Lixin Wei1, Meng Chao2, Xuanrui Dai1, Xinlei Jia1,3, Xiaoheng Geng3, Haiying Guo3. 1. School of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China. 2. Gas Production Branch of Daqing Oilfield Co. Ltd., Daqing 163453, China. 3. College of Chemical Engineering and Safety, Binzhou University, Binzhou 256600, China.
Abstract
Various flooding technologies were applied in the middle and late stages of the oilfield, which made the heavy oil emulsion receive much concern because of its high stability and separation difficulty. In our paper, alcohol molecules were used as initiators and multibranched block copolymers were synthesized through open-loop polymerization technology. A variety of novel modified block polyether demulsifiers with demulsification activity were finally synthesized through water-soluble modification and oil-soluble modification, which achieved efficient demulsification of heavy oil emulsions. Hydrophile-lipophile balance (HLB) values and surface tension were used to characterize demulsifiers. In addition, their demulsification efficiency was evaluated by measuring the amount of dehydration in the separated heavy oil emulsion experiments. The experimental results showed that within 5 h, the demulsification effect of the water-soluble demulsifier is better than that of the oil-soluble demulsifier. When the HLB value of the demulsifier reaches a certain value, the dehydration rate and the demulsification effect reach the highest point. When the amount of demulsifier is 50 μg/g and the demulsification temperature is 85 °C, the dehydration rate of the water-soluble demulsifier X-6 reached 91%, the water quality was clear, and the demulsification effect reached its peak. This work will provide a novel and efficient demulsifier for demulsification and dehydration of heavy oil emulsions.
Various flooding technologies were applied in the middle and late stages of the oilfield, which made the heavy oil emulsion receive much concern because of its high stability and separation difficulty. In our paper, alcohol molecules were used as initiators and multibranched block copolymers were synthesized through open-loop polymerization technology. A variety of novel modified block polyether demulsifiers with demulsification activity were finally synthesized through water-soluble modification and oil-soluble modification, which achieved efficient demulsification of heavy oil emulsions. Hydrophile-lipophile balance (HLB) values and surface tension were used to characterize demulsifiers. In addition, their demulsification efficiency was evaluated by measuring the amount of dehydration in the separated heavy oil emulsion experiments. The experimental results showed that within 5 h, the demulsification effect of the water-soluble demulsifier is better than that of the oil-soluble demulsifier. When the HLB value of the demulsifier reaches a certain value, the dehydration rate and the demulsification effect reach the highest point. When the amount of demulsifier is 50 μg/g and the demulsification temperature is 85 °C, the dehydration rate of the water-soluble demulsifier X-6 reached 91%, the water quality was clear, and the demulsification effect reached its peak. This work will provide a novel and efficient demulsifier for demulsification and dehydration of heavy oil emulsions.
Oil is the most important
energy and strategic material in the
world and its demand has increased rapidly with the growing global
economy. In the process of oil exploitation, due to the composition
of the crude oil, the flooding process, and even the distribution
of underground crude oil, water is always produced during the processing
and refining of crude oil.[1−3] The presence of water in crude
oil and natural surface-active substances in petroleum causes emulsification
of crude oil under conditions of temperature and shear.[4,5] At present, about 80% of the crude oil in the world is recovered
in the form of an emulsion.[6]With
the large-scale exploitation of conventional oil resources
in various countries, heavy oil has attracted much attention because
of its huge reserves.[7] Canada, the United
States, China, Venezuela, Indonesia, and other countries are all rich
in heavy oil resources. In recent years, thermal oil recovery technology
has gradually been replaced by thermochemical oil recovery technology;
the main method is to increase the recovery of heavy oil using surfactants
or polymers as oil displacement agents.[8,9] However, surfactants
and polymers will aggregate on the oil–water surface to form
a rigid, stable, viscoelastic interface film, which will further improve
the stability of the heavy oil emulsion and destroy the continuity
of demulsification technology of the heavy oil emulsion.[10−12] The demulsification technology for heavy oil emulsions can be divided
into three categories: mechanical, chemical, and biological, of which
chemical is the most economical and commonly used method of demulsification.
