Prior to a hydraulic fracturing treatment, the estimated fracture length may be estimated with knowledge of certain physical properties of the proppant and transport fluid such as fluid viscosity, proppant size and specific gravity of the transport slurry as well as fracture geometry and the treatment injection rate. The estimated fracture length may be determined by the equation:
(DPST)B=qi×(1/A)×CTRANS×(d2prop)×(1/μfluid)×(ΔSGPS) (I)
wherein:
- DPST is thus the estimated propped fracture length;
- B is the exponent from the Power Law equation describing the transport slurry velocity vs. distance for the fracture geometry;
- qi is the injection rate per foot of injection height, bpm/ft.; and
- A is the multiplier from the Power Law equation describing the transport slurry velocity vs. distance for the fracture geometry;
- CTRANS, the transport coefficient, is the slope of the linear regression of the ISP vs. MHVST.
d
prop is the median proppant diameter, in mm.;
- μfluid is the apparent viscosity of the transport fluid, in cP; and
- Δ SGPS is SGprop−SGfluid, SGprop being the specific gravity of the proppant and
- SGfluid being the specific gravity of the transport fluid.
The minimum horizontal flow velocity, MHVST, for transport of the transport slurry based upon the terminal settling velocity of the proppant, Vt, may be determined in accordance with Equation (II):
MHVST, =Vt×10 (II)
Via rearrangements of the same derived equations, a model for optimizing the transport fluid, proppant, and/or treating parameters necessary to achieve a desired propped fracture length may further be determined.