JOGCE Journal of Oil, Gas and Coal Engineering Vol. 3(1), pp. 023-033, August, 2018. © www.premierpublishers.org. ISSN: 0767-0974 Re search Article The New Capillary Number Parameterization for Simulation in Surfactant Flooding Mustapha Abdullahi School of Chemical Engineering and Analytical Science, University of Manchester, Manchester M13 9PL, UK Email: [email protected], Tel: +447388119656 The Capillary number hypothesis is very empirical in Surfactant flooding Enhanced Oil Recovery (EOR) method. which is of modest experience on the North Sea and many other offshore platforms. The capillary number drives the force wetting processes, which is controlled by the balance between capillary and viscous forces. The mobilization of oil trapped in pores of water- wet rock is steered by capillary number that is typically within specific ranges (ퟏퟎ−ퟓ to ퟏퟎ−ퟒ). There is high uncertainty and confusion in the parameterization of capillary number formula, as every quantity is given on a macroscale level. As demonstrated herein, a new microscopic capillary number parameterization was proposed. This paper is written to improve the numerical formulation of capillary number in surfactant flooding model. The new formula for capillary number was derived based on existing equations as a function of residual oil saturation and tested. Thus, the proposed mobility mechanism easily accounts for a broader critical range of capillary number (ퟏퟎ−ퟔ to ퟏퟎ−ퟒ) in comparison with available models with a critical capillary number (ퟏퟎ−ퟓ to ퟏퟎ−ퟒ). We used an existing model to quantify the effect of capillary number on a miscible and immiscible relative permeability curves by computing the interpolation parameter 푭풌풓 as a tabulated function of the Logarithm (base 10) of the capillary number using a new capillary number formulation. Keywords: Critical capillary number; Capillary number; capillary desaturation; miscibility; Interpolation parameter. INTRODUCTION Up to two-thirds of the crude oil remains trapped in the 푢 is Darcy’s velocity, µ is the viscosity of the displacing reservoirs after primary and secondary recovery in an fluid, is the interfacial tension between oil and the average oil reservoir (Yan and Qiu, 2016). EOR is then surfactant solution, ∆p is the density difference between required to optimise the depletion, as the remaining oil is the phases, g is acceleration due to gravity and d is a trapped in the pore structure of the reservoir. characteristic dimension taken here as the pore diameter. The fluid flow in porous media is mainly governed by three The role of interfacial tension and capillary number in a forces: gravitational force, viscous force and capillary dynamic air-liquid interface during an immiscible fluid forces. These three forces are integrated through the displacement flow driven by pressure was investigated by Capillary number (푁푐) and the bond number (퐵표) defined Yan & Qiu (2016). The critical capillary number was by: studied analytically, and they derived the theory regarding the critical capillary number with the wettability effect in a 푢휇 pressure-driven capillary tube. Their results show that the 푁푐 = (1) critical capillary number is associated with the contact angle, slip length and capillary radius. Basante (2010) ∆푔푑2 conducted a laboratory experimental work using two 퐵 = 표 (2) sandstone cores to demonstrate the effect of capillary The New Capillary Number Parameterization for Simulation in Surfactant Flooding Abdullahi M. 024 number on mobility control. The result of the experiment where 휆푤 and 휆표are constants for water and oil relative shows that raising the flow rate by a factor of 10 permeability, respectively, for the same rock type. With the (0.03ml/min to 0.3 ml/min) will decrease the oil recovery sandstone cores associated with the fluids in Shen’s factor considerably. The water-oil relative permeability experiment, the curve fitting of the experimental data leads characterises two-phase flow, and it’s difficult to determine to 휆표=2.006 and 휆푤 =3.807 (Shen et al., 2006). the functional form in a reservoir study. The addition of various chemical agents (For example, Surfactant) during Xu et al. (2011) conducted experiments to determine the chemical flooding in oil production will significantly change surfactant’s performance, such as the relationship the interfacial tension and increase the degree of difficulty between surfactant concentration and oil/water interfacial in measurement. Shen et al. developed an improved tension and the relationship between the surfactant method of measuring water-oil relative permeability concentration and the water viscosity. Their results show curves, shown that the relative permeabilities of both water that oil/water interfacial tension will decrease as the