---

INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Horizontal permeability		mD
Vertical permeability		mD
Perforation spacing		ft
Perforation length		ft
Perforation phasing angle		°

---

---

OUTPUT   VARIABLES   &   GRAPHS

Perforated Horizontal Well	Factor
♦  Productivity Ratio (PR)

Productivity Ratio Of Perforated Horizontal Completions

PR is widely employed in evaluating the effects of perforating parameters on well productivity. PR is defined as the ratio of the ratio of productivity index (PI) of a perforated well to the PI of an openhole well.

Tang et al presented semi-analytical correlations to estimate PR for cased-hole horizontal completions. PR is modelled as a function of perforation anisotropy and perforating parameters (perforation density, phasing and penetration). The PR correlation is given as:

PR = a₀ + a₁F + a₂F²

  F = f₁(kzr) + f₂(L_p) + f₃(SPF)

  f₁(kzr) = b₀ + b₁ln(k_z/k_r) + b₂ln²(k_z/k_r)

  f₂(L_p) = c₀ + c₁L_p + c₂L_p²

  f₃(SPF) = d₀ + d₁SPF + d₂SPF²

where
     SPF = shot per foot = perforation density = reciprocal of h_perf, 1/ft
     h_perf = perforation spacing = vertical distance between perfs rows, ft
     L_p = penetration length = length of perforation tunnel, ft
     k_zr = k_v/k_h
     k_h = horizontal permeability of formation, mD
     k_v = vertical permeability of formation, mD
     θ = perforation phasing angle = angular sparation between neighbouring perforations, degrees
     a₀,a₁,a₂,b₀,b₁,b₂, c₀,c₁,c₂,d₀,d₁,d₂ = Phasing-dependent constants tabulated in Tang et al.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Tang Y., Ozkan E., Kelkar M. & Yildiz T.; Fast and accurate correlations to compute the perforation pseudoskin and productivity of horizontal wells; paper SPE-71638, 2001.
• Karakas M. & Tariq S.M.; Semianalytical productivity models for perforated completions; SPEPE, Feb., 1991, p. 73-82.
• Economides M.J., Hill A.D. & Ehlig-Economides C.; Petroleum Production Systems; PTR Prentice Hall Inc. Englewood Cliffs, NJ, 1994, chap. 5.