Modelling the Apparent Viscosity of Water Confined in Nanoporous Shale: Effect of the Fluid/Pore-Wall Interaction

Abstract The viscosity of nanoconfined fluid is a crucial parameter for evaluating the flow back of the fracturing fluid in unconventional reservoirs. Generally, the viscosity is an intrinsic property defined as the internal friction among fluid molecule themselves. However, the effect of the fluid/pore-wall interaction on the viscosity of fluid at the nanoscale becomes significant. Due to this strong confinement, two abnormal flow behaviors have been discovered, including an extremely high water-flow rate in hydrophobic nanotubes and an extremely slow capillary filling rate in hydrophilic nanochannels. Thus, understanding such contradictory hydrodynamics is helpful to estimate the flow performance of fracturing liquid in both organic pores and inorganic pores of shales. In this work, a concept of apparent viscosity of nanoconfined fluid is proposed, where the activation energies (indicating the energy barrier needed to be overcome for fluid motion) caused by both the fluid/ fluid interaction and fluid/pore-wall interaction are modeled. For the case with only fluid/fluid interaction, the apparent viscosity reduces to the bulk-phase viscosity, and this traditional case has been well studied. Thus, we mainly focus on the additional interaction energy caused by the pore walls during the motion of water molecules. To solve this problem, the fluid/pore-wall interaction, including an intermolecular term, an electrostatic term and a structural term, is considered to modify the Eyring's viscosity theory. Due to a repulsion term (e.g., the structural force) and an attraction term (e.g., the intermolecular force and the electrostatic force) both introduced in the surface interaction, the integrated interaction energy of fluid and pore-wall can be either positive or negative, which depends on the relative value of repulsion and attraction controlled by the pore-wall wettability. Finally, the contact angle of the pore surface is calculated by a DLVO theory (describing gas/water/solid interactions) related to the fluid/pore-wall interaction properties. The continuous viscosity profile of fluid confined inside nanochannels with different wettability and size can be directly obtained by the proposed method. Result shows that: (i) the presence of the pore-wall significantly influences the apparent viscosity of fluid. For a strongly hydrophilic channel with the contact angle approaching to zero, the average viscosity of first layer (assuming the monolayer thickness is 0.35 nm) can be 3∼4 times higher than that of the bulk phase; whereas for a strongly hydrophobic case, the first-layer viscosity is about 2∼3 times lower. Thus water molecules with the extremely high-viscosity close to the hydrophilic wall can be regarded as a sticking layer as the immobile state, and those with the low-viscosity near the hydrophobic wall can be regarded as the rare-density vapor due to the surface depletion effect. (ii) The average viscosity of the confined fluid is a function not only of the wettability but also of the confinement. When the pore dimension decreases to serval nanometers, the portion of water molecules in the interface region increases relative to the total water molecules present in entire nanopores, and the average viscosity is dominated by the apparent viscosity of fluids near the wall. Besides, (iii) it is worth noting that the effect of pore wall on the apparent viscosity reduces sharply, the apparent viscosity approaches to the bulk-phase viscosity when the fluid-wall distance is about 0.7-1.2 nm, corresponding to two or three molecular layers. In this work, the viscosity of the nanoconfined fluid has been successfully modeled by considering both the fluid-fluid interaction and the fluid-wall interaction. We try to pave a path for characterizing the water flow behavior in both hydrophilic and hydrophobic nanopores, and further guide to simulate the imbibition characteristic or the flowback performance of the fracturing liquid in shale gas/oil reservoirs.

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