# Numerical and experimental investigation on the effect of retrograde vaporization on fines migration and drift in porous oil reservoir: roles of phase change heat transfer and saturation

- 333 Downloads
- 1 Citations

## Abstract

Retrograde vaporization effects on oil production are nearly unprecedented to reservoir engineering community, and its relation to formation damage should be explored. For this purpose, this paper elucidates the importance and role of this phenomenon and its phase change heat transfer (PCHT) on fines migration and subsequent, permeability damage in porous rocks bearing oil and gas. Initially, a fine particle energy conversion equation was successfully acquired by combining fine particle mass balance and general energy equations. Moreover, the computational fluid dynamic model (CFD) was adopted for performing numerical modeling. A 2D CFD model using FEA-Comsol 5.0 version was used to simulate the retrograde vaporization of reservoir fluids. Pore walls are designed as non-adiabatic, and therefore, a modified Dittus-Boelter mass transfer model is provided for a fine particle detachment under PCHT. Hence, from the simulation results it was observed that there is a high degree of heat release during reservoir fluid phase change that is from oil to gas for decreasing pressure and increasing saturation time. This heat transfer from the oil and gas influxes contributes in the expulsion and migration of in situ fines in porous media. Also, an increasing rate of enthalpy was achieved that produces a non-isentropic flow, which is required to mobilize the fines in porous medium, and a satisfactory phase transition simulation outputs were obtained and presented as well. Altogether, these factors play a significant role in the fine particle eviction from the pore chamber, thereby plugging in the pore throat and consequently, decreasing the well productivity during transient flow.

## Keywords

Retrograde vaporization Fines migration Phase change heat transfer Arc length Enthalpy## List of symbols

- W
Water

- O
Oil

- G
Gas

*U*Carrier fluid velocity

- \(\dot{W}\)
Work transfer per second

- \(\dot{m}\)
Mass flow rate

- RV
Retrograde vaproization

- PTT
Phase transition time

- DOF
Degrees of freedom

- PW
Production well

- CFD
Computational fluid dynamics

- FEA
Finite element analysis

- PCHT
Phase change heat transfer

*c*Suspended fines concentration

*t*Time

*k*Permeability

*gz*Potential energy

- \(T_{\text{s}}\)
Rock surface temperature

- \(S_{\text{wog}}\)
Water–oil–gas saturation

- \(k_{\text{ro}}\)
Relative permeability of oil

- \(k_{\text{rw}}\)
Relative permeability of water

- \(k_{\text{rg}}\)
Relative permeability of gas

- \(k_{\text{rwg}}\)
Relative permeability of water–gas

- \(k_{\text{rog}}\)
Relative permeability of oil–gas

- \(k_{\text{row}}\)
Relative permeability of oil–water

- \(k_{\text{rgl}}\)
Relative permeability of gas–liquid

*ϕ*Porosity

- \(\alpha\)
Drift delay factor

- \(\sigma_{\text{a}}\)
Concentration of attached particles

- \(\sigma_{s}\)
Concentration of strained particles

- \(\frac{P}{\rho }\)
Flow energy

- \(\frac{{v^{2} }}{2}\)
Kinetic energy

- \(\nabla \left( {s + \gamma } \right)\)
Overall change in entropy (

*s*) and surface energy (*γ*) in porous media

## Introduction

Zeinijahromi et al. (2011) analyzed the induced formation damage effects on water cut during waterflooding. It was revealed from various studies that there was fines migration during coreflood test with changes in water chemistry and temperature. In this case, the authors have given importance to mobility control during waterflooding. In earlier research, the particle detachment model was combined with a Dietz model for a layer cake reservoir under waterflooding with constant injection and production rate to examine the fines migration effect and induced permeability reduction in the sweep efficiency of the reservoir. They developed and extended an analytical model to waterflooding with pressure drop between injection and production wells.

