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Gas lift installation design methods
The two gas lift installation design methods given in this page can be classified as:
- The decreasing injection-gas pressure design in API^{[1]}
- A variation of the decreasing injection-gas pressure design that considers valve performance at each station. ^{[2]}
Valves with small production-pressure factors, F_{p}, are recommended for the decreasing injection-gas pressure installation design method. Valves with a small F_{p} (under 0.2) are sensitive primarily to a change in the injection-gas pressure. A decrease in the surface operating injection-gas pressure for each lower gas lift valve is essential to ensure the closure of upper unloading valves after gas injection has been established through a lower operating valve. This design is particularly applicable when the available injection-gas pressure is high relative to the required depth of lift and an additional incremental decrease in injection-gas pressure can be added between valves.
If gas lift valves with large ports are required to pass sufficient gas rates for unloading and lifting a well, the design that incorporates valve performance should be used. Generally, if the operating valve is not near the packer, the calculated point of gas injection will be bracketed by installing at least one valve below the calculated operating valve depth in the event there is a slight error in the well information or a change in well conditions.
Constant decrease in the operating injection-gas pressure for each succeeding lower gas lift valve
This installation design method (following API) is based on all gas lift valves having the same port size and a constant decrease in the operating injection-gas pressure for each succeeding lower gas lift valve. The gas lift valve selection must be based on a port size that allows the injection-gas throughput required for unloading and gas lifting the well. This installation design method is recommended for gas lift valves with a small production-pressure factor. When the ratio of the port area to the bellows area is low, the decrease in the injection-gas pressure between gas lift valves, based on the additional tubing-effect pressure for the top valve, is not excessive. The effect of bellows-assembly load rate on the performance of the gas lift valves is not considered in the installation design calculations. Safety factors included in these design calculations should allow sufficient increase in the operating injection-gas pressure, which is necessary to provide the valve-stem travel for adequate injection-gas passage through each successively lower unloading gas lift valve without excessive interference from upper valves.
Selection of a constant injection-gas pressure decrease, or drop, in the surface operating-injection-gas pressure for each succeeding lower gas lift valve should not be arbitrary, as proposed in some design methods. The pressure decrease should be based on the gas lift valve specifications to minimize the possibility of upper valves remaining open while lifting from a lower valve. The additional tubing-effect pressure for the top gas lift valve is a logical choice for this decrease in the operating injection-gas pressure between valves. Closing or reopening of an injection-pressure-operated gas lift valve is partially controlled by the production-pressure effect, which is equal to the production-pressure factor for the valve multiplied by the difference flowing-production pressure at the top valve depth.
The flowing-production pressure at an unloading-valve depth changes from the transfer pressure, (P_{pfD})_{min}, to a higher flowing-production pressure after the next lower valve becomes the operating valve. The additional tubing-effect pressure is the difference between (P_{pfD})_{min} and the maximum flowing-production pressure, at the unloading valve depth, (P_{pfD})_{max}, after the point of gas injection has transferred to this next lower valve. As the unloading gas lift valve depths increase, the distance between valves and the difference between (P_{pfD})_{min} and (P_{pfD})_{max} decrease. Although the additional tubing-effect pressure decreases for lower valves, the injection-gas requirement for unloading increases with depth. An increased stem travel, or stroke, is usually needed for the lower valves to generate the larger equivalent port area necessary for the higher injection-gas requirements with the lower pressure differentials that occur across these deeper valves. A constant decrease in the operating injection-gas pressure equal to the additional tubing-effect pressure for the top valve allows a greater increase in the injection gas above initial opening pressure for lower gas lift valves.
Another application for this simplified design method depends on the relationship between the available injection-gas pressure and the flowing-production pressure at the maximum depth of lift. When the injection-gas pressure significantly exceeds this flowing-production pressure, an arbitrary decrease in the injection-gas pressure, ΔP_{io}, can be added to the additional production-pressure effect for the top valve for calculating the spacing and the initial opening pressures of the unloading gas lift valves. The total decrease in the injection-gas pressure is distributed equally between each successively lower unloading gas lift valve rather than having a sizable injection-pressure drop across the operating gas lift or orifice-check valve. This procedure reduces the possibility of multipoint gas injection through upper unloading gas lift valves by ensuring that these valves remain closed after the point of gas injection has transferred to the next lower gas lift valve.
Determination of valve depths
Because this final injection-gas pressure is unknown until the installation is designed, a pressure difference of at least 100 to 200 psi between the unloading P_{ioD} and P_{pfD} traverses is assumed for locating the deepest-valve depth. This assumption of (P_{ioD} – P_{pfD} = 100 to 200 psi) should ensure calculation of the operating valve depth. The static bottomhole pressure, P_{wsd}, and temperature, T_{wsd}, generally are referenced to the same depth, which is the lower end of the production conduit, D_{d}. The steps for establishing the gas lift valve depths follow.
1. Calculate the maximum unloading GLR based on the maximum injection-gas rate available for unloading and the maximum daily design total fluid rate.
where
q_{giu} | = | maximum unloading injection-gas rate, Mscf/D, |
q_{lt} | = | total liquid (oil + water) daily production rate, B/D, |
R_{gl} | = | maximum unloading GLR, scf/STB, |
and | ||
R_{glu} | = | maximum unloading GLR, scf/STB. |
2. Calculate with a multiphase-flow computer program or determine from an appropriate gradient curve the unloading flowing-production pressure at the lower end of the production conduit, P_{pfd} at D_{d}, based on the installation design R_{gl} and q_{lt}.
