Table 1.
A summary of the main scaling groups devised to model spontaneous imbibition.
| Authors | Dimensionless time | Comments |
|---|---|---|
| Lucas (1918) and Washburn (1921) |
|
This model predicted that the cumulative volume imbibed is proportional to the square root of time. However, it is invalid in cases where gravity force is dominating and high permeability zones. |
| Mattax and Kyte (1962) |
|
The model was based in Darcy’s law to develop a scaling group for two-phase flow. The equation imposes restrictions on the core shape, relative permeability, viscosity ratios, effect of gravity and capillary pressure profile. On the other hand, this analysis help understands recovery behavior from fracture-matrix, water drive reservoirs. |
| Reis and Cil (1993) |
|
This model scales linear imbibition profiles for two-phase flow. It was developed through combing Darcy law and mass balance. In fact, the scaling groups was based on the first simple, closed-form, semi-analytical model that incorporates the key petrophysical properties without any empirical parameters. However, many assumptions have been made in the development of this model limiting its applicability. |
| Ma et al. (1997) |
|
This model incorporated new definition of the characteristic length and a viscosity ratio term enabling the scaling of imbibition oil recovery data for different core sizes, boundary condition, and oil and water viscosities against dimensionless time. However, this equation can only predict the behavior of strongly water-wet systems. |
| Li and Horne (2006) |
|
This model is considered the first general scaling group for different rock systems in both counter-current and co-current imbibition. It was developed based on a thorough theoretical analysis of fluid-flow mechanisms. Nevertheless, measuring the parameters governing the flow and the rock properties in the lab is time consuming and expensive, hence causing a severe set-back to the feasibility of this model. |
| Schmid and Geiger (2012) |
|
This model accounts for the effect of all flow and rock properties on spontaneous imbibition where it serves as the master equation for scaling imbibition recovery. It works well with water-wet and mixed-wet cases, and characterizes SI by the cumulative inflow without the need of any fitting parameters. However, this model ignores viscous and gravity forces and is only valid for a certain time range where t < t*. |