A model of the proppant flowback: setup of the theoretical framework

Abstract

Proppant flowback control is one of the main issues in hydraulic fracture modeling since the propping agent maintains the crack in an open state and therefore provides oil inflow to the wellbore. The main objective of this paper is to determine the conditions that can lead to proppant flowback during the direct operation of the well. The main outcome of this paper is an evolution criterion for proppant flowback occurrence, which takes the external pressures affecting the proppant particles, the proppant properties, and the crack opening width into account. We propose a two-component continuum model consisting of the proppant and the oil to find the stress-strain state of the proppant and thereby to obtain the stress components in the evolution criterion. We solve both a stationary problem for estimating the probability of the proppant flowback occurrence under regular conditions as well as a transient problem for taking the possibility of fast changing external conditions into account.Communicated by Francesco dell'Isola. MSC2010: 70E50, 70E55, 74B15, 74F10, 76S05.