A New Approach Toward Improving our Understanding of ...

J. Sustainable Energy Eng., Vol. 4, No. 1, September 2016 37

*Corresponding author: [email protected]

DOI: 10.7569/JSEE.2016.629508

A New Approach Toward Improving our Understanding of Electrically Enhanced Coalescence

J. P. Wagner* and J. B. Nelson

Texas A&M University, Department of Nuclear Engineering, Separations Group, College Station, TX 77843-3133

Received March 15, 2016; Accepted August 15, 2016

Abstract: Coalescence rate data are presented for both well-defined water-in-oil (W/O) emulsions [different conductivity waters ranging from tap to reverse osmosis (RO) water dispersed in a light oil - Isopar M and stabilized with Paranox 100 surfactant] and “real world” crude oils using a 2-liter Teflon insulated electrostatic coalescer. The dramatic effect that changes in the electrical conductivity of two different light crude oils – Shell Brunei and Nigerian, have on increasing coalescense are demonstrated for A.C. fields at 1,000 Hz. while dispersed phase conductivity effects are shown for the same frequency and type using Isopar M/water emulsions. Resort to use of published analytical or theoretical treatments on electrostatic coalescence were unsuccessful in either explaining or correlating the data presented herein. An inspectional analysis of the charge transport conservation equations used to analyze static charge generation accompanying flow of hydrocarbon fuels, coupled with the accepted principles for two-phase flow was used to delineate the principal independent variables that coalescence rate depends upon. Dimensional analysis using the Buckingham π method and Langhaar’s matrix formulation in the mass (M), length (L), time (T) and Charge (coulomb, C) formulation was used to show that the dimensionless coalescence rate is a function of seven independent dimensionless groups. For the fixed geometry employed herein and for Isopar M emulsions, only the ratio of two dimensionless groups (i.e., π7/π6) was needed to correlate A.C. data at 60 and 120 Hz with a regression coefficient, R2, ranging from 0.86 to 0.94. The physical significance of the groups are discussed and future studies are recommended.

Keywords: Electrostatic coalescence, dimensional analysis, key dimensionless groups, dispersed phase electrical conductivity, light and intermediate crude oils, charge transport conservation equations

J. P. Wagner and J. B. Nelson: A New Approach Toward Improving our Understanding

38 J. Sustainable Energy Eng., Vol. 4, No. 1, September 2016

DOI: 10.7569/JSEE.2016.629508

1 Objective and Scope

The primary objective of this study was to improve our understanding of the performance of electrostatic coalescers especially under conditions where the elec-trical conductivity of the oil phase was varied using “so-called” antistatic additives, which we will term electrical conductivity modifiers. To achieve this goal a critique of published literature dealing with electrostatic coalescence was first initiated. Since no published theory could explain the dramatic increases in coalescence rate we obtained when the oil phase conductivity of light and intermediate crude oils were varied, a resort to collection of new data was initiated. This required the preparation of a well-characterized emulsion that would not vary from one test to the next. This was achieved using RO water (16.7% by vol.) mixed with Isopar M (83.3% by vol.) that was stabilized with Paranox 100 at room temperature, and subsequently tested under externally imposed A.C. fields at 60 and 120 Hz.

The second objective of our study was to show the influence that varying the electrical conductivity of both the oil phase and the dispersed water phase has on increasing coalescence rate for both “real world” crude oils and Isopar M emulsion systems.

2 Background Literature

Commercial applications of electrostatic separations have been in practice for nearly 100 years. However, well-known examples are limited to crude oil desalt-ing, distillate treating [1, 2] and removal of catalyst fines from cat cracker bottoms [3]. Of these three examples, crude oil desalting (which involves blending up to l0 wt.% of water with the crude to create a fine dispersion usually with or without addition of a surfactant and resolving this mixture under an externally imposed electric field) is the most widely practiced in terms of total throughput of product. In practice the salt is generally contained as in-situ brine. The blended water is then used to dilute the brine followed by a subsequent dehydration step.

A lesser-known example involves selective extraction of aromatic hydrocarbons from catalytic reformates using n-methylpyrrolidone as solvent with provisions for electrically improving settling in a mixer-settler operation [4]. More recently, there have been laboratory and analytical efforts addressing cross-flow electrofiltration in dealing primarily with synthetic fuels, such as coal-derived liquids [5–10].

It has been well known that electric fields can be used to augment mass transfer processes [11]; in particular, an increase of the mass transfer rate from around 3 to 10 fold [12, 13] has been demonstrated in extraction columns as compared to the “no-field” base case. Such results offer the potential for significant reductions in investment capital through use of smaller sized pressure vessels. Additionally, this methodology offers a compact alternative for separations that minimizes the space requirements, reduces the liquid inventories and improves the feasibility for total enclosure. In contrast to gravity settling, it also affords: lower operational costs,



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reduced civil engineering and capital cost requirements, fast response for control purposes and a considerable reduction in evaporative, entrainment, and degrada-tion losses of solvents [14].

