This paper examines an application of method of characteristics (MOC) to evaluate utilization of nanoparticles to mitigate fines migration. Deepwater reservoirs are poorly consolidated, strongly heterogeneous and less consolidated with high pressure, temperature, porosity and permeability. All these features increase the possibility of troublesome sand production. It has been shown that nanoparticles can effectively reduce double layer repulsive forces between sand particles through changing the associated zeta potentials; the reduction of repulsive forces between loose particles would maintain integrity of the rock texture. However, our understanding on the effectiveness of nanoparticles to mitigate sand production has been limited to some experimental studies serving as proof of concept. In practice, this paper also provides an efficient and simple model to optimize fines migration treatment via injection of nanoparticles.

In this paper, we develop an analytical model to study the interplay between adsorption of nanoparticles and their geochemical effects on fines migration and the consequent sand production. There are two governing mechanisms: 1) adsorption of nanoparticles on the surfaces of fines particles; 2) the positive contribution of adsorbed nanoparticles on integrity of the rock texture. We define a fictitious attachment reaction for which we interpret the existing lab results as the rate of reaction.

We consider nanoparticle adsorption front as borders of distinct regions. At upstream of adsorption front, adsorbed nanoparticles improve coalescence of particles; whereas at the downstream, dynamic detachments of fine particles occur. Similarly, adsorption of nanoparticles on the grain surface occurs only at the upstream of adsorption front. The main contribution of this work is to evaluate the propagation of adsorption front, and fine particles and nanoparticle concentration profile along the sand pack. We use method of characteristics and present a graphical solution to determine optimal concentration of nanoparticles required to reduce maximum sand production. We define mitigation index (MI) to describe the contribution of nanoparticles to mitigate fines migration.

The analytic solution is verified by numerical simulation. This model provides a novel and efficient approach to describe the impact of nanoparticles to mitigate fines migration. In practice, this method can be used to design an effective treatment for sand control in deepwater reservoirs as well as other type of reservoirs that suffer from fines migration problems.

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