6.4 WP9: Hydraulic Fracturing

6.4.1 Stress shadows and interference

Read the paper “Roussel, N. P., and Sharma, M. M. (2011). Optimizing fracture spacing and sequencing in horizontal-well fracturing. SPE Production and Operations, 26(02), 173-184.” https://doi.org/10.2118/127986-PA.

1. Calculate the point of principal stress reversal (isotropic point in Fig. 11 of the paper) with a constant pressure and plane-strain solution utilizing your FreeFEM++ linear elasticity code. Use all parameters as in Table 1. Note: $\Delta S_{yy} = \nu (\Delta S_{xx}+\Delta S_{zz})$.
2. Repeat the previous task for fracture width 6 mm, 8 mm, and 10 mm. Plot stress reversal distance as a function of fracture width. Hint: You may need to calculate the required net pressure from the analytical solution.

Figure 6.1: $S_{Hmax}$ direction around a propped hydraulic fracture (Roussel and Sharma, 2011).

6.4.2 Coupled hydraulic fracturing modeling

A single hydraulic fracture treatment will be performed in a tight sandstone. The hydraulic fracture height is expected to be $h_f$ = 170 ft. The tight sandstone has a plane-strain modulus $E' = 8.9 \times 10^6$ psi. The (two-wing) injection rate will be 50 bbl/min (constant) during 1 hour.

Compute:

1. The expected fracture half-length $x_f$, fracture width at the wellbore $w_{w,0}$, and net pressure $p_{n}$ as a function of time with the PKN model (no leak-off) assuming the fracturing fluid has a (constant) viscosity 2 cP.
2. The expected fracture half-length $x_f$, fracture width at the wellbore $w_{w,0}$, and net pressure $p_n$ as a function of time with the PKN model (no leak-off). Now the fracturing fluid has a viscosity 2 cP with no proppant (initial 10 min), and increases in steps of 10 min with 2 cP in each step (due to increasing proppant concentration).
3. What should you do to your solution in order to consider leak-off? Justify and explain briefly the algorithm to calculate $x_f$, $w_{w,0}$, and $p_n$.

Hint: convert all quantities to the SI system first