3. Calculate the unloading flowing-pressure-at-depth gradient above the point of gas injection, g_{pf}, by subtracting the wellhead U-tubing (unloading) wellhead pressure, P_{whu}, from the flowing-production pressure, P_{pfd} at D_{d}, and dividing by the reference datum depth, D_{d}.
The traverse above the point of gas injection will actually be a curved line representing a fluid density that typically becomes increasingly less dense as it travels toward the surface. An exception to this is the case of high GLRs at low pressures where the pressure traverse may reverse slope near the surface. However, a straight line is used because it will be easier to calculate the flowing-production pressure at valve depth, P_{pfD}, than with an actual curved flowing-pressure-at-depth traverse. This assumption normally will give a slightly more conservative design.
4. Calculate the static injection-gas pressure at the lower end of the production conduit, P_{iod} at D_{d}, using Eq. 3 and the static injection-gas pressure-at-depth gradient, g_{gio}, by subtracting the surface injection-gas pressure, P_{io}, from P_{iod} at D_{d} and dividing by the reference datum depth, D_{d}.
where
g_{gio} | = | static injection-gas pressure at depth gradient, psi/ft |
P_{io} | = | injection-gas pressure at surface, psia, |
P_{ioD} | = | injection-gas pressure at depth, psia, |
D_{d} | = | reference datum depth (usually lower end of production conduit) for bottomhole temperature and pressures, ft |
5. Calculate the unloading gas lift valve temperature-at-depth gradient, g_{Tvu}, by assuming a straight line and subtracting the surface unloading flowing wellhead temperature, T_{whu}, from the bottomhole temperature, T_{wsd} at D_{d}, and dividing by the reference datum depth, D_{d}.
6. Calculate the depth of the top gas lift valve, D_{v1}, on the basis of the surface kick-off or average field injection-gas pressure, P_{ko}, static-load fluid gradient, g_{ls}, and the wellhead U-tubing unloading pressure, P_{whu}, with either Eqs. 5, 6, or 7. Eq. 47 is used in this example. The flowing wellhead pressure, P_{whf}, and the wellhead unloading U-tubing pressure, P_{whu}, are considered equal in the API Design.
or
where
D_{v1} | = | depth of top valve, ft, |
P_{ko} | = | surface kick-off or average field injection-gas pressure (optional), psig, |
P_{whu} | = | surface wellhead U-tubing (unloading) pressure, psig, |
ΔP_{sD} | = | assigned spacing pressure differential at valve depth, psi, |
g_{ls} | = | static load (kill)-fluid pressure gradient, psi/ft, |
and | ||
g_{gio} | = | injection-gas pressure-at-depth gradient, psi/ft. |
7. Calculate the minimum flowing-production pressure, (P_{pfD1})_{min}, the injection-gas pressure, P_{ioD1}, and the unloading gas lift valve temperature, T_{vuD1}, at the top valve depth by multiplying the appropriate gradient by the valve depth, D_{v1}, and adding to the appropriate surface values (where n = 1 for top valve):
8. Calculate the depth of the second gas lift valve, D_{v2}, where n = 2, on the basis of the assigned minimum decrease in surface injection-gas pressure, Δp_{io}, for spacing the gas lift valves and the P_{ioD} traverse. A valve-spacing differential of approximately 20 to 30 psi will usually be sufficient for most 1.5-in.-OD gas lift valves. However, 1-in.-OD valves with large ports may require a higher Δp_{io}. This can be checked by calculating the additional production-pressure effect, ΔP_{pe1}, using Eq. 19 after the valve depths are calculated for the assigned Δp_{io}. The distance between valves and valve depth are calculated as follows:
Solve for D_{bv}.
and
The decrease in surface injection-gas pressure for calculating D_{v2} is ΔP_{io}, and for D_{v3} is 2 (ΔP_{io}), and for D_{v4} is 3 (ΔP_{io}), and this procedure continues for each successively lower valve.
Repeat calculations in Step 7 at second valve depth by calculating (P_{pfD2})_{min}, P_{ioD2}, and T_{vuD2} with Eqs. 11, 12, and 13.
Repeat calculations in Step 8 for D_{bv} and D_{v3} with Eqs. 15 and 16.
Repeat Steps 7 and 8 until the maximum desired valve depth, D_{v(max)}, is attained. When the calculated distance between gas lift valves, D_{bv}, is less than an assigned minimum distance between valves, D_{bv(min)}, use D_{bv(min)}.
Valve port sizing and test-rack opening pressure calculations
The port size selection is based on the maximum depth of lift and the final operating injection-gas pressure for spacing the deepest valve. The port size and the test-rack setting pressures of the gas lift valves are calculated as follows:
1. Determine the port size for the type of gas lift valves to be installed in the installation on the basis of the unloading and operating injection-gas requirements. Correct the injection-gas rate for the actual gas gravity and temperature at each valve depth with Eq. 12.
where
C_{gT} | = | approximate gas gravity and temperature correction factor for choke charts, dimensionless, |
T_{gD} | = | gas temperature at valve depth, °R, |
Determine from Fig. 2 the port ID needed to pass the required injection-gas rate with the pressure differential available at the operating valve. When an orifice-check valve is selected for the bottom valve, the upstream injection-gas pressure, P_{1}, should be equal to or less than the injection-gas initial valve opening pressure of the last unloading valve, corrected to the depth of the orifice-check valve. The pressure differential across the orifice-check valve is the difference between P_{1} and the downstream flowing-production pressure, P_{2}, at the valve depth.
