Literature review on numerical simulation based works associated with capillary pressure and capillary trapping capacity

A comprehensive literature review on capillary pressure, and capillary trapping capacity, including the motivation of current studies are discussed in this section.

Capillary pressure, capillary trapping capacity, and current research motivation

When pores/pore throats in a porous medium are occupied by two immiscible fluids, a pressure difference exists at the fluid-fluid interface due to surface tension. This difference in the phase pressures is termed as the capillary pressure.

In other words, the capillary pressure is the difference between the non-wetting fluid pressure (Pnw) and the wetting fluid pressure (Pw) across the interface. It is the function of the wetting phase saturation (Sw). The relationship between capillary pressure and saturation is called the capillary pressure curve, and mathematically expressed by Equation 2.1.

“P” _”c” (“S” _”w” )”=” “P” _”nw” “- ” “P” _”w” 2.1

The capillary trapping capacity is the product of reservoir rock porosity and non-wetting phase residual saturation (Zhou et al.

2011), and mathematically expressed in the Equation 2.2.

## C_trap “=?” S_nr 2.2

Where s Ctrap, is the capillary trapping capacity, ? is the rock porosity and Snr is the non-wetting phase saturation. The capillary pressure-saturation relationship of scCO2-brine system within a reservoir rock is of major practical importance in a CCS project. With the help of this unique relationship, the movement and safe storage of injected and trapped CO2 into the subsurface reservoirs can understand better. The study of capillary pressure resulted in direct assessment of capillary trapping capacity of CO2 within a CCS project. Thus, in this investigation, a numerical approach is employed to analyse the effect of inlet fluid flow rate and wettability (in terms of contact angle) on pore-scale scCO2 capillary pressure for various drainage and imbibition cycles for a sand pack and sandstone forwarded by scCO2 capillary trapping capacity.

Literature review on capillary trapping capacity

Widenschild et al. (2011) conducted core-flood experiments to estimate effects of interfacial tension, viscosity, and fluid flow rate on capillary trapping on synthetic glass beads. Results showed that for initial non-wetting phase saturation values are optimized at decreasing non-wetting phase viscosities and low drainage flow rates. For residual non-wetting phase saturation values, the observed situation was opposite. However, they suggested further research work in this regard. Iglauer et al. (2011) investigated the impact of the initial non wetting-phase saturation and porosity on the residual non wetting-phase saturation on sand packs and consolidated sandstones. Results represented that the optimal porosity for CO2 storage was around 22% for measured maximum trapping capacity of 11%. Pentland et al. (2011) estimated primary drainage capillary pressure and the relationship between initial and residual non?wetting phase saturation through core-flooding experiments for a scCO2?brine system in Berea sandstone. Their results demonstrated that the observed maximum trapped CO2 saturation was 35%, which was less than the maximum trapped saturation of 48% for an equivalent n?decane/brine experiment in Berea sandstone. Pini et al. (2012) showed the influence of sub-core scale capillary heterogeneity on fluid saturation at pore-scale for CO2-water system. They have conducted laboratory experiments and measures fluid saturation with micro-CT scanner. Suekane et al. (2010) investigated the micro level mechanism of residual gas trapping on Berea sandstone. They have used micro-CT scanner to observe the fluid distribution in Berea and Tako sandstones. Moreover, they investigated the influence of capillary number and injected amount of water on residual trapping for glass beads. Results showed that low-porosity reservoir rocks were good for residual trapping.

Pore scale modelling is beneficial to study various petro-physical parameters (such as capillary pressure) under different wettability conditions. With the advancement in numerical modelling, these various wettability conditions can be assigned as contact angles in numerical models. Thus, it is relatively convenient to examine the numerical outcomes of various drainage and imbibition cycles in terms of capillary pressure and capillary trapping capacity. As, oil and gas industry have desire to store more CO2 safely within geological sources for a safer environment, this numerical estimation procedures of capillary pressure will add much to the future research and technology.

Some important parameters central to this study

## Capillary Number

The capillary number is the dimensionless ratio of the viscous to capillary force. It is denoted by Nc. When Nc> 1, then the viscous force dominate over capillary force and vice versa. Generally, the value of Nc ~10-6 for flow through pores in the reservoir. According to Chatzis and Morrow (1984) the equation for capillary number is,

## N_c=?v/? (2.3)

## Where,

## Nc =capillary number

µ = fluid viscosity

## v = fluid velocity

? = surface tension

In this work, the fluid velocity values were considered to ensure that the capillary number remained greater than 10-6. So, fluid velocities can be used to investigate their influence on fluid residual saturation, thus on the shape of the fluid relative permeability curves as described by Krevor et al. (2012). Moreover, as fluid relative permeability values are used in this work to predict capillary pressures, the capillary numbers greater than 10-6 imposed an effect on capillary pressure values.