3D numerical simulation of the enhanced oil recovery process using nanoscale colloidal solution flooding

Journal Pre-proof 3D simulation of the enhanced oil recovery process using nanoscale colloidal solution flooding

Mohammad Hemmat Esfe, Saeed Esfandeh PII:

S0167-7322(19)34388-0

DOI:

https://doi.org/10.1016/j.molliq.2019.112094

Reference:

MOLLIQ 112094

To appear in:

Journal of Molecular Liquids

Received date:

4 August 2019

Revised date:

21 October 2019

Accepted date:

7 November 2019

Please cite this article as: M.H. Esfe and S. Esfandeh, 3D simulation of the enhanced oil recovery process using nanoscale colloidal solution flooding, Journal of Molecular Liquids(2019), https://doi.org/10.1016/j.molliq.2019.112094

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© 2019 Published by Elsevier.

Journal Pre-proof

3D Simulation of the Enhanced Oil Recovery Process Using Nanoscale colloidal solution Flooding Mohammad Hemmat Esfe1, Saeed Esfandeh1,2* 1

Department of Mechanical Engineering, Imam Hossein University, technical campus, Tehran, Iran 2,*

Department of Mechanical Engineering, Jundishapur University of technology, Dezful, Iran *Corresponding Author: [email protected]

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Abstract

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The purpose of this study is to model nanoscale colloidal solution injection into porous media with the aim of enhancing oil recovery (EOR). In the present study, by focusing on the mechanism of changing the thermophysical properties of the injected fluid, including its viscosity due to the presence of nanoparticles, and using the FEM method, a model is developed. Finally, with the aid of the proposed model, the effect of nano-fluid injection flow rate, nanoparticle volume fraction and the effect of media porosity on the EOR process has been investigated. According to the results, an increase in the injection nanofluid flow rate from 0.1 to 0.5 ml/min, there has been a sensible positive effect on accelerating the EOR process. Nanofluid with the flow rate of 0.3 ml/min selected as the optimum flow rate with 94% success in trapped oil extraction at the same time with 0.5 ml/min. On the other hand, three solid volume fraction of nanofluids analyzed and according to results increasing the nanoparticle volume fraction even though it has a significant effect on the change in the thermophysical properties of the base fluid, but in the end, it has had a poorly positive impact on the enhanced oil recovery process. According to the

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results of the model at a constant flow rate the medium with a lower porosity (0.217 in present study), oil recovery by nanoscale colloidal solution occurs max 36% faster that oil extraction in medium with high porosity (0.4 in present study) after the same time from the start of flooding. It should be noted that in all three simulated porosity in present study, the oil extraction was fully completed after 4200 seconds from the start of flooding. In order to have more real simulation, the problem is define time dependent and the porous medium simulated for about 90 minutes time period.

Keywords: Enhanced Oil Recovery; Nanofluid; Flooding; Porous Media; Nanoscale Colloidal Solution; Nanoparticles

Highlights:  



Simulation of Enhancement Oil Recovery Using Nanofluid Flooding over time A constant injection in a media with lower porosity had a faster oil extraction Enhancement of inlet flow rate improves recovery factor

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1. Introduction Today, the major part of the world oil production is supplied by old reservoirs. Improving oil recovery after the primary and secondary recovery stages from these reservoirs is a major concern of companies and governments. The enhanced oil recovery methods are referred to as processes in which it is tried to enhance crude oil extraction, whose extraction by conventional

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methods (i.e., primary and secondary recovery methods) is not possible or affordable, by using

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energy out of the oil field or the injection of materials into reservoirs. Typically, only 20 to 40 percent of the oil can be extracted with primary and secondary recovery methods; while by using

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enhanced oil recovery techniques or EORs, 30-60% of the reservoir capacity can be recovered. By reducing the discovery of new oil reservoirs in the last decade, it is believed that enhanced oil

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recovery technologies play a key role in supplying global energy demand in the coming years

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[1].