Earlier patent literature results by Wagner [15–17] have shown that certain difficult to resolve emulsions can be electrostatically separated on a small pilot plant scale by the utilization of high frequency A.C. fields. These emulsions include: l) crude refinery and petroleum tanker sludges, 2) oil-continuous emulsions contaminated with electrically conductive catalyst fines and 3) liq-uid membrane emulsions with high water content (up to about 50%). Prior to these studies, emulsions with suspended fines and solids were particularly dif-ficult to resolve even when A.C. fields at frequencies in excess of 60 Hz were applied [18]. In addition, severe resolution difficulties were earlier observed with electrically conductive liquids even when frequencies as high as 1000 Hz were utilized [19].

Highlights of some of the results contained in Refs. 15–17 are presented here to illustrate the capability of the process. For example, a crude tank sludge with an initial analysis of 24.8 wt.% water, 73.5 wt.% oil, and 1.7 wt.% inorganic solids with electrical conductivity of 7.27 × 10–7 Siemens/cm was dehydrated to no detectable water as per the standard micro-distillation method of Dean and Stark. Another example included the dehydration of and removal of particles from an emulsion containing approximately 48 wt.% conductive catalyst fines, 49 wt.% oil and around 3 wt.% water. No water was found in the raffinate oil or in the sidestream containing the solid particulates when analyzed as per the standard method of Dean and Stark.

Additional results obtained at Texas A&M University conclusively demonstrate the potential for removal of metallic species from hydrocarbon continuous media including ionized metallic species such as lead, iron and zinc [20, 21]. Texas A&M guayule resin having the characteristics (pour point, heat of combustion, and flash point) of a heavy oil, was blended with reverse osmosis water at a proportion of 10 vol.% along with surfactant Breaxit 7151 (0.5% by weight) and a test series was conducted in a 2-liter glass electrostatic coalescer vessel [20–22] with vertical cylin-drical geometry. The surfactant stabilized emulsion was readily resolved under the electrical field while under gravitational effects alone, up to around 12 hours of set-tling time was required to obtain roughly comparable separations for Na+, Mg++, K+ and Ca++. However, for a heavy metal such as Pb++, electrostatic treatment removed approximately a 10-fold higher amount of metallic species in a residence time of only 22 minutes as compared to the 12-hour gravitational settling. It is currently unclear why slightly better results were obtained for Na+, Mg++, K+ and Ca++ under gravitational settling; however, the possibility of binding of salts known to uptake naturally in plants from soils to complex proteins in the resinous mixture come to mind. Considering that liquid inventories will build up to enormous quantities in 12 hours requiring storage in large tanks or vessels and that the aforementioned metallic species are present in one’s blood stream (i.e., are non-toxic in normal con-centrations), electrostatic separation is clearly preferred over gravitational settling.



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Recent results by Lee [23] at Texas A&M on both surrogate waste oils and used gasoline engine automotive crankcase oils further illustrate toxic metals removal capabilities. For a surrogate waste oil emulsion (reverse osmosis water-in-Isopar M) containing 104.5 ppm of nickel (II) 2-ethylhexanoate) stabilized with 0.25 wt.% Paranox 100 as surfactant, removal efficiencies of up to 99.1% were obtained in batch-mode tests under 60 Hz pulsed D.C. field. In batch-mode tests with diluted used motor oil, the removal of magnesium and sodium were roughly around the 50% range without extra additives. However, with the addi-tion of 0.7 wt.% Nalco 7715 (a emulsion breaker), the average zinc and calcium concentrations in the aqueous phase were more than doubled (67 and 86 ppm, respectively) as compared to that without addition of Nalco 7715 under both A.C. and pulsed D.C. fields at 60 Hz (26 and 42 ppm, respectively). The elec-tricity cost (i.e., around $ 0.38 per 1000-bbl or 0.23 cents per ton for a crude oilwith specific gravity 0.8 at 60 Hz of A.C. or pulsed D.C. electric field) to pro-cess an equivalent 1000 barrels quantity of emulsion is comparable to actualfull-scale “desalting” costs using coalescers designed by NATCO [24]. (NATCOGroup was acquired by Cameron in November 2009. Cameron has recently beenacquired by Schlumberger effective April 2016.) These values are almost negli-gible as compared with the thermal or encapsulation methods at $50 to $200 perton of effluent.

Additional test results with “real world” light and intermediate crude oils have shown increases in coalescence rate up to 600% by using certain types of elec-trical conductivity modifiers as compared to the identical test condition without the additive [25–27]. This methodology when combined with improved electrode and coalescer designs as demonstrated by Lee [23] offers great potential for dra-matic throughput increases in treating “real-world” oily wastes using significantly reduced sizes for the electrostatic coalescers.

Methods to increase metallic species removal efficiency [20] include: increasing feed residence time (i.e., reducing emulsion flow rate for the test system), increas-ing system operating temperature to reduce viscosity and interfacial tension gradients and promote film drainage between droplets, coalescer staging (e.g., operating several coalescers in series should easily improve extraction efficien-cies up to the 99% range or even higher excluding any other improvements), and changes of coalescer geometrical and operating parameters.

2.1 Mechanisms of Separation

Various mechanisms have been proposed to explain electrostatic separations in liquid media. The mechanisms involve phenomena such as [28]: chain formation, dielectrophoresis, electrophoresis, formation of intermolecular bonds, dipole coa-lescence, electrofining and random collisions. A two-step model involving chain formation and coalescence has been suggested for dispersions containing a water content of less than 10% by volume and droplet size in the range of 5–30 µm [29].