2. Record the gas lift valve specifications, which include the effective bellows area, A_{b}, port area, A_{p}, (A_{p} /A_{b}), (1 – A_{p} /A_{b}), and the production-pressure factor, F_{p}.
3. Calculate the injection-gas initial opening pressure at depth of the top gas lift valve,
where
P_{ioD1} | = | injection-gas pressure at valve depth, psig, and |
P_{oD1} | = | injection-gas initial gas lift valve opening pressure at valve depth, psig. |
4. Calculate the test-rack set opening pressure of the first valve (n = 1), P_{vo1}, with Eqs. 16 and 17 or 18.
or
where
C_{T} | = | temperature correction factor for nitrogen from P_{bvD} to P_{b} at 60°F, dimensionless, |
P_{bvD} | = | nitrogen-charged bellows pressure at valve temperature, psig, |
(P_{pfD}) min | = | minimum flowing-production pressure at valve depth, psig, |
and | ||
P_{vo} | = | test-rack valve opening pressure at 60°F, psig. |
Some designers prefer Eq. 18, which does not require calculation of P_{bvD} and gives the same result.
5. Calculate the injection-gas initial opening pressure of the second gas lift valve at depth (n = 2) with Eq. 19.
6. Calculate the maximum flowing-production pressure opposite the top unloading valve immediately after the point of gas injection has transferred to the second (lower) valve, (P_{pfD1})_{max}. (P_{pfD1})_{max} is shown graphically in Fig. 3 and can be calculated with Eq. 20.
7. Determine if the assumed decrease in surface injection-gas pressure, ΔP_{io}, is sufficient for the required gas lift valve port size by calculating the additional production-pressure effect, ΔP_{pe1}, at the top valve:
If ΔP_{pe1} is less than or equal to the assumed ΔP_{io}, proceed with the design. If ΔP_{pe1} is greater than the assumed ΔP_{io}, then set ΔP_{io} = ΔP_{pe1} and recalculate the spacing design. This is a conservative approach, and many operators use actual operating experience to determine which ΔP_{io} to use.
Repeat Steps 3 and 4 calculations for the second gas lift valve. Repeat Steps 3, 4, and 5 calculations for remaining gas lift valves. If the operating valve is an orifice-check valve, determine the orifice ID for lifting the well on the basis of the calculated upstream and downstream pressures, P_{1} and P_{2}.
Example 1
Well information for continuous-flow installation design (API Design Technique).
- Tubing size = 2 7/8-in. OD.
- Tubing length, D_{d} = 6,000 ft.
- Maximum valve depth, D_{v(max)} = 5,970 ft.
- Static bottomhole pressure at D_{d}, P_{wsd} = 1,800 psig at 6,000 ft.
- Daily production rate = 800 STB/D.
- Water cut = 50% (f_{w} = 0.50).
- Formation GOR = 500 scf/STB.
- Oil gravity = 35°API.
- Gas gravity, γ_{g} = 0.65.
- Produced-water specific gravity, γ_{w} = 1.08.
- Bottomhole temperature, T_{wsd} = 170°F at 6,000 ft.
- Design unloading wellhead temperature, T_{whf} = 100°F.
- Load-fluid pressure gradient, g_{ls} = 0.46 psi/ft.
- U-tubing wellhead pressure, P_{whu} = 100 psig.
- Flowing wellhead pressure, P_{whf} = 100 psig.
- Static fluid level = 0 ft (well loaded with kill fluid).
- Surface kick-off injection-gas pressure, P_{ko} = 1,000 psig.
- Surface operating injection-gas pressure, P_{io} = 1,000 psig.
- Maximum unloading injection-gas rate, q_{giu} = 800 Mscf/D.
- Operating daily injection-gas rate, q_{gi} = 500 Mscf/D.
- Wellhead injection-gas temperature, T_{gio} = 100°F.
- Assigned valve-spacing pressure differential at valve depth, ΔP_{sD} = 50 psi.
- Test-rack valve setting temperature, T_{vo} = 60°F.
- Assigned minimum decrease in surface operating injection-gas pressure between valves, ΔP_{io} = 20 psi.
- Minimum distance between valves, D_{bv(min)} = 150 ft.
- Gas lift valves: 1.5-in.-OD nitrogen-charged with A b = 0.77 in. 2 and sharp-edged seat.
Solution—Calculation of valve depths
The pressure traverses used to establish the gas lift valve depths are drawn on pressure/depth worksheets in Figs. 3 and 5. 1. Calculate maximum injection GLR with
2. Determine the flowing-production pressure P_{pfd} at D_{d} from the appropriate gradient curves in Fig. 4 for 800 B/D and 1,000 scf/STB:
Actual Depth, ft | Chart Depth, ft | Pressure, psig |
0 | 725 | 100 |
6,000 | 6,725 | 900 |
P_{pfd} = 900 psig at 6,000 ft, where P_{pfd} is the flowing-production pressure at the lower end of the production conduit, D_{d}.
3. Calculate g_{pfa} with Eq. 2.
4. Calculate the operating injection-gas pressure at the lower end of the production conduit using Eq. 3 and g_{gio} with Eq. 4. P_{iod} = 1,154 psig at 6,000 ft (calculated).
Because the difference between P_{pfd} and P_{iod}, (P_{iod} – P_{pfd} = 1,154 – 900 = 254 psi), exceeds 200 psi, the maximum valve depth of 5,970 ft can be attained.
5. Calculate the unloading gas lift valve temperature at depth gradient with Eq. 5.
6. Calculate the depth of the top gas lift valve with Eq. 47.
7. Calculate the minimum flowing-production pressure, (P_{pfD1})_{min}, injection-gas pressure, P_{ioD1}, and the unloading flowing temperature, T_{vuD1} at D_{v1} of 1,957 ft with Eqs. 11 through 13.
