Dynamic modelling of injectivity evolution in unconsolidated sands

Fluid injection into unconsolidated formations serves many different purposes in the oil and gas industry. EOR projects require fluid injection at sustained high flow rates into the reservoir for years. Depending on the matrix properties and injection conditions, individual grains may be detached from the sand matrix and carried away by the fluid. During well shut-ins, pressure transients are generated and the direction of the flow is reversed allowing the grains to be transported and deposited near and even inside the wellbore. The deposited grains may plug the pores around the wellbore and decrease the injectivity, a phenomenon often observed at injection wells targeting unconsolidated formations. In order to address this issue, we implement a model consisting of partial differential equations solved through the numerical finite element methods that decomposes the porosity into mobile and immobile solid phases plus the liquid phase. The mass exchange from mobile to immobile solid phases is dependent on the deposition and erosion rates that are a function of the pressure gradient and stress concentrations around the wellbore. The system uses appropriate scales in size and time as well as appropriate field parameters. The results show how the porosity evolves over time around a hypothetical wellbore; the erosion reduces the pressure gradient until the erosion is negligible. The injection rate, the initial porosity heterogeneity and inter-grain forces (degree of consolidation) proved to have a significant impact on the matrix erosion. Simulations that emulate the effect having gravel and frac-packs were also performed evidencing that the different completion systems help to reduce the formation of high porosity channels around the wellbore during fluid injection.