 0.75*4*3*4 = 36points) were randomly selected and the other 25% (i.e. 0.25*4*3*4 = 12points) were used to validate the model. Moreover, the average value of the triplicates in experimental results was used for the calculations. The A1 , A2 , B1 and B2 coefficients were estimated by minimizing the distance between the experimental and simulated data (Equation (21)) using the AIU-PPSO optimization algorithm [44]. The estimated/optimized values of the coefficients for the three crude oil samples are presented in Table 6.

The sensitivity of  parameter to Volw,init and Ir can be analyzed by studying the A and B variable in Equation (22). Based on the results of parameter estimation (Table 6) and Equations (23), (24), the range of variation of the B variable is much larger than the A . This issue denotes that the variation of the  is more sensitive to the initial water content (Volw,init). The effect of ultrasonic intensity appears to be sufficiently expressed through the

u12 in Equation (6). However, the assumption made in droplet pair model to incorporate the effect of ultrasonic intensity can be compensated through the  parameter. Here, it should be noted that the  parameter would have a sensible functionality to the concentration of injected demulsifier in the preparation of samples. However, since in this work a constant amount of demulsifier (50ppm) was used during the experiments, it was not meaningful to propose any functionality for that. The comparison between the simulated and experimental dehydration rate of the validation points for the three crude oil samples are presented in Table 7. The error shown in Table 7 is calculated by Equation (21).

22

As can be seen in Table 7, the error of the model to predict the dehydration rate at the validation points was acceptable. Although, the biggest error was seen for the Cheshmeh Khosh crude oil samples. This can be associated with the high concentrations of asphaltene and resin in the crude oil which was not well addressed in the model. Furthermore, the highest local deviation from the PBE model was specifically realized at the points with a high value of irradiation time/ultrasonic intensity. This could be due to the insufficient proficiency of the model to predict the ultrasonic cavitation threshold to avoid the overestimation of the model.

6. Conclusion This work presented an experimental and theoretical study on the pretreatment of crude oil using low-frequency ultrasonic field coupled with chemical demulsifiers. A simplified PBM was proposed to explicate the experimental data. The results of the experiments showed that it is not possible to completely omit the consumption of chemical demulsifier. However, for a W/O emulsion, it would be possible to decrease the injection of demulsifier by 50% using an appropriate irradiation time and intensity of ultrasonic waves. Based on the experiments, for a W/O emulsion with a definite initial water content, the increase of irradiation time is more effective than the increase of acoustic intensity in boosting the dehydration rate as the acoustic cavitation is delayed. The results of electrostatic experiments verified the potential of the ultrasonic waves in pretreatment of W/O emulsion. The salt/water contents that is reached in the electrocoalescence process after the ultrasonic and chemical treatment could be comparable. The PBM using the derived coalescence model, generated unbiased results for the amount of separated water in bottle test that presented a decent agreement with experimental data. The droplet-pair model showed to be a proper approach in predicting the coalescence frequency. Based on the parameters estimated for the aggregation frequency coefficient, the frequency of aggregation has a significant functionality on the initial water content. The ideas that are suggested to improve the model is to (a) consider a multidimensional distribution of the ultrasonic waves, (b) add the surface tension force to the balance equation of body forces, and (c) obtain a functionality for the concentration of demulsifier in the equation of coefficient of aggregation.

23

Acknowledgments The authors would like to thank the Iranian Central Oil Fields Company (ICOFC) for providing informational and financial supports. Also, the authors are grateful to the Radman Sanaat Nasr Company for its technical consultation in constructing the ultrasonic setup.

Appendix A: In this section, the detailed experimental data of the ultrasonic tests is provided. The results of the experiments for Gachsaran1, Gachsaran2, and Cheshmeh Khosh crude oil samples are presented in Tables 5-7, respectively.

Table 1: Dehydration rate (%) of the ultrasonic tests for the Gachsaran1 crude oil samples Ir = 0.25 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

74.40 82.18 87.84 92.59

72.88 80.24 86.51 90.63

71.24 78.39 83.92 89.10

69.27 79.94 85.93 80.27

Ir = 0.5 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

74.40 82.29 87.55 92.93

72.88 80.01 86.14 92.02

71.24 77.67 83.02 88.39

69.27 80.26 85.56 79.37

Ir = 0.75 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

74.40 81.92 87.63 93.27

72.88 79.93 85.01 90.20

71.24 78.49 83.90 88.69

69.27 79.60 85.91 79.91

24

Ir = 1 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

74.40 80.92 86.30 92.66

72.88 79.79 86.63 92.27

71.24 78.31 85.02 91.32

69.27 80.24 86.81 80.28

25

Table 2: Dehydration rate (%) of the ultrasonic tests for the Gachsaran2 crude oil samples Ir = 0.25 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

75.54 85.47 90.12 97.06

74.05 82.35 87.99 93.08

72.20 81.40 87.48 92.70

69.45 81.59 86.49 81.26

Ir = 0.5 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

75.54 82.86 88.14 94.29

74.05 80.08 85.66 93.34

72.20 79.50 84.34 90.09

69.45 80.26 85.58 79.61

Ir = 0.75 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

75.54 83.72 89.51 95.66

74.05 81.54 86.26 92.50

72.20 78.12 83.59 88.32

69.45 79.88 85.79 80.54

Ir = 1 (W/cm3) Volw,init tr(s)

0 1 2 5

10

15

20

25

75.54 80.92 85.99 91.94

74.05 79.70 85.78 92.04

72.20 78.19 83.95 90.73

69.45 80.55 86.32 80.51

26

Table 3: Dehydration rate (%) of the ultrasonic tests for the Cheshmeh Khosh crude oil Samples Ir = 0.25 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

68.56 76.37 81.69 86.79

67.01 71.95 79.24 81.40

64.26 73.34 77.59 77.67

63.81 69.19 74.80 71.63

Ir = 0.5 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

68.56 75.36 79.33 86.07

67.01 70.94 77.23 82.53

64.26 73.64 79.87 77.74

63.81 70.38 76.71 72.69

Ir = 0.75 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

68.56 74.99 79.64 86.39

67.01 74.97 81.12 84.32

64.26 73.78 77.81 77.08

63.81 69.63 76.93 73.15

Ir = 1 (W/cm3) Volw,init(%) tr(s)

0 1 2 5

10

15

20

25

68.56 75.51 81.85 87.29

67.01 72.65 80.04 85.21

64.26 74.21 80.51 78.62

63.81 71.33 78.99 74.84

Nomenclature a

diameter of droplet (m)

a1

diameter of the smaller droplet (m) 27

aˆ

ratio of the smaller droplet diameter to the larger droplet diameter

B  v, t 

birth aggregation (mol.m-3.s-1)

C (ai , a j )

coalescence frequency of the particles with diameter ai and a j

delectrodes

distance between the electrodes (m)

D12

relative diffusivity due to Brownian motion

D  v, t 

death aggregation (mol.m-3.s-1)

Dd

diffusion coefficient of dispersed phase (m2.s-1)

E

electrical field (N/C)

Eac

average energy density of the acoustic field (j.m-3)

F

acoustic contrast factor

FF

objective function of optimization (minimization) for parameter estimation

g

gravity acceleration (m.s-2)

G

particle growth

Gs 

near-field relative mobility function

Hs 

near-field relative mobility function

I

unit tensor

Ir

ultrasonic intensity (W.cm-3)

k

wave number of the acoustic field (1/m)

K

Boltzmann constant (kg.m2.s-2.k-1)

Ls 

far-field relative mobility function

M

mass of separated water in bottle test

Ms 

far-field relative mobility function

N

number of drops

N exp

number of experimental points

Ni

number of drops with size of class “i”

n

number density of particles (1.m-3)

r

droplets’ center-to-center distance (m)

s

dimensionless droplet separation

t

time (s)

tr

Irradiation time (s)

28

T

temperature (K)

ud

droplet velocity (m/s)

u12

relative velocity of two droplets (m/s)

u

velocity of a droplet due to the body forces (m/s)

v

particle volume (m3)

Vol

volume (m3)

V

voltage (kg·m2·s−3·A−1)

W

ratio of the drag force to the buoyancy force

x

position of the droplet relative to the pressure antinode (m)

xi

pivot of class “i” (m)

Y

ratio of the first ultrasonic force to the buoyancy force

z

special position (m)

Greek symbols



viscosity (kg·m−1·s−1)

ˆ

ratio of the water viscosity to the oil viscosity



density (kg.m-3)

ˆ

ratio of the water density to the oil density

ˆ

ratio of the water compressibility to the oil compressibility

12

total interparticle force potential

d

dehydration rate

Subscripts

cal

calculated by model

exp

experimental value

init

initial (t=0)

o

oil phase

sep

separated water

tot

total water

w

water phase

Abbreviations

29

AC

alternative current

API 

American Petroleum Institute degree

SARA

Saturate, Aromatic, Resin and Asphaltene

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Figure 1. Ultrasonic system for the crude oil pretreatment. Figure 2. The main components of the ultrasonic transducer. Figure 3. The batch electrostatic cell and its power source. Figure 4. The effect of irradiation time on dehydration rate of the emulsion: (a) Ir = 0.5W.cm-3 & Volw,init % = 20, (b) Ir = 1.0W.cm-3 & Volw,imit % = 25. Figure 5. The effect of acoustic intensity on dehydration rate of the emulsion: (a) tr = 5mins & Volw,init % = 15, (b) tr = 2mins & Volw,init % = 25. Figure 6. The effect of initial water content on dehydration rate of the emulsion: (a) Ir = 0.25 W.cm-3 & tr = 2mins, (b) Ir = 0.75 W.cm-3 & tr = 5mins. Figure 7. Analysis of the desalted samples: (a) water content, (b) Salt content

Table 4: Characteristics of the crude oils

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Crude 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) Salinity concentration ppm (IP 77-72) Water content % (ASTM D4007-02)

Cheshmeh Gachsaran1 Gachsaran2 Khosh 21 28 31.5 20.3 21.4 19.1 20.7 18.1 22.6 1.1 0.5 2.4 15.9 14.1 19.3 18 23 21 21 19 28 -

Table 5: Preparation and experimental conditions of the two samples Control Ultrasonic Sample Sample

Parameter Initial Water Content (%)

15

15

Initial Salt Content (g/m )

3000

3000

Demulsifier Injection (ppm)

100

50

Ultrasonic field intensity of (W/cm3)

-

1

Irradiation time (min)

-

5

Electrostatic field Intensity (KV/cm)

1

1

Electrostatic time (min)

20

20

3

Table 6: The coefficients of the aggregation frequency parameter (  ) Crude Oil

A1

A2

B1

B2

Cheshme Khosh

1.009×10-9

-2.845×10-10

0.6674

-0.7979

Gachsaran1

1.796×10-9

-6.791×10-10

-0.232

-0.04143

Gachsaran2

2.331×10-9

-8.516×10-10

-0.429

-0.02919

Table 7. Simulated and experimental dehydration rate of the validation points: (a) Gachsaran1, (b) Gachsaran2, (c) Cheshmeh Khosh crude oil samples. (a)

Irradiation time (min)

Ultrasonic intensity (W/cm3)

Initial water content (%)

d ,exp (%)

d ,cal (%)

2 5 5 5

1.0 0.25 0.75 1.0

10 10 10 10

86.3 92.6 93.3 92.7

90.57 84.42 85.51 85.20

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(b)

(c)

1 1 5 2 5 5 1 5

0.25 1.0 0.5 0.75 0.75 1.0 1.0 1.0

15 15 15 20 20 20 25 25

80.2 79.8 92.0 83.9 88.7 91.3 80.2 80.3 Error (%)

85.63 87.87 95.34 77.19 92.75 84.19 73.23 82.86 6.29

Irradiation time (min)

Ultrasonic intensity (W/cm3)

Initial water content (%)

d ,exp (%)

d ,cal (%)

1 5 5 2 5 2 5 5 5 1 2 5

1.0 0.5 0.75 0.75 0.5 1.0 0.5 0.75 1.0 0.75 1.0 0.75

10 10 10 15 15 20 20 20 20 25 25 25

80.9 94.3 95.7 86.3 93.3 83.9 90.1 88.3 90.7 79.9 86.3 80.5 Error (%)

86.27 98.17 88.31 79.09 85.26 74.19 88.58 91.36 95.04 80.51 78.58 83.17 5.83

Irradiation time (min)

Ultrasonic intensity (W/cm3)

Initial water content (%)

d ,exp (%)

d ,cal (%)

1 1 2 5 5 5 2 2 5 1 1 2

1.0 0.75 1.0 0.5 0.75 1.0 0.5 0.75 0.5 0.5 1.0 0.25

10 15 15 15 15 15 20 20 20 25 25 25

75.5 75.0 80.0 82.5 84.3 85.2 79.9 77.8 77.7 70.4 71.3 74.8 Error (%)

65.31 75.67 75.32 83.74 81.58 82.92 71.33 71.24 64.84 81.76 75.42 86.41 7.65

35

Highlights: - The feasibility of using ultrasonication in the crude oil pretreatment as studied. - A low-frequency ultrasonic setup was designed to perform the experiments. - A population balance model was developed to interpret the experimental data. - An aggregation model was developed to predict the coalescence of droplets. - The results showed the proper performance of ultrasonic demulsification.

36