(P_{pfD1})_{min} = 100 + 0.1333 (1,957) = 361 psig. P_{ioD1} = 1,000 + 0.0257 (1,957) = 1,050 psig. T_{vuD1} = 100 + 0.0117 (1,957) = 123°F.
8. Calculate D_{bv} for depth of second valve, D_{v2}, where ΔP_{ioD2} = 20 psi, using Eqs. 16 and 17:
Repeat Step 7: Calculate (P_{pfD2})_{min}, P_{ioD2}, and T_{vuD2} at valve depth D_{v2} = 3,429 ft. (P_{pfD2}) min = 557 psig, P_{ioD2} = 1,088 psig, and T_{vuD2} = 140°F.
Repeat Step 8: Calculate depth of third valve, D_{v3} , where ΔP_{ioD3} = 40 psi. D_{bv} = 1,061 ft and D_{v3} = 4,490 ft.
Repeat Step 7: Calculate (P_{pfD3})_{min}, P_{ioD3}, and T_{vuD3} at valve depth D_{v3} = 4,490 ft. (P_{pfD3}) min = 699 psig, P_{ioD3} = 1,115 psig, and T_{vuD3} = 152°F.
Repeat Step 8: Calculate depth of fourth valve, D_{v4}, where ΔP_{ioD4} = 60 psi. D_{bv} = 752 ft and D_{v4} = 5,242 ft.
Repeat Step 7: Calculate (P_{pfD4})_{min}, P_{ioD4}, and T_{vuD4} at valve depth D_{v4} = 5,242 ft. (P_{pfD4}) min = 799 psig, P_{ioD4} = 1,135 psig, T_{vuD4} = 161°F.
Repeat Step 8: Calculate depth of fifth valve, D_{v5}, where ΔP_{ioD3} = 80 psi. D_{bv} = 520 ft and D_{v5} = 5,762 ft.
Repeat Step 7: Calculate (P_{pfD5})_{min}, P_{ioD5}, and T_{vuD5} at valve depth D_{v5} = 5,762 ft. (P_{pfD5})_{min} = 868 psig, P_{ioD5} = 1,148 psig, and T_{vuD5} = 167°F.
The calculated valve spacing for the sixth valve, D_{v6}, would exceed the maximum valve depth, D_{v(max)}, of 5,970 ft. Because an orifice-check valve will be placed in the bottom wireline-retrievable valve mandrel, no test-rack valve setting information is required. This completes the valve spacing calculations. A graphical representation of the valve installation design is shown in Fig. 5.
Solution—Determination of gas lift valve port size and calculation of test-rack opening pressures The gas lift valves port ID and test-rack opening pressure calculations are given next.
1. Determine the port size required for the gas lift unloading valves and the operating orifice-check valve orifice ID. The upstream injection-gas pressure, P_{1} , is based on P_{oD5} of the last unloading valve using Eq. 17 corrected to the orifice-check valve depth of 5,970 ft.
P_{1} = 1,068 + 0.0257 (5,970 – 5,762) = 1,073 psig at 5,970 ft.
The downstream flowing-production pressure, P_{2}, is equal to the minimum flowing-production pressure at 5,970 ft with Eq. 6.
P_{2} = 100 + 0.1333 (5,970) = 896 psig at 5,970 ft. ΔP_{ov} = 1,073 – 896 = 177 psi across the orifice-check valve.
From Fig. 2, the required equivalent orifice size is near 14/64 in.; therefore, the next largest gas lift valve port ID is 1/4 in. This size is sufficient for all of the upper unloading valves because they have a higher injection-gas operating pressure and a greater differential pressure between P_{ioD} and (P_{pfD})_{min}. An equivalent orifice size of 12/64 in. to 13/64 in. is required to pass the operating injection-gas rate of 500 Mscf/D.
2. Record the valve specifications for a l.5-in.-OD gas lift valve having a 1/4-in.-ID port with a sharp-edged seat where A_{b} = 0.77 in.^{2} from Table 1.
(A_{p}/A_{b}) = 0.064, (1 – A_{p}/ A_{b}) = 0.936, and F_{p} = 0.068.
3. Calculate P_{oD1} with Eq. 13 : P_{oD1} = 1,050 psig at 1,957 ft.
4. Calculate P_{bvD1} with Eq. 14 for C_{T1} = 0.876 (Calculated for T_{vuD1} = 123°F).
5. Calculate Pvo_{1} with Eq. 15: P_{vo1} = = 942 psig at 60°F.
6. Calculate P_{oD2} with Eq. 17: P_{oD2} = 1,088 – 20 = 1,068 psig at 3,429 ft.
7. Calculate (P_{pfD1})_{max} with Eq. 18:
8. Calculate ΔP_{pe1} with Eq. 19: ΔP_{pe1} = 0.068 (652 – 361) = 20 psi.
Because the ΔP_{pe1} of 20 psi is the same as the assumed ΔP_{io} of 20 psi for spacing, a pressure differential of 20 psi can be used for setting the valves. Note that if 1-in.-OD valves had been used in this design, F_{p} = 0.188 for a 1/4-in.-ID port and ΔP_{pe1} would be 55 psi. Repeat Steps 6, 4, and 5 for remaining gas lift valves:
P_{oD2} = 1,035 psig at 3,429 ft, P_{bvD2} = 1,035 psig, C_{T2} = 0.847 for T_{vuD2} = 140°F, and P_{vo2} = 937 psig.
