Modeling of Nanoparticles Transport and Aggregation Kinetics in Porous Media Using Quadrature Method of Moments
- Elsayed Abdelfatah (Chemical and Petroleum Engineering Department, University of Calgary, Calgary, Canada) | Maysam Pournik (Mechanical Engineering Department, University of Texas at Rio Grande Valley, Texas, USA)
- Document ID
- Society of Petroleum Engineers
- SPE International Conference and Exhibition on Formation Damage Control, 19-21 February, Lafayette, Louisiana, USA
- Publication Date
- Document Type
- Conference Paper
- 2020. Society of Petroleum Engineers
- Quadrature Method of Moments, Aggregation, Nanoparticles, Population Balance Equation, Formation Damage
- 22 in the last 30 days
- 22 since 2007
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Nanotechnology has attracted great attention from the oil and gas industry because of its potential in applications such as drilling fluids, stimulation fluids, and enhanced oil recovery. The key challenge for nanoparticle injection into porous media is to maintain stable dispersion to harness its potential while preventing the formation damage. This work presents a mathematical and numerical tool to study the evolution of nanoparticle size and its effect on nanoparticle transport in porous media.
Population Balance Equation (PBE) representing the evolution of nanoparticle size was modified to include different nanoparticle interaction mechanisms; nanoparticles- nanoparticles and nanoparticles-porous media interactions. This model allows to study the interactions and aggregation kinetics of nanoparticle in porous media. PBE is coupled with the fluid flow model represented by the continuity equation and Darcy equation. The finite volume method was used for the discretization of the continuity equation and Darcy equation. PBE involves a continuous integration of an infinite number of nanoparticle and it was converted into a discrete number of moments for efficient computation using Quadrature method of moments (QMOM) coupled with Wheeler algorithm.
The evolution of nanoparticle aggregates sizes due to mixing and physicochemical effects in porous media significantly affects nanoparticle transport and retention in porous media as demonstrated by multiple experimental works in the literature. However, nearly most of the mathematical models to date ignore the change in nanoparticle aggregates sizes during the transport process in porous media. The model developed here considered those missed interactions and was used to match several experiments from the literature. The model shows that as the collision efficiency increases because of the high salinity or high temperature, the size of the nanoparticles would increase significantly. These large aggregates would cause plugging of small pores. However, the collision efficiency could be decreased significantly using the steric stabilization mechanism and the nanoparticles could effectively transport in porous media. It was also found that as the injection rate decreases, the retention of the nanoparticles increases significantly. This is mainly because the shear rate is too low to cause the breakage of the large aggregates formed during the transport.
This work presented an efficient numerical model capable of describing the nanoparticles-nanoparticles and nanoparticles-porous media. The model will help to understand and effectively interpret experimental results of nanoparticle transport in porous media including the effect of nanoparticle aggregation.
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