Gas Lift Valve Mechanics

Overview

Gas lift valves are the critical control elements in a gas lift system. They regulate the flow of injection gas from the annulus into the tubing at specific depths. Understanding valve mechanics is essential for proper valve spacing, pressure setting, and troubleshooting.

The most common type is the Injection Pressure Operated (IPO) valve, which opens and closes based on casing (injection) pressure.

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IPO Valve Construction

An IPO valve consists of:

The bellows area ($A_b$) is larger than the port area ($A_p$). The ratio $R = A_p/A_b$ is a key valve parameter, typically 0.05-0.20.

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Dome Pressure

Temperature Effect

The nitrogen dome is charged at the test rack temperature (60°F) but operates at valve temperature. The charge is sealed, so its density is fixed and the dome pressure follows the real-gas law:

$$\frac{P_{d,2}}{z_2 T_2} = \frac{P_{d,1}}{z_1 T_1}$$

Where:

• $P_d$ = dome pressure, absolute
• $T$ = absolute temperature
• $z$ = nitrogen compressibility factor at the dome's own state

The z factors are nitrogen's, not the lift gas's: a gauge pressure, or the lift-gas z, gives the wrong answer. PO.GL.Valve.Pdome solves this with nitrogen's critical constants (Guo et al. 2007, Eq. 13.58), and dome pressure rises with temperature.

Test Rack Opening

The valve is set at 60°F on a test rack with the tubing side open to the atmosphere, so the test rack opening pressure is the opening-pressure balance below with $P_t$ = 14.7 psia (Eq. 13.57). PO.GL.Valve.TRO returns it in absolute pressure.

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Opening and Closing Pressures

Force Balance

At the moment of opening, the forces on the valve stem balance:

Closing force = Dome pressure × bellows area, plus any spring $$F_{close} = P_d \times A_b + S_t \times (A_b - A_p)$$

Opening force = Casing pressure on bellows + Tubing pressure on port $$F_{open} = P_c \times (A_b - A_p) + P_t \times A_p$$

Opening Pressure

Setting $F_{open} = F_{close}$ and solving for $P_c$ gives the opening pressure (Guo et al. 2007, Eq. 13.42):

$$P_{vo} = \frac{P_d}{1 - R} + S_t - \frac{R}{1 - R} P_t$$

Tubing pressure on the port helps open the valve, which is why it enters with a minus sign. Without a spring ($S_t = 0$):

$$P_{vo} = \frac{P_d - R \times P_t}{1 - R}$$

All pressures are absolute.

Closing Pressure

Once the valve is open, the pressure under the port is close to casing pressure, so casing pressure acts on the whole bellows area. The valve closes when it falls to (Eq. 13.43):

$$P_{vc} = P_d + S_t (1 - R)$$

Without a spring, the closing pressure is the dome pressure. PO.GL.Valve.Pvc takes no spring, so it returns $P_d$ and $R$ has no effect on it.

Valve Spread

Without a spring:

$$\text{Spread} = P_{vo} - P_{vc} = \frac{R}{1 - R} (P_d - P_t)$$

Key observations:

• Spread depends on the dome-to-tubing pressure difference and the port-to-bellows ratio $R$
• Larger port → larger $R$ → larger spread → less precise control
• Higher tubing pressure → smaller spread, because tubing pressure helps open the valve

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Gas Throughput

Thornhill-Craver Equation

The gas flow rate through a gas lift valve operating in subcritical flow:

$$q_{sc} = 155.5 \times C_d \times A_p \times P_1 \times \sqrt{\frac{2g}{k-1} \times \frac{M}{RT_1} \times \left[\left(\frac{P_2}{P_1}\right)^{2/k} - \left(\frac{P_2}{P_1}\right)^{(k+1)/k}\right]}$$

Where:

• $q_{sc}$ = gas rate at standard conditions (Mscf/d)
• $C_d$ = discharge coefficient (0.60-0.85)
• $A_p$ = port area (in2)
• $P_1$ = upstream pressure (psi)
• $P_2$ = downstream pressure (psi)
• $k$ = specific heat ratio ($c_p/c_v$)
• $M$ = gas molecular weight
• $T_1$ = upstream temperature (degR)

Critical Flow

When the pressure ratio drops below the critical ratio:

$$\frac{P_2}{P_1} \le \left(\frac{2}{k+1}\right)^{k/(k-1)}$$

The flow becomes sonic (critical), and increasing the downstream pressure drop no longer increases flow rate. For natural gas ($k \approx 1.28$), the critical ratio is approximately 0.55.

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Production Pressure Effect (PPE)

Concept

In practice, the tubing (production) pressure at valve depth affects both valve opening and gas throughput. The PPE factor quantifies this influence:

$$PPE = \frac{P_t \times R}{1 - R}$$

This is the tubing effect in the opening pressure above: it is subtracted from $P_d/(1-R)$. Higher PPE means:

• Lower opening pressure for the same dome pressure
• Opening pressure more sensitive to tubing pressure changes
• A wider spread, since a larger $R$ raises both PPE and the spread

Design Implications

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Valve Spacing

Principles

1. Top valve depth set by kickoff pressure available
2. Subsequent valves spaced to maintain pressure differential for unloading
3. Operating valve is the deepest valve — injection point for steady-state production
4. Each valve must close before the next one is uncovered

Pressure Drop Per Valve

Each successive valve requires slightly lower opening pressure to ensure sequential operation:

$$\Delta P_{valve} = 15-30 \text{ psi per valve}$$

This drop accounts for:

• Dome pressure setting tolerances
• Ensuring upper valves close before lower ones open
• Providing a margin of safety

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Troubleshooting

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Related Topics

• Gas Lift Overview — System design and optimization
• VFP Overview — Tubing pressure calculations for lift design
• IPR Overview — Inflow performance at operating conditions

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References

1. Winkler, H.W. and Smith, S.S. (1962). Gas Lift Manual. CAMCO Inc.

2. Takacs, G. (2005). Gas Lift Manual. PennWell Books.

3. API Recommended Practice 11V6 (2008). "Design of Continuous Flow Gas Lift Installations Using Injection Pressure Operated Valves." American Petroleum Institute.

4. Brown, K.E. (1980). The Technology of Artificial Lift Methods, Vol. 2a. PennWell Books.

5. Guo, B., Lyons, W.C. and Ghalambor, A. (2007). Petroleum Production Engineering, Section 13.5. Gulf Professional Publishing.

6. Economides, M.J., Hill, A.D., Ehlig-Economides, C., and Zhu, D. (2013). Petroleum Production Systems, 2nd Edition. Prentice Hall.