**10. Relative order of magnitude calculations — Supplemental power**

Using the hypothetical pressure losses that might occur for the generic scenario being consid‐ ered, presuming a certain number of effective perforations (broken down, and closely enough aligned with the local minimum principal stress7 ), additional pumping requirements (above

<sup>6</sup> In fact, this is approximate. For multiple, closely spaced fractures the width of the fractures is generally reduced. This was proposed by Nolte ,1997, [60] and Jeffrey et al., 1997 [62]. Germanovich et al., 1997, showed the complexity of the interaction with internal fractures being preferentially closed by encompassing external fractures.

openhole requirements) are estimated. This depends strongly on the number of effective perforations. The number of effective perforations is strictly governed by gun characteristics, especially phasing and density as well as in-situ conditions. It appears that for typical perfo‐ ration diameters the casing hole perforation diameter is a secondary parameter – unless it becomes extremely small.

Using the same generic reservoir, the power requirements for lifting and to overcome the estimated pressure losses in the perforations and the multiply fractured region are shown in Figure 4, using additional assumptions shown below.

hset setting depth for pump -- 500 m TVD

3 12 *<sup>m</sup>*

D = (10)

/s/m. The greater the half-length of the

), additional pumping requirements (above

*q L*

Apply this relationship to estimate the pressure drop. On a meter by meter basis it is possible to assume that the fracture width would be the width of an openhole fracture (assume 2 mm constant along the wellbore length) divided by the number of effective perforations;<sup>6</sup> similarly for the flow rate per fracture. For 60° phasing and 6 spf, one can envision something over six effective perforations per meter, giving an effective width of 0.33 mm (as opposed to 2 mm for an openhole bi-winged fracture). Assuming a velocity of 2.5 m/s through each perforation, the required perforated wellbore length (net perforated length) would be 160 m (see earlier) and

zone of multiple fractures (distance away from wellbore), Lm, the greater the pressure losses. Assume 5 m (Weng [12] found a typical transition at about 15 ft. in some of his calculations), the pressure loss can be estimated as 27 kPa (4 psi). The key variables are of course the number of effective perforations per unit length (phasing and spm) and the length over which linkage would occur. The presumption is that the length required for linkage can be reduced when the stimulation is carried out by breaking down all perforations, drilling at acceptable angles, and initiating at low rate. The troublesome aspect of this logic here is that more perforations give a higher pressure drop – so the ideal situation would be to use fewer, which is counter-intuitive and would increase the perforation tunnel losses. Figure 3 shows order of magnitude pressure losses for first order approximations of losses through the perforation tunnels themselves (see

Figure 2) and from the friction estimated in the multiply fractured region.

interaction with internal fractures being preferentially closed by encompassing external fractures.

**10. Relative order of magnitude calculations — Supplemental power**

Using the hypothetical pressure losses that might occur for the generic scenario being consid‐ ered, presuming a certain number of effective perforations (broken down, and closely enough

6 In fact, this is approximate. For multiple, closely spaced fractures the width of the fractures is generally reduced. This was proposed by Nolte ,1997, [60] and Jeffrey et al., 1997 [62]. Germanovich et al., 1997, showed the complexity of the

*mf*

Δpmf pressure loss for flow through the multiply fractured region

q volumetric flow rate in each fracture per unit height

the total inflow per meter would need to be 6.9 x 10-4 m3

aligned with the local minimum principal stress7

Lm half-length of multiply fractured zone *<sup>w</sup>*¯average aperture for each connecting fracture

where:

h unit height

m dynamic viscosity

374 Effective and Sustainable Hydraulic Fracturing

*<sup>p</sup> <sup>h</sup> <sup>w</sup>* m

hreservoir nominal depth to midpoint of producing fracture(s) -- 2,000 m TVD

hf length fracture communicates with wellbore -- 10, 20, 50, 100, 500 m

η pump efficiency (dimensionless) … 0.50 was used

**Figure 3.** Total pressure loss through perforations and near-wellbore region for 60,000 BWPD (0.11 m3/sec) – Comple‐ tion Losses. The legend shows the nominal perforation diameter through the casing and the number of shots per me‐ ter connecting with the fracture. The abscissa is the actual contact length of the fracture along the wellbore. For practical lengths and open perforations, this type of loss is inconsequential.

This might be considered in terms of incremental cost. Figure 5 shows that with enough connectivity these costs could be manageable. An overall economics evaluation would be required.

<sup>7</sup> Sometimes referred to as a secondary minimum principal stress. This strictly indicates the minimum principal stress at the borehole wall, not necessarily aligned with the far-field minimum principal stress.

