Hydraulic fracturing, or “fracking,” is widely used to stimulate production from oilor gas deposits. A deep well is lined with a steel pipe. A large volume of water is pumpedinto the well at a pressure sufficient to fracture the rock formation at the bottom. A slurrycontaining “proppants” (sand or ceramic particles) is then pumped into the formation, theparticles acting to keep the cracks open when the applied pressure is released.Suppose the (smooth) pipe diameter is 15 cm and the well depth is 2.3 km. The flow rateduring the water-only phase is to be 0.21 m 3 /s, which is predicted to give P = 44 MPa at thewell bottom, based on what is known about the geology. It is planned to use 60 °C water, forwhich μ = 0.467×10−3 Paꞏs and ρ = 0.983×103 kg/m 3 at atmospheric pressure. If theseproperties are constant throughout the pipe, what pressure P must be maintained at the top?[~ 32 MPa]
Hydraulic fracturing, or “fracking,” is widely used to stimulate production from oil
or gas deposits. A deep well is lined with a steel pipe. A large volume of water is pumped
into the well at a pressure sufficient to fracture the rock formation at the bottom. A slurry
containing “proppants” (sand or ceramic particles) is then pumped into the formation, the
particles acting to keep the cracks open when the applied pressure is released.
Suppose the (smooth) pipe diameter is 15 cm and the well depth is 2.3 km. The flow rate
during the water-only phase is to be 0.21 m 3 /s, which is predicted to give P = 44 MPa at the
well bottom, based on what is known about the geology. It is planned to use 60 °C water, for
which μ = 0.467×10−3 Paꞏs and ρ = 0.983×103 kg/m 3 at atmospheric pressure. If these
properties are constant throughout the pipe, what pressure P must be maintained at the top?
[~ 32 MPa]
Step by step
Solved in 2 steps with 3 images
