CYP2C9

Figure 6.10 shows the comparison of the calculated BHP from the measured treating pressure and the simulated one during the main fracturing. The simulated pressure matches well with the calculated one, which proves the reliability of the modeled fracture propagation and closure.

Figure 6.10 Comparison of the calculated BHP from the measured treating pressure and the simulated during the main fracturing 2

Figure 6.11 shows the fracture pattern with width distribution and proppant mass distribution per unit area at shut-in and closure. At the end of the injection (t = 87 min), the fracture got a half-length of 84 meters and a height of 63 meters (Figure 6.13 a). It is noteworthy in Figure 6.11 b, that there is a maximum value appearing along the fracture length at the depth of -4439 m by the proppant mass per unit area at shut-in. The proppant mass per unit area (Eq. (6.1)) is defined as,

𝑀𝑝

𝐴 = 𝑤𝑓∗ 𝐶𝑝∗ 𝜌𝑝 (6.1)

where Mp is proppant mass [kg], A is fracture area [m2], wf is fracture width [m], Cp is proppant

volume concentration [%], ρp is proppant density [kg/m3].

For fracture 2 the dimensionless fracture conductivity (FCD)is 12.2. Figure 6.12 shows fracture

width, proppant volume concentration and proppant mass per unit area along the fracture length at shut-in. The fracture width reduced along the facture length. The proppant volume concentration hat reached the maximum value of 65% from x = 74 m. According to the (Eq. (6.1)), the proppant mass per unit area is equal to the product of the facture width and proppant volume concentration. So, at x = 74 m the proppant mass per unit area has reached the maximum value of 15.6 kg/m2_{. That is the reason for the maximum value appearance along the} fracture length by the proppant mass per unit area at shut-in.

At t = 650 minutes (563 min after shut-in), the width shows the same contour distribution as the proppant, which indicates that the fracture got already in contact with the proppant and no more closure would happen there.

Figure 6.11 Fracture pattern with width distribution (a) and proppant mass distribution pro area (b) at shut-in (t = 87 min) and closure (t = 650 min) during the main fracturing 2

Figure 6.12 Fracture width, proppant volume concentration and proppant mass per unit area along the fracture length at shut-in (z = -4439 m) during the main fracturing 2

(a) (b)

Figure 6.13 (a) Temporal developments of the fracture half-length and height during the main fracturing; (b) Temporal developments of the fracture and the proppant concentration at perforation during the main fracturing 2

Figure 6.14 shows the comparison between FLAC3Dplus _{and FracPro by the fracture half-length,} height and average fracture width at shut-in and closure. The differences between them are small and acceptable i.e. can be neglected.

Figure 6.14 Comparison between FLAC3Dplus _{and FracPro by the fracture geometry at shut-} in and closure during the main fracturing 2

Figure 6.15 shows the comparison of the fracture volume and the injection volume. After t = 650 minutes the fracture volume stays constant, which means that the fully closure is reached. Figure 6.16 shows the comparison between FLAC3Dplus _{and FracPro by the injection volume,} fracture volume and leak-off at shut-in and closure. The differences between them are small.

Figure 6.15 Comparison of the fracture volume and the injection volume during the main fracturing 2

Figure 6.16 Comparison between FLAC3Dplus _{and FracPro by the injection volume, fracture} volume and leak-off at shut-in and closure during the main fracturing 2

The viscosity distribution and the formation temperature are shown in Figure 6.17. The largest fluid viscosity value is 0.87 Pa∙s at shut-in. And the temperature around the perforation is 50 °C, which is coinciding with the injection temperature. Because of the gel breaking during the hydraulic fracturing, the largest fluid viscosity reduced to 0.65 Pa∙s at closure. And because of the energy transport the formation temperature gradually comes back to the initial reservoir temperature.

Figure 6.17 Fracture pattern with Fluid viscosity (a) and reservoir temperature (b) at shut-in (t = 87 min) and closure (t = 650 min) during the main fracturing 2

6.1.3 Simulation results of frac-stage 3

Figure 6.18 shows the comparison of the calculated BHP from the measured treating pressure and the simulated one during the main fracturing. The simulated pressure matches well with the calculated one, which proves the reliability of the modeled fracture propagation and against closure.

Figure 6.18 Comparison of the calculated BHP from the measured treating pressure and the simulated during the main fracturing 3

Figure 6.19 shows the fracture pattern with width distribution and proppant mass distribution per unit area at shut-in and closure. At the end of the injection (t = 100 min), the fracture got a half-length of 94 meters and a height of 76 meters (Figure 6.21 a). At t = 1000 minutes (900 min after shut-in), the width shows the same contour distribution as the proppant, which indicates that the fracture got already in contact with the proppant and no more closure would happen there. Figure 6.21 b shows the temporary development of the widths and the concentration distribution at perforation. From t = 223 min the proppant concentration at perforation has already reached 65%. For frac-stage 3 the dimensionless fracture conductivity (FCD)is 19.2.

Figure 6.20 shows fracture width, proppant volume concentration and proppant mass per unit area along the fracture length at shut-in and at the depth of -4432 m. The fracture width reduced along the facture length. The proppant volume concentration hat reached the maximum value of 65% from x = 79 m. According to the Eq. (6.1), the proppant mass per unit area is equal to the product of the facture width and proppant volume concentration. So, at x = 74 m the proppant mass per unit area has reached the maximum value of 16.4 kg/m2_{. That is the reason} for the maximum value appearance along the fracture length by the proppant mass per unit area at shut-in (Figure 6.19 b).

