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INPUT   DATA

Title

Horizontal length		ft
Wellbore radius		ft
Drainage radius		ft
Formation thickness		ft
Permeability		mD
Skin factor
Wellflowing pressure		psi
Reservoir pressure		psi
Reservoir temperature		° F

#	Pressure	Viscosity	Compressibility
	(psia)	(cp)
1
2
3
4
5
6
7
8

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OUTPUT   VARIABLES  &   GRAPH

	Wellflowing pressure	Reservoir pressure	Gas flow rate
	(psi)	(psi)	(Mscf/day)
Horizontal well
Vertical well

Horizontal Well Performance (Gas)

The pseudosteady-state flow of gas into an horizontal well is represented by the following equation:

Where:

   Q_g = gas flow rate Mscf/day
   h = thickness, ft
   k= permeability, md
   T = temperature, ° Rankine
  L = length of horizontal well, ft
  r_eh = drainage radius of horizontal well
  r_w = wellbore radius, ft
  a = half the major axis of the drainage ellipse, ft
  s = skin factor
   ψ _r = average reservoir pseudo-pressure
   ψ _wf = wellflowing pseudo-pressure

Note that drainage radius (ft) is derivable from drainage area A (acres) as follows:
  r_eh = √[43560A/π]

The pseudo-pressure is defined by the following integral equation:

Where:

   ψ(p) = pseudo-pressure at pressure p, psi²/cp
   p_b= an arbitrary base pressure (< p), psia
   μ = viscosity of gas, cp
   z = gas compressibility factor

  (Note that μ and z are both functions of pressure. μ increases with pressure. z takes a value of 1 at zero pressure, then initially drops as pressure increases and eventually rises at higher pressures.)

Numerical integration is performed here using the trapeziodal rule with p_b = 0.

For radial flow into a Vertical well,  r′_w = r_w .

BIBLIOGRAPHY

• Ahmed T.; Reservoir Engineering Handbook; Pennwell Publ Co, Tulsa, Oklahoma, 2000, chap. 8.
• Joshi S.; Horizontal Well Technology; Pennwell Publ Co, Tulsa, Oklahoma, 1991.