Page 214 - Introduction to Petroleum Engineering

HYDRAULIC FRACTURING 201
In a fracture, the proppant pack may include contaminating particulates of various
sizes plus any remaining fracturing fluids that will decrease permeability below that
of the previous equation. Permeability will also decrease if proppants break under
stress, if proppant is embedded in fracture walls, and if fracture walls spall in the
presence of liquids. As a result, the actual permeability of proppant in a fracture
will be lower than the estimate from the previous equation.

Example 10.12 Proppant Permeability
Find the permeability of a proppant pack with porosity of 0.38 and average
particle diameter of 0.063 cm.
Answer
3
.
.
1 (038 ) (0 063cm ) 2
−6
×
k = = 37810 cm 2
.
150 (10. ) 2
− 38
2
Using the unit conversion 1 darcy = 9 87 10. × − 9 cm , we obtain proppant perme-
ability k = 383 darcies.
The mass of proppant in a fracture typically ranges from 50 000 to 500 000 pounds.
This mass m relates to the size of the fracture and properties of the proppant pack:
p
φ
m = ρ p Aw(1 − ) = ρ p Lwh(1 − ) φ (10.21)
ee
p
where ρ is the density of proppant particles, A is the fracture area, w is the fracture
p
width, ϕ is the porosity of the pack, L is the end‐to‐end length of the fracture, and h
ee
is the fracture height. The units for Equation 10.21 can be any consistent set of units.
10.5.1 Horizontal Wells
Horizontal wells in very‐low‐permeability formations such as shales are typically
cased, cemented, and fracked with 10 or more stages starting at the “toe” of the well
and working back to the “heel” where the well bends up to the surface. In each stage,
the casing must be perforated, then the formation is fracked, and finally a plug is
placed in the casing on the heel side of the perforations to isolate the fracked interval
from the next stage. To efficiently finish all these stages, service companies have
developed hardware and methods to cycle quickly from perforating to fracking and
to plugging. In some methods, the casing or liner is not cemented. In other methods,
ball‐drop plugs are combined with the casing to isolate one frack stage from another.
No doubt, fracking technology will continue to evolve.
The permeability of shale formations is in the range of microdarcies and lower.
With such low permeability, the relative conductivity (defined in Eq. 10.18) of the
propped fracture can be increased with smaller fracture permeability.