One of the new approaches in the field of enhanced oil recovery is the use of nanotechnology-

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based methods [2]. Adding nanoparticles to the base fluid causes changes in the properties of base fluid such as viscosity [3-5], thermal conductivity [6-8], thermal convection [9] and boiling

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heat transfer [10-13]. Also many researchers studied different thermophysical and nonthermophysical properties of various nanofluids in laboratory to analyze nanofluids feasibility

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for using in cooling and heat transfer systems [14-19]. Among the potential applications of nanotechnology in oil and gas industries, nano-fluid injection into oil reservoirs or nano-flooding is one of the new methods of Chemical Enhanced Oil Recovery (CEOR) which has attracted considerable attention in scientific communities. In this method, the special properties of nano-fluids are used to improve the ability to transfer crude oil and facilitate the extraction and enhanced oil recovery. Nanofluids are of the nanotechnologybased fluids and stable engineered suspensions that contain particles, fibers or tubes in the range of 1 to 100 nm. The higher stability of the particles in the fluid, the adjustable properties (such as the heat transfer coefficient, surface wettability) and the reduction in the power required for fluid pumping, are among the advantages of nanofluids compared to common solid-liquid suspensions

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Journal Pre-proof [20]. With the injection of nanofluid into oil reservoirs, it is possible to extract more than 50% of the reservoir capacity, which is currently unavailable by primary and secondary recovery methods and even some of the methods for enhanced oil recovery (such as polymer injection and surfactant injection) [21]. In recent years, several studies have been carried out on the experimental study of nano-flooding to enhance oil recovery. In these studies, the positive effect of flooding has been observed by nano-fluids containing different nanoparticles and in different operating conditions on the amount of oil recovery from the porous media, compared with water flooding. The performance

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and efficiency of the EOR process are usually performed using experiments involving rheology

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(change in viscosity), surface tension, wettability, and core flooding. Experimental studies on the use of nanofluids in the EOR have focused on the effect of different nanoparticles, on the

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mentioned properties, and consequently on the amount of oil recovered from the porous medium

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[22]. SiO2, TiO2, CuO, Al2O3 nanoparticles are among the substances used in these experimental studies [21], [23-30].

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When nanoparticles are used to enhance oil recovery, recognizing and understanding the mechanism of nanoparticle action for developing EOR methods by nano-flooding is necessary in

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practice. In recent experimental studies, interactions of nanofluid, oil and porous media have shown some of the mechanisms of EOR action. Despite this, EOR mechanisms with the help of

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nano-flooding are still not fully understood. Among the suggested mechanisms in previous

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studies in this area, disjoining pressure, pore channels plugging, surface tension reduction, changes in the wetting properties of rock and improvement in transfer properties of injected fluid, such as conduction coefficient, specific heat capacity, and viscosity of injected fluid with the presence of nanoparticles are the important ones that cause to increase in the percentage of oil recovery from the media [21], [22], [31-36]. Since most studies in the field of nano-flooding have been experimental studies, modeling can be used by researchers in advancing the process more efficiently and can be considered as an effective step in the industrialization of this process. For this purpose, the results of the models can be complementary for experiments. In spite of the frequency of experimental studies in the EOR area with the help of nano-flooding, few studies have been performed on numerical and simulation of this process. Nano-flooding 3

Journal Pre-proof modeling with the purpose of EOR can be carried out by modeling the flow transfer of nanoparticles in porous media. In the modeling of flow transfer containing nanoparticles, the surface loads of the nanoparticles, and the surface of the rock are often considered in the porous medium during flow transfer. The absorption of nanoparticles in porous media is related to the wettability change phenomenon of the rock surface, which is an effective factor in determining the capillary pressure and relative permeability curves. Therefore, the change in the capillary pressure and relative permeability of the phases due to the change in the wettability of the environment is used to model and simulate the process [37]. In the following, the most important

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numerical studies in the EOR area are studied through nano-flooding.

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Ju et al. [24] have numerically analyzed the mechanism of enhanced oil recovery by using polysilicon hydrophilic fatty acid nanoparticles (LHP) due to the wettability change of the porous

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media. InThis study, a two-phase mathematical model is proposed for one dimensional geometry

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in which the migration and absorption of LHP nanoparticles and the change in the wettability of the reservoir's rock medium due to this migration is proposed as a mechanism for EOR process.

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In the development of this model, transfer equations of nanoparticles in a porous medium have been used in which the accumulation rate of nanoparticles is also considered due to the trapping

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of nanoparticles in the cavities and bottlenecks of the medium. The model proposed by Ju et al. [24], is the expansion of the equations for the transfer of nanoparticles in the porous medium,

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based on the proposed formulation of Liu and Sivan [38] and it is a model for the migration of particles in micron in porous media. With the help of this model, the change in relative and

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effective permeability of water and oil phases and also the change in the oil recovery rate after injection of water containing nanoparticles is quantitatively calculated. Also, the calculation of the distribution of nanoparticle concentrations, decrease of porosity, and absolute permeability of the medium through absorption of nanoparticles in cavities and bottlenecks of the porous media and the efficiency of oil recovery process have been done with this model. At the end of the study, Ju et al. [24] concluded that, despite the decrease in the permeability of the porous medium due to the deposition of nanoparticles in it, the oil recovery rate of the environment with the help of hydrophilic LHP nanoparticles has clearly improved. The findings of this study have been repeated in a similar study by Ju et al. [39].

