A model of fluid expulsion from compacting tight sedimentary rocks based on the Toggle-Switch algorithm

Abstract

Expulsion of fluids from tight rocks is an important process in sedimentary basins for phenomena such as distribution of overpressure and primary migration of hydrocarbons. This paper shows that the “Toggle Switch” (TS) algorithm of Miller and Nur is well-suited to model expulsion of brine by hydraulic fracturing from tight rocks undergoing compaction. Local random overpressure is generated in the TS algorithm using a void ratio function with random compaction length. The TS algorithm equilibrates critical fluid pressure by local exchange of excess fluid. We show that the algorithm gives net migration of fluid upwards, because the least compressive stress is decreasing towards the surface. The random void ratio makes the total expulsion rate from the layer intermittent. In the limit of zero cell size the expulsion rate approaches a mean value. When the rock has a random strength, it is shown that critically pressured clusters remain after the TS algorithm has been applied. The implementation of the algorithm is mass conservative, which ensures that the expelled mass is exactly the mass of pore fluid lost by compaction. Expressions are derived for the rate of fluid expulsion and for an effective fracture permeability.