P_{oD3} = 1,075 psig at 4,490 ft, P_{bvD3} = 1,051 psig, C_{T3} = 0.828 for T_{vuD3} = 152°F, and P_{vo3} = 929 psig.
P_{oD4} = 1,075 psig at 5,242 ft, P_{bvD4} = 1,057 psig, C_{T4} = 0.815 for T_{vuD4} = 161°F, and P_{vo4} = 919 psig.
P_{oD5} = 1,068 psig at 5,762 ft, P_{bvD5} = 1,055 psig, C_{T5} = 0.805 for T_{vuD5} = 167°F, and P_{vo5} = 907 psig.
An orifice-check valve is recommended for the sixth valve at 5,962 ft. The orifice ID should be 1/4 in. to pass sufficient gas to gas lift the well. A tabulation form for these calculations is given in Table 2.
When injection-gas pressure is high, relative to depth of lift
An additional incremental decrease in the injection-gas pressure can be added to the calculated decrease to ensure unloading a gas lift installation when the injection-gas pressure is high, relative to the required depth of lift. The flowing-production pressure at the depth of lift limits the maximum injection-gas pressure that can be used in terms of contributing to the lift process. The higher available injection-gas pressure cannot be utilized in this installation. An excessive injection-gas pressure drop across the operating valve represents an inefficient energy loss. Distributing the decrease in the injection-gas pressure between each successively lower unloading gas lift valve prevents multipoint gas injection through upper gas lift valves after the point of gas injection transfers to a lower valve. In other words, the gas lift installation can be unloaded without valve interference, and the unloading process is apparent from the injection-gas pressure recording at the surface. A high available injection-gas pressure, relative to the depth of lift, may exist in areas where both shallow and deep wells are being gas lifted with injection gas from the same system. The flowing-production pressure in the shallow wells limits the injection-gas pressure that can be used to gas lift these wells.
High rate continuous-flow installation design
The application of the injection-gas rate throughput performance for injection-pressure-operated gas lift valves is illustrated in the high daily liquid rate continuous-flow installation design. The importance of valve performance data for high daily injection-gas rates is shown, and their unimportance for low-injection-gas-rate installation designs is illustrated. Valve performance data is of no value in selection of the top two unloading gas lift valves in this installation. For these two upper valves, an assumed reasonable decrease in the surface injection-gas pressure of 20 psi for each valve ensures unloading the well and these upper valves remaining closed while lifting from a lower valve. When the required daily injection-gas rate increases for lifting from the third and fourth gas lift valves, valve performance information becomes very important. A pressure-vs.-depth plot for this continuous-flow installation is shown in Fig. 7.
Although the flowing-production transfer-pressure-traverse method for locating the depths of the valves may require an additional valve, or valves, in some installations, this design method has several advantages in wells requiring a high daily injection-gas rate for unloading. Because the injection-gas requirement to uncover the next lower valve is reduced, smaller valve ports can be used and the increase in the injection-gas pressure to stroke the valve stem is less. The unloading operations are faster because of the lesser difference in injection-gas requirement between unloading valves. This fact is of more importance after an injection-gas supply interruption when several wells must be unloaded and the total-system available daily injection-gas volume is limited. The chance of heading and surging with a smaller port is reduced because a change in flowing-production pressure has a lesser affect on the valve-stem position. Bubble-tight seats are easier to achieve with small ports.
The surface origin and final downhole termination pressures for the flowing-production transfer-pressure traverse are arbitrary. The 20% in this example for locating the surface transfer-pressure traverse is widely used. The unloading injection-gas requirements for uncovering each lower valve increase as that percentage decreases and decrease as that percentages increases. The flowing-production transfer pressure at datum depth should be at least 100 to 200 psi less than the available design operating injection-gas pressure at the same depth. This flowing-production transfer pressure at datum depth should also be less than the flowing-production pressure at the same depth based on the design daily production rate and maximum total gas/liquid ratio (GLR).
The multiphase-fluid-flow correlation selected for these calculations can significantly affect the results. Several assumptions for calculating the depths of the unloading valves are very conservative in this example (e.g., assuming a load-fluid pressure gradient below an unloading valve after significant bottomhole-pressure drawdown and the assigned valve spacing pressure differential of 50 psi at the next lower valve depth). These design calculations provide a comprehensive understanding of the overall well unloading process and operations. The installation designer can modify the assumptions on the basis of the availability and accuracy of the known well information.
A lower-than-the-design daily liquid-production rate is assigned for spacing the unloading valves until the flowing-bottomhole-pressure drawdown results in a calculated daily production rate that exceeds the assigned rate. Typical assigned unloading daily liquid rates would be 200 to 400 B/D for 2 3/8-in.-OD tubing and 400 to 600 B/D for 2 7/8-in.-OD tubing. When the calculated flowing-bottomhole-pressure drawdown results in a higher than the assigned unloading daily liquid production rate for the flowing-production transfer pressure at the depth of the operating unloading valve, this higher rate is used for spacing the next lower unloading valve. A 1,000-B/D unloading rate is assigned for unloading valves before a higher liquid rate occurs from a flowing-bottomhole-pressure drawdown in this high-productivity well with large tubing. The assigned design flowing-wellhead temperature of 120°F is between the ambient surface temperature and the flowing-well fluids temperature at the design daily production rate from the well.
