**6. Perforation skin — Pressure loss during injection**

the benefits of casing, cementing and perforating in the short-term override the costs of degradation with time, and whether these completions jeopardize well or system produc‐

**• Pressure Losses.** For commercial purposes, single well rates are high. It is often argued that pressure losses will be too extreme. Simple calculations to follow explore some of these

Pending successful isolation (casing and cementing), it is still necessary to complete the well. What are the methods for carrying this out? Perforating is the first logical choice. Abrasive jetting is also a possibility and may in fact ultimately turn out to be preferable. Alternatively, diversion is advocated as a methodology for isolation in openhole – and there is good logic for this, if the diverter can tolerate incremental pressures between fracturing events. Diversion could be considered in open or cased hole scenarios to maximize fracture contacts with the

To effectively develop multiple fracture systems, wellbore isolation seems to be a natural requirement. One legitimate possibility is diversion. This technology is decades old. For example, Spencer, 1970, [4] stated that "For many years solid materials have been used down hole as temporary barriers for diverting injected fluids. A typical operation involves adding the solids to a carrier fluid which is then pumped down hole. This solid laden fluid will be pumped into existing fractures and fissures. As the solids lodge and wedge in the openings and cracks within the formation, they reduce the flow … As the flow decreases due to the action of additional solids blocking the fluid path, the pressure continues to rise until another region of the formation fractures and provides a different path for the fluid to follow." Waters et al., 2009, [5] document more recent use in openhole hydraulic fracturing for shale produc‐ tion. Stalker et al., 2009, [6] show rudimentary calculations of the pressures that could be

Suppose that diversion is not appropriate in a particular openhole scenario. Possibly there are not enough pre-existing discontinuities intersecting the wellbore. This could mean that the pressure increments between diversions in an open hole would be so large that previously diverted zones would start to take fluid. Possibly there are pre-existing fractures that need to be avoided, and so on … If this is the case, a cased and cemented completion could be a rationale decision. Presuming that adequate pumping capacity can be installed, the primary concern has been "How much fluid can be economically delivered through a perforated completion during production?". Whether it is in the geothermal domain or the oil and gas domain, this

anticipated. Geothermal applications have been described by Petty, 2012 [7].

mechanisms, and suggest that this may or may not be the case.

**4. Using diversion in openhole situations**

**5. How to develop multiple fracture systems**

is a relevant question.

tivity and economics.

364 Effective and Sustainable Hydraulic Fracturing

wellbore.

A substantial amount of work has been done to understand pressure drop that occurs through perforations. One facet of this research has been to evaluate the pressure loss in a complicated perforation connection from the wellbore to the formation during injection. Eftaxiopoulos and Atkinson, 1996, [8] provided an elegant mathematical approximation. This built on earlier work by Yew and Li, 1988, [9] as well as Yew et al., 1989 [10]. These latter authors applied three-dimensional elasticity to assess hydraulic fracture growth from inclined wells. This is a situation that does promote complicated interconnection with the main hydraulic fracture and where a perforated completion may offer significant advantages over open hole. Initiation, propagation and linkage of fractures formed from individual perforations were considered. Yew et al., 1993, [11] continued these evaluations. A landmark practical presentation of these concepts was provided by Weng et al., 1993 [12].

In 1991, Behrmann and Elbel [13] carried out laboratory block testing to study the complex interconnection of multiple fractures growing from perforations. These authors suggested the strong potential role of a microannular fracture link. "In both cases, despite ideal laboratory conditions, clean wellbore and casing, and short cement interval, the wellbore annulus is pressurized during any pumping treatment. Therefore, in the absence of any optimally oriented defects (perforations), fractures will initiate as though the completion were openhole. Fracturing pressure will obviously be higher than in open hole, but initiation sites and extension geometry will be the same. Thus, it is theoretically possible to have different fractureinitiation sites with identical perforation orientations if two wells have substantially different wellbore damage."

