Gas Well Deliverability

Overview

Gas well performance differs fundamentally from oil wells due to:

• High flow velocities — Gas compressibility creates turbulence near wellbore
• Pressure-dependent properties — μg, ρg, Z vary significantly with pressure
• Non-Darcy flow — Inertial/turbulent effects at high rates
• Pseudo-pressure — Required for rigorous gas flow analysis

Gas well deliverability analysis determines:

• AOF (Absolute Open Flow) — Maximum theoretical rate
• Productivity — Relationship between rate and pressure drawdown
• Backpressure curve — Rate vs. (p²) or pseudo-pressure relationship
• Completion efficiency — Skin effects and damage quantification

Darcy vs. Non-Darcy Flow

Darcy Flow (Laminar)

At low velocities, gas flow follows Darcy's law (linear relationship):

Or in pseudo-steady state using real gas pseudo-pressure:

Where real gas pseudo-pressure is:

Applicability: Low rate wells, high permeability, large wellbore radius.

Non-Darcy Flow (Turbulent)

At high velocities, inertial (turbulent) effects become significant. The Forchheimer equation adds a rate-squared term:

Where:

• $\beta$ = turbulence factor (or inertial resistance coefficient), ft⁻¹
• Second term represents non-Darcy (turbulence) pressure drop

This leads to the backpressure equation:

Or:

Physical interpretation:

• $a$ term: Darcy (laminar) flow
• $b$ term: Non-Darcy (turbulent) flow
• At high rates, turbulence dominates (b term >> a term)

Non-Darcy Coefficient (D)

The non-Darcy flow coefficient quantifies turbulence:

Where:

• $F$ = turbulence factor (dimensionless, typically 1-100)
• Higher D → More turbulence, steeper backpressure curve

Typical D values:

• Low perm tight gas (0.1 md): D = 0.001 to 0.01
• Moderate perm (1 md): D = 0.0001 to 0.001
• High perm (100 md): D = 0.00001 to 0.0001

Estimating D (Jones-Blount-Glaze Correlation)

Where $\beta$ (turbulence factor) can be estimated from:

Data needed: k, h, rw, T, γg, μg (all at average reservoir conditions).

Backpressure Testing

Four-Point Test Procedure

1. Shut in well → measure pR (stabilized)
2. Flow at rate q₁ → measure pwf,1 (stabilized)
3. Flow at rate q₂ → measure pwf,2 (stabilized)
4. Flow at rate q₃ → measure pwf,3 (stabilized)
5. Flow at rate q₄ → measure pwf,4 (stabilized)

Calculating a, b (or n)

Plot $(p_R^2 - p_{wf}^2)$ vs. $q_{sc}$ on log-log paper.

Slope = n (deliverability exponent):

• n = 1.0 → Pure Darcy flow (no turbulence)
• n = 0.5 → Fully turbulent flow
• n = 0.6 to 0.8 → Typical gas wells

Backpressure equation:

Or modern form:

Absolute Open Flow (AOF):

Pseudo-Steady State Gas Flow

For bounded reservoirs (closed drainage volume), use pseudo-steady state equations.

PSS Darcy Flow

Where:

• $r_e$ = external drainage radius, ft
• $r_w$ = wellbore radius, ft
• $s$ = skin factor (dimensionless)

PSS Non-Darcy Flow

Combining:

Where:

Time to Pseudo-Steady State

Before PSS is reached, gas wells exhibit transient flow. Time to reach PSS:

For Gas (Low Compressibility Liquid)

Where:

• $t_{PSS}$ = time to PSS, hours
• $\phi$ = porosity, fraction
• $\mu_g$ = gas viscosity, cP
• $c_t$ = total compressibility, psi⁻¹
• $r_e$ = drainage radius, ft
• $k$ = permeability, md

Typical values:

• High perm (100 md), small drainage (500 ft): tPSS ≈ 5 hours
• Low perm (0.1 md), large drainage (2000 ft): tPSS ≈ 2000 hours

Skin Factor and Wellbore Effects

Total Skin Factor

Components:

• $s_{damage}$: Formation damage near wellbore
• $s_{perforation}$: Perforation geometry and density
• $s_{partial penetration}$: Limited perforated interval
• $s_{deviation}$: Deviated well effects
• $s_{turbulence}$: High-velocity non-Darcy effects

Effective Wellbore Radius

Positive skin reduces effective wellbore radius:

Where:

• $r_w'$ = effective wellbore radius, ft
• $r_w$ = actual wellbore radius, ft
• $s$ = skin factor

Example:

• rw = 0.5 ft, s = +5 → rw' = 0.0034 ft (147× reduction!)
• rw = 0.5 ft, s = -3 → rw' = 10.0 ft (20× increase from stimulation)

Equivalent Skin for Fractures

Hydraulically fractured wells can be represented by equivalent negative skin:

Where:

• $x_f$ = fracture half-length, ft

Example: xf = 200 ft, rw = 0.5 ft → sfrac = -6 (excellent stimulation).

Drainage Radius Calculations

For circular drainage area:

Where $A$ = drainage area, ft²

Common well spacings:

• 160 acres: re ≈ 1490 ft
• 80 acres: re ≈ 1053 ft
• 40 acres: re ≈ 745 ft

Functions Covered

The following functions implement gas well deliverability calculations. See each function page for detailed parameter definitions, Excel syntax, and usage examples.

Related Documentation

• WellFlow Overview — Well performance concepts
• Vogel IPR — Oil well IPR (different from gas)
• Vertical Flow Correlations — Tubing flow (Hagedorn-Brown, Gray)
• Gas Properties — Z-factor, viscosity, pseudo-pressure
• Horizontal Wells — Horizontal gas well productivity

References

1. Lee, J. and Wattenbarger, R.A. (1996). Gas Reservoir Engineering. SPE Textbook Series Vol. 5. Richardson, TX: Society of Petroleum Engineers.

2. Economides, M.J., Hill, A.D., Ehlig-Economides, C., and Zhu, D. (2013). Petroleum Production Systems, 2nd Edition. Upper Saddle River, NJ: Prentice Hall. Chapter 4: Gas Well Deliverability.

3. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Cambridge, MA: Gulf Professional Publishing. Chapter 13: Gas Well Testing.

4. Guo, B., Lyons, W.C., and Ghalambor, A. (2007). Petroleum Production Engineering: A Computer-Assisted Approach. Burlington, MA: Gulf Professional Publishing.

5. Jones, L.G., Blount, E.M., and Glaze, O.H. (1976). "Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence." SPE-6133-MS, presented at SPE Annual Fall Technical Conference, New Orleans, LA, October 3-6.