The demulsification rate of the heavy oil emulsion can be increased
by adding a small amount of the demulsifier. At the same time, factors
such as the demulsification temperature and the amount of the demulsifier
affect the demulsification rate. The above factors can be optimized
by further research.[13−15] Novel demulsifiers such as ionic liquid demulsifiers
or magnetic demulsifiers are currently being researched. Ezzat et
al.[16] synthesized a novel amphiphilic ionic
liquid demulsifier using dialkyl-substituted imidazoles as the head
group and combining with acetate and 4-(trifluoromethoxy) phenyl borate
anion. Abdullah et al.[17] synthesized amphiphilic
ionic liquids (AILs) and formed the corresponding IL (GEB-CL). The
chloride ion was replaced by a trifluoroacetic acid (TFA) ion to form
the second IL (GEB-TFA), which had a strong ability to reduce the
surface tension and IFT. Atta et al.[18] prepared
a new type of an ionic surfactant using cashewnut oil as a raw material
and put forward a viewpoint that the single surfactant as a heavy
oil dispersant and a demulsifier had a good effect through experimental
analysis. Al-Lohedan et al.[19] prepared
a new amphiphilic Gemini ionic liquid (GILs) using poly(ethylene terephthalate)
(PET). The results of characterization and performance evaluation
showed that the demulsification efficiency increases with the increase
in the water content. Alves et al.[20] synthesized
five different chemical surfactants based on castor oil and determined
that the demulsification effect of MACO1 was better at 60 °C
through characterization of the synthesized surfactants and the demulsification
experiment of the bottle test method. Ali et al.[21] synthesized a novel demulsifier P (MMA-AA-DVB)/Fe3O4 magnetic submicron ion and studied the demulsification
performance of the demulsifier in a heavy oil–water emulsion.
Although the research on novel demulsifiers for heavy oil emulsions
has broad application prospects, further research is needed, and the
existing technologies cannot comprehensively surpass traditional chemical
demulsifiers in terms of the synthesis process, application scope,
and demulsification effect. The demulsifying ability is manifested
by controlling the hydrophile–lipophile balance values and
destroying the stable and rigid interface film formed by the surfactant,
polymer, and the like at the oil–water interface.[22−24] Block polyether demulsifiers were gradually applied to crude oil
demulsification in the 1940s. The block polyether demulsifier mainly
consists of a polymerization reaction between an initiator and propylene
oxide (PO) and ethylene oxide (EO) under the action of a catalyst
and forms a hydrophobic block of poly(propylene oxide) (PPO) and a
hydrophilic block of poly(ethylene oxide) (PEO).[25−27] Demulsifier
compounding, chain extension, and cross-linking are common modification
methods for demulsifiers.[28] Water-soluble
modification and oil-soluble modification use active hydrogen groups
in the demulsifier to react with other active molecules, which can
change the hydrophilic and lipophilic properties, increase the molecular
weight and the number of branches of the demulsifier molecule, and
improve the demulsification effect.[29]The purpose of this work is to study the synthesis of a novel modified
polyether demulsifier for heavy oil emulsions. In our paper, a series
of block-modified polyether demulsifiers were synthesized by changing
the ratio of propylene oxide (PO) and ethylene oxide (EO). Demulsifiers
were characterized by surface activity and hydrophile–lipophile
balance (HLB) values. Through bottle test analysis and determination
of the optimal block-modified polyether demulsifier, the purpose of
improving the efficient demulsification of heavy oil demulsifiers
at this stage was achieved and it provided a reference for the synthesis
of polyether demulsifiers.
Results and Discussion
Determination of the Content
of a Cross-Linker
Oil-soluble
demulsifiers modified with 10% PM-200 solutions of different qualities
were synthesized, and demulsification dehydration experiments were
carried out by the bottle test method, and the demulsification rates
of different oil-soluble modified demulsifiers in 5 h were recorded.
The amount of the demulsifier added was 50 μg/g and the demulsification
temperature in the water bath was set at 85 °C. The demulsification
dehydration experiment results are shown in Figure . It can be seen that as the amount of modified
cross-linking agent increases, the demulsification rate of the oil-soluble
demulsifier increases first and then decreases after 5 h. When the
dosage is 4% of the mass of the polyether demulsifier, the demulsification
rate reaches the highest. This is because when the amount of the cross-linking
agent is small, appropriately increasing the amount of the cross-linking
agent can improve the demulsification rate. When the concentration
of the cross-linking agent is too high, the diffusion speed of the
demulsifier in the process of demulsification is reduced and the demulsification
rate is reduced at the same demulsification time.