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Journal Pre-proof El-Amin et al. [40-43] have presented different models for calculating the transfer of nanoparticles in a two-phase flow within a porous medium. The models presented by these researchers consist mainly of 5 PDE equations, which are related to pressure, phase saturation, nanoparticle concentration, nanoparticle volume in porous cavities, and also the volume of nanoparticles trapped in the bottlenecks of porous medium. In these models, porosity and permeability changes of the environment due to the accumulation and fouling of nanoparticles in porous bed cavities have been considered. In another study, Abdolfattah et al. [2] considered the mechanism of the wettability change to

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provide the mathematical modeling of the EOR process using nanoparticles. The adsorption of

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nanoparticles in the porous medium causes its wettability change. The wettability change of the cavity wall of the porous medium means that the medium resistance to the flow of oil and water

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phases varies, and due to this, the relative permeability of the two phases change. Abdolfattah et

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al. developed a mathematical model based on the Liu and Sivan [39] equations, emphasizing on the mechanism of changing the wettability of the medium. In this case, the changes in porosity,

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the absolute permeability of the medium, wettability, capillary pressure and relative permeability of the two phases during the flooding process and the accumulation of nanoparticles in the

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porous medium have been considered. Finally, the effect of parameters such as the concentration of nanoparticles, the size of nanoparticles, and the grain size of the porous media and the flow

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rate of the injected fluid have been calculated.

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In the models presented for simulating the nano-flooding, the emphasis was often on the mechanism of changing the wettability of the medium due to the accumulation of nanoparticles during the injection period of the fluid. But, as mentioned earlier, changing the wettability properties is one of the suggested mechanisms for explaining the effect of nanofluids injection in order to increase the oil recovery. The changes in nano-fluid thermophysical properties, such as density and viscosity, are also considered as other proposed mechanisms that have not been investigated in two-phase modeling of nanoparticles in porous media. The purpose of the present study is to simulate the EOR process by flooding, taking into account the changes in the thermophysical properties of the injected fluid due to the presence of nanoparticles in it. For this purpose, empirical equations for the effective properties of nano-fluids have been used in this study. In addition, the heat transfer equations have been also considered in this modeling.

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Journal Pre-proof Finally, the effect of important parameters in the EOR process with the help of nano-flooding has been simulated by the proposed model. In the following, we describe and develop the hypotheses and equations of the model. A time dependent (90 minutes) simulation give researchers more clear view about the effect of changing each parameter on quality and speed of oil extraction from porous media.

2. Numerical Simulation Computational fluid dynamics is a method through which computer simulations are used to

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analyze systems including fluid flow, heat transfer, and their lateral phenomena, such as chemical reactions. The ability to study critical and specific situations in a process, facilitate

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equipment design, reduce response time and costs associated with research, and obtain complete

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and detailed information of the process, are the benefits of the CFD method compared to experimental studies [44]. FEM methods, which is one of the common methods for CFD studies,

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has been used in present modeling. COMSOL multiphysics software that is used for simulation in present study that its main structure is totally based on FEM as a numerical method.

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Commercial packages for CFD are traditionally based on finite volume methods. This is due to the fact that basically all of the larger commercial packages for CFD have the same ancestors.

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But finite element methods are widely used by the numerical analysis community to study numerical methods for fluid flow. There is a vast amount of work described in scientific

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publications regarding CFD and finite element methods especially in EOR process and porous media simulation [45-52]. The hypotheses and equations used to simulate the behavior of the

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process of nano-flooding into the porous medium are discussed below. In the following, the assumptions, governing equations and input parameters of the model have been discussed: 2.1. Assumptions: The proposed model has been extended based on the following assumptions: 

Assuming that the nanoparticles flow easily in the water phase (which is selected as the base fluid for flooding operation), the water and nanoparticle mixture has been considered as a homogeneous phase. In other words, the relative velocity of the water phase and the nanoparticles are negligible and equal to zero. Therefore, the effect of nanoparticles on the behavior change of flooding process has been studied. 6

Journal Pre-proof 

The porous medium has been considered homogeneous.



The flow of nano-fluid and oil phases in porous media follows the Darcy’s two-phase law.