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Chain formation is characterized by the formation of chains of droplets that lie in the direction of maximum field strength and do not start or end in a particular electrode, and the chain grow by migration of single droplets in the direction that is generally perpendicular to the chain itself. As a result of the water droplets chain for-mation, a very low resistance path been developed between the electrodes and this is obviously considered to be responsible for the “sparking” or “arcing” that occurs in electrostatic coalescers with uninsulated electrodes.

Dielectrophoresis refers to the relative movement of drops with respect to the suspending medium as a result of an inhomogeneous electric field distribution. The movement is in the direction of the areas of higher electrical potential and is observed in both A.C. and D.C. fields.

Electrophoresis is the migration of charged droplets under a uniform elec-tric field toward the electrodes as a result of an applied potential gradient. This phenomenon takes place only in areas in proximity to the electrodes under unidirectional D.C. fields.

Rupture of existing intermolecular bonds at the interface between droplets, with the creation of new ones, or simply the rearrangement of molecular bonds have also been suggested as another mechanism to explain separations. Waterman [2] has distinguished two mechanisms that promote separation: dipole coalescence and electrofining. Dipole coalescence results from forces between droplets that have acquired an induced dipole. In A.C. fields, inter-droplet attraction takes place, causing the rupture of the separating, non-conductive film. In D.C. fields, droplets migrate back and forth between electrodes colliding and coalescing in their zig-zag trajectories [29, 30]. Electrofining includes the phenomena of elec-trophoresis, D.C. induced dipole coalescence and collision as a result of charged droplets moving in opposite or the same direction [2].

Film drainage theory has also been used to explain electrostatic coalescence. This approach divides the coalescence process into three general stages: approach of one drop to another, formation and thinning of the film trapped between inter-faces and rupture of the film. The second stage is believed to be the slowest and therefore the rate determining step [31]. It has been observed that when two drops approach each other, the trapped liquid film drains and the formation of a dim-pled film that thins with time is observed [32, 33]. A critical film thickness can be attained at which the film becomes unstable and ruptures. Film stability depends on the sign and magnitude of the disjoining pressure as well as the presence of surfactants or stabilizers [34]. Several models on film thinning are available. These are based on London-van der Waals forces [32], electrical double layer forces [33] or a combination of these forces [35]. Drop-flat surface or drop-drop coalescence have been considered in these studies.

Attempts to model coalescence based on the postulate of electric charge in con-ductive droplets have appeared as early as the 19th century. Rayleigh established that there is a limiting charge under which conductive drops of a given volume remain stable. Once this limit is exceeded the drops will disintegrate. For stable



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droplets, charge in excess of the Rayleigh limit value has been experimentally measured [36]. This is attributed to increased surface area of oscillating droplets when they deviate from spherical shapes. The Rayleigh principle has also been used to improve mass transfer rates by combining the processes of electrical disin-tegration and coalescence [37].

An important factor, that has restricted the commercialization of electrostatic processes, is that heretofore a valid theory that can be used to fully explain elec-trostatic processes is still not available [36–38]. No published approach was able to predict the behavior of the data (i.e., neither the magnitude of the increase nor the dependence on the electrical conductivity of the phases) shown in Figures 1–3 for coalescence of Shell Brunei and Nigerian crude oils and for Isopar M emulsions made with water of different electrical conductivities. Here dramatic increases in separation rates were achieved when the conductivity of both the oil and aque-ous phase were increased. Lack of success in obtaining a better understanding of electrostatic coalescence can be attributed to the complexity that arises from a large number of experimental dependencies involved in this phenomenon. This is illustrated later in the section on Dimensional Analysis following an outlining of the equations that must be solved in order to obtain the important dependencies of the coalescence phenomena.

3 Experimental Setup

The electric power supply module consisted of two Elgar Model 3001 single-phase power amplifiers (Elgar Corporation, San Diego, CA) operating in tandem. Both

Figure 1 The influence of conductivity modifier #1 on coalescence of shell brunei crude oil emulsion (83 oil/17 water % volume).

0

20

40

60

80

0 1 2 3 4 5 6Imposed electrical eld strength (kV/cm) - 1000 Hz, A.C.

Oil

phas

e di

seng

agem

ent r

ate

(ml/m

in) Untreated

30 ppm100 ppm

Conductivity of emulsion (S/cm)*10–10

9.2721.661.8


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43

Untreated1300 ppm

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8Imposed electrical eld strength (kV/cm) - 1000 Hz, A.C.

Oil

phas

e di

seng

agem

ent r

ate

(ml/m

in)

Conductivity of emulsion (S/cm)*10–9

3.3725.2

Figure 2 The influence of conductivity modifier #1 on coalescence of nigerian crude oil emulsion (83 oil/17 water % volume).

1000.00

100.00

10.00

1.002.70 4.05 5.41 6.76 8.11

Imposed electrical eld strength (kV/cm) - 1000 Hz, A.C.

Isop

ar M

pha

se d

isen

gage

men

t rat

e (m

l/min

) Conductivity ofemulsion (S/cm)*10–10

Conductivity ofwater (S/cm)*10–4

3.20.1

0.51

9.300.13

0.027

TapDistilledRO

Figure 3 Coalescence of isopar m emulsions made with different waters (83 isopar/17 water %volume).