Simplified mathematical gas lift valve performance model
Because performance equations for specific gas lift valves are not available from gas lift valve manufacturers, a simplified gas lift valve performance computer model was used to illustrate the calculations in this paper. The model is based on static force-balance equations and several simplifying assumptions. This computer model describes qualitatively the injection-gas rate throughput of unbalanced, single-element gas lift valves using the Thornhill-Craver equation (Eq. 22).
where
q_{gsc} | = | gas-flow rate at standard conditions (14.7 psia and 60°F), Mscf/D, |
C_{d} | = | discharge coefficient (determined experimentally), dimensionless, |
A | = | area of orifice or choke open to gas flow, in.^{2}, |
P_{1} | = | gas pressure upstream of an orifice or choke, psia, |
P_{2} | = | gas pressure downstream of an orifice or choke, psia, |
g | = | acceleration because of gravity, ft/sec^{2}, |
k | = | ratio of specific heats (C_{p}/C_{v}), dimensionless, |
T_{1} | = | upstream gas temperature, °R, |
F_{du} | = | pressure ratio, P_{2}/P_{1}, consistent absolute units, |
For this computer model, the gas lift valve has a square sharp-edged seat and the stem tip is a carbide ball with a 1/16-in. larger outside diameter (OD) than the bore ID of the valve seat. The equivalent port area for a partially open valve is defined by the lateral surface area of the frustum of a right circular cone. The frustum area is generated between the surface of the ball and the valve seat-line as the valve stem moves away from its seat. The bellows-assembly load rate is assumed to be linear for the stem travel required to attain a given equivalent port area, and there is no increase in nitrogen-charged bellows pressure during this stem travel. The flow restriction and the pressure loss, resulting from a check-valve assembly, are not included in the gas lift valve model calculations. The same gas gravity, ratio of specific heats, and discharge coefficient are used for all calculations.
There are many unknown dynamic quantities in terms of actual areas and pressures acting on these areas as the gas-flow rate through a valve changes with valve-stem travel. For the valve performance calculations with a partially open port, the injection-gas pressure is assumed to act over the effective bellows area minus the port ball/seat contact area. Regardless of the valve-stem position, the flowing-production pressure is applied over the entire port ball/seat contact area. These assumptions should result in the calculated injection-gas rate being less than the actual rate. As the ball on the valve stem moves away from its seat during an increase in injection-gas pressure, the two areas over which the opening pressures are applied will change. The bellows area exposed to the injection-gas pressure increases and the flowing-production pressure approaches the injection-gas pressure downstream of the port as the equivalent port area increases in the variable-orifice throttling mode. This pressure is difficult to define accurately because of the varying pressure loss as the equivalent port area changes with valve-stem travel.
Although several of the assumptions for the mathematical valve model are known to be approximate, the predicted performance illustrates, with reasonable accuracy, the manner in which an unbalanced, injection-pressure-operated, single-element gas lift valve operates in a well. The valve performance curves, in the continuous-flow installation design, were calculated using the performance model described in Simplified mathematical gas lift performance model. The coefficient for Eq. 23 is based on the Thornhill-Craver coefficient of 155.5, a gas gravity of 0.65, ratio of specific heats of 1.26, discharge coefficient of 0.865, and acceleration caused by gravity of 32.174.
A_{pe} | = | valve port equivalent area open to gas flow, in.^{2} |
P_{atm} | = | atmospheric pressure, psia |
P_{ioD} | = | injection-gas pressure at valve depth, psig |
R_{du} | = | ratio of downstream pressure/upstream pressure, psia |
Determination of valve depths
The procedure for referencing the static bottomhole pressure, P_{wsd}, and temperature, T_{wsd}, to the lower end of the production conduit, D_{d}, is the same as for the lower-injection-gas-rate continuous-flow installation design in Example Problem 2 in Gas lift installation design methods.
1. Determine the static operating injection-gas pressure at the lower end of the production conduit, P_{iod}, with Eq. 24 and calculate the static operating injection-gas pressure at depth gradient, g_{gio}, with Eq. 25. The same operating injection-gas pressure at depth gradient, g_{gio}, is used for all calculations regardless of the surface injection-gas pressure. This is not a recommended procedure; particularly, for high injection-gas pressures in deep wells. The injection-gas pressures at depth should be calculated on the basis of the actual:
- Surface pressures
- Gas properties
- Temperature
The constant g_{gio} was used in the following installation design to simplify the calculations.
where
2. Calculate the gas lift valve unloading temperature-at-depth gradient, g_{Tvu}, with Eq. 26 on the basis of the assigned unloading flowing-wellhead temperature, T_{whu}, and the static bottomhole temperature, T_{wsd}, in the well. The assigned unloading flowing-wellhead temperature should be between the ambient surface temperature and the flowing-well fluids temperature at the design maximum daily production rate from the well.
3. Calculate the surface flowing-production transfer pressure, P_{pt}, on the basis of the assigned flowing-production transfer-pressure valve-spacing factor at the surface, f_{pt}. The assigned f_{pt} will generally range between 0.15 and 0.25 (15 to 25%).
P_{pt} = P_{whf} + f_{pt}(P_{io} - P_{whf})
4. Calculate the flowing-production transfer pressure at the lower end of the production conduit, P_{ptd}, and the flowing-production transfer pressure at depth gradient, g_{pt}. The recommended minimum pressure difference, ΔP_{ptd}, between the flowing-production transfer pressure at the lower end of the production conduit, P_{ptd}, and the operating injection-gas pressure at the same depth, P_{iod}, should be at least 100 to 200 psi or greater and can be based on operating experience in the area.
5. Determine from the appropriate set of gradient curves, or calculate using a reliable multiphase-flow computer program, the flowing-production pressure at the lower end of the production conduit, P_{pfd} at D_{d}, on the basis of the maximum operating total GLR, R_{glt} (operating daily injection-gas plus formation-produced gas rates), and the installation design total daily liquid rate (oil + water), q_{lt}.