Figure 1
Five hour emulsion breaking
rate of different doses of a cross-linking
agent.
Five hour emulsion breaking
rate of different doses of a cross-linking
agent.
Hydrophile–Lipophile
Balance (HLB) Values of a Polyether
Demulsifier
The above experimental method is used to determine
the hydrophile–lipophile balance (HLB) values, and the measurement
results are shown in Figure , where D is a polyether demulsifier, W is a water-soluble
modified polyether demulsifier, and O is an oil-soluble modified polyether
demulsifier. As shown in Figure that in the same series, the water-soluble modified
polyether demulsifier has the highest HLB value and high hydrophilicity,
the polyether demulsifier itself is second, and the oil-soluble modified
polyether demulsifier has the lowest HLB value. For different series
of HLB values, as the proportion of EO and PO in the molecular weight
in the X-1 to X-8 series increases, the HLB values and hydrophilicity
of polyether demulsifiers and water-soluble polyether demulsifiers
increase. The oil-soluble modified polyether demulsifier has a relatively
stable overall HLB value in the X-3 to X-6 series, and the HLB value
of other series decreases significantly.
Figure 2
X-series demulsifier
HLB value measurement.
X-series demulsifier
HLB value measurement.
Surface Tension of a Polyether
Demulsifier Solution
The surface tension of the polyether
demulsifier and the modified
polyether demulsifier aqueous solution was measured by the pendant
drop method. The measurement results are shown in Figure . The surface tension of a
polyether demulsifier aqueous solution and water-soluble modified
and oil-soluble modified polyether demulsifiers has the same tendency.
When the concentration is 1–50 mg/L, the surface tension decreases
rapidly; after 50 mg/L, it decreases slowly and finally stabilizes
at about 37.2 mN/m. The surface tension–concentration curve
of the water-soluble polyether aqueous solution is slightly lower
than that of the polyether aqueous solution, and both the polyether
and water-soluble modified polyether curves are lower than the oil-soluble
modified polyether curve. This showed that the water-soluble modified
polyether aqueous solution was slightly better than the polyether
aqueous solution in its ability to reduce surface tension. The ability
of oil-soluble modified polyether aqueous solution to reduce surface
tension was lower than that of polyether and water-soluble modified
polyether aqueous solutions. From the perspective of the final effect,
all three polyethers could effectively reduce surface tension, and
at the same time had better displacement and replacement capabilities
and higher surfactivity.
Figure 3
Surface tension of polyether and modified polyether
aqueous solutions.
Surface tension of polyether and modified polyether
aqueous solutions.
Demulsification Mechanism
Analysis
After the demulsifier
was added to the heavy oil emulsion, the high surface activity of
the demulsifier could pass through the external phase of the emulsion
to reach the oil–water interface, and the demulsifier with
higher hydrophilic properties reached the oil–water interface
faster. The block polyether demulsifier synthesized in this experiment
has high surface activity, can reduce the interfacial tension, preferentially
adsorbs on the oil–water interface, and replaces the asphaltene
molecules at the oil–water interface. A large number of demulsifier
molecules are adsorbed on the oil–water interface in this way,
and an interface film with lower stability is formed. Under the action
of heating or shaking, the macromolecules in the emulsion made irregular
Brownian motions and collided with other macromolecules, causing the
interface film to rupture, and the water in the internal phase broke
through the interface film and entered the external phase to agglomerate
to achieve the purpose of oil–water separation. Figure shows the demulsification
mechanism of the demulsifier.
Figure 4
Demulsification mechanism of demulsifier.
Demulsification mechanism of demulsifier.
