Gas lift traverses are computed incrementally from the wellhead node down to reservoir node. There are multiple scenarios in which ProdX can compute a gas lift traverse and gas lift valve diagnostics, depending on the available data.

During the course of valve diagnostic calculations, a valve state is determined by the application. The following states can be detected:

In the absence of known gas lift valve depths, ProdX will compute a pure injection traverse and production traverse (using the total gas rate = produced + injected gas). Then the spread between these traverses is analyzed to find the deepest point at which the difference is greater than a minimum delta pressure (45 psi, by default). This is assumed to be the gas lift depth of injection. The production and injection traverses are modified below this depth to remove the injected gas from the traverse rates.

With known valve depths and unknown R and PTRO values, the design case surface opening and closing pressures (PSO, PSC) are used to determine which valve(s) are open.

To perform this calculation, the injection pressure at surface is compared to each valve's PSO. Valves in which the injection pressure is above PSO are deemed open, and valves in which the injection pressure is below PSC are deemed closed. Valves which have injection pressures between PSC and PSO are indeterminant but assumed closed for modeling.

Next, a production and injection traverse are computed simultaneously from surface to the first open valve using a total gas rate of produced + injected gas for the production traverse. At the first open valve, the modified Thornhill-Craver (TC) equation or API RP 11 V2 is used to compute the gas flow rate through the valve, depending on configuration and available data. See below sections for more information.

Any remaining injection gas that cannot pass through the first open valve will be assumed to travel to the next open valve or deepest/orifice valve. The traverse is continued downward using this methodology, modifying the produced and injected gas rate accordingly by depth and passage through open valves. Any valves deeper than the intersection of the production and injection traverses are considered submerged.

With known valve depths, R, and PTRO values, a more comprehensive calculation can occur.

First, a production and injection traverse are computed simultaneously from the surface node down to the first gas lift valve. The production traverse assumes a total gas rate of produced gas + injected gas from the surface to the first valve. At the first valve, downhole opening and closing pressures are computed by calculating the dome pressure (closing, PVC), and then using the r-value and production pressure to determine opening pressure (PVO). See section below for more details on opening and closing pressure calculations. Then, using the injection pressure at depth, a comparison is made to PVO/PVC to determine if that valve is open, closed, or "likely closed" (indeterminant state with injection pressure between PVC and PVO).

If the valve is open, the modified Thornhill-Craver (TC) equation (default) or API RP 11 V2 is used to compute the gas flow rate through the valve, depending on configuration and available data. See below sections for more information.

Any remaining injection gas that cannot pass through the first open valve will be assumed to travel downward. The traverses continue downward, with gas rates modified accordingly to the next valve, where the previous step is repeated to check valve status and flow rate through the valve, if applicable. Any valves deeper than the intersection of the production and injection traverses are considered submerged.

The following diagram illustrates the methodology

The downhole closing pressure of a valve is equal to its dome pressure at depth. First the estimated dome pressure at 60 degF is calculated using

Pd' - dome pressure at 60 degF PTRO - test rack opening pressure R - r-ratio

Then, the final downhole PVC is calculated through an iterative method using an equation of state with an estimation of nitrogen compressibility from Sage and Lacy.

The dome / PVC pressure is used to compute the downhole opening pressure (PVO) using

PVO - downhole opening pressure PVC - downhole closing pressure Pprod - production presssure R - r-ratio

The downhole PVO and PVC values are converted to surface pressures (PSO and PSC) through a traverse from downhole node to surface node.

To compute gas passage through an open valve, one method ProdX can leverage is the Modified Thornhill-Craver equation

Qgi - gas flow rate, Mscf/d Cd - discharge coefficient (see below) Ap - valve seat flow area, in2 P1 - injection pressure, psia g - acceleration due to gravity, 32.16 ft/s2 k' - specific heat ratio of injection gas, Cp / Cv r - pressure ratio of production pressure / injection pressure γg - specific gravity of injection gas Z - z-factor of injection gas T - absolute temperature of injection gas, degR

If configured and detailed valve experimental data is available, ProdX can analyze the appropriate flow model to use following API RP 11 V2. The first step is calculating the transition injection pressure between orifice to throttling flow using

Ptran - transition injection pressure, psi Pd - dome pressure at depth, PVC, psi Fe - dynamic Ap/Ab ratio from valve test data

If the injection pressure is greater than Ptran, then the orifice model is used.

The Orifice Model assumes the gas lift valve operates as a simple orifice, where the flow through the valve is governed by standard orifice flow equations. This is used when the valve is fully open, and the flow rate is not restricted by mechanical components like a throttling stem.

Key Assumptions:

Orifice Flow:

Where:

Choked Flow:

If the pressure drop (ΔP\Delta PΔP) exceeds the critical pressure ratio, the gas reaches sonic velocity (choked flow), and the flow rate is no longer influenced by downstream pressure.

The critical pressure ratio (Ptubing/Pcasing) for choked flow depends on the specific heat ratio γ.

Used for unloading valves and when the valve is designed as a simple orifice with no stem to restrict the flow.

If the injection pressure is less than Ptran, then the throttling model is used.

The Throttling Model applies when the gas lift valve includes a throttling stem or other internal mechanism that modulates the flow. The stem changes the effective flow area dynamically, altering the gas flow rate through the valve.

Key Assumptions:

Where:

The stem position affects the flow area Aeff, which is calculated based on the r-ratio (port-to-bellows area ratio) and the bellows deflection due to the pressure differential across the valve.

Throttling Mechanism:

Used for operating valves where the valve modulates the gas injection rate based on operating conditions. More common in continuous gas lift systems where precise control of gas injection is needed.