The P_{pfd} calculation (or determination from gradient curves) determines if the tubing size restricts the maximum design daily production rate and whether a higher injection-gas pressure is recommended. If P_{pfd} is less than P_{ptd}, the tubing size does not appear to restrict the design production rate, and the available injection-gas-line pressure appears to be adequate. The final maximum daily production rate will be controlled by the productivity of the well. If P_{pfd} is greater than P_{ptd}, a higher operating injection-gas pressure is necessary to achieve the assigned maximum depth of lift for this design method.
6. Determine the depth of the top gas lift valve, D_{v1}. The top unloading valve depth is calculated using Eqs. 31, 32, or 33 on the basis of the terms defined for the equation or can be located graphically.
or
where
D_{v1} | = | depth of top valve, ft, |
P_{ko} | = | surface kick-off or average field injection-gas pressure (optional), psig, |
P_{whu} | = | surface wellhead U-tubing (unloading) pressure, psig, |
ΔP_{sD} | = | assigned spacing pressure differential at valve depth, psi, |
g_{ls} | = | static load (kill)-fluid pressure gradient, psi/ft, |
and | ||
g_{gio} | = | injection-gas pressure-at-depth gradient, psi/ft. |
7. Calculate the flowing-production transfer pressure, P_{ptD(n)} , the operating injection-gas pressure, P_{ioD(n)}, and the unloading valve temperature, T_{vuD(n)}, at the gas lift valve depth, D_{v(n)}.
8. Calculate the flowing bottomhole pressure, P_{wfd(n)}, while lifting from the gas lift valve at depth, D_{v(n)}, based on the flowing-production transfer pressure, P_{ptD(n)}, and the static load (kill) fluid pressure gradient, g_{ls}, to determine whether the calculated daily liquid rate, q_{lc(n)}, based on Productivity Index, PI, exceeds the assigned unloading daily liquid rate, q_{lu(n)}.
If P_{wfd(n)} < P_{wsd}, calculate q_{lc(n)}.
The static load (kill)-fluid pressure at depth gradient is recommended for calculating the valve depths after flowing-bottomhole-pressure drawdown. The time required to recover all load (kill) fluid that entered the reservoir during workover is unknown. It may require days, or weeks, before normal formation-fluids production returns. When reservoir fluids begin to re-enter the wellbore, the flowing-pressure-at-depth gradient below an operating unloading valve will normally decrease and formation free-gas production will reduce the injection-gas requirement.
9. Calculate the daily injection-gas rates, q_{gi(n)}, on the basis of the assigned unloading or calculated daily producing liquid rate in Step 8 if q_{lc(n)} > q_{lu(n)}. Assume injection-gas/liquid ratios, R_{gli(n)}, that result in flowing-production pressures, P_{pfD(n)}, at the valve depth, D_{v(n)}, that bracket the flowing-production transfer pressure, P_{ptD(n)}. Values of P_{pfD(n)} for varying R_{dlt} can be calculated or determined from gradient curves. Then calculate the q_{gi(n)} for the P_{ptD(n)} after the assumed R_{dlt} equals the calculated R_{dlt}.
10. Calculate the increase in the injection-gas pressure, ΔP_{ioc(n)}, above injection-gas initial valve opening pressure, P_{oD(n)}, for the valve to pass the required daily injection-gas rate, q_{gi(n)}, to establish the P_{ptD(n)} in Step 9 on the basis of the valve port ID, bellows-assembly spring rate, B_{sr} = B_{lr} (A_{b}) in Appendix A, the P_{oD(n)} and the P_{ptD(n)}. The injection-gas rate through a gas lift valve for an assumed P_{ioD(n)} greater than P_{oD(n)} is calculated with the equations in Appendix A. Similar to Step 9, the increase in the injection-gas pressure, P_{ioD(n)}, above P_{oD(n)} to attain the q_{gi(n)} in Step 7 can be determined graphically or calculated using a curve-fitting routine. The calculated increase in the injection-gas pressure, ΔP_{ioc(n)}, is equal to the difference between the P_{ioD(n)} that results in the required q_{gi(n)} and the P_{oD(n)} of the valve.
11. Compare the assigned minimum surface injection-gas pressure decrease between valves, ΔP_{ioa}, (represents the assigned minimum surface design injection-gas pressure increase above P_{oD(n)} for stroking a valve) to the calculated injection-gas pressure increase in Step 10. If the calculated surface injection-gas pressure increase in Step 10, ΔP_{ioc(n)}, is less than ΔP_{ioa}, use this assigned injection-gas pressure decrease, ΔP_{ioa} (ΔP_{io(n)} = ΔP_{ioa}). Then calculate the sum of the ΔP_{io(n)} values, ΣΔP_{io(n)}, required for calculation of the injection-gas initial gas lift valve opening pressure at depth of the next lower valve, P_{oD(n)}. The ΣΔP_{io(n)} equals zero for the top gas lift valve in Eq. 37.
12. Calculate the depth of the next lower valve, D_{v(n+1)}, below the operating unloading valve with a load (kill)-fluid g_{ls} traverse (no formation production fluids) below the valve. The top and the second valve depths, D_{v1} and D_{v2}, respectively, are based on the assigned surface operating injection-gas pressure, P_{io}. The following equation is used for calculating the depths of the second and lower valves until the assigned maximum valve depth or minimum distance between valves is reached.
