Copyright © the author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. 

DOI: 10.14800/IOGR.425  

Received July 5, 2018; revised August 30, 2018; accepted September 18, 2018. 

*Corresponding author: ouodi7@gmail.com                                                                                                                                                                                    1 

Incorporation Of Homogenizer In 
Nanoemulsion Injection Scheme For 

Enhanced Oil Recovery 

 
Uchenna Odi*, Devon Energy, Houston, USA 

 
 

Abstract 

This work presents a theoretical approach of incorporating a homogenizer within a nanoemulsion injection 

scheme for enhanced oil recovery (EOR). Nanoemulsions are kinetically stable emulsions stabilized by 

surfactants with droplet sizes ranging from 20 to 500 nm and have the potential to deliver chemical agents 

depending on their application. For EOR, nanoemulsions have the potential to be more effective than the 

often used microemulsion which are thermodynamically stable and thus may break due to the 

heterogeneous conditions inherent in oil and gas reservoirs. There are two primary categories of 

nanoemulsion formulation which are high energy methods and low energy methods. High energy methods 

involve creating nanoemulsions using a high energy process such as high pressure homogenization. These 

methods can be expensive due to the energy applied to the nanoemulsion formulation process. Low energy 

methods involve manipulating the chemistry of the oil and surfactant formulation and are thus low cost due 

to the low energy input. Current technology illustrates that nanoemulsion size control is relatively 

straightforward using high energy methods such as high pressure homogenization.  

Injecting incompressible fluids into a reservoir requires substantial energy in the form of pumps. 

Incorporating a homogenizer in the injection scheme gives an opportunity for the homogenizer to utilize 

the high energy inherent in the injection process. This is illustrated using the mechanical energy balance 

that combines the potential, kinetic, friction, and homogenizer pressure drops inherent in the incorporation 

of a homogenizer in the injection of nanoemulsions. Analysis shows the relative contributions of each of 

these pressure effects in the overall determination of the bottom hole injection pressure. 

Incorporating a homogenizer into a nanoemulsion EOR process would schematically give direct control 

over nanoemulsion size while conserving energy by using the high energy inherent in an EOR injection 

process. This would be a novel direct approach of controlling the stability of nanoemulsions (by controlling 

the size) while not producing extra costs associated with high energy nanoemulsion creation methods. The 

describe procedure illustrates how to design an injection performance curve that can schematically give 

control of nanoemulsion size. 

Introduction 

Nanoemulsion EOR is an emerging smart fluid technology that has the potential to substantially increase 

ultimate recovery rates of reservoirs in the tertiary stages of recovery. Nanoemulsion formation is 

characterized as two methods which are high energy and low energy (Koreleva and Yurtov 2012). Low 

energy methods, which include phase inversion (by temperature or composition) and spontaneous 

emulsification, have been demonstrated but control of nanoemulsion diameter is not as straightforward as 

high energy methods. High energy methods which include high shear stirring, ultrasonic emulsification and 

high pressure homogenization are more energy intensive (and thus expensive) but give greater control of 

nanoemulsion diameter and therefore control of stability. A breakdown of nanoemulsion stability can be 

caused by gravitational separation (creaming/sedimentation), flocculation, coalescence, and Ostwald 

ripening (McClements 2012). Kinetic stability is critical to avoiding nanoemulsion breakage. Kinetic 

mailto:ouodi7@gmail.com


   

2 

stability of a nanoemulsion can be maintained as long as the energy barrier height between the 

nanoemulsion and separated state of the surfactant and oil mixture is greater than 20kT, where k is the 

Boltzman constant and T is the absolute temperature (McClements 2012). In addition, McClements has 

remarked that radius’s less than 90 nm show ability to avoid gravitational separation 

(creaming/sedimentation) due to Brownian forces dominating gravitational forces.  

Some authors have commented on the use of nanoemulsions for EOR. Del Gaudio et al. (2007) remarked 

on the potential application of nanoemulsions to deliver chemical agents that can increase oil recovery. In 

addition, Del Gaudio et al. were successful in creating several nanoemulsion formulations for EOR (Del 

Gaudio et al. 2013). Mandal et al. (2012) showed that nanoemulsions (consisting of mineral oil and a series 

of nonionic ethoxylated surfactants) in a core flood setup increased oil recovery up to 30% more after a 

water flood. Mandal et al. (2012) and Del Gaudio et al. (2007 and 2013) methods of nanoemulsion 

preparation were both categorized as low energy methods which have indirect control over nanoemulsion 

size. No authors have commented on the simultaneous injection of nanoemulsions of EOR while controlling 

nanoemulsion size. The original work here utilizes an existing nanoemulsion fluid and illustrates how to 

create injection performance curves that have the ability to control nanoemulsion size. Control of 

nanoemulsion size is essential for successful nanoemulsion EOR. 

A high energy nanoemulsion system is presented in this work that utilizes the existing energy inherent 

in EOR injection to create and inject stable nanoemulsions. This process is verified by merging the theory 

of nanoemulsion creation into the mechanical energy balance of an EOR injection process. As examples, 

several nanoemulsion injection scenarios are presented that utilize this process using an example 

nanoemulsion, vertical well configuration, and several homogenizer dimensions. 

Statement of Theory and Definitions 

Consider the diagram in Figure 1 which illustrates an injection scheme that is connected to a nanoemulsion 

formulation process which includes a mixing system, centrifugal pump and high pressure homogenizer. 

The first stage of this process is the mixing process. The purpose of the mixer is to create low energy 

emulsions by mixing the brine, surfactant, and oil phases together. In addition the mixer can also be used 

to mix already prepared nanoemulsions. After this mixing stage, the mixture is transported to the second 

stage by a centrifugal pump. The centrifugal pump pressurizes and transports the emulsion mixture to the 

third stage which is the high pressure homogenizer. The purpose of the homogenizer is to further reduce 

the nanoemulsion diameter to a desired value that ensures kinetic stability (radiuses less than 90 nm) 

(McClements 2012). After going through the homogenizer, the fluid is transported (still using the head of 

the centrifugal pump) to the fourth stage which is transport through the wellbore to the reservoir’s sand 

face. As an assumption, every stage in the nanoemulsion injection process occurs at a steady state injection 

rate.  