and oil phases will increase with decreasing interfacial surfactant concentration increase, surfactant flooding has tension (Shen et al., 2006). the capacity of enhancing oil recovery. Their results show that the optimum surfactant concentration is 2%, which A logarithm relationship exists between water-oil two- can improve oil recovery by the percentage of 0.22. Ren phase relative permeability and interfacial tension (Shen et et al. (2018) used both numerical and analytical method to al., 2006). characterise the migration, trapping and accumulation of Base on several experiments, relative permeability is 퐶푂2 in a saline aquifer during geological sequestration. considered as a function of saturation, interfacial tension, They used a 1D two-phased-flow model and solved the and properties of core pore only (Shen et al., 2006). model equations using the method of characteristics. Their results demonstrated that the 퐶푂2accumulated by (3) permeability hindrance is greater than that accumulated by 퐾 = 푚 (푆∗ )푛푤 푟푤 푤 푤 capillary trapping. ∗ 푛표 퐾푟표 = 푚표(1 − 푆푤) (4) Alquaimi et al. (2018) proposed a new capillary number where 푚푤 and 푚표 are coefficients of water and oil relative definition for fractures that depends on force balance and permeability functions respectively incorporates geometrical characteristics of the fracture ∗ Note that 푚푤 is the water relative permeability at 푆푤 = model. They conducted an experimental desaturation ∗ 1 and 푚표 is the oil relative permeability at 푆푤 = 0, procedure to test their capillary number definition and respectively. quantify the relationship between the pressure and By definition above, trapped ganglions. Bryan & Kantzas (2009) performed (5) core flooding experiments to investigate how Alkali- 푚 = (퐾∗ ) 푤 푟푤 푆표푟 Surfactant flooding can lead to improved heavy oil ∗ 푚표 = (퐾푟표)푆푤푐 (6) recovery. It was determined from their results that the performance of surfactant alone was not sufficient to Therefore the normalise formula can be derived from the emulsify oil, but can only increase the water-wetting of the two relative permeability equations above: glass, but the combination of alkali and surfactant can reduce the oil-water interfacial tension and oil/water (7) emulsions will be produced. Furthermore, their results 퐾∗ = (푆∗ )푛푤 푟푤 푤 show that the mechanism of emulsification and ∗ ∗ 푛표 퐾푟표 = (1 − 푆푤) (8) entrainment, which occurs during high rate flow in lower permeability cores is not as efficient in recovering The exponential indexes, 푛푤 푎푛푑 푛표 are found to be related additional oil. to interfacial tension and the pore size distribution parameters, 휆푤 and 휆표 (Brooks and Corey, 1964), as Laforce et al. (2008) used analytical solutions to study the development of multi-contact miscibility in simultaneous (9) water and gas (SWAG) injection into a reservoir, they 푛표 = 푛표(푤표,휆표) considered the application of 퐶푂2 storage in enhanced oil 푛푤 = 푛푤(푤표,휆푤) (10) recovery using a fully compositional one-dimensional and three-phase flow through porous media. Their results A particular relation between exponential constants and demonstrate that miscibility does not develop when the interfacial tension was derived, and the two-phase relative fraction of water in the injection mixture is sufficiently high permeability model from the relative permeability and define the minimum gas fraction necessary to achieve equations above has the form(Shen et al., 2006): miscibility and highlights the importance of improved relative permeability models. ∗ ∗ [표.9371.푙표푔(휎푤표)+휆푤] (11) 퐾푟푤 = (푆푤) Lohne et al. (2012) investigated the influence of capillary ∗ ∗ [0.1960.푙표푔(휎푤표)+휆표] forces on segregated flow behind the displacement front 퐾푟표 = (1 − 푆푤) (12) The New Capillary Number Parameterization for Simulation in Surfactant Flooding J. Oil, Gas Coal Engin. 025 by numerical simulations of homogeneous and 퐹 = 1 − [(훼푁 )푛 + 1]−1 (13) 푘푟 푐 heterogeneous models. Their results show that the positive effect of gravity segregation is that the oil floats Where 푛 ≃ −0.75 seems to fit data they conducted by up, accumulates under low permeable rocks and thereby laboratory measurements. The scaling parameter α is increases the effective horizontal oil mobility. They found used to fit the measured data. the magnitude of the incremental oil production to increase with increasing curvature of oil relative permeability. Thus, by referring to the latest previously published Hence, the positive effect of decreasing IFT is larger in literature on the miscibility development in surfactant mixed-wet formation than in water-wet formations. flooding, it can be concluded that the capillary number and Keshtkar et al. (2016) developed an explicit composition the interfacial tension plays a vital role in accurately and explicit-saturation