Hydraulic Fracturing at Scale

Part 7, Part 7: Fracturing the Rock

Learning objectives

Scale up from a minifrac to a production fracture: length, width, and height
Read the PKN intuition, width grows with net pressure and length and shrinks with stiffness
Explain height containment by stress contrast: high-stress shales cap the fracture
Distinguish the mechanics (this course) from the flow that follows (Reservoir course)

From a Diagnostic to a Highway

The minifrac opened a short fracture to measure the stress; a production hydraulic fracture grows one large enough to drain the rock, sometimes hundreds of meters long. The mechanics that set its shape are captured by the classic PKN intuition (Perkins-Kern-Nordgren): a fracture is held open by the net pressure, the amount by which the fluid pressure exceeds $S_{hmin}$ hmin, and its maximum width scales as $w \sim \dfrac{p_{net}\,L}{E'}$ net,LE′, growing with net pressure and half-length $L$ and shrinking with the rock's plane-strain stiffness $E'$ . Stiff rock opens narrow fractures; soft rock opens wide ones; and pumping harder (more net pressure) or longer (more length) widens them. This is a scaling relation for intuition, not a design code, but it captures the levers a completion engineer actually pulls.

The figure grows a fracture as you inject and shows the single most important design constraint: height containment. A hydraulic fracture wants to grow in every direction, but it is stopped in height where it meets rock of higher $S_{hmin}$ hmin. Because the fracture opens against $S_{hmin}$ hmin, a bounding layer with a higher minimum stress, typically a stiffer, more clay-rich shale, is harder to open and caps the fracture, keeping it in the pay zone. The $S_{hmin}$ hmin profile against depth, the same profile the leak-off tests and minifracs of this part measure, is therefore the master control on fracture height: contrast in $S_{hmin}$ hmin between the reservoir and its bounding shales is what keeps a frac from growing out of zone into water or into a fault. A good completion targets a reservoir with strong stress barriers above and below.

Where This Course Stops

An honest boundary: this course covers the mechanics of the fracture, how big it grows and which way it goes, but not the flow through it, how many barrels the propped fracture ultimately produces. That production side, fracture conductivity, proppant transport, and the reservoir-simulation of drainage, belongs to the Reservoir Modeling course, which owns it in its unconventional-reservoirs chapter. The division is clean: geomechanics decides where the fracture goes and what shape it takes; reservoir engineering decides what flows out of it. The two meet at the fracture geometry this section produces. The mechanics are now complete, from the fracture gradient that is the ceiling, through breakdown and propagation, precise measurement by minifrac, and the height-contained production fracture. The last section of this part turns to a property that the industry loves and the physics distrusts: brittleness, and whether it really predicts frac-ability.

References

Perkins, T. K., & Kern, L. R. (1961). Widths of hydraulic fractures. Journal of Petroleum Technology, 13(9), 937-949.
Nordgren, R. P. (1972). Propagation of a vertical hydraulic fracture. SPE Journal, 12(4), 306-314.
Economides, M. J., & Nolte, K. G. (2000). Reservoir Stimulation (3rd ed.). Wiley.