If D_{v(n+1)} exceeds D_{v(max)}, D_{v(n+1)} = D_{v(max)}, and P_{ptD(n)} is calculated with Eqs. 39 and 40.
and
Orifice-check valve calculations
The deepest (bottom) operating valve of choice in many continuous-flow installations is an orifice-check valve. Because an orifice-check valve is always fully open, there are no dynamic valve performance calculations required. The published orifice or choke equations or charts are used to select the proper orifice or gas lift valve seat ID and determine the injection-gas rate throughput. Orifice-check valve calculations for the bottom valve are outlined in detail in the following high-rate continuous-flow installation design in the following Example Problem.
Problem 2
Well data for installation design using unbalanced, nitrogen-charged, injection-pressure-operated gas lift valves for unloading.
- Tubing size = 4 1/2 -in. OD (ID = 3.958 in.), and length = 6,000 ft.
- Casing size = 8 5/8-in. OD, 44 lbm/ft (ID = 7.725 in.).
- Datum depth for bottomhole pressures and temperature, D_{d} = 6,000 ft.
- Bottomhole temperature at D_{d}, T_{wsd} = 170°F.
- Shut-in (static) bottomhole pressure at D_{d}, P_{wsd} = 2,000 psig.
- Maximum depth for bottom valve, D_{v(max)} = 5,900 ft.
- Productivity index (gross liquid), PI = 6.3 B/D/psi.
- Oil gravity = 35°API (γ_{o} = 0.850).
- Gas specific gravity (air = 1.0), and γ_{g} = 0.65.
- Water specific gravity, γ_{w} = 1.08.
- Water fraction, f_{w} = 0.50 (50%).
- Formation GOR, R_{go} = 400 scf/STB.
- Formation GLR, R_{glf} = 200 scf/STB.
- Assigned minimum daily unloading production rate, q_{lu} = 1,000 B/D
- Design total (oil + water) daily production rate, q_{lt} = 5,000 B/D.
- Wellhead U-tubing unloading pressure, P_{whu} = 100 psig.
- Surface flowing wellhead pressure, P_{whf} = 100 psig.
- Static load (kill)-fluid pressure gradient, g_{ls} = 0.468 psi/ft.
- Unloading wellhead temperature, T_{whu} = 120°F (basis for calculation of P_{vo}).
- Wellhead injection-gas temperature, T_{gio} = 120°F.
- Surface kick-off injection-gas pressure, P_{ko} = 1,400 psig (at wellsite).
- Surface operating injection-gas pressure, P_{io} = 1,400 psig (at wellsite).
- Assigned daily injection-gas rate, q_{gi} = 2,000 Mscf/D.
- Minimum assigned surface injection-gas pressure decrease between valves, ΔP_{io} = 20 psi. (Represents minimum surface injection-gas pressure increase for stroking gas lift valve).
- Valve spacing design line percent factor at surface = 20% (f_{pt} = 0.20).
- Minimum transfer-production-pressure difference (P_{iod} – P_{ptd}) at D_{d}, ΔP_{ptd} = 200 psi.
- Valve-spacing pressure differential at valve depth, ΔP_{sD} = 50 psi.
- Minimum distance between valves D_{bv(min)} = 400 ft.
- Gas lift valve test-rack setting temperature, T_{vo} = 60°F.
- Gas lift valves: 1.5-in.-OD wireline-retrievable, unbalanced, single-element, nitrogen-charged bellows with A_{b} = 0.77 in.^{2}, B_{lr} = 600 psi/in., and square sharp-edged seat.
Solution—Calculation of valve depths
1. P_{iod} = 1,617 psig at 6,000 ft , and g_{gio} = = 0.03617 psi/ft.
2. g_{Tvu} = = 0.008333° F/ft.
3. P_{pt} = 100 + 0.20 (1,400 – 100) = 360 psig at wellhead.
4. P_{ptd} = 1,617 – 200 = 1,417 psig at 6,000 ft, and g_{pt} = = 0.1762 psi/ft.
5. R_{glf} = = 400 scf/STB, and R_{glt} = 200 + 400 = 600 scf/STB.
P_{pfd} = 1,227 psig at 6,000 ft for 5,000 B/D, and R_{glt} = 600 scf/STB (R_{gli} + R_{glf}) using the Ros multiphase-flow correlation. Because P_{pfd} is less than P_{ptd} by 390 psi (1,617 – 1,227), the tubing size does not appear to restrict the design production rate and the available injection-gas-line pressure seems adequate. The final maximum daily production rate will be controlled by the reservoir productivity of this well.
Top valve depth calculations
7. P_{ptD1} = 360 + 0.1762 (2,778) = 849 psig at 2,778 ft. P_{ioD1} = 1,400 + 0.03617 (2,778) = 1,500 psig at 2,778 ft. T_{vuD1} = 120 + 0.008333 (2,778) = 143°F at 2,778 ft.
8. P_{wfd1} = 849 + 0.468 (6,000 – 2,778) = 2,357 psig at 6,000 ft for g_{ls} traverse below D_{v1}. Because P_{wfd1} > P_{wsd}, there is no flowing-bottomhole-pressure drawdown.
9. Refer to Table 1 with values of P_{pfD1} and q_{gi1} for assumed varying total-injection GLRs, R_{glt} = R_{gli}, and to the intersection of P_{ptD1} = 849 psig with the tubing performance curve in Fig. 8, where q_{gi1} = 104 Mscf/D.
10. Refer to Table 1 with values of P_{ioD1} vs. q_{gi1} based on equations in Simplified mathematical gas lift performance model and the intersection of the gas lift valve performance curve in Fig. 2 with q_{gi1} