Numerical Modeling of the Conductivity of the Particle Monolayer with Reduced Size

Abstract

Fractures filled with a proppant monolayer play an important role in the hydraulic fracture network. Predicting the conductivity of these fractures is the basis of fracture network optimization. However, little attention has been paid to the conductivity of the proppant monolayer. The change of conductivity under various conditions is currently not fully understood. Therefore, in this paper, the conductivity variation under different conditions are simulated. The reduction of particle size was calculated by existing analytical models. The permeability variation was calculated through computational fluid dynamics (CFD) combined with COMSOL Multiphysics. The controlling factors of conductivity under a proppant monolayer were identified. Simulation results indicate that elastic parameters, closure pressure, and proppant distribution have significant influence on conductivity, while creep parameters, such as rock viscosity and time, have limited influence on conductivity. Moreover, the changes in permeability, porosity, and tortuosity with variation of embedment were analyzed. Results indicated that with an increase in embedment, the permeability and porosity decrease as expected. The main reduction (nearly half) emerges in the first 20% of proppant embedment. Furthermore, the permeability of a single particle deviates largely from the prediction of Carman-Kozeny (CK) equation. The tortuosity of proppant particle increases with a decrease in particle size due to embedment. A modification of the Carman-Kozeny equation is proposed to address this influence.

An Experimental Study on the Particle Size and Shape Distribution of Coal Drill Cuttings by Dynamic Image Analysis

“…Distribution. The mathematical models used to describe the particle size distribution of broken coal samples commonly include the Gaudin-Schuhmann distribution, the lognormal distribution, the fractal particle size distribution, and the Rosin-Rammler distribution [34,[37][38][39][40][41][42].…”

Numerical Modeling of Proppant Embedment in Viscoelastic Formations with the Fractional Maxwell Model

“…However, several mechanisms may result in the loss of fracture conductivity, such as fines migration, proppant diagenesis, proppant crushing, − and proppant embedment, which is defined as proppant particles being embedded into the rock mass under pressure, causing a reduction in the fracture width and conductivity . Among these mechanisms, proppant embedment has been investigated via experiments, − numerical simulation, − and analytical modeling. − However, as has been confirmed by a larger number of laboratory experiments conducted with proppants to reproduce the in situ fracturing process, laboratory observations greatly overestimate the conductivity of real wells. , This great discrepancy may arise because in these studies, the underground rocks are often regarded as elastic/elastoplastic. , However, increasing reservoir depth, high temperature, high pressure, and high stress may result in extreme geological conditions, which may transform the mechanical properties of reservoir rocks from elastic to viscoelastic or viscoplastic . Hard rocks can also exhibit time-dependent deformation , under such extreme conditions.…”