*F*

_{l},

*F*

_{e},

*F*

_{g}, and

*F*

_{d}, respectively. These four major forces are determined by the torque balance that in turn constitutes the mechanical equilibrium of attached particles. Fines adhering to the surfaces of the pore of the relatively higher porosity and permeability porous formations can be released by colloidal, hydrodynamic, and thermodynamic forces, and these forms of induced fines are identified to be a more common occurrence in sandstone formations, especially water-wet rocks. These particles, releasing from and adhering to the pore surface, avail the potential energies of London–van der Waals attraction and electrical double layer repulsion, respectively (Khilar and Fogler 1998). The former force is the attraction energy at the interface between the fine particle and pore wall and contributes to its attachment strength. The latter force describes the formation of electric double layers at the surface of the pore and around the fine particle which overlap and expand. This process repels the fines from the surfaces and induces the migration in the porous medium.

There is also a report of slow transport and fines drift in the porous rocks. For instance, Oliveira et al. (2014) studied this same phenomenon of slow mobilization of reservoir fines in porous media, and specifically, authors have reported from experiments that the speed of mobilized fines drift is considerably lower than the carrier fluid (water) velocity. It should be noticed that this fine drifting can be a sum of different particle micro-motions like rolling over the surface of the rock and sliding in the walls of the rock pores. Hence, it is necessary to investigate the RV effect on the clay fines drift and stagnation in porous media. Most researchers are unaware that the retrograde vaporization and well-known phenomenon in gas reservoirs during pressure drop near wellbore is retrograde condensation, in which, there will be a liquid from the gas phase due to reduction. As a result, the well will experience liquid loading effect and production loss. Likewise, the retrograde vaporization process also has a tremendous effect on the well productivity; the only difference is that this phenomenon will occur in oil reservoirs. To the best of our knowledge, till date this retrograde vaporization process and mechanism in oil reservoirs and its effect on natural reservoir fines have not been addressed yet. Hence, we have conducted mathematical and numerical modeling to understand this phenomena and our modeling results were good.

## Modeling methodology

- $$\nabla \left( {s + \gamma } \right) =\, {\text{Overall }}\;{\text{change}}\;{\text{in}}\;{\text{entropy}}\; \left( s \right)\,{\text{and}}\; {\text{surface}}\;{\text{energy}}\;\left( \gamma \right){\text{in}}\;{\text{porous}}\;{\text{media}}$$
Entropy and surface energy rises during particle detachment from pore wall.

Entropy and surface energy declines during particle straining in pore throat and also during particle re-attachment.

The \({\text{Plus}}\;{\text{or}}\;{\text{minus}} \left( \pm \right)\) sign indicates increase and decrease in entropy and surface energy.

Since Eqs. 3 and 4 consider the variable drift delay factor, we shall take the waterflooding as permeating fluid for fines surface detachment and have divided the porous media into three sections to describe the energy change.

*Section* *1* During waterflooding (flow in pore space) there is an increase in kinetic energy (including fluid energy) and velocity. Subsequently, there are no production and creation of entropy and new surface. Here the potential energy may remain constant. In this location, there is no presence of fines or if there is a particle, it is firmly attached to the rock surface. Here the particle is not affected during fluid flow velocity.

*Section* *2* In this location, the fines are detached from the pore wall and after particle detachment there is a production of entropy and surface energy resulting in the creation of new surface. Over here, the detached particles are suspended in water and some particles are strained and plugged in the pore throat. The new surface energy increases the volume of the pore chamber for more fluid storage. In this part, the kinetic energy and velocity of fluid is in equilibrium and there is a rise in potential energy.

Additionally, during particle suspension or suspension flow the particles will undergo a collision with pore walls and as a result the particle will lose its momentum. After losing momentum, it is again reattached to the rock surface and then there is a decline in available entropy and surface energy (Kampel 2007). Furthermore, some particles may undergo a slow mobilization over rock surface, this is because of the decrease in the fluid momentum and internal energy (including enthalpy).

*Section* *3* At this location, the suspended particles are captured or strained in pore throat. Here there is a loss in entropy and surface energy. Also, the fluid kinetic energy and velocity will exhibit an exponential decline. Mainly at this point, there is a huge amount of potential energy, since the pore chamber is filled with water that is suspended with fines (colloid). It should be noted that already in Sect. 2 there is a creation of new surface space (due to fines detachment).

Collectively or in a straightforward manner, it can be stated or proposed that Eqs. 3 and/or 4 are fines energy conversion equation or in other words, we hereby propose that by adding a general energy equation to fines mass balance equation yields energy conversion equation for fine particles in porous media. It can be clearly seen that two different equations are equated to yield an energy conversion equation for fines transport in porous media.