In 1995, Romero et al. [14] presented numerical evaluations related to near-wellbore injec‐ tion pressure losses attributed to communication (perforations), fractures (turning and twisting) and multiple fractures. Their interest was in mitigating high treatment pressure and unanticipated screenouts. They allocated a near-wellbore pressure loss to the sum of these three effects – perforation pressure drop, turning/twisting or tortuosity and perfora‐ tion misalignment. For the perforations themselves, they considered the perforation tun‐ nels as orifices. That relationship is (see Crump and Conway, 1988, [15], Lord et al., 1994, [16] Shah et al., 1996 [17]):

$$
\Delta p\_{\text{perfavorable}} = 0.2369 \frac{Q^2 \rho}{N\_p^2 d^4 C\_d^2} \tag{2}
$$

openhole, the contact area is explicitly defined. In cased hole, injection restrictions through individual perforations may force a larger contact area along the wellbore with linked fractures evolving from perforations, feeding into the pre-existing fracture at some small distance from

Do Perforated Completions Have Value for Engineered Geothermal Systems

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

367

These considerations of pinch points are appealing, but may not work equally well during

At the other end of the spectrum are production-related publications which have either assumed a high permeability formation without hydraulic fractures, or have agglomerated complicated near wellbore effects into a choke skin. Karakas and Tariq, 1991, [23] provide a summary of these effects. Since these tend not to reveal a great deal of information about specific losses in the near-wellbore area other than an overall skin, they are only summarized

A comparative analysis is done to assess the magnitude of perforation friction losses. Tor‐ tuosity associated with shear fractures intersecting the wellbore can be included using methods proposed by Weng, 1993, [12] and Haney et al., 1995, [57] with the assumption that they work for production in the same fashion that they do for hydraulic fracturing. The simplest possible representation of near-wellbore pressure loss, ignoring tortuosity, is that the pressure drop is strictly due to orifice losses using calculations that can be readily inferred from Bernoulli's

the well. See also Massaras et al., 2007 [22].

here (refer to Appendix I).

TD to reservoir top 2000 m

Net to gross 1

Inclination 0°

Reservoir net thickness 500 m

Perforated reservoir thickness up to 500 m

required mass flow rate per well 100 kg/sec

Required volumetric flow rate 62,000± BWPD (sand face)

Average reservoir temperature 200°C

Average bottomhole fluid density1

Average viscosity 0.14 cP

production, with the pressure gradient into the wellbore.

**7. Perforation skin — Pressure loss during production**

**8. Relative order of magnitude calculations — Pressure losses**

equation along with a discharge coefficient, Cd. Consider a hypothetical case:

, 877.6 kg/m3

where:

Q total flow rate, BLPD

ρ fluid density, lbm/gal

Np number of contributing perforations

d perforation nominal diameter, inch

Cd orifice discharge coefficient

Depending on the upstream Reynolds' number and the roundness of the edges, the discharge coefficient can range from less than 0.5 to approximately 1. It has been empirically expressed as (El Rabba et al., 1997 and 1999 [18]):

$$\mathbf{C}\_d = \left(1 - e^{-\frac{2.2d}{\mu^{0.1}}}\right)^{0.4} \tag{3}$$

where:

d perforation diameter through the casing, inch

μ apparent viscosity, cP

The pressure drop due to fracture turning was also approximated, as was microannular flow. Romero et al. [14] stated that, "If the fluid exits the well through the perforation, it must traverse the microannulus and pass the restriction area before, entering the main body of the fracture. A geometry effect occurs in which the rock moves away from the cement resulting in a channel around the annulus with a width of [w<sup>2</sup> /16rw] at the fracture entrance, where w is the fracture width, and rw the wellbore radius. In addition, an elastic response (Poisson's effect) occurs in which the fracture opening results in a movement of the rock towards the wellbore." This results in a pinch point during injection – a similar restriction with opposing geometry (but widest where the pressure is highest) is anticipated during production. Gulrajani and Romero, 1996, [19] acknowledged the importance of diagnostic measurements with rate changes to determine near-wellbore losses during injection, where the pressure losses associated with near-wellbore effects could be approximated by the injection rate to a suitable power. If there are insufficient perforations, the pressure loss varies with the rate squared. If tortuosity dominates, the pressure loss varies with the square root of the rate. Similar considerations have been published by Manrique et al., 1997, [20] and by Behrmann and Nolte, 1998, [21] who discussed fracture contact with deviated wellbores. Communicating with a fracture intersect‐ ing the hole at an oblique angle may actually be an advantage for a cased hole scenario. In openhole, the contact area is explicitly defined. In cased hole, injection restrictions through individual perforations may force a larger contact area along the wellbore with linked fractures evolving from perforations, feeding into the pre-existing fracture at some small distance from the well. See also Massaras et al., 2007 [22].

These considerations of pinch points are appealing, but may not work equally well during production, with the pressure gradient into the wellbore.