2.2. Governing equations The two-phase Darcy equations which ultimately lead to the determination of the distribution of the pressure inside the medium and the saturation of the phases during the flooding operation, are

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as Eq.s 1 to 7 that are governing equations of COMSOL Multiphysics software:

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(2)

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𝜅 ∇. (𝑝) 𝜇

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𝐮=

(1)

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∂ϵ𝑃 𝜌 + ∇. (𝜌𝐮) = 0 ∂t

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∂ϵ𝑃 𝑐1 + ∇. (𝑐1𝐮) = ∇. (𝐷𝑐 ∇𝑐1) ∂t

(4)

𝜌 = 𝑠1 𝜌1 + 𝑠2 𝜌2

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𝑐1 = 𝑠1 𝜌1

(3)

(5)

1 𝜅𝑟1 𝜅𝑟2 = 𝑠1 + 𝑠2 𝜇 𝜇1 𝜇2

(6)

𝑠1 + 𝑠2 = 1

(7)

The parameter Dc represents the capillary penetration coefficient which has been considered constant in the model. Also, the variables 𝜅𝑟1 and 𝜅𝑟2 in effective viscosity equation are the relative permeabilities of the two nano-fluid and oil phases which are related to the saturation 7

Journal Pre-proof distribution of phases through permeability models. In this study, the Brooks-Corey model has been used to determine the relative permeabilities of each phase. The Brooks-Corey model has been introduced to the model: (3+2⁄𝜆𝑃 )

(8)

𝑘𝑟1 = 𝑠1

(1+2⁄𝜆𝑃 )

𝑘𝑟2 = (1 − 𝑠1 )2 (1 − 𝑠1

(9)

)

Where, λp = 2 shows the value for distribution of the size of the cavities index. In order to

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determine the thermophysical properties of the phases, it is necessary to consider the heat

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transfer equations in the model. For this purpose, the heat transfer equation in porous media has been used, in which the effective thermophysical properties is an average of the properties of

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𝐪 = −𝑘𝑒𝑓𝑓 ∇𝑇

(10)

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∂T + 𝜌𝐶𝑃 u. ∇𝑇 + ∇. 𝑞 = 𝑄 ∂t

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(𝜌𝐶𝑃 )𝑒𝑓𝑓

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nano-fluid phase, the oil phase, and the porous rock:

(𝜌𝐶𝑃 )𝑒𝑓𝑓 = 𝜃𝑃 𝜌𝑃 𝐶𝑃,𝑃 + (1 − 𝜃𝑃 )𝜌𝐶𝑃

(11)

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(12)

𝑘𝑒𝑓𝑓 = 𝜃𝑃 𝑘𝑃 + (1 − 𝜃𝑃 )𝑘

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(13)

2.3. Calculation of Nano-fluid Thermophysical Properties Estimation of thermophysical properties of nanofluid in single-phase models is done by empirical models. In this section, relationships have been used to determine the effective thermophysical properties of nano-fluids in this study. 2.3.1. Nano-fluid thermal conductivity coefficient

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Journal Pre-proof The Maxwell-Garnet empirical model has been used to calculate the nano-fluid thermal conductivity coefficient, which correlates the thermal conductivity of the nano-fluid with the following relation to the conductivity coefficient of fluid, the nanoparticle, and the volume fraction of the nanoparticles: 𝑘𝑠 + 2𝑘𝑓 − 2𝜑(𝑘𝑓 − 𝑘𝑠 ) 𝑘𝑒𝑓𝑓 = 𝑘𝑓 [ ] 𝑘𝑠 + 2𝑘𝑓 + 𝜑(𝑘𝑓 − 𝑘𝑠 )

(14)

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2.3.2. Nano-fluid density

The nano-fluid density is related to the density of the fluid, the density of the nanoparticles, and

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the volume fraction of the nanoparticles according to the Eq.15. According to this equation, the

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nano-fluid density increases with increasing volume fraction.

(15)

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𝜌 = (1 − 𝜑)𝜌𝑓 + 𝜑𝜌𝑠

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2.3.3. Nano-fluid specific heat

𝐶𝑝 =

(1 − 𝜑)𝜌𝑓 𝐶𝑝𝑓 + 𝜑𝜌𝑠 𝐶𝑝𝑠 𝜌

(16)

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2.3.4. Nano-fluid viscosity

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The Eq.16 can be used to calculate the specific heat of the nano-fluid:

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The experimental Pak & Chu’s model has been used to calculate the nano-fluid viscosity: 𝜇𝑛𝑓 = (1 + 39.11𝜙 + 533.9𝜙 2 ) 𝜇𝑓

(17)

2.4. Input parameters of the problem As mentioned, the purpose of the modeling is to study the effect of nano-flooding on the amount of oil recovery from porous media. The geometry of this problem can be seen in the Fig.1. In this case L is the length of the cylinder and D is its diameter. In this study, the L/D ratio has been considered equal to unit. The diameter and length of the cylinder have been assumed to be equal to 0.04 m. The side surface of the presented model is adiabatic (n.q=0) and also with no fluid flow (n.ρu=0), the inlet boundary is considered with a certain flow rate or velocity and the outlet is considered with a certain pressure (pressure outlet boundary condition). Also a temperature, 9

Journal Pre-proof pressure and Initial saturation of nanofluid phase in system are considered as initial conditions of the problem. The inlet flow is pure nanofluid that enters to the porous media to extract trapped

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oil inside core.