All four stages are linked and have an associated effect on one another. As an example, the emulsion 

diameter after the pumping stage can be large enough to warrant multiple passes through the homogenizer. 

Multiple passes through the homogenizer will reduce the overall bottom hole pressure. If the bottom hole 

pressure is less than the reservoir pressure than no injection can take place. Therefore, it is important to 

consider emulsion size in conjunction with a mechanical energy balance so that the bottom hole injection 

pressure is above the reservoir pressure. 

 



   

3 

 

Figure 1—Nanoemulsion injection system. 

 

Nanoemulsion Size Control. The emulsion mixture goes through several processes that have the ability to 

impart energy in various forms which may have wide implications on nanoemulsion size. The primary 

difference in each of the processes is the turbulent energy of dissipation. Each process imparts a form of 

energy onto the emulsion. For the mixer, it has been remarked that the turbulent energy of dissipation is in 

the order of 10-100 W/kg (Davis 1987). This range is miniscule when compared to homogenizers and other 

high energy methods which are 108 W/kg and greater (Davis 1987). Davis (1987) proposed a widely used 

expression for emulsion diameter as a function of the turbulent energy of dissipation and emulsion 

properties. The expression for emulsion diameter, dne, is conveyed in the following relationship.  

𝑑𝑛𝑒 = (
4

𝐶1𝐶2
)

3/5

(1 + (
√𝐶2

4
)

𝜇𝐷𝜀1/3𝑑𝑛𝑒
1/3

𝜎
)

3/5

(𝜎3/5𝜌𝐶
−3/5

𝜀−2/5),…………...……………………………(1) 

where C1 and C2 are constants equal to 0.7 and 2 respectively; µD is the dispersed phase viscosity; ε is the 

turbulent energy of dissipation; ρC is the density of the continuous phase; and σ is the interfacial tension 

between the oil and aqueous phases. The turbulent energy of dissipation is the key factor in controlling the 

nanoemulsion diameter. Using Davis’s equation and assuming the physical properties of a typical emulsion, 

it is possible to see the relationship between the energy of dissipation and emulsion droplet size. This 

relationship is expressed in the following figure for emulsions where the continuous phase density is 

approximately 1000 kg/m3 and the interfacial tension is .001 N/m. 

 



   

4 

 

Figure 2—Turbulent energy of dissipation as a function of emulsion droplet size using Davis's expression. 

 

Figure 2 (in diameter length scales) illustrates that stable nanoemulsions (radiuses less than 90 nm or 

180 nm diameter) can be made using turbulent energy of dissipations greater than approximately 5×103 

MW/kg for dispersed phase viscosities of approximately .001 Pa*s. To make stable nanoemulsions with an 

increased dispersed phase viscosity of .01 Pa*s, results in a required turbulent energy of dissipation of 

approximately 3×106 MW/kg or greater. To make stable nanoemulsions with a decreased dispersed phase 

viscosity of .0001 Pa*s, results in a required turbulent energy of dissipation of approximately 7×102 or 

greater. These results indicate that amount of energy needed to reduce emulsion size substantially increases 

as the dispersed phase viscosity increases. Additionally, these results show that the energy of dissipation 

can be used to directly control nanoemulsion size.  

For a homogenizer, the energy of dissipation can be directly controlled using the dimensions of the 

homogenizer. These dimensions are illustrated in Figure 3.  

 

 

Figure 3—Homogenizer valve cross section (rotate along axis of symmetry for complete cross section, not 

drawn to scale). 

 

Using this active zone, the energy of dissipation for the homogenizer is the following (Hakansson 2007). 

𝜀𝐻 =
𝛥𝑃𝐻𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
,……..………………………………………….....……………………………..(2) 

Where rin is the homogenizer inlet radius, rout is the homogenizer outlet radius, hgap is the gap height of the 



   

5 

homogenizer, Q is the volumetric flow rate of emulsion, ρM is the density of the emulsion, and ΔPH is the 

pressure drop through the homogenizer. Several homogenizers placed in series is equivalent to multiple 

passes through one homogoenzier. The energy of dissipation for N passes through the homogenizer is 

derived to be the following (see Appendix). 

𝜀𝐻 =
𝑁𝛥𝑃𝐻𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
,.……………………………………….…………...…………………………...(3) 

Observing the expressions for the energy of dissipation from one pass in the homogenizer and N passes 

through a homogenizer, it is evident that the total turbulent energy of dissipation is directly proportional to 

the number of passes or number of identical homogenizers in series. When several homogenizers are placed 

in series together, the equivalent total energy of dissipation can be found by substituting the energy of 

dissipation for each individual homogenizer. This results in the following expression for the total energy of 

dissipation. 

𝜀𝐻 = 𝜀𝐻1
+ 𝜀𝐻2

+ ⋯ + 𝜀𝐻𝑁
= ∑ 𝜀𝐻𝑖

𝑁
𝑖=1 ,.…………………..…………………..………………………(4) 

This result states that for identical homogenizers in series, the total energy of dissipation is the summation 

of their respective turbulent energies of dissipation. This conclusion can be extended to multiple emulsion 

droplet reducing machines in series. The sum of their turbulent energies of dissipations can be used to 

effectively determine resulting droplet size. As an example, consider an emulsion with properties listed in 

Figure 4 that undergoes several passes using a homogenizer with specifications listed in Figure 4. This 

emulsion’s size is simulated in Figure 4 as a function of number of passes in the homogenizer. A decay 

relationship, first proposed by Hatton et al. (2014) described the eventual decline of emulsion size as the 

number of passes. This relationship is described in the following expression.  