## Results and discussions

This section discusses the CFD modeling results and the curves obtained.

### Effect of retrograde vaporization on fines drift in porous rocks

During the retrograde vaporization process, there will be a high release of heat and will be transferred to the surroundings. This type of heat release during the RV process or during phase transition is called the phase change heat transfer. During this time, the reservoir may experience a higher temperature and it is also possible due to the presence of the gas phase. This high temperature enhances the pore surface thermal conductivity and as a result the electrostatic force, which hold fines on the rock surface, becomes weak. Subsequently, the fines will be detached and suspend in the fluid, and will be transported by the carrier fluid. It is actually complicated to establish a formation damage framework for this fines migration problem.

Before critically analyzing the fines drift mechanism, the readers should be aware that at this time the reservoir is saturated with three phases, namely gas-oil–water in the order top-middle-bottom. It is assumed that during PCHT process itself some amount of reservoir fines are detached and suspended in the oil phase, and during PTT, the suspended fines in the oil phase migrate to the gas phase. The particle is jumping from the liquid to gas phase and also colliding with the upper pore wall. Simultaneously, oil–water phase sloshing may occur in the pore chamber (Abbaspour and Hassanabad 2010; Greenspan 2005). Consequently, there will be a loss in the fluid momentum and surface energy in the lower pore wall as well.

*U*” shaped curve was acquired, which indicates the feasibility of non-Newtonian flow in the porous medium due to differences in the saturated fluid physical properties. Figure 9 shows the variation of total enthalpy with respect to increasing temperatures.

It can be observed from Fig. 9 that for all fluid phase transition times the enthalpy of the reservoir fluids increases rapidly for increasing temperature. It can be viewed from this figure that in beginning the enthalpy release rate is sluggish and after 30 °C there is a high degree of enthalpy release for all phase transition times and after that it stabilizes steadily.

*W*>

*O*> G) density. As a result reservoir fluid will undergo a state of stagnation, where there will not be any fluid movement in the porous path. Moreover, increasing saturation can decrease the porosity and permeability of the reservoir rocks. As it is evident from Fig. 12 that at no multi-component fluid saturation the porosity of the reservoir rocks is noted between 0.2 and 0.3. After a gradual increase in the saturation of three-phase fluids, the porosity decreases steadily reaching the lowest value below 0.05. It can be observed that the porosity decline is higher for the 540 s phase transition time and lesser for zero seconds. Implying, that the rock porosity plummet sharply for higher phase transition time.

## Conclusions

- (1)
A new equation for perturbations in the porous medium energy change was obtained by combining the pore surface fines mass balance and general energy equations. This has led to the creation of the fines energy conversion equation. We have demonstrated and validated this equation based on theoretical and numerical modeling.

- (2)
Retrograde vaporization simulation revealed that there was a tremendous amount of heat release during the fluid phase change process. This heat release and saturation detach and suspend the fines in the three-phase fluids. Consequently, it will roll and collide within the pore walls and drift along with the liquid–gas flow. Importantly, fines degrees of freedom are gradually getting arrested due to fluid phase density difference.

- (3)
During fluid phase change heat transfer, there is an increase in the enthalpy of a new phase for the elevated reservoir temperature. The fines drift was identified in the region between the start of phase transition and saturation. The relative permeability of oil decreases with increasing saturation and also, relative permeability of oil–gas phase and water–gas phase decreases for increasing gas relative permeability. In addition, rock porosity decreases for increasing water–oil–gas saturation with respect to increasing phase transition time. Finally, this work is validated with experimental modeling and revealed good agreement.

- (4)
Therefore, the quantification and analysis of formation damage due to fines migration in oil reservoirs that undergo two- to three-phase flow is critical and important for optimizing the production loss. Initially, these factors must be seriously taken into consideration before the start of water injection. The experimental study of RV phenomenon and its interaction with low to high salinity water injection will be explored in our future work. Furthermore, our future work will also explore the RV effects on the EOR/IOR performances due to fines migration and it was already reported that fines migration can increase the water–oil relative permeability in porous rocks and expand the rock surface energy, which ultimately increase the mobility ratio and oil recovery rate (Hussain et al. 2013; Zeinijahromi et al. 2011). Therefore, in the near future, we will make numerical and thermal investigations on the effects of retrograde vaporization on the enhanced or improved oil recovery rate by taking natural reservoir fines into an account.