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Fig. 1. Geometry of the investigated model.

The boundary conditions governing the problem can be summarized as Table. 1: Table 1. Boundary conditions.

The left base of cylinder The right base of cylinder

s1 = 1

N = −n. ρu =

𝑃 = 𝑃𝑜𝑢𝑡

Side surface of cylinder Initial condition

0 𝑠1 = 𝑠𝑤

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𝜌𝑛𝑓 𝑄𝑖𝑛 𝐴

𝑇 = 𝑇𝑖𝑛

−n. 𝐷𝑐 ∇𝑐1 = 0

−n. q = 0

−n. ρu = 0

−n. q = 0

𝑃 = 𝑃𝑖𝑛𝑖𝑡

𝑇 = 𝑇𝑖𝑛𝑖𝑡

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3. Results and discussion 3.1. Mesh independency analysis The mesh independency study on the meshing results for flooding of a porous medium was

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carried out using water containing aluminum oxide nanoparticles (volume fraction of 0.01). Fig.2

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shows the effect of changing the number of meshes used in the modeling process (or, consequently, the effect of the mesh size) on the percentage variation of recovered oil from the

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medium in terms of the porous filled volume. As it can be seen, after increasing the number of meshes (or reducing the mesh size) to around 25000 meshes, there is no significant change in the

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curve and the results will be fitted and are match to each other. However, the results of the

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saturation distribution of three-dimensional phase over time showed that selecting less than 148000 meshes in the defined geometry cause irregularities and heterogeneities. Therefore, mesh

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number 6 (according to Table 2 information) is selected as an optimal mesh number and is used in all of the simulations below. Thus, the amount of recovered oil percentage that is calculated

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from the media is independent of the mesh size, and the saturation distribution curves have sufficient quality and heterogeneity. As stated a list of number of mesh sizes in studied is

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presented in Table 2. Also tetrahedron meshes have been used for meshing the geometry defined in present study (Fig. 3).

Table 2. Number of different meshing to study the independence of model results from meshing. Row number Number of mesh

1

2

3

4

5

6

7

1881

3767

12906

25783

107145

148276

315723

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#1

70

#2

60

#3 50

#4

40

#5

30

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#6

20

0 0.5

1

1.5

2

2.5

3

3.5

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0

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10

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PV Injected

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Fig. 2. Mesh independency control.

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Recovery Factor %

80

Fig.3 Geometry with applied mesh

12

4

4.5

#7

Journal Pre-proof In the following table 3 has presented the parameters introduced to the modelling and simulation process in present study. Table 3. Model input parameters for simulating the nano-flooding process. Description

Unit

Value

Variable

Temperature of input flow

𝐾

300

𝑇𝑖𝑛

System initial temperature

K

300

𝑇𝑖𝑛𝑖𝑡

Initial pressure

atm

1

𝑃𝑖𝑛𝑖𝑡

Pressure of output flow

atm

1

𝑃𝑜𝑢𝑡

-

0.237

𝑠𝑤0

Operational parameters

Initial saturation of nanofluid phase in

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system

𝑚𝑙/𝑚𝑖𝑛

Permeability of porous media

𝑄𝑖𝑛

𝒎𝟐

10−11

kappa

-

0.217

por

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Media porosity

0.5

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Input flow rate of nanofluid

Density of solid matrix

𝑘𝑔⁄𝑚3

2714

ρ_p

solid matrix

Specific heat of solid matrix

𝐽⁄𝑘𝑔. 𝐾

851

cp_p

𝑊 ⁄𝑚. 𝐾

2.2

k_p

Density of nanoparticles

𝑘𝑔⁄𝑚3

3970

ρ_s

Specific heat of nanoparticles

𝐽⁄𝑘𝑔. 𝐾

765

cp_s

𝑊 ⁄𝑚. 𝐾

40

k_s

Solid volume fraction of nanofluid

-

0.01

phi

Density of oil

𝑘𝑔⁄𝑚3

878

ρ_o

Specific heat of oil

𝐽⁄𝑘𝑔. 𝐾

2776

cp_o

𝑊 ⁄𝑚. 𝐾

0.25

k_o

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Properties of

Thermal conductivity coefficient of

oxide nanoparticle

Thermal conductivity coefficient of nanoparticle

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(Aluminum)