𝑑𝑛𝑒 = 𝑑∞ + 𝐴𝑛𝑒−𝑁/𝑁𝑏,...…………………………………..………………..…………………………(5)
 

Where An is a parameter in the fit, Nb is the number of passes until emulsion breakage and d∞ is the emulsion 

size after an infinite amount of passes. The parameter An can be quantified by understanding that before the 

emulsion enters the homogenizer, the parameter NH is 0. Therefore, 𝑑𝑛𝑒 = 𝑑∞ + 𝐴𝑛 which is essentially 

the initial emulsion diameter size before homogenization. Figure 4 illustrates this best fit line using the 

previous relationship and the simulated data.  

 

Figure 4—Simulated emulsion as a function of homogenizer passes.  

Because the sum of the turbulent energy of dissipations is the total contribution of the energy imparted 

onto the emulsion, the emulsion diameter is then a function of the total turbulent energy of dissipation along 

with the specific properties of the emulsion. For the Nanoemulsion Injection System, the total energy of 

dissipation can be modeled using the following expression. 



   

6 

𝜀𝑇 = 𝜀𝑀 + 𝜀𝐶𝑃 + 𝜀𝐻,..………………………..………………………………………………………..(6) 

Where εM is the turbulent energy of dissipation for the mixer, εCP is the turbulent energy of dissipation for 

the centrifugal pump, and εH is the turbulent energy of dissipation for the homogenizer(s). The starting point 

of the nanoemulsion injection system is the mixer. The turbulent energy dissipation for a mixer is function 

of the impeller diameter and impeller speed. The expression for the turbulent energy of dissipation in a 

mixer is represented in the following expression (Morales et al. 2013). 

𝜀𝑀 = 𝜅𝑀𝑁𝑀
3 𝐿𝑀,………..…………………..…………………………………………………………..(7) 

Where κM is the mixing turbulent energy of dissipation for the mixer, Nm is the mixing impeller angular 

velocity, and Lm is the mixing impeller diameter. The mixing system used in this work has the general 

ability to mix the aqueous and oil phases for pressurization through the centrifugal pump. All specifications 

for the mixing system are listed in Table 1. 

 

Table 1—Mixing system specifications. 

Mixing Impeller Diameter .232 m 

Mixing Turbulent Energy of Dissipation  0.0019 

Mixing Impeller Angular Velocity 150 RPM 

 

To determine the emulsion size as a result of passing through a centrifugal pump requires quantifying 

the turbulent energy of dissipation for the centrifugal pump. The turbulent energy dissipation for a 

centrifugal pump is a function of the hydraulic power performed on the fluid. Specifically, it can be 

represented using the following expression (Morales et al. 2013). 

𝜀𝐶𝑃 = 𝜅𝐶𝑃
𝛥𝑃𝐶𝑃𝑄

𝜌𝑀𝑉𝐶𝑃
,.……………………..………………..….…………………………………………..(8) 

Where κCP is the fraction of total dissipated energy by turbulence for the centrifugal pump, ∆PCP is the 

change in pressure caused by the centrifugal pump and VCP is the volume of the centrifugal pump. Using 

the previous expression and the Davis expression for emulsion diameter, it is possible to estimate the 

emulsion size as a result of pumping the emulsion product from the mixing system through the centrifugal 

pump. The resulting high pressured emulsion from the centrifugal pump is the premix feed into the high 

pressure homogenizer. Emulsion size can be further controlled by using the homogenizer’s ability to pass 

the emulsion mixture through several homogenizer passes. It is possible to incorporate emulsions size 

control in the injection scheme of nanoemulsions by performing a mechanical energy balance on the 

nanoemulsion injection system.  

Description and Application of Equipment and Processes 

The injection bottom hole pressure is a function of the fluid changes due to the pump, potential energy, 

kinetic energy, and friction (with full discussion in the Appendix). A homogenizer can be added to this 

conventional setup by adding another pressure drop attributed to 𝑁 passes through the homogenizers in 

series. Quantitatively this pressure drop is  𝑁∆𝑃𝐻. The bottom hole pressure from the mechanical energy 

balance across an injection system incorporating a homogenizer is then represented using the following 

equation. 

𝑃𝐵𝐻𝑃 = 𝑃𝑡ℎ + 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓 − 𝑁𝐻𝛥𝑃𝐻,..…………….…………………………………………(9) 

Where Pth is the pressure contribution due to the pump, ∆PPE is the pressure drop due to potential energy, 

∆PKE is the pressure drop due to kinetic energy, and ∆Pf is the pressure drop due to friction. Using the 

previous expression, nanoemulsion size control can be incorporated into the mechanical energy balance. 

The primary challenge in implementing the nanoemulsion injection scheme is ensuring that there is enough 

pressure to inject and enough turbulent energy of dissipation to control the nanoemulsion size. These goals 

are counterintuitive because ensuring emulsion radiuses of 90 nm or less (for stability) requires large 

turbulent energies of dissipation which correspondingly require large pressure drops through the 



   

7 

homogenizers. Large pressure drops through multiple homogenizers would reduce the bottom hole injection 

pressure to values less than the reservoir pressure which would result in nanoemulsion injection failure. 

Conversely, only ensuring bottom hole pressures larger than the reservoir pressure would result in small 

pressure drops in the homogenizers which would then result in low turbulent energies of dissipation. 

Radiuses greater than 90 nm would then be created and would cause nanoemulsion failure because these 

diameters are outside the stable nanoemulsion class. A generalized algorithm can be created that ensures 

that nanoemulsions with radiuses less than 90 nm (diameter less than 180 nm) are created with sufficient 

pressure for injection against a reservoir pressure, Presv.  

Illustrated in Figure 5, this algorithm shows that for a limit of Nlimit homogenizers in series it is possible 

to create stable nanoemulsions by systematically going through a three step checklist after each 

homogenizer pass. After each homogenizer pass, this checklist consists of first verifying if 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is 

true. If 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is false than there can be no injection of nanoemulsion. If 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is true then the 

second point on the checklist, 𝑑𝑛𝑒 ≤ 180 nm, needs to be checked. If the second point, 𝑑𝑛𝑒 ≤ 180 nm, is 

false then the emulsion needs another pass through a homogenizer. If 𝑑𝑛𝑒 ≤ 180 nm is true then the third 

point on the checklist, 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣, needs to be checked. If the third point, 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣, is false than 

there can be no injection of nanoemulsion. If 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣 is true, than there is successful nanoemulsion 

injection. Applying this algorithm for a desired nanoemulsion injection rate, it is possible to create stable 

nanoemulsions with sufficient injection pressure. 

 

 

Figure 5—Generalized nanoemulsion injection algorithm. 

 

Proper homogenizer dimensions can be used to mitigate the two conflicting goals of nanoemulsion 

injection and nanoemulsion size control. Homogenizer dimensions can do this by creating enough turbulent 

energy of dissipation to reduce emulsion diameter at moderate homogenizer pressure drops that minimize 

the deduction from the bottom hole injection pressure. To adequately compare homogenizer performance, 

Innings and Tragardh (2007) proposed dimensionless groups and length scales which are represented in the 



   

8 

following expressions.  

𝑁𝑅𝑒, 𝐺𝑎𝑝 =
𝜌𝑀𝑄

2𝜋𝑟𝑜𝑢𝑡𝜇𝑀
,..…………………………….……………………………………………………(10)

 

 𝑁𝐺,𝐾𝑜𝑙 =
ℎ𝐺𝑎𝑝

𝜂
,……………………..…………………………………………………………………...(11)

 

𝜂 = (
𝜇𝑀

𝜌𝑀𝜀
)

1

4,…………………….…………..…………………………………………………………(12)

 

𝑙0 = 𝜂 ⋅ 𝑁𝑅𝑒, 𝐺𝑎𝑝

3

4,.……………………..……………………………………………………………...(13) 

Where NRe,Gap is the gap Reynolds number, NG,Kol is the turbulent gap height, ƞ is the Kolmogorov length 

scale, and l0 is the largest eddy scale. These groups can be used to compare the performance of different 

homogenizer dimensions. They will also give insight on homogenizer dimensions that are essential to 

successful nanoemulsion injection. 

Presentation of Data and Results 

To illustrate the effectiveness of the Nanoemulsion Injection system a Tween 80/Span 80 and diesel fuel 

nanoemulsion injection is simulated using nanoemulsion experimental data from Noor El-Din et al. (2013). 

Specifically, this system is a water in oil nanoemulsion that contains 9 wt% water and 10 wt% active 

surfactants (53.3wt% Tween 80 and 46.7wt% Span 80) in the aqueous phase and diesel fuel as the oil phase. 

Noor El-Din et al. (2013) measured the HLB of the aqueous phase as 10, the critical micelle concentration 

of the mixed surfactant system as 14.3x10-4 mol/L, and the interfacial tension between the oil and aqueous 

phase at the critical micelle concentration as 3.8 mN/m. Noor El-Din et al. (2013) also measured the density 

and kinematic viscosity of the nanoemulsion system for different volume fractions of the aqueous phase 

illustrated in Figure 6 and Figure 7. Using the density and kinematic viscosity as functions of temperature, 

dynamic viscosity values were determined as a function of temperature. As previously discussed, 

nanoemulsion viscosity and density are critical parameters in the calculation of the bottom-hole injection 

pressure. These parameters are essential in quantifying viscosity and density changes caused by temperature 

increases in the injection tubing as the nanoemulsion is transported from the homogenizer and through the 

wellbore to the reservoir’s sand face.  

 

 

Figure 6—0-9 wt% Water and 10 wt% Surfactant Mixture (53.3 wt% Tween 80 and 46.7 wt% Span 80) in 

Diesel Nanoemulsion Density as Function of Temperature (Noor El-Din et al. 2013). 

 



   

9 

 

Figure 7—0-9 wt% Water and 10 wt% Surfactant Mixture (53.3 wt% Tween 80 and 46.7 wt% Span 80) in 

Diesel Nanoemulsion Kinematic Viscosity as Function of Temperature (Noor El-Din et al. 2013). 

 

Noor El-Din et al. (2013) experimental nanoemulsion diameter was measured as 49.55 nm and was 

obtained using a high pressure homogenizer. For this work, 49.55 nm is the target diameter because it 

represents the minimum diameter obtained experimentally. Using this target diameter, Noor El-Din’s 

emulsion properties, and a test injection rate of 1000 STB/day (159 m3/day), homogenizer gap heights were 

determined for four cases of homogenizer dimensions. Homogenizer gap heights were determined by first 

solving for the turbulent energy of dissipation for a diameter equal to 49.55 nm. From there, the turbulent 

energy of dissipation was used along with user defined homogenizer inlet and outlet radiuses to solve for 

the gap height in the homogenizer turbulent energy of dissipation expression. Using this procedure, gap 

heights were determined for four homogenizer dimensions labeled accordingly in the following table along 

with their characteristic properties. 

Observing Table 2, it is apparent that the pressure drop is reduced for the same turbulent energy of 

dissipation as the homogenizer dimensions progress from Production Scale to the 2nd Proposed Nano Scale. 

This is an important result because it shows that the homogenizer pressure drop can be reduced without 

adversely affecting the homogenizer’s ability to produce nanoemulsions. In addition, turbulence is 

increased as the homogenizer dimensions progress to the 2nd Nano Scale which may be an indication that 

more energy is utilized in the process of reducing the emulsions diameter. 

A vertical well configuration with a target reservoir temperature of 99oC (210oF) and other parameters 

listed in Table 3 was used to illustrate the nanoemulsion injection system. Using the vertical well 

configuration, several homogenizer scenarios indicated in Table 2 were simulated. 

 

Table 2—Homogenizer Dimensions (dne=49.55 nm, Q=1000 STB/Day (159 m3/Day), Temp.=60oF (15.6oC)). 