Demulsification Experiment
A series
of modified block
polyether demulsifiers were tested for demulsification using the bottle
test method. The demulsifier addition amount and the water bath demulsification
temperature were 50 μg/g and 85 °C. The demulsification
test results are shown in Figures –7. As shown in Figure , the overall demulsification rate of the water-soluble modified
polyether demulsifier is above 80%, while the maximum demulsification
rate of the oil-soluble modified polyether demulsifier reaches 70%
and the minimum demulsification rate is less than 5%. The overall
demulsification rate of the oil-soluble demulsifier is significantly
lower than that of the water-soluble modified demulsifier. As the
molecular weight of the X-series demulsifier increases, the demulsification
rate of the water-soluble modified demulsifier gradually increases,
and the X-6 series has the highest demulsification rate, reaching
91%. When the molecular weight increases again, the demulsification
rate decreases slightly and remains stable. The larger the proportion
of EO and PO added to the molecules of the modified demulsifier, the
higher the molecular weight and hydrophilicity of the water-soluble
modified demulsifier. Before the hydrophilicity reached a proper value,
as the hydrophilicity increased, the oil–water interface adsorbed
by the demulsifier increased, the oil–water interface tension
was weakened, the interface film strength was reduced, and the demulsification
rate increased. When the hydrophilicity was too large, the number
of demulsifiers dissolved in water increased, which caused the reduction
of the oil–water interface of the remaining demulsifiers, and
the demulsification rate decreased slightly. Before the demulsifier
dissolved in water reached saturation, the demulsification rate was
stable.
Figure 5
Demulsification rate of X-series demulsifier.
Figure 7
Dehydrated volume of water-soluble modified
demulsifier per hour.
Demulsification rate of X-series demulsifier.Figure shows that the demulsification speed of the X-6 series
is higher than that of other series of water-soluble modified demulsifiers,
reaching the highest point of the demulsification rate. With the increase
of the proportion of polyether demulsifiers by EO and PO, the demulsification
rate and demulsification speed of demulsifiers also increased. However,
the demulsification speeds of X-7 and X-8 series polyether demulsifiers
between 2 and 3 h are lower than other X series. The demulsification
speed increased again between 3 and 5 h and reached the average demulsification
rate. This phenomenon indicated that the demulsification speed was
related to the proportion of EO and PO in the polyether demulsifier.
The effect of the proportion of EO and PO on the demulsification rate
was relatively small. When the proportion of EO and PO approached
a certain value, the demulsification efficiency and demulsification
rate reached the maximum. Figure shows the amount of dehydration
per hour of a water-soluble modified polyether demulsifier. The X-6
series water-soluble modified block polyether demulsifier has a higher
dehydration volume and dehydration speed than other series before
3 h. Although X-7 and X-8 series polyether demulsifiers have the highest
dehydration volumes and dehydration speeds in the 4th hour, the overall
dehydration volumes and dehydration speeds are lower than X-6 series
water-soluble modified polyether demulsifiers.
Figure 6
Demulsification rate
of a water-soluble modified polyether demulsifier
per hour.
Demulsification rate
of a water-soluble modified polyether demulsifier
per hour.Dehydrated volume of water-soluble modified
demulsifier per hour.
Conclusions
High-efficiency
demulsifier is an inevitable trend in the development
of demulsifiers in the future and plays an important role in the demulsification
of crude oil emulsions. In our paper, a series of modified block polyether
demulsifiers were synthesized and used for demulsification of heavy
oil emulsions. Both polyether demulsifiers and modified polyether
demulsifiers could effectively reduce surface tension. Among them,
water-soluble modification had the strongest ability to reduce surface
tension. When the appropriate hydrophilic–hydrophobic HLB value
was reached, the breaking rate and breaking rate of the demulsifier
reached the highest point. The dehydration test of the block polyether
demulsifier was carried out through the bottle test method, which
confirmed that for the Liaohe heavy oil, the water-soluble modification
of the demulsifier was better than the oil-soluble modification. The
demulsification speed and demulsification rate were related to the
proportion of EO and PO in the polyether demulsifier. Finally, the
X-6 series demulsifier was optimal. The X-6 series demulsifier could
reach the 91% dehydration rate at a dehydration temperature of 85
°C and a demulsifier dosage of 50 μg/g.
Experimental
Section
Materials
Ethylene oxide (EO) and propylene oxide (PO)
were provided by the laboratory. Formaldehyde (40 wt %), nonylphenol,
xylene, methanol, 2-phenylmethane diisocyanate (MDI), and potassium
hydroxide were purchased from the Tianjin Tianli Chemical Reagent
Co., Ltd. Triethylenetetramine was purchased from the Tianjin Comeo
Chemical Reagent Co., Ltd. Glycerol was provided by the Tianjin Damao
Chemical Reagent Factory. Epichlorohydrincas was purchased from the
Shanghai Zhanyun Chemical Co., Ltd. The oil-in-waterheavy oil emulsion
used for demulsification evaluation was obtained from the Liaohe Oilfield.