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Properties of

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solid matrix

Oil properties in 300 K

Water properties in 300 K

Thermal conductivity coefficient of oil

4.038

μ_o

Oil viscosity

𝑃𝑎. 𝑠

Water density

𝑘𝑔⁄𝑚3

997.6

ρ_w

Specific heat of water

𝐽⁄𝑘𝑔. 𝐾

4181

cp_w

𝑊 ⁄𝑚. 𝐾

0.6056

k_w

Thermal conductivity coefficient of water Water viscosity

13

𝑃𝑎. 𝑠

× 10−2

8.55 × 10−4

μ _w

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3.2. Results obtained 3.2.1. Validation of results using experimental data

In order to validate the model, the results of the model are compared with extracted data related

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to an experimental study [27]. In this study, an aluminum oxide nanoparticle was used to enhance oil recovery from a porous cylindrical core with a diameter of 4.15 and a length of 5.78

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cm.

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Core characteristics used in the experimental study to investigate the flooding process by

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aluminum oxide nano-fluid showed in Table 4[27].

Table 4. Specifications of the core.

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Core characteristics

Amount 4.15

Length (cm)

5.78

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Diameter (cm)

Permeability of media (mD)

110.4

Porosity percentage

17.5

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In Fig.4, the results obtained from the model for the changes in the percentage of oil recovered

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from the medium versus pore volume have been compared with experimental results. As it is clear from this chart, the model follows well the behavior of experimental data.

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Fig.4. Comparison of curve variations of the percentage of oil recovery from porous media for porous filled volume

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obtained from model with experimental data [27].

Then, with the help of developed model, simulation of nano-flooding process and investigation

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of the effect of different parameters on the amount of oil recovered from porous media has been investigated.

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3.2.2. Effect of Injected nano-fluid flow rate

In order to investigate the effect of injection nano-fluid flow rate into the medium, the variation

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of saturation and oil recovery from the medium were compared in three different flow rates of

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0.5 ml/min, 0.3 ml/min and 0.1 ml/min (Containing aluminum nanoparticle with a volume fraction of 0.01) (Considering constant value of other parameters). It is natural that by reducing the flow rate of nanofluid in porous medium, more time is needed to remove oil from the medium. This effect can be seen by comparing the saturation charts in a constant time over three different variable flow rates. For this purpose, the saturation distribution of the medium in 960th second has been presented in Fig.5 for the three flow rates. As these saturation distribution profiles indicate, reducing the debit from 0.5 ml/min to 0.1 ml/min, the lower amount of water replaced the original oil contained in the medium. Pressure distribution profiles during flooding times for different flow rates of the input nanofluid are also shown in Fig.6. As it is known, the pressure distribution at different times from the start

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Journal Pre-proof of the flooding process, like the distribution of oil saturation, will ultimately lead to a constant

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pressure for the entire medium.

Q=0.3 ml/min

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Q=0.5 ml/min

Q=0.1 ml/min

Fig. 5. Effect of nanofluid input flow rate on oil saturation distribution in 960th second after flooding.

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Journal Pre-proof Q=0.3 ml/min

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Q=0.5 ml/min

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Q=0.1 ml/min

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Fig. 6. Effect of nanofluid input flow rate on pressure distribution in 960th second after flooding.

Fig.7 shows the variation of the oil recovery curve in terms of the filled porous volume of the

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medium. As it is known, the variation of the inlet nano-fluid flow rate does not significantly

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affect this curve. However, changes in the oil recovery percentage versus flooding time can be better compared and interpreted. For this purpose, Fig.8 shows the variation curve for oil

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recovery from the medium plotted according to the time passage during the water flooding process. As it can be seen, the changes are more tangible and understandable in this chart. By reducing the inlet nano-fluid flow rate in the medium, at a given time, the percentage of

ur

recovered oil decreases. For example, at 2500th second since the start of the flooding process, for

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the flow rate of 0.5 ml/min, almost all of the medium oil has been removed by the nano-fluid. At the same time, at the flow rate of 0.3 ml/min, 94% of the primary oil and for a flow rate of 0.1 ml/min, only 53% of the primary oil is removed by nano-fluid injection. So more time is needed for removing all trapped oil in lower flow rates like 0.1 ml/min. In other word, modeling shows that for lower input flow rates, it can be expected that the primary oil will eventually be removed from the medium, although this will happen later and for this purpose, more time is needed for flooding.