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power source units are capable of supplying from 0 to 130 volts A.C. ( alternating current). A frequency oscillator (Elgar Model 400SD) is built into one of the power sources and it allows the frequency range to be varied between 45 and 3000 Hz. The high voltage field needed for electrostatic coalescence experiment was made possible by applying a NWL Model 25644 single-phase transformer (NWL Transformer and Power System, Bordentown, NJ) connected in series with the two Elgar power sources. The transformer can step up the A.C. voltage from 115 V to 20 kV (rms) A.C. at a maximum current draw of 250 mA, and is, thus, rated at 5 kVA of power.

A custom-built rectifier module including links between a diode-bridge, a capacitor-bank, and a series of resistor-arrays, provided different waveform out-puts. The five possible output forms are as follows: 1) standard A.C., 2) half-wave rectified (referred as pulsed D.C. herein), 3) half-wave rectified and smoothed, 4) full-wave rectified, and 5) full-wave rectified and smoothed. Only A.C. at 60,120 and 1,000 Hz was used herein. The power supply and the frequency oscillatorwere both calibrated by a 50 MHz Tektronix Model 2225 Oscilloscope connectingwith a 1000:1 Tektronix Model P6015 high voltage attenuation probe before thecoalescence experiments were performed. Figure 4 shows an exploded view of the2 liter Teflon insulated coalescence test cell.

The coalescer and all energized parts were secured in cages shielded with ¼ inch thick Plexiglas plate and the whole system also incorporates a set of inter-locking switches that activates a safety cut-out circuit if any door entry of the cage is opened while the unit is energized. In addition, the surrounding floor area was completely covered with corrugated Switchboard Mats (Lab Safety Supply, Janesville, WI), which has a dielectric strength up to 3 × 106 V/m, to ensure mini-mization of the high voltage hazard.

The charged or “hot” electrode was used for all tests but for the dimensional anal-ysis study was constructed according to specifications given in the patent literature by Wagner [17]. The inner support and conductor were fashioned from 10 gauge, copper wire, concentrically surrounded by a 6.35 mm O.D. (0.25 in.), 0.76 mm (0.03 in.) thick Teflon tube. Tap water was used to fill the gap between the wire and the tubing. The electrode was shaped into a spiral configuration, with as many turns as possible in order to closely approximate a flat electrode. The ground plate was a perforated steel plate connected to ground by a copper wire. A cross-shaped, sprin-kler type, emulsion distributor identical to that used by Figueroa and Wagner [20] was located 0.03 m. below the hot electrode (see Table 1 for dimensions of test setup).

The hot electrode for the dimensional analysis tests was similar to that used ear-lier by Lee, Sams and Wagner [24]. It consisted of a 10 gauge copper wire enclosed with flexible lightweight spaghetti Teflon tubing (2.7 × 10–3 m inside diameter, wall thickness 2 × 10–4 m) to form a grid with two vertical stems as illustrated in Figure 4. Interface level was kept constant at about 1.8 × 10–2 m below the insulated electrode.

All of the valves, fittings, adapters and tubing connections were primarily made of chemically inert fluoropolymer materials (including Teflon PFA, FEP, and PTFE)


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45

Table 1 Coalescer dimensions.

Component Dimension

Diameter 0.15 m.

Length 0.11 m.

Volume 1.94 × 10–3 m3

Separation between electrodes 0.065 m.

Distance from hot electrode to interface 0.018 m.

Height of interface from bottom ground electrode 0.047 m.

Figure 4 Exploded view of coalescence cell.

Water phase valve

Lower end plate

Viton O-ring

Ground plate

Distributor

Glass wall

Electrode

Viton O-ring

Upper end plate

Vent

Loading valve

Oil phase valve



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to ensure that the entire electrostatic coalescence system provided high electrical resistance, low coefficient of friction, excellent crack- and stress-resistance, and also was compatible with handling of highly corrosive or eroding fluid for future studies.

4 Experimental Measurements

The principal parameters examined in this study were electrical conductivity, vis-cosity of the oil and the emulsion formulations, interfacial tension using the stand-ard ring method, electrical voltage waveforms and frequencies, and field strength across the electrodes. The emulsion droplet mean diameter (0.2 µm) and size distribution determined by a Malvern ZetaSizer 3 were identical to that used by Figueroa and Wagner [20] and Figueroa [22].

Current draw from different applied voltage amplitudes in the coalescer, emul-sion feed rates, and changes in physicochemical parameters was not reported herein and is to be the subject of future efforts. After coalescence, the oil overflows or raf-finates were collected and analyzed for residual water content using the Dean and Stark micro-distillation method. Water levels were generally less than around 0.1% by volume in the raffinate phase. This is indicative of a high quality separation.

The viscosity of the liquid was measured using a Brookfield DV-III Programmable Viscometer/Rheometer (Brookfield Engineering Laboratories, Inc., Stoughton, MA) equipped with a CP-40 Cone Spindle and a TC-200 circulating water bath for precise temperature control. All of the samples were allowed to equilibrate to a preset temperature of 25 °C while the measurements were taken. The data used herein were taken at ambient conditions.

The phase disengagement rates of the raffinate and aqueous phases were measured using graduated cylinders and a stopwatch. Emulsion feed rate to the coalescer was regulated using the rheostat control on the feed pump.

5 Emulsion Preparation

The preparation procedure started with weighing 7.0 g of Paranox 100 (a polyamine surfactant from EXXON Chemical Company, Linden, NJ) in an empty 8-liter capacity stainless steel beaker then adding 1200mL of Isopar M (a lightiso-paraffinic oil from EXXON Chemical Company) and allowing them to sit anddissolve for at least 8 hours. Then the mixture was stirred at 1,000 rpm for 1 minuteafter which 200 mL of Reverse Osmosis water was evenly added to the beakerduring a 30-second interval while using a Tekmar Super Dispax SD-45 laboratorysized Homogenizer (Tekmar Company, Cincinnati, OH) stirring at 1,000 rpm.Once all of the water was added, the emulsion was allowed to continue mixing atthe same speed for additional six minutes. The stability of the emulsion was deter-mined to be acceptable if no noticeable phase disengagement occurred for a periodbetween 12 and 24 hours. Immediately following preparation, the emulsion wastransferred to the reservoir tank and then the coalescence experiment was started.



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It was important to have a stable emulsion in order to minimize variations in the droplet size distribution, which would lead to errors in correlating the data.

6 Operating Procedures

The insulated electrode was positioned parallel to the ground plate and the oil/water interface. The cross-type distributor introduced the emulsion below the hot electrode into the oil phase above the interface and allowed it to flow radially outward and parallel to the insulated electrode. No evidence of arcing or short-circuiting occurred over the range of imposed potential gradients.

After the electrical field was fully established, the emulsion was pumped into the coalescer at a gradually increasing flow rate before a very thin band of unre-solved emulsion was observed at the interface. The interface was maintained at constant level by carefully regulating the output flows of the disengaged phases, both oil phase overflow from the top and water drained out from the bottom of the coalescer. The maximum coalescence rates were attained by measuring the volume of oil overflows collected in graduated cylinders over fixed time periods while simultaneously monitoring the emulsion pumping rates and allowing that no unresolved emulsion accumulated at the oil-water interface.

Between changes in voltage or frequency, any unresolved emulsion that accu-mulated at the oil/water interface was “electrically clarified” before adjusting the electrical signal to another level. This clarifying procedure proceeded with increasing applied voltage to approximately a maximum value of 15 kV (p-p) under no flow conditions, and the system was kept at this high potential gradi-ent for several minutes until all of the residual emulsion at the interface was resolved. This insured that precisely the same starting condition took place for each run.

All coalescence experiments conducted herein were carried out at room temperature.

7 Charge Transport Conservation Equations

The charge transport conservation equations applicable to understanding the behavior accompanying charge generation and transport during fluid flow situ-ations in low dielectric constant, low conductivity liquids (e.g., typical refined and unrefined hydrocarbons including crude oils) utilized herein are due to Gavis [39–42]. The nature of the boundary conditions for different flow situations as well as similitude principles based on these equations is given by Wagner [43]. Starting with the most generalized equation given below

∂∂

dqrt

L D q q q q D q qr

rr r r r r r r= + + ∇ − + +( / ) [ * /( ) ] [( ) ]/ / *2 1 2 1 21 1 12 2 2

−− ⋅ ∇ + + + ∇ ⋅ ∇ + ∇( / ) [ /( ) ] ( ) /(/ * *d y12 21 1 2 2L q q q D q D q qr r r r r r r r r r r rv ++ 1)

(1)



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whereq q FC v v U L

t t FC L r L

r r r

r o r o o

= = ∇ = ∇

= = ( ) ∇ = ∇

/ /

/ /

o

t y y ee 2 2 2 2

D* = (D+ – D–)/(D+ + D–), is the ionic diffusivity ratiod = (D*to)

1/2 is the Debye electrical double layer thickness, andd1 = Uto is a characteristic length based on velocity times a characteristic electri-

cal relaxation time and L and U are length and velocity characteristics of a particu-lar system and τo is the relaxation time of the original solution before transport has occurred and is given by,

to = eeo/[D* F2 Co/Rg Ta]

one sees that a solution to this equation even for simple geometries and single phase flow is difficult even for simple boundary conditions and steady flow conditions.

Simplified forms of the charge transport conservation equation readily follow [39–43] and are only illustrated for:

Equal ionic diffusivities D+ = D–, or D* = 0 then Equation 1 becomes

∂∂

d dqrt

L q q q L q q qr

rr r r r r r r r r= ∇ − + − ⋅ ∇ + +( / ) [( ) ] ( / ) [ /(/2 1 22 2

121 v 11 1 2) ]/ *

∇ ⋅ ∇r r r rq y (2)

andFor small charge density qr = q/FCo << 1, then Equation 2 reduces [39–43] to

∂∂

d dqrt

L q q L qr

rr r r r r r= ∇ − − ⋅ ∇( / ) ( / )2 2

1 v (3)

or in non-reduced form

∂t d

qt

D q q L qo∂

= ∇ − − ⋅ ∇2

1/ ( / )v (4)

where it is similar to the equation for convective diffusion with a source term.Even Equation 4 is difficult to solve for two-phase flow conditions and when

one does not know the boundary condition (e.g., is it a drop-drop or drop- interface type of interaction), little good will be accomplished by providing solutions since they will not relate to reality. Nevertheless, the equations are useful since an inspectional analysis provides one with important electrokinetic parameters useful in a dimensional analysis. These parameters when coupled with surface tension, viscosity and droplet size provide the independent parameters necessary in performing a generalized dimensional analysis.

7.1 Dimensional Analysis

We will assume that coalescence rate (or oil phase disengagement rate), E, is the independent variable and we have a mono-dispersed charged droplet distribution



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under the influence of an electric field. Furthermore, we will utilize the fact that throughput data for industrial coalescers are based on correlations relating emulsion or dispersion flow or feed rate (e.g., barrels/day-ft2 of electrode cross-sectional area for a specific crude oil type) to the density difference (i.e., density of water - density of oil) divided by the viscosity of the continuous or oil phase –(dw – do)/µ. Ιn addition, we will assume the M (mass), Length (L), time (T), Charge (Q in coulombs) system and the matrix formulation given by Langhaar [44]. This allows us to formulate the following matrix.

k1 k2 k3 k4 k5 K6 k7 k8 k9 k10 k11 k12

E Im Ae Ac Lhi m rw – ro D* t0 FC0 fI a

M 1 0 0 0 0 1 1 0 0 0 1 0

L 0 0 2 2 1 –1 –3 2 0 –3 0 1

T –1 –1 0 0 0 –1 0 –1 1 0 –2 0

Q 0 1 0 0 0 0 0 0 0 1 0 0

Solution to a set of algebraic equations based on the above matrix allows one to solve the resultant matrix and obtain a total of eight dimensionless groups as illustrated below [45]:

p t p t p p

p p m t1 0 2 0 0

33

24

2

5 6 0

= = ( ) = =

= = ( )E I FC a A a A a

L a ai m e c/ / / / /

/ /

φ

φii w ia D ap r r t p t7 03

02

8 02= −( ) =/ /φ

Now, according to the Buckingham p Theorem a functional relationship between p1 and the other p’s exists in terms of simple powers. By maintaining as many of the above groups constant one can develop a relationship between these correlating groups. This approach shows that the dimensionless feedrate or throughput of the emulsion, p1, is a function of the independent dimensionless groups p2…….. p8 or

p p p p p p p p1 2 3 4 5 6 7 6= B a b c d e f g

where B is a constant. Based on recent data in our lab, it appears that only π6 and p7 (i.e., the ratio of p7 to p6 or alternatively p6 to p7) are needed to correlate experi-mental coalescence rate data (see Figure 5). Here the data illustrate a reasonable fit as the regression coefficient, R2, ranges from 0.94 to 0.86. Other parameters which were fixed or kept constant, such as the cross-sectional area of the energized elec-trode, cross-sectional area of the coalescer, etc., would need to be varied for scale-up purposes for larger-sized vessels.

The physical significance of the ratio of the correlating parameters p7/p6 given by:

p p r r m t7 02

06/ / /= −( )

×

w a



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is to follow. First the density difference term divided by the viscosity is precisely the term used to scale up industrial coalescer behavior. It is implicit here that in order to enhance coalescence behavior one should operate at elevated temperature in order to reduce the viscosity to achieve good settling of water droplets; thus, industrial coalescers are designed to operate at temperatures typically ranging from 250–300 °F. However, the significance of the term a2/τ0 has not been recog-nized by other investigators. This is probably due to industrial processors gener-ally blending water with the crude oil across a mixing valve at around a 10 psi pressure drop to create a dispersion or emulsion for which the a2/τ0 is effectively a constant (i.e., the droplet size is fixed by the power dissipation across the mixing valve and the relaxation time for the dispersion or emulsion doesn’t change much from that of the oil itself). However, it should be emphasized that t0 can easily be varied by 105 for refined petroleum products as clearly shown in Ref. 43 and Refs. 25–27 for crude oils through variations in electrical conductivity. However, for unrefined crude oils one is limited by how much the electrical conductivity can be varied since too conductive of a medium can lead to premature arcing before coalescence is achieved.

The ratio of π7/π6 may be interpreted in a number of different ways. First, since m/rD* is the mass transfer Schmidt number, Sc, based on the mean dif-fusivity of ions in solution, then multiplying both numerator and denominator by D* one can define a modified Schmidt number based on density differences as follows

Sc D Dw w∆∆= −( )

= ( )

∗

−

∗m r r m r/ /0 0

Now one has

p p t7 62

01/ / /= [ ]×

∗Sc a D∆

Here D*t0 is the square of the equilibrium Debye electrical double layer thickness

s t=

∗D 0

1 2/ based on the mean ionic diffusivity. Since the Schmidt number for

liquids generally doesn’t change by more than a factor or around 2, one sees that the controlling term is [ka2/D*ee0] upon substituting for t0. Again since the drop-let size is fairly large (i.e., the power dissipation per volume of fluid is small in a 10 psi pressure drop across a mixing valve), D* doesn’t vary much, is typically around 2 for hydrocarbon liquids, e0 is a constant, then the controlling variable is k, the electrical conductivity. The group [ka2/D*ee0] is dimensionless, and, thus, may be interpreted as the ratio of the square of the characteristic droplet diameter to the square of the Debye double layer thickness.

If one leaves the ratio of p7/p6 as such

p p r r m t7 6 02

0/ / /= −( )

×

w a



DOI: 10.7569/JSEE.2016.629508

and rewrites the [(rw – ro)] as ∆rw–o then p7/p6 may be rewritten in more familiar terms as

p pr t

m7 60 0/

/=

[ ]−∆ w a a

where ∆rw–o[a/t0 ]a/m has the units of a modified Reynolds number. Τherefore, p7/p6 may be interpreted as a ratio of electrokinetic forces to viscous forces.

The physical significance of

p t8 02

=∗D a/

is clear since D*τ0 is the square of the equilibrium Debye double layer thickness;

that is it is the ratio of square of the Debye double layer thickness to a character-istic droplet size squared. It is contained implicitly in the ratio of π7/π6 and will probably not have any significance in improving the correlation of the data given in Figure 5.

As an alternative to plotting π1 versus the ratio of π7/π6 once could also plot π1 versus π6/π7. Then the ratio of π6/π7 becomes

p p s6 72 2/ /= Sc a∆

where Sc∆

2/a2 may be interpreted as an electrokinetic Schmidt number, Sc∆e, based

on the density difference between the water and oil phase.

Figure 5 Results of dimensional analysis.

y = 2E+23x1.3619

R2 = 0.9422

y = 2E+22x1.2954

R2 = 0.8605

y = 1E+23x1.341

R2 = 0.9008

0.01

0.1

1

10

100

1000

1.00E-19 1.00E-18 1.00E-17 1.00E-16 1.00E-15 1.00E-14

PI 7/PI 6

PI 1

60 Hz (8 & 9 kV) 120 Hz (8 & 9 kV) Both frequencies

Power (60 Hz (8 & 9 kV)) Power (120 Hz (8 & 9 kV))Power (both frequencies)



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The current draw term

p t2 0 03

= ( )× ( )Im / /FC a

is not easily interpretable. Rearranging p2 and multiplying both numerator and denominator by the imposed potential ψ one obtains.

p yy t

2

03

0

=I

FC am

/

Therefore, π2 may be interpreted as the total power dissipated during the coalescence process divided by the power required to collapse a charged droplet.

However, using the definition for electrical conductivity in terms of the mean ionic diffusivity [43]

k = CoF2D*/RgTa

and substituting for FC0 and rearranging one gets for π2

pt

20

2

=

×

( )

∗I D a

R T

F ka

m

g a

/

/

Now the term RgTa/F/ka may be interpreted similarly to that of the conventional Arrhenius expression using the dimensionless groups in Catchpole and Fulford [46] as the ratio of the potential energy of the fluid to the activation energy of a charged droplet. The second term in the numerator is π8 and has been interpreted previously.

The physical significance of the groups π7 and π6 upon rewriting are as follows:

p r r tr t t

7 03

02 0 0 0

= −( ) =

( )

×−

w Iw

Ia

a a a/

/ /φ

φ

∆

p m t6 0= ( )/ / a iφ

where π7 is the product of inertia forces acting on a droplet times the ionic forces acting on the droplet under the influence of the electrical field divided by surface or interfacial tension force and π6 is the ratio of viscous forces acting on the droplet divided by the product of the ionic forces acting on the droplet times the surface or interfacial tension forces.

Thornton [47] was apparently the first investigator to use dimensional analy-sis to correlate experimental data on charged droplets for the system (water-in-n-heptane) over a limited range of system variables. Here the normalized droplet diameter was characterized by only two dimensionless groups, one of which contains the dielectric constant and the other a density difference. One immedi-ately notes the absence of the electrical conductivity of n-heptane and the fluid viscosity. Closer inspection, however, reveals that fluid electrical conductivity and



DOI: 10.7569/JSEE.2016.629508

temperature were also not considered as independent variables in the analysis. Here it is demonstrated that a more generalized dimensional analysis based on an inspectional analysis of the charge transport equations along with the assump-tion of two-phase flow applied to a charged droplet reveals that as many as seven independent dimensionless groups (the eight group is the dependent dimension-less throughput or coalescence rate) influence charged droplet or coalescence rate behavior. That the electrical conductivity is an experimental parameter of impor-tance is supported by extensive data obtained in our laboratories for coalescence of light and intermediate crude oil emulsions [25–27].

8 Discussion and Conclusions

It is well known that electrostatic coalescence is not only influenced by the volt-age, oscillating frequency and waveform type of the applied electric field, but also by coalescer geometry, electrode configuration, operating temperature, agitation speed of mixing, volume phase ratio, and physical-chemical properties of the emulsion constituents (e.g., oil-phase density, viscosity, dielectric constant, electri-cal conductivity, water droplet size, surfactant concentration, etc.).

To date, there is no valid theory that can explain the complex dependencies of all of these variables with emulsion separation rate, nor is there any easy method to isolate individual factors or to generalize the entire contributions to the whole process. Consequently, it is very difficult to make indisputable comparisons between many different researchers’ results. The differences in coalescer configu-ration employed and various definitions of parameters arbitrarily chosen to evalu-ate the emulsion separation rates by many researchers further complicated the comparison procedure [48–50].

