Leakoff

One-dimensional (Carter) fluid leakoff representations are commonly applied for low-permeability, stimulation hydraulic fracturing.

    (5)

Van den Hoek, 2000 stated: "It is well-known that [Equation (5)] only works properly if the fracture propagation rate is large compared to the leak-off diffusion rate. If this is not the case, the use of [Equation (5)] can lead to overestimation of fracture length. For example, in waterflooding under fracturing conditions, this overestimation may be up to two orders of magnitude.^, In this case [Equation (5)] needs to be replaced by a proper description of the reservoir fluid flow around the fracture." Differences in leakoff between linear (Carter) leakoff in low permeability stimulation on one hand and pseudo-radial leakoff in high permeability waterflooding on the other hand are demonstrated in Figure 4, from van den Hoek, 2000.

Figure 4.       A comparison between the dimensionless leakoff rate (Q_lD=mQ_l/{2pkhDp}) versus dimensionless time (t_D=k/{fmc}) for various leakoff methodologies. Carter indicates conventional one-dimensional fluid loss. Gringarten indicates Gringarten et al.'s solution (1974) for transient elliptical diffusivity for a stationary, infinite conductivity line fracture. Settari indicates an elliptical leakoff formula from Settari, 1980.Pseudo-radial is a late-time approximation of the transient elliptical flow solution from Koning, 1988. Numerical is a numerical model solution for fully transient elliptical flow around a propagating hydraulic fracture for arbitrary pump rates, as developed by van den Hoek, 2000. (this figure is after van den Hoek, 2000).