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Fig. 7. Inlet flow rate effect on recovery factor of oil.

Fig. 8.Speed of recovery factor in various flow rates.

3.2.3. The effect of the nanoparticle volume fraction

In order to investigate the effect of volume fraction of injected nano-fluid into the medium on the results, the saturation and oil recovery percentage variations during the nano-flooding process, in 18

Journal Pre-proof for four different volume fractions of inlet nanofluid (with constant consideration of the other parameters) have been compared. The investigated solid volume fractions are ϕ = 0, 0.01, 0.025 and 0.04. Thermal conductivity coefficient, specific heat and density of selected nanoparticle (Al 2O3) are 40 (W/m.K), 765 (J/kg.K) and 3970 (kg/m3), respectively.

Fig.9 indicate the effect of increasing volume fraction on the average nano-fluid properties. As it is known, with increasing nanoparticle volume fractions in the nano-fluid, all the average

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properties of the nano-fluid (except for the specific heat capacity) increase over time.

Fig. 9. Solid volume fraction versus thermophysical properties.

The variations of the three-dimensional profiles of the saturation phase of the oil phase and the pressure over time for the various volume fractions of nanoparticles have been presented in Figures 10 and 11, respectively. As is clear from the comparison of these results, the effect of the nanoparticle volume fraction on saturation distribution is not very clear; however, increasing the volume fraction weakly reduces the oil saturation in a given flooding process time. This positive 19

Journal Pre-proof effect can be observed in the graph of changes in the percentage of oil recovered from the

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medium (Fig.12).

Phi=0.01

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Phi=0

Phi=0.025

Phi=0.04 Fig. 10. Oil saturation distribution in different solid volume fractions (960th second).

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Phi=0.01

Phi=0.04

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Phi=0.025

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Fig. 11. Pressure distribution in different solid volume fractions (960th second).

As shown in Fig.12, increasing the volume fraction of nanoparticles in the injected nano-fluid improves the flooding process of the medium and the outflow of oil from it. This positive effect of nano-fluids is also mentioned in previous experimental studies. The reason for this positive effect can be attributed to the improvement of nano-fluid thermophysical properties after adding more nanoparticles to the base fluid. As noted earlier, increasing the volume fraction improves the average properties of the nano-fluid mixture and the oil in the porous medium. Of course, this positive effect is not remarkable due to the parameters introduced to the model; because according to the model results, the use of pure water in the flooding process has also led to the

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Journal Pre-proof enhanced oil recovery from the medium. It is expected that changing the parameters of the model and including the permeability and the definition of a suitable capillary pressure model, which is a demonstration of the interaction of two nano-fluid and oil phases, will give more accurate heat transfer and mass transfer between two phases, so that the significant effect of nanoparticle

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volume fraction can be observed more clear.

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Fig. 12. Effect of nanofluid solid volume fraction on recovery factor.

3.2.4. The effect of porosity of the medium

In order to investigate the effect of porosity of porous media on the results, the variations of saturation and recovery percentage of oil during the nano-flooding process containing aluminum nanoparticles (volume fraction of 0.01) for three different core porosity values of 0.217, 0.3 and 0.4 (with constant parameters) were compared. Increasing the porosity of the medium means more volume accessible by phases. It is obvious that in the process of flooding for a given flow rate of nano-fluid injection into the medium, by increasing the porosity of the medium, more time is needed to recover the entire primary oil of the medium. This is what happened in Fig.13 at the saturation distribution for porosity of 0.3 and 22

Journal Pre-proof 0.4. As it is known, with the increase of porosity, in the second 2360 after the flooding process began in a medium with a porosity of 0.4, still some amount of water remains while for the same period of flooding in a medium with a porosity of 0.217, almost all of the medium oil was extracted. According to the saturation distribution profiles, in Fig. 14, the distribution of the pressure inside the porous medium for different porosity values over time from the onset of the

𝑝𝑜𝑟 = 0.3

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𝑝𝑜𝑟 = 0.217

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flooding process has been presented.

𝑝𝑜𝑟 = 0.4 Fig. 13. Effect of porosity on oil saturation distribution after 2360th second.

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𝑝𝑜𝑟 = 0.3

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𝑝𝑜𝑟 = 0.217

𝑝𝑜𝑟 = 0.4

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Fig. 14. Effect of porosity on oil saturation distribution after 2360th second.