Waterman [2] first suggested that the performance of coalescing crude oil emul-sion was equally as well in A.C. and D.C. fields, but Hsu and Li [51] pointed out that an A.C. source was much superior to a D.C. source for liquid membrane demulsification processes. However, Bailes and Larkai [52], Wakeman [53] and Figueroa and Wagner [20] all suggested that pulsed D.C. fields gave the best coalescence efficiency. Figueroa [22] also concluded specifically that a pulsed D.C. waveform achieved emulsion separation rate between 1.2 to 1.5 times higher than that obtained from an A.C. signal of the same rms applied field strength at a fre-quency of 600 Hz.

In contradiction with the experimental results obtained by Figueroa [22] and Figueroa and Wagner [22], Lee, Sams and Wagner [24] recently found that at the same 400 Hz frequency with applied field strength about 1.9 × 102 kV(rms)/m, the A.C. field gave rise to a coalescence rate of almost 345 mL/min, which was 303% higher than the 114 mL/min achieved by applying a pulsed D.C. field. On the other hand, at the same frequency, in order to attain an equivalent coales-cence rate, the applied field strength for a pulsed D.C. field would be 15.7% higher than that for an A.C. field (e.g., at frequency of 600 Hz, for oil phase overflow



DOI: 10.7569/JSEE.2016.629508

rate of about 550 mL/min, pulsed D.C. field needed an applied strength of 2.50 × 102 kV(rms)/m as compared to that only about 2.16 × 102 kV(rms)/m was needed for an A.C. field).

With the noted lack of agreement among different investigators, especially even within our own laboratory, it was decided to study the coalescence of a well-defined Isopar M /RO water emulsion system. Excellent reproducibility of emul-sion properties such as droplet size and electrical conductivity was achieved from one test to the next and, thus, changes in these parameters could be eliminated as potential errors or scatter in the data.

Our results indicate that the dimensionless separation rate π1 is a function of only the ratio of two dimensionless groups π7/π6 or π6/π7 depending on ones pref-erence. The regression coefficient, R2, which varied from 0.94 to 0.86 is indicative of reasonable accuracy.

Further study is needed to extend the study from the model emulsion system Isopar M/ RO water to “real-world” crude oils. Additionally, the current draw term π2 in our dimensional analysis needs to be examined over a range of frequen-cies and imposed potential gradients.

Acknowledgments

The authors wish to acknowledge the generous support from the Texas Higher Education Coordinating Board for their Advanced Technology Program and Technology Development & Transfer Program. Without this support the present study could not have been undertaken. Two of us (J.P.W. and J.B.N.) wish to acknowledge additional strong support and collaborative efforts from NATCO Group, Inc., and Nalco/Exxon Energy Chemicals, Inc.; additionally, the labora-tory support in conduct of the experiments and Dean and Stark water analyses by Dr. Jerry Zoeller is also gratefully acknowledged.

Nomenclature

Ae: cross-sectional area of energized electrode (L2)Ac: cross-sectional area of coalescer (L2)A: characteristic mass medium diameter of the emulsion obtained from a

Malvern ZetaSizer 3 particle size/Zeta Potential analyzer (a = 0.2 µm )Co: concentration of ions in bulk of fluid, (moles/m3)D+,-: Ionic diffusivity of positive or negative ions, (L2/t or m2/s)D: mean diffusivity of positive and negative ions, (D+ – D-)/2, (m2/s)D*: (D+ – D-)/(D++ D-), ionic diffusivity ratio, (m2/s)E: the feedrate of the emulsion, (M/s)F: Faraday number [96,500 Coulombs/mole, (C/mol)]FC0: initial total concentration of ions in solution which may be obtained from

the measured electrical conductivity and standard equations in Ref. 43.



DOI: 10.7569/JSEE.2016.629508

Im: the current draw measured across a dropping resistor (1000 Ω) in series with the ground electrode of the coalescer (not utilized herein), (A)

k: Fluid conductivity, Siemens/m (S/m)L: characteristic length, (m)Lhi: distance from energized electrode to oil/water interface, (m)M: Mass, (kg)Q: charge in Coulombs, (Q)q: charge density, (C/m3)qr: reduced charge density, dimensionlessRg: gas constant, (8.32 V-C/K-mole)Re: Reynolds number, dimensionlessSc: Mass Transfer Schmidt number, dimensionlessTa: Absolute temperature, (K)t, T: Time, [seconds, (s)]tr : reduced or dimensionless time, (t/ τo)U: characteristic flow velocity, (m/s)v: flow velocity, (m/s)vr: reduced flow velocity, dimensionlessvr: reduced vectoral flow velocity, dimensionless

Subscripts

r: reduced or dimensionless variableo: initial value of a parameter or oil phasew: refers to water or aqueous phase

Greek Symbols

δ: (D*τo)1/2 is the Debye electrical double layer thickness, (m)

δ1: Uτo is a characteristic length based on velocity times an electrical relax-ation time, (m)

∆: property difference∇: mathematical symbol for gradient∇2: mathematical symbol for Laplacian operatorε: dielectric constant of liquid, dimensionlessεo: permittivity of free space, a constant equal to 8.85 x 10-12 s/-mµ: Fluid viscosity, kg/m-sρ: Fluid density, kg/m3(ρw – ρo): density difference between heavy (water) and light phases (oil)π: Constant number Piτo: electrical relaxation time, s; τo = εεo/kψ: potential, (V)ψr: reduced potential, dimensionlessφi : surface or interfacial tension, (kg/s2)



DOI: 10.7569/JSEE.2016.629508

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