Modeling counter-current spontaneous imbibition and its scaling application to underground gas storage

Abstract

Spontaneous imbibition (SI) is a process by which a liquid (e.g., water or oil) is naturally drawn into a partially saturated porous medium under capillarity. Understanding the SI and its mechanisms have broad applications, particularly to underground gas storage in deep aquifers or depleted reservoirs. For instance, injecting CO₂ under the supercritical conditions into subsurface, known as CO₂ sequestration, is a practical solution to reduce greenhouse gases in the atmosphere and help fight climate change. Modeling and scaling the counter-current SI has been a long- standing issue, and various approaches have been proposed in the literature. In this study, to model the SI we generalize fractional flow theory (GFFT) using fractional derivatives and apply non- Boltzmann scaling. In our approach, the imbibition distance is proportional to the time to the power 𝛼/2 in which 𝛼 is fractional order (0 < 𝛼 < 2). We analyzed the SI data reported in literature including 25 sandstones, 2 diatomites, carbonates, clay samples, 6 synthetic porous media and silty clay soil samples. By plotting the normalized liquid recovery against the dimensionless time, we found that the non-Boltzmann transformation (variable α) yielded a better collapse in the SI data than the Boltzmann transformation (𝛼 = 1). More specifically, results showed that 𝛼 ranged between 0.88 and 1.54. Also, we fit the solution of GFFT to experimental and stimulation data reported in literature including soil, clay and carbonate samples to show that non-Boltzmann transformation model the SI resulting in variable α values accurately than the traditional Boltzmann approach (fixed α=1). We demonstrate that the variation in 𝛼 value can be attributed to contact angle of the fluid, dynamic viscosity, fracture dynamics and pore structure. However, further investigations are still required. Using the GFFT, we expect to more accurately predict the rate and amount of fluid that can spontaneously imbibe into a porous medium if characteristics such as porosity, permeability, initial and maximum saturations, viscosity, and wettability are known.