Fig.15 has provided the changes in the percent of oil recovered from the medium in terms of porous volume filled with nano-fluid. As it is clear from this diagram, porosity variations (at least at porosities above 0.217) have little effect on the change in the percentage of oil recovered from the medium in terms of filled porous volume. Of course, this cannot mean that porosity is not affected by the process of oil recovery by nano-flooding. Since the change in the porosity of the medium, such as the change in the flow rate of the nano-fluid, can affect the filling time of the medium by the nano-fluid, in this case, the comparison of changes in the percentage of recovered oil in terms of time can lead to better understanding and interpretation.

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Fig. 15. Effect of porosity on recovery factor.

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Fig.16 shows the effect of medium porosity on changes in the oil recovery percentage of the core

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in terms of the time since the start of the flooding process. As it is known, at the time of 2000 seconds after the flooding operation, for the porosity of 0.217, the percentage of recovered oil

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from the medium has reached about 100% while the percentage of recovered oil at this time for the medium with a porosity of 0.3 was 93 percent and for a medium with porosity of 0.4 was 76

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percent. Therefore, it can be concluded that at a constant flow rate in a medium with lower

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rapidly.

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porosity (considering the conditions of this problem), oil recovery by nano-fluid occurs more

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Fig. 16. Effect of porosity on recovery factor speed.

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4. Conclusion

In this study, it is tried to provide a model to simulate nano-flooding process for a cylindrical

•

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core. The most important issues mentioned in this study can be summarized as follows: To determine the distribution of pressure and saturation in the porous medium, a two-

experimental data.

Determination of effective nanofluid properties in the model was conducted with the help

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•

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phase Darcy model was used and the results of the model were verified using previous

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of previous experimental models. The Maxwell-Garnet model was used to determine the nano-fluid thermal conductivity coefficient, and the Pak and Cho model was used to determine the effective nano-fluid viscosity. •

Using the proposed model, the effect of volumetric flow rate of injected nano-fluid, the volume fraction of nanoparticles present in the nanofluid composition, and the porosity of the medium on the EOR process was simulated and studied.

•

Modeling shows that for lower inlet flow rate, it can be expected that the primary oil will eventually be removed from the medium, although this will happen later and for this purpose, more time is needed for flooding.

•

The oil recovery process could be stopped after 2400 sec and 3600 sec after the start of flooding with the flow rates of 0.5 (ml/min) and 0.3 (ml/min) respectively. Because all 26

Journal Pre-proof trapped oil will be extracted from the porous medium after presented times and no more flooding is needed. •

Flooding with flow rate of 0.1(ml/sec) need more time than 5400 sec for fully oil extraction based on its recovery factor-time curve that is not reached to its maximum amount.

•

Flooding with flow rate of 0.5 (ml/min) is max 56% faster in releasing trapped oil in comparison to flooding with flow rate of 0.1 (ml/min).

•

Also, according to the results of the model at a constant flow rate in a medium with a

Max 36% oil extraction improvement for porosity of 0.217 in comparison to porosity of

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•

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lower porosity, oil recovery by a nano-fluid occurs faster.

0.4 at the same elapsed time from the start of flooding (1500 sec). Reaching 100% of oil recovery in cores with porosities of 0.217, 0.3 and 0.4 needs 2000

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•

sec, 3000 sec and 3800 sec flooding time respectively in the same solid volume fraction

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Studies on the volume fraction of nanoparticles indicate that nanoparticles can improve the process of washing the oil from the porous medium due to the improvement in the

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effective properties of the injected fluid. However, according to the model's forecast, this positive effect has been shown to be weak. It seems that the combination of empirical equations related to the effective properties of nano-fluids with nanoparticles transfer

ur

equations in a porous medium can provide a better analysis of the behavior of the EOR process with the help of nano-flooding. This is something that can be considered in the

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•

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and flow rate.

next few studies to bring the results as close as possible to actual results.

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Suggested Reviewers:

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[email protected]

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Centre for Energy Technology, School of Mechanical Engineering, The University of Adelaide, AdelaideAustralia

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Mohammad Mohsen Sarafraz

State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, College of Materials Science and Engineering, Donghua University, Shanghai 201620, China

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Fateme Zabihi

[email protected]

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Omid Mahian

Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand

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mohammadmohsen.sarafra [email protected]

Journal Pre-proof Graphical abstract Inlet flow rate effect on recovery factor of oil

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Oil distribution in different solid volume fractions

Increasing 𝜑 weakly reduces the oil saturation

𝑄𝑖𝑛 =0.1 ml/min

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Increasing 𝑄𝑖𝑛 causes improvement in recovery factor

𝜑=0

𝜑 = 0.04

𝑄𝑖𝑛 =0.5 ml/min

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