#### **11. Erosion of perforations**

Figure 6 shows velocities through individual perforations in the generic geothermal system being considered. While the erosive capabilities of clean fluids are not always certain, twophase and solids-entrained fluids will have significant erosive potential. In conservative engineering applications, Simpson, 1968, [58] argued for velocities between 2.5 and 3 m/s. Considering that time-dependent enlargement of the perforations will stabilize the erosive potential and that the most important role of the perforations is before the well is in use (e.g., to promote multiple hydraulic fracturing) erosion is probably a benefit – reducing the pressure drop.

perforated completions cannot accommodate the volumes required for economical geothermal

**1.** Pressure losses through perforation tunnels per se are theoretically small. More perfora‐

**2.** Twisting and to a lesser extent turning of fractures initiating from perforations can cause greater pressure losses. Smaller densities can reduce this friction if the alignment of the

**3.** It seems that perforated completions for geothermal wells can be designed to minimize near-wellbore losses and improve economics. The calculations done to support this only have a relative order of magnitude reliability and further numerical and empirical

**Additional Costs for Perforation Losses**

25.4 mm, 13.12 Effective spm 12.7 mm, 13.12 Effective spm 25.4 mm, 6.56 Effective spm 12.7 mm, 6.56 Effective spm

Do Perforated Completions Have Value for Engineered Geothermal Systems

http://dx.doi.org/10.5772/56211

377

1 10 100 1000

**Fracture Contact Length Along Wellbore (m)**

**Appendix I — Pressure losses during production (Literature survey)**

The most cited work for perforation pressure losses is usually Karakas and Tariq, 1991 [23], Although their skin values were designed for permeable formations, the methodology is useful for thinking about pressure losses that might be incurred. They incorporated additive skin components that accounted for vertical and horizontal convergence and phasing. Inclination mechanical skin can also be considered. Presume that the perforation skin for a vertical well

production should be carefully reconsidered. The key findings:

tions and larger shots reduce this component further.

evaluation is necessary to generalize this observation.

**Figure 5.** Incremental daily cost estimate for pressure losses through the perforations.

wellbore falls within acceptable limits.

1

10

100

**Incremental Daily Cost (\$U.S.)**

can be represented as:

1000

10000

**Figure 4.** Power requirements to lift 60,000 BWPD (0.11 m3/sec) and to accommodate the required pressure drop through the perforations for a 50 percent efficiency. The legend shows the nominal perforation diameter through the casing and the number of shots per meter connecting with the fracture. The abscissa is the actual contact length of the fracture along the wellbore.

#### **12. Summary**

There are supplementary costs associated with casing, cementing and perforating geothermal production and injection wells that are to be hydraulically fractured. There are also operational costs related to overcoming near-wellbore losses as well as minor losses through perforation tunnels themselves. However, the advantages of ensuring extended contact along the wellbore with perforated completions could be substantial. At the very least, assertions that cased and perforated completions cannot accommodate the volumes required for economical geothermal production should be carefully reconsidered. The key findings:

**11. Erosion of perforations**

376 Effective and Sustainable Hydraulic Fracturing

0.01

0.1

1

Openhole

Lifting

25.4 mm, 13.12 Effective spm 12.7 mm, 13.12 Effective spm 25.4 mm, 6.56 Effective spm 12.7 mm, 6.56 Effective spm

10

**Hydraulic Power (kW)**

the fracture along the wellbore.

**12. Summary**

100

1000

drop.

Figure 6 shows velocities through individual perforations in the generic geothermal system being considered. While the erosive capabilities of clean fluids are not always certain, twophase and solids-entrained fluids will have significant erosive potential. In conservative engineering applications, Simpson, 1968, [58] argued for velocities between 2.5 and 3 m/s. Considering that time-dependent enlargement of the perforations will stabilize the erosive potential and that the most important role of the perforations is before the well is in use (e.g., to promote multiple hydraulic fracturing) erosion is probably a benefit – reducing the pressure

**Power Requirements**

1 10 100 1000

**Fracture Contact Length Along Wellbore (m)**

**Figure 4.** Power requirements to lift 60,000 BWPD (0.11 m3/sec) and to accommodate the required pressure drop through the perforations for a 50 percent efficiency. The legend shows the nominal perforation diameter through the casing and the number of shots per meter connecting with the fracture. The abscissa is the actual contact length of

There are supplementary costs associated with casing, cementing and perforating geothermal production and injection wells that are to be hydraulically fractured. There are also operational costs related to overcoming near-wellbore losses as well as minor losses through perforation tunnels themselves. However, the advantages of ensuring extended contact along the wellbore with perforated completions could be substantial. At the very least, assertions that cased and


**Additional Costs for Perforation Losses**

**Figure 5.** Incremental daily cost estimate for pressure losses through the perforations.