Figure 6.19 Fracture pattern with width distribution (a) and proppant mass distribution pro area (b) at shut-in (t = 100 min) and closure (t = 1000 min) during the main fracturing 3

Figure 6.20 Fracture width, proppant volume concentration and proppant mass per unit area along the fracture length at shut-in (Z = -4432m) during the main fracturing 3

(a) (b)

Figure 6.21 (a) Temporal developments of the fracture half-length and height during the main fracturing; (b) Temporal developments of the fracture and the proppant concentration at perforation during the main fracturing 3

Figure 6.22 shows the comparison between FLAC3Dplus _{and FracPro by the fracture half-length,} height and average fracture width at shut-in and closure. The differences between them are small and can be neglected.

Figure 6.23 shows the comparison of the fracture volume and the injection volume. After t = 1000 minutes the fracture volume stays constant, which means that the fully closure is reached. Figure 6.24 shows the comparison between FLAC3Dplus _{and FracPro by the injection volume,} fracture volume and leak-off at shut-in and closure. The difference between them is very small.

Figure 6.22 Comparison between FLAC3Dplus and FracPro by the fracture geometry at shut- in and closure during the main fracturing 3

Figure 6.23 Comparison of the fracture volume and the injection volume in the main fracturing during the main fracturing 3

Figure 6.24 Comparison between FLAC3Dplus _{and FracPro by the injection volume, fracture} volume and leak-off at shut-in and closure during the main fracturing 3

The viscosity distribution and the formation temperature are shown in Figure 6.25. The largest fluid viscosity value is 0.87 Pa∙s at shut-in. And the temperature around the perforation is 50 °C, which is coinciding with the injection temperature. Because of the gel breaking during the hydraulic fracturing, the largest fluid viscosity reduced to 0.64 Pa∙s at closure. And because of the energy transport the formation temperature gradually comes back to the initial reservoir temperature.

Figure 6.25 Fracture pattern with Fluid viscosity (a) and reservoir temperature (b) at shut-in (t = 100 min) and closure (t = 1000 min) during the main fracturing 3

6.1.4 Simulation results of frac-stage 4

Figure 6.26 shows the comparison of the calculated BHP from the measured treating pressure and the simulated one during the main fracturing. Except the unstable section at the end of the injection, which is caused by pre-mature screen out, the simulated pressure matches well with the calculated one, which proves the reliability of the modeled fracture propagation and closure.

Figure 6.26 Comparison of the calculated BHP from the measured treating pressure and the simulated during the main fracturing 4

Figure 6.27 shows the fracture pattern with width distribution and proppant mass distribution per unit area at shut-in and closure. At the end of the injection (t = 110 min), the fracture got a half-length of 100 meters and a height of 86 meters (Figure 6.28 a). The reason of the maximum value appearance along the fracture length by proppant mass per unit area at shut-in is the same with fracture 2 and 3 (Figure 6.27 b). At t = 740 minutes (630 min after shut-in), the width shows the same contour distribution as the proppant, which indicates that the fracture got already in contact with the proppant and no more closure would happen there. Figure 6.28 b shows the temporary development of the widths and the concentration distribution at perforation. From t = 200 min the proppant concentration at perforation has already reached 65%. For frac-stage 4 the dimensionless fracture conductivity (FCD)is 22.6.

Figure 6.27 Fracture pattern with width distribution (a) and proppant mass distribution pro area (b) at shut-in (t = 110 min) and closure (t = 740 min) during the main fracturing 4

Figure 6.28 (a) Temporal developments of the fracture half-length and height during the main fracturing; (b) Temporal developments of the fracture and the proppant concentration at perforation during the main fracturing 4

Figure 6.29 shows the comparison between FLAC3Dplus _{and FracPro by the fracture half-length,} height and average fracture width at shut-in and closure. The differences between them are

small and can be neglected.

Figure 6.29 Comparison between FLAC3Dplus and FracPro by the fracture geometry at shut- in and closure during the main fracturing 4

Figure 6.30 shows the comparison of the fracture volume and the injection volume. After t = 740 minutes the fracture volume stays constant, which means that the fully closure is reached. Figure 6.31 shows the comparison between FLAC3Dplus _{and FracPro by the injection volume,} fracture volume and leak-off at shut-in and closure. The difference between them is very small.

Figure 6.30 Comparison of the fracture volume and the injection volume during the main fracturing 4

Figure 6.31 Comparison between FLAC3Dplus _{and FracPro by the injection volume, fracture} volume and leak-off at shut-in and closure during the main fracturing 4

The viscosity distribution and the formation temperature are shown in Figure 6.32. The largest fluid viscosity value is 0.87 Pa∙s at shut-in. And the temperature around the perforation is 50 °C, which is coinciding with the injection temperature. And because of the energy transport the formation temperature gradually comes back to the initial reservoir temperature.

Figure 6.32 Fracture pattern with Fluid viscosity (a) and reservoir temperature (b) at shut-in (t = 110 min) and closure (t = 740 min)