## Notes

### Acknowledgements

The corresponding authors thank the management of Sathyabama Institute of Science and Technology for their financial and technical assistances.

## References

- Abbaspour A, Hassanabad M (2010) Comparing sloshing phenomena in a rectangular container with and without a porous medium using explicit nonlinear 2-D BEM-FDM. Trans B Mech Eng 17:93–101Google Scholar
- Alhuraishawy A, Bai AK, Wei M, Geng J, Pu J (2018) Mineral dissolution and fine migraton effect on oil recovery factor by low-salinity water flooding in low-permeability sandstone reservoir. Fuel 220:898–907CrossRefGoogle Scholar
- Bashtani F, Ayatollahi S, Habibi A, Masihi M (2013) Permeability reduction of membranes during particulate suspension flow; analytical micro model of size exclusion mechanism. J Membr Sci 435:155–164CrossRefGoogle Scholar
- Chequer L, Vaz A, Bedrikovetsky P (2018) Injectivity decline during low salinity waterflooding due to fines migration. J Pet Sci Eng 165:1054–1072CrossRefGoogle Scholar
- Dullien F (1992) Porous media: fluid transport and pore structure, 2nd edn. Academic Press, San Diego, pp 35–75Google Scholar
- Greenspan D (2005) A particle model of fluid sloshing. Math Comput Model 41:749–757CrossRefGoogle Scholar
- Hussain F, Zeinijahromi A, Bedrikovetsky P, Badalyan A, Carageorgos T, Cinar Y (2013) An experimental study of improved oil recovery through fines-assisted waterflooding. J Pet Sci Eng 109:187–197CrossRefGoogle Scholar
- Kampel G (2007) Mathematical modeling of fines migration and clogging in porous media. Georgia Institute of Technology, AtlantaGoogle Scholar
- Khilar K, Fogler H (1998) Migrations of fines in porous media, 1st edn. Kluwer Academic Publishers, Dordrecht. ISBN 978-90-481-5115-8CrossRefGoogle Scholar
- Oliveira M, Vaz A, Siqueira F, Yang Y, You Z, Bedrikovetsky P (2014) Slow migration of mobilised fines during flow in reservoir rocks: laboratory study. J Pet Sci Eng 122:534–541CrossRefGoogle Scholar
- Raha S, Khilar K, Kanpur P (2007) Regularities in pressure filtration of fine and colloidal suspensions. Int J Miner Process 84(1–4):348–360CrossRefGoogle Scholar
- Robinson B (1993) Production problems. In: Thompson D, Woods A (eds) Development geology reference manual. AAPG, Tulsa, pp 492–495Google Scholar
- Santos A, Bedrikovetsky P, Fontoura A (2008) Analytical micro model for size exclusion: pore blocking and permeability reduction. J Membr Sci 308:115–127CrossRefGoogle Scholar
- Tistory (2018) What is waterflooding? (Water Injection). Plant Eng. http://plant-engineering.tistory.com/267
- Yang Y, Siqueira F, Vaz A, You Z, Bedrikovetsky P (2016) Slow migration of detached fine particles over rock surface in porous media. J Nat Gas Sci Eng 34:1159–1173CrossRefGoogle Scholar
- You Z, Yang Y, Badalyan A, Bedrikovetsky P, Hand M (2016) Mathematical modelling of fines migration in geothermal reservoirs. Geothermics 59:123–133CrossRefGoogle Scholar
- Zeinijahromi A, Lemon P, Bedrikovetsky P (2011) Effects of induced fines migration on water cut during waterflooding. J Pet Sci Eng 78(3–4):609–617CrossRefGoogle Scholar
- Zeinijahromi A, Farajzadeh R, Bruining J, Bedrikovetsky P (2016) Effect of fines migration on oil–water relative permeability during two-phase flow in porous media. Fuel 176:222–236CrossRefGoogle Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.