The physiochemical characteristics of Liaohe heavy oil are shown in Table .
Table 1
Physiochemical Characteristics of
Liaohe Heavy Oil
density (kg·m–3)
dynamic viscosity (50 °C) (mPa·s)
gum (%)
asphaltene (%)
acid value (mgKOH·g–1)
pour point (°C)
sulfur
content (%)
957.6
893.1
15.69
9.57
2.07
18
0.158
Synthesis of a Novel Modified Polyether Demulsifier
Nonylphenol (82.3 g) and triethylenetetramine (158.4 g) were put
into a three-necked flask. The three-necked flask was put in an oil
bath, which was heated to 50 °C under stirring at 330 rpm for
30 min. Xylene (223.6 mL) was introduced dropwise into a three-necked
flask, and the oil bath was heated to 70 °C to completely dissolve
nonylphenol and was then cooled to 35 °C. The formaldehyde solution
(82 g) was added dropwise using a separatory funnel within 1.5 h.
The molar ratio between nonylphenol, triethylenetetramine, and formaldehyde
was 1:2:2. The condenser tube was connected to a three-necked flask,
and the temperature of the reflux water was increased at 105 °C
for 1 h, and then the oil bath was gradually heated at 120 °C
until bubbles were seen inside the solution. Xylene was recovered
after 2 h of heat preservation and reflux. The temperature was increased
to 150 °C for 3 h and the reflux water was observed for 1 h.
Finally, the temperature of the oil bath was gradually increased to
200 °C, and the temperature was maintained for 0.5 h. The three-necked
flask was cooled to 155 °C and the initiator was obtained.The initiators and a small amount of potassium hydroxide as a catalyst
were added to the autoclave. N2 was used to replace the
air in the autoclave and then the vacuum pump was used to pump out
the gas in the autoclave, and the operation was stopped after the
pressure indication reached the negative pressure. Propylene oxide
(PO) was slowly introduced from the open feed port. The mass ratios
of the initiator to the propylene oxide (PO) were 1:69, 1:99, 1: 139,
and 1: 199. After the completion of the feed, the feeding valve was
closed and the temperature was increased to 110 °C to perform
the polymerization reaction. The reaction ended when the pressure
reading returned to negative pressure and remained stable. A small
amount of potassium hydroxide was added to the autoclave again; ethylene
oxide (EO) was introduced into the autoclave in a second polymerization
reaction. After the reaction was completed, the polyether demulsifier
was formed. The mass ratios of ethylene oxide (EO) to propylene oxide
(PO) were 1:3.7 and 1:2.7. The final polyether demulsifiers X-1 to
X-8 were formed. The molecular weights of X-1 to X-8 increase as the
ratio of ethylene oxide (EO) to propylene oxide (PO) increases. The
reaction formula is shown in Figure . Table shows the synthesis ratio of the polyether demulsifier.
Figure 8
Polymerization
formula of demulsifiers.
Table 2
Synthetic
Ratio of the Polyether Demulsifier
demulsifier samples
molecular weight
initiator:PO
PO:EO
X-1
0.845 × 105
1:69
3.7:1
X-2
0.967 × 105
1:69
2.7:1
X-3
1.071 × 105
1:99
3.7:1
X-4
1.117 × 105
1:99
2.7:1
X-5
1.327 × 105
1:139
3.7:1
X-6
1.448 × 105
1:139
2.7:1
X-7
1.879 × 105
1:199
3.7:1
X-8
1.956 × 105
1:199
2.7:1
Polymerization
formula of demulsifiers.
Modification
of a Novel Modified Polyether Demulsifier
Epichlorohydrin
was used for water-soluble modification of demulsifiers.
The generated polyether (100 g) was put into a four-necked flask,
heated to 55 °C in a water bath, and stirred at a speed of 300
rpm. When the temperature reached 55 °C, potassium hydroxide
(1.2 g) was put into a four-necked flask and stirred for 20 min. After
increasing the temperature to 70 °C, epichlorohydrin was dropped
into the four-necked flask using a separatory funnel. After the dropwise
addition was completed, the temperature was increased to 85 °C
and was maintained for 2 h. The temperature was lowered to 60 °C,
and methanol (70 g) and water (30 g) were added to obtain a water-soluble
block polyether demulsifier (50 wt %). Figure shows the synthetic reaction formula of
the water-soluble modified demulsifier.