 Production Scale Pilot Scale 1st Proposed Nano scale 2nd Proposed Nano scale 

rout, mm 16 4 2 1 

rin, mm 15 3 1 0.5 

hgap, µm 170 291 413 696 

∆PH, MPa 5,290 2,050 1,250 524 

ε, MW/kg 677,000 677,000 677,000 677,000 

NRe,Gap 2,140 8,570 17,200 34,300 

ƞ, µm 59.6 59.6 59.6 59.6 

l0, mm 18.8 53.1 89.3 150.2 

NG,Kol 2.85 4.89 6.93 11.7 

 



   

10 

Table 3—Well parameters. 

Pipe Roughness 0.0006 

Tubing Inner Diameter 0.0762 m (3 inches ) 

Surface Temperature 15.6oC (60oF) 

Geothermal Gradient 8.33oC per 304.8 m, (15oF per 1000 ft) 

Injection Tubing Length 3048 m (10000 ft) 

Inclination Angle 90o 

Total Depth 3048 m (10,000 ft) 

Change in Depth 3.048 m (10 ft) 

 

The results of these simulations are illustrated in Figure 8 through Figure 11. Observing the pressure 

contributions illustrated in Figure 8, it is apparent that the bottom hole injection pressure increases for the 

same nanoemulsion injection rate as the homogenizer dimensions progress from Production Scale to the 

2nd Proposed Nano Scale. This occurs primarily because the pressure drop due to homogenization is 

minimized as the homogenizer dimensions progress from the Production Scale to the 2nd Proposed Nano 

Scale. A reduction of the homogenizer pressure drop ensures larger range of positive bottom hole injection 

pressures. 

 

 

(a) 

 

(b) 

 

(c) 

 

(d) 

Figure 8—Bottom Hole Pressure and Pressure Drops for Nlimit = 1 (a) Production Scale (b) Pilot Scale (c) 1st 

Proposed Nano Scale (d) 2nd Proposed Nano Scale. 



   

11 

 

(a) 

 

(b) 

 

(c) 

 

(d) 

Figure 9—Turbulent Energy of Dissipation for Nlimit = 1 (a) Production Scale (b) Pilot Scale (c) 1st Proposed 

Nano Scale (d) 2nd Proposed Nano Scale. 

 

As a consequence of extending the bottom hole pressure over a larger range of injection rates for specific 

homogenizer dimensions, there is a larger range of turbulent energies of dissipation and thus a larger range 

of emulsion diameters. This is portrayed in Figure 9 and Figure 10 which show that as the homogenizer 

dimensions progress from the Production Scale to the 2nd Proposed Nano Scale there is larger amount of 

energy dissipated in the creation of smaller diameter emulsions. 

Observing all the presented homogenizer dimensions, it is apparent that the 2nd Proposed Nano Scale had 

the largest impact on emulsion diameter reduction. The injection range in which positive injection pressures 

and kinetically stable emulsion diameters occurred for this homogenizer was an injection flow rate of 32 

m3/Day at a bottom hole injection pressure of 251 MPa to an injection flow rate of 107 m3/Day at a bottom 

hole injection pressure of 0.585 MPa.  

When compared to the 2nd Proposed Nano Scale, the other homogenizer specifications did not have the 

same success in reducing the emulsion diameters as conveyed by Table 4. Overall, all of the homogenizers 

exhibited the same trend of having the emulsion diameters decrease. This decrease was limited by the 

homogenizer pressure drop. Because of this, it is essential to choose the right homogenizer dimensions so 

as to ensure stable nanoemulsions and adequate nanoemulsion injection. 

 

Table 4—Minimum Diameters Obtained for Nanoemulsion Injection. 

 
Minimum 

Diameter, nm 

Injection Rate at Minimum 

Diameter, m3/Day 

Bottom Hole Pressure at 

minimum Diameter, MPa 

Production Scale 235 20.2 0.259 

Pilot Scale 138 39.7 0.530 

1st Proposed Nano Scale 105 58.0 0.492 

2nd Proposed Nano Scale 67.8 107 .585 

 



   

12 

 

(a) 

 

(b) 

 

(c) 

 

(d) 

Figure 10—Emulsion Diameter for Nlimit = 1 (a) Production Scale (b) Pilot Scale (c) 1st Proposed Nano Scale 

(d) 2nd Proposed Nano Scale. 

  

In addition to the homogenizer dimension study presented earlier, an additional study was conducted to 

see if adding homogenizers in series according to the algorithm presented in Figure 5 is beneficial. This 

scenario was conducted using the dimensions of the 2nd Proposed Nano Scale. The emulsion diameter 

results are illustrated in Figure 11. These results show that increasing the amount of homogenizers results 

in no beneficial decrease in nanoemulsion diameter. This occurs because increasing the amount of 

homogenizers correspondingly increases the total homogenizer pressure drop. Increasing the total 

homogenizer pressure limits the bottom hole injection pressure range which thus reduces the injection rate 

range of how far the emulsion diameter can be reduced. 

 



   

13 

 

(a) 

 

(b) 

 

(c) 

Figure 11—Diameter using 2nd Proposed Nano Scale (a) Nlimit=1, (b) Nlimit=3, (c) Nlimit=5. 

Economics 

Equipment and transportation costs are the primary differences between onsite and offsite production of 

nanoemulsions for the oil field. Onsite production of nanoemulsions which utilizes a homogenizer 

incorporated into an EOR injection scheme requires capital investment due to homogenizers, mixers, and 

centrifugal pumps. While a single homogenizer and single mixer could be sized accordingly to service 

several wells in a field (estimated total capital cost ranging from 1-10 million USD), the cost of several 

centrifugal pumps for injection depends on the number of wells in a field. Because of this, the total cost of 

the nanoemulsion injection system depends on the number of wells utilized in the field. The final decision 

to use the onsite option depends on if the capital costs of the onsite implementation are less than the 

transportation costs to deliver offsite produced nanoemulsions.  

Regardless of the choice between onsite and offsite options, the one similarity between these two options 

is the chemical cost associated with creating the nanoemulsion. Nanoemulsions fundamentally contain oil, 

water, and surfactants. Considering these components it is possible to determine the chemical cost per 

volume of a nanoemulsion by utilizing the following equation.  

