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

2

*p d*

r

D = (2)

(3)

24 2 0.2369 *perforations*

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

> 0.1 0.4 2.2

m

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

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

/16rw] at the fracture entrance, where w is the fracture

æ ö ç ÷ = - ç ÷ è ø

*d*

1

*C e <sup>d</sup>*

*<sup>Q</sup> <sup>p</sup> NdC*

where:

where:

μ apparent viscosity, cP

Q total flow rate, BLPD ρ fluid density, lbm/gal

366 Effective and Sustainable Hydraulic Fracturing

Np number of contributing perforations d perforation nominal diameter, inch

as (El Rabba et al., 1997 and 1999 [18]):

d perforation diameter through the casing, inch

around the annulus with a width of [w<sup>2</sup>

Cd orifice discharge coefficient

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 here (refer to Appendix I).