Figure 9
Synthetic reaction formula
of the water-soluble modified demulsifier.
Synthetic reaction formula
of the water-soluble modified demulsifier.The oil-soluble modification adopted the modification method of
adding an appropriate cross-linking agent. The generated polyether
(100 g) and xylene (50 g) were put into a four-necked flask and heated
in a water bath to 60 °C. A 10% PM-200 xylene solution was slowly
dropped into the four-necked bottle using a separatory funnel. At
the same time, a glass rod was used to dip the solution in a four-necked
flask and test the drawing length. When the length of the drawn wire
reached 3–4 cm, dropwise addition of the 10% PM-200 xylene
solution was stopped. Finally, xylene (46.8 g) was added to obtain
an oil-soluble block polyether demulsifier (50 wt %). Figure shows the schematic diagram
of chemical synthesis of modified polyether. Figure shows the structural formula of the demulsifier
after cross-linking.
Figure 10
Schematic diagram of chemical synthesis of modified polyether
demulsifiers.
Figure 11
Structural formula of the demulsifier
after cross-linking.
Schematic diagram of chemical synthesis of modified polyether
demulsifiers.Structural formula of the demulsifier
after cross-linking.
X-3 synthesized above was selected
for the oil-soluble modification
experiment. PM-200 solutions (10%) of different qualities, such as
2, 4, 6, 8, and 10% of the mass of polyether demulsifier, were added
to the oil-soluble modification experiment. The demulsification and
dehydration experiments of five oil-soluble modified demulsifiers
in the bottle test method were carried out.
Hydrophile–Lipophile
Balance (HLB) Value Determination
The cloud point method
was used to measure the HLB value of the
synthesized X-series demulsifier. A 10% aqueous solution of the synthesized
X-series demulsifier was placed in a test tube equipped with a thermometer,
and the liquid level was controlled at 50 mm. The test tube was heated
in an oil bath, and the temperature was gradually increased to observe
the transparency of the solution. After the solution appeared turbid,
the value was read and recorded on the thermometer immediately. After
the experiment, the HLB value was calculated according to the formula.
The calculation formula is as follows:where X is
the cloud point
of a 10% block polyether demulsifier aqueous solution.
Surface Tension
Measurement
The Kruss DSA100 contact-angle
measuring instrument was used for measuring polyether demulsifiers
and modified polyether demulsifiers. Polyether aqueous solutions with
different concentrations were prepared, including concentrations of
0.01, 0.1, 1, 10, 50, 100, 300, 500, 103, and 104 mg/L. The prepared
polyether demulsifier aqueous solution was heated in a water bath
and the temperature was set at 80 °C. The surface tension measurements
of a polyether aqueous solution with different concentrations were
carried out using the pendant drop method and a 1 mL disposable syringe.
Determination of the Water Content in Heavy Oil
Heavy
oil was heated to a flowing state in a water bath at 80 °C; the
diesel oil was used as a solvent, poured into a round bottom flask,
and a few pieces of shard were added. The cleaned and dried receiving
bottle and a straight tube condenser were connected to a round bottom
flask and then the round bottom flask was heated. The experiment ended
when the volume of the liquid in the receiver no longer changed; the
volume of the liquid in the receiver was read and recorded. Finally,
the instrument was disassembled and cleaned.
Demulsification Test
A series of block polyether demulsifiers
were tested for demulsification using the bottle test method. The
heavy oil emulsion was heated to a flowing state using a water bath,
and the upper emulsion of the heavy oil was taken and stirred in a
beaker. The taken emulsion was poured into a test bottle and 50 μg/g
demulsifier was added to the test bottle using a micropipette. The
test bottle was shaken by hand until the demulsifier and emulsion
were completely mixed, and then the test bottle was placed in the
designated water bath. Each group of test bottles retained a set of
blank control measurements. The volume of water released at different
times was observed and recorded. The demulsification rate of each
demulsifier was measured according to the proportion of the volume
of separated water, and the calculation formula is as follows:where W is the
demulsification
rate of the heavy oil emulsion by the demulsifier, VT is the volume of water separated from the heavy oil
emulsion, and VO is the volume of water
contained in the heavy oil emulsion.