𝐶𝑁𝐸 = 𝜌𝑀 (
𝑓𝑚,𝑊𝐶𝑊

𝜌𝑊
+ 𝑓𝑚,𝑆𝐶𝑆 + 𝑓𝑚,𝑂𝐶𝑂),.………………………………………………………….....(14)

 
Where fm,W is the mass fraction of water in the nanoemulsion, CW is the cost per volume of water, ρW is the 

density of water in the nanoemulsion, fm,S is the mass fraction of surfactants in the nanoemulsion, CS is the 

cost per mass of surfactants in the nanoemulsion, fm,O is the mass fraction of oil phase in the nanoemulsion, 

and CO is the cost per mass of oil in the nanoemulsion. Considering the nanoemulsion investigated in this 



   

14 

work and the chemical costs of each component the nanoemulsion costs is approximately $5.98 per liter. 

This costs is relatively expensive due to the expensive cost of surfactants (Tween 80 is $114 per gallon, 

Span 80 is $96.20 per liter) and diesel (3.65 per gallon). In addition, the majority of the investigated 

nanoemulsion is diesel by mass. These costs are lab scale and can be further reduced using carefully selected 

suppliers or cheaper chemical substitutes when scaled up to field use. To ensure profitability for the 

nanoemulsion injection system, the current commodity price of oil must be more than the cost of delivering 

the nanoemulsion to the reservoir.  

When considering the numerous possible nanoemulsions (water in oil and oil in water) it is possible to 

determine the range of chemical cost associated with nanoemulsion formulation by using MonteCarlo 

simulation. These simulation results using the uniform distributed parameters in Table 5 and a range of 800 

kg/m3 to 1200 kg/m3 for the nanoemulsion density gives a nanoemulsion cost ranging from $.0044 to $21.62 

per liter. Additional specifics regarding the possible nanoemulsion costs are illustrated in Figure 12. 

 

 

(a) 

 

(b) 

Figure 12—Results of MonteCarlo Simulation of Nanoemulsion Cost (a) Probability Distribution Function 

(b) Cumulative Distribution Function. 

 

Table 5—Parameters for montecarlo simulation of nanoemulsion cost. 

 Water Phase Surfactant Phase Oil Phase 

Minimum Mass Fraction .01 .01 .01 

Maximum Mass Fraction .90 .10 .98 

Minimum Density 1000 - - 

Maximum Density 1200 - - 

Minimum Cost $.01 per barrel $.01 per kg $.01 per kg 

Maximum Cost $10 per barrel 100 per kg 10 per kg 

 

These results show that it is important to have low cost surfactants and low cost oil. Having low cost 

nanoemulsion components ensures that the margin between nanoemulsion chemical cost and oil price is 

large enough to justify nanoemulsion EOR.  

Conclusions 

It is theoretically possible to create nanoemulsions within an EOR injection scheme. Proof of this concept 

is accomplished by incorporating the production of nanoemulsions into the mechanical energy balance. 

Successful nanoemulsion injection is strongly dependent on the homogenizer dimensions. Inadequate 

homogenizer dimensions cause too much of a pressure drop or too small of an energy of dissipation. Proper 



   

15 

homogenizer dimensions have adequate pressure drops with substantial turbulent energies of dissipation 

that reduce the emulsion to stable nanoemulsion sizes. Utilizing the 2nd Proposed Nano Scale, it is possible 

to combine the production of nanoemulsions into a nanoemulsion injection scheme.  

Acknowledgement 

ENI is gratefully acknowledged for promoting this research towards understanding implementation of 

nanoemulsion EOR in the field. MIT is also acknowledged for collaboration. 

Conflicts of Interest 

The author(s) declare that they have no conflicting interests. 

References 

Del Gaudio, L., Bortolo, R., and Lockhart, T. P. 2007. Nanoemulsions: A New Vehicle for Chemical Additive 

Delivery. Paper presented at the 2007 SPE International Symposium on Oilfield Chemistry. Houston, TX, 28 

February-2 March. SPE-106016-MS. 

Del Gaudio, L., Lockhart, T. P., Belloni, A., et al. 2013. Process for the Preparation of Water-in-Oil and Oil-in-Water 

Nanoemulsions. U.S. Patent Application 13/845,515, filed March 18, 2013. 

Economides, M. J., Hill, A. D., and Ehlig-Economides, C. 1994. Petroleum Production Systems. Englewood Cliffs, 

N.J.: PTR Prentice Hall. 

Hakansson, A. 2007. Dynamic Modelling of High Pressure High Pressure Homogenizer. Master Thesis. Department 

of Food Technology, Engineering and Nutrition. Lund University, Sweden. 

Hakansson, A., Tragardh, C., and Bergenstahl, B. 2009. Dynamic Simulation of Emulsion Formation in a High 

Pressure Homogenizer. Chemical Engineering Science 64(12):2915-2925.  

Hatton, T. A., Doyle, P. S., Doyle, G. A., et al. 2014. Nanoemulsions: Mechanistic Evaluation of Formation, Stability 

and Applications. Massachusetts Institute of Technology. 

Innings, F. and Tragardh, C. 2007. Analysis of the Flow Field in a High-Pressure Homogenizer. Experimental 

Thermal and Fluid Science 32(2):345-354.  

Mandal, A., Bera, A., Ojha, K., et al. 2012. Characterization of Surfactant Stabilized Nanoemulsion and Its Use in 

Enhanced Oil Recovery. Paper presented at the 2012 SPE International Oilfield Nanotechnology Conference. 

Noordwijk, The Netherlands, 12-14 June. SPE-55406-MS. 

McClements, D. J. 2012. Nanoemulsions Versus Microemulsions: Terminology, Differences, And Similarities. Soft 

Matter 8(3):1719-1729.  

Morales, R., Pereyra, E., Wang, S., et al. 2013. Droplet Formation Through Centrifugal Pumps for Oil-Water 

Dispersions. SPE Journal 18(2013):172- 178. SPE-163055-PA. 

Noor El-Din, M. R., El-Hamouly, S. H., Mohamed, H. M., et al. 2013. Water-in-Diesel Fuel Nanoemulsions: 

Preparation, Stability, and Physical Properties. Egyptian Journal of Petroleum 22(2013):517-530. 

The MathWorks. 2014. Centrifugal Pump. 

http://www.mathworks.com/help/physmod/hydro/ref/centrifugalpump.html?refresh=true.  

Appendix 

Energy of Dissipation through a Homogenizer Derivation. The energy of dissipation using the 

homogenizer dimensions can be quantified by assuming that the major fragmentation and coalescence 

occurs in the gap just after the Seat and before the Forcer as a consequence of the pressure drop through 

the gap. Using this active zone, the energy of dissipation for the homogenizer is the following (Hakansson 

2007). 

𝜀𝐻 =
𝛥𝑃𝐻𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
,………….…….……………………………………………………………..(A1)

 

 

Where rin is the homogenizer inlet radius, rout is the homogenizer outlet radius, hgap is the gap height of the 

homogenizer, Q is the volumetric flow rate of emulsion, ρM is the density of the emulsion, and ΔPH is the 

pressure drop through the homogenizer expressed as the following (Hakansson et al. 2009). 

𝛥𝑃𝐻 =
𝜌𝐶

4
(

𝑄

2𝜋𝑟𝑖𝑛ℎ𝑔𝑎𝑝
)

2

+
5𝜌𝐶𝜇𝐶

3/5𝑄7/5

(2𝜋)7/5ℎ𝑔𝑎𝑝
3 (

1

𝑟𝑖𝑛
2/5

+
1

𝑟𝑜𝑢𝑡
2/5

) +
𝜌𝐶

2
(

𝑄

2𝜋𝑟𝑜𝑢𝑡ℎ𝑔𝑎𝑝
)

2

…...…………….………..(A2)

 

http://www.mathworks.com/help/physmod/hydro/ref/centrifugalpump.html?refresh=true


   

16 

Substituting the pressure drop expression in the turbulent energy of dissipation expression results in the 

following expression which illustrates that the turbulent energy of dissipation is a function of the 

homogenizer dimensions which are rin, rout, and hgap.  

  

𝜀𝐻 = (
𝜌𝐶

4
(

𝑄

2𝜋𝑟𝑖𝑛ℎ𝑔𝑎𝑝
)

2

+
5𝜌𝐶𝜇𝐶

3/5𝑄7/5

(2𝜋)7/5ℎ𝑔𝑎𝑝
3 (

1

𝑟𝑖𝑛
2/5 +

1

𝑟𝑜𝑢𝑡
2/5) +

𝜌𝐶

2
(

𝑄

2𝜋𝑟𝑜𝑢𝑡ℎ𝑔𝑎𝑝
)

2

) (
𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
).……(A3) 

Ideally, it is desired to create nanoemulsions after one pass in the homogenizer. However it may not be 

possible to do this depending on the dimensions of the homogenizer. Because of this, it is important to 

model the homogenizer for N passes. This can be done by first considering homogenizers with the same 

dimensions in series as illustrated in Figure 13a. These homogenizers have the same pressure drop through 

them (∆𝑃𝐻1
= ∆𝑃𝐻2

= ⋯ = ∆𝑃𝐻𝑁) and therefore have the same turbulent energy of dissipation (𝜀𝐻1
=

𝜀𝐻2
= ⋯ = 𝜀𝐻𝑁). Effectively, this means that each homogenizer has the same ability to change emulsion 

size. 

 

 

(a) 

 

(b) 

Figure 13—Pressure Drops in a Series of Homogenizers (a) Individual in Series (b) Summation of Individual 

in Series. 

 

As the emulsion passes through each homogenizer, it has a pressure drop equal to the summation of 

pressure drops as illustrated in Figure 13b. Using the analogy presented in the previous figure, it is possible 

to deduce the total turbulent energy of dissipation as a result of passing through a series of these 

homogenizers. This expression is derived by starting with the expression for turbulent energy of dissipation 

and the total pressure drop through the homogenizer. 

𝜀𝐻 =
𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
[𝛥𝑃𝐻1

+ 𝛥𝑃𝐻2
+ ⋯ + 𝛥𝑃𝐻𝑁

]...…………………..…………………………...(A4) 

Multiplying out the pressure drop terms results in the following expression. 

𝜀𝐻 =
𝛥𝑃𝐻1𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
+

𝛥𝑃𝐻2𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
+ ⋯ +

𝛥𝑃𝐻𝑁
𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
........……………………………(A5)

 

 

There are two conclusions that can be made from the previous expression. Since ∆𝑃𝐻 = ∆𝑃𝐻1
= ∆𝑃𝐻2

=

⋯ = ∆𝑃𝐻𝑁, there are N pressure drops with a pressure drop of ∆𝑃𝐻. Therefore, the total pressure drop 

through the system of homogenizers is  𝑁∆𝑃𝐻 . Using this statement, the first conclusion is the final 

expression for the turbulent energy of dissipation for N homogenizers in series. 

𝜀𝐻 =
𝑁𝛥𝑃𝐻𝑄

𝜋(𝑟𝑜𝑢𝑡
2 −𝑟𝑖𝑛

2 )ℎ𝑔𝑎𝑝𝜌𝑀
......………………………………………..…………………………………...(A6) 

 

Mechanical Energy Balance. Nanoemulsion injection is possible when the bottom hole injection pressure 

(PBHP) at the reservoir’s sand face is greater than the pressure in the reservoir. The bottom hole injection 

pressure is determined by first performing an energy balance on the injection system which includes 

everything downstream from the pump to the sand face of the reservoir system. The following equation 

describes the energy balance for a production/injection system (Economides et al. 1994) excluding a 

homogenizer. 



   

17 

𝑑𝑃

𝜌𝑀
+

𝑢𝑑𝑢

𝑔𝑐
+

𝑔

𝑔𝑐
𝑑𝑧 +

2𝑓𝑓𝑢2𝑑𝐿

𝑔𝑐𝐷
+ 𝑑𝑊𝑠 = 0,..….…………………..……………………………………(A7) 

where P corresponds to pressure, u is the injection velocity, z is the height from the injection site to the 

reservoir’s sand face, ff is the friction factor, D is the wellbore diameter, and Ws is the shaft work. Integrating 

the previous equation from the injection site (Stage 2) to the reservoir’s sand face (Stage 4) and solving for 

the total pressure drop leaves the following expression. 

𝛥𝑃 = 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓.....………………..………………………………………………..……..(A8) 

The total pressure drop, ΔP, is the pressure loss experienced from transporting a fluid from the pump to 

the reservoir’s sand face (without a homogenizer). This pressure drop is the sum of pressures which include 

the pressure increase due to the weight of fluid (ΔPPE, potential energy), the pressure loss due to decreasing 

the diameter of flow (ΔPKE, kinetic energy), and the pressure loss due to friction (ΔPf). It is possible to 

determine each of these contributions by first dividing the length of the wellbore into NL segments with 

each segment being of length dL. The pressure drop due to kinetic energy in a section of pipe can be 

determined using the following relationship. 

𝛥𝑃𝐾𝐸 =
8𝑄2

𝜋2𝑔𝑐
∑ 𝜌𝑀𝑖 (

1

𝐷𝑖
4 −

1

𝐷𝑖−1
4 )

𝑁𝐿
𝑖=1 .……………………………..……………………………..……..(A9) 

The parameter i corresponds to the ith segment along the length of the wellbore. The pressure drop due 

to potential energy can be determined using the following relationship. 

𝛥𝑃𝑃𝐸 =
𝑔

𝑔𝑐
∑ 𝜌𝑀𝑖𝑑𝐿𝑖 𝑠𝑖𝑛 𝜃𝑖

𝑁𝐿
𝑖=1 .………………………………..…………………………………….(A10) 

The parameter ϴ is the angle of well inclination. The pressure drop due to friction can be determined 

using the following relationship. 

𝛥𝑃𝑓 =
2

𝑔𝑐
∑

𝜌𝑀𝑖𝑓𝑓𝑖𝑢𝑖
2𝑑𝐿𝑖

𝐷𝑖

𝑁𝐿
𝑖=1 .……………………….………………………………………………….(A11) 

The fanning friction factor, ff, for the ith segment can be determined by first calculating the Reynolds 

Number (NRe) illustrated in the following expression (Economides et al., 1994).  

𝑁𝑅𝑒 =
𝜌𝑀𝑢𝐷

𝜇𝑀
,.………………………………………………………………………………………...(A12) 

where μM is the viscosity of the nanoemulsion mixture. Using the Reynolds Number, the fanning friction 

factor can be calculated using the laminar (NRe ≤2100) or turbulent (NRe >2100) flow regimes (Economides 

et al. 1994). 









































































2100for    
1497

82572
log

04525

70653
log4

2100for                                                                                        
16

Re

2-
89810

Re

10981

Re

Re

Re

N
N

.

.

ε

N

.

.

ε

N
N

f ..

RR

f ,……………….(A13) 

The parameter, εR, is the relative pipe roughness. Incorporating the pressure contribution due to the pump 

(Pth) it is possible to determine the bottom hole injection pressure, PBHP, using the following relationship. 

𝑃𝐵𝐻𝑃 = 𝑃𝑡ℎ + 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓...…………………………………………………………...….(A14) 

The pressure contribution due to the pump can be determined by using a pumping curve (for a centrifugal 

pump) and common affinity laws that scale pump performance as a function of required injection rate 

(Mathworks 2014). These affinity laws can be utilized by first relating the required injection rate, Q, and 

the pumps impeller angular velocity, ω, to the rate provided by the pumping curve, Qcurve, and the pumping 

curve’s angular velocity, ωcurve. This relation is expressed as the following equation.  

𝑄𝑐𝑢𝑟𝑣𝑒 = 𝑄 (
𝜔𝑐𝑢𝑟𝑣𝑒

𝜔
).....………………..….………………………………………………………...(A15) 

The pressure contribution due to the pump can then be determined by first finding its equivalent, Pth,curve, 

on the pumping curve using Qcurve. The pressure contribution due to the pump can be determined using the 

following equation. 























curve

M

curve

curvethth PP







2

, ,.………….……..…………………………………………………….(A16) 

where ρcurve refers to the reference density in the centrifugal pump used to make the pumping curve. The 



   

18 

centrifugal pump used in this work is a high capacity pump that has the ability to increase the pressure of 

the nanoemulsion from the mixing stage. A synthetic pumping curve in conjunction with pump affinity 

relationships were used to describe the relationship between the pressure and flow rate for the centrifugal 

pump. The pumping curve used for this work is illustrated in Figure 14. Previously discussed pump affinity 

laws were used to scale the pumping curve for several impeller angular velocities. In addition, the pump 

had several more specifications listed in Table 6. 

 

 

Figure 14—High capacity centrifugal pump curve. 

 

Table 6—Centrifugal pump parameters. 

Pump Impeller Diameter (Morales et al. 2013) .231775 m 

Fraction Turbulent Energy of Dissipation (Morales et al. 2013) 0.0019 

Pump Active Volume .05 m3 ( 50 L) 

Pump Impeller Angular Velocity 5000 RPM 

 
Uchenna Odi is a Data Scientist at Devon Energy Corporation. He was previously a Research Scientist 
at ENI Petroleum and a Visiting Scientist at the Massachusetts Institute of Technology on behalf of ENI. 
He holds a B.S. degree in chemical engineering and an energy focused executive MBA both from the 
University of Oklahoma. He also holds M.S. and Ph.D. degrees in petroleum engineering from Texas A&M 
University. His interests are in optimization algorithms, risk analysis, emulsion systems, enhanced oil 
recovery, carbon dioxide sequestration, reservoir fluids, and machine learning.