PETE5373_HW#4

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Apr 3, 2024

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Advanced Well Stimulation ( PETE 5373) Spring 2024 HW#4 Due date: 04/03/2024 Total: 40 points 1. Calculate the effective stress on the proppant (called closure stress in the proppant charts) and find the permeability. (10 points) Assume the following parameters: • d S hmin /d z = 0.7 [psi/ft] • d P wf /d z = 0.1 [psi/ft] a. In general, how does proppant size affect proppant permeability according to the Figures 6.2 and 6.6? b. Fill out the table below assuming you are using 20/40 proppant size. Depth [ft] Effective Closure Stress ( S hmin – P wf ) [psi] Brady Sand Permeability [D] Bauxite Permeability [D] 1,000 5,000 10,000 Note : The units for proppant permeability are Darcies [D]. The permeability in formations requiring hydraulic fracturing are usually reported in milli-Darcies [md].

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2. Answer the questions below based on the McGuire-Sikora plot. (10 points) a. What happens to the J / J o when you increase relative conductivity (RC)? b. What happens to the J / J o when you increase the fracture length (2 L )? c. What can you do to get greater fracture length for a given fracture treatment? d. What can you do to improve your RC for a given fracture treatment?

3. Find the most cost-effective fracture design strategy by evaluating the possible combinations of the following parameters. There are 4 possible combinations. (20 points) Proppant – 20/40 size, Bauxite ($1.0/lb) or Brady Sand ($0.1/lb), (use the permeability you calculated in problem 1 for this depth Fracture Length – 0.1 or 1.0 times the reservoir radius a. Fill in the table below for South Texas tight sandstone (Frio Formation) Assume the following parameters: • Depth: z = 10,000 [ft] • Formation permeability: k = 0.01 [md] • Fracture width: w = 0.1 [inch] • Drainage Area: A = 40 [acres] Note: The Frio is a hard rock, so it is hard to get a real fat fracture. A propped fracture width of 0.1 inch is typical in hard rock. Proppant Type Relative Conductivity (RC) Ratio of Fracture Length to the Reservoir Radius ( L / r e ) Productivity Index Ratio ( J / J o ) Brady Sand 0.1 1.0 Bauxite 0.1 1.0

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b. Fill in the table below for Gulf of Mexico frac-pack Assume the following parameters: • Depth: z = 10,000 [ft] • Formation permeability: k = 100 [md] • Fracture width: w = 1.0 [inch] • Drainage Area: A = 40 [acres] Note: The formations in Gulf of Mexico are typically poorly cemented or unconsolidated sands. The rock is very soft and easy to deform, so hydraulic fractures are typically fat (large opening). Proppant Type Relative Conductivity (RC) Ratio of Fracture Length to the Reservoir Radius ( L / r e ) Productivity Index Ratio ( J / J o ) Brady Sand 0.1 1.0 Bauxite 0.1 1.0

c. Based on your results, come up with some general design rules with regard to fracture length and proppant permeability (both parameters we can control in our frac designs) for high permeability versus low permeability formations. Recognize that the more proppant you pump, the more expensive your fracture treatment will be (you cannot just say pump the fattest, longest fracture with the highest permeability proppant every time).