In the conventional view of hydraulic fracturing, the rate of leakoff is determined by one (or a combination) of three mechanisms:

- Reservoir fluid viscosity/compressibility effects
- And the formation of a filter cake associated with particulate matter that was suspended in the fracturing fluid.

The widely accepted model of filter cake formation was introduced by Carter. Assume that a particulate-laden fluid (in blue above) contacts a rock interface (i.e., a fracture face, in red above) and a pressure difference, *Δp*, exists between the fracture and the porous rock. As solvent (with viscosity, μ) flows into the porous rock (black and white pattern above) at a velocity, *u _{l}*, the particulates form a filter cake (in yellow above) of permeability,

The thickness of an incompressible filter cake grows at a rate that is proportional to the throughput of filtrate:

where a indicates the factor by which the particulates are concentrated during the transition from the suspension to the filter cake. Combining Eqs. 1 and 2 yields Eq. 3.

Eq. 4 presents a solution to Eq. 3.

where *t _{exp}* is the time of first exposure to filter cake for the element of fracture face of interest. The key result in Eq. 4 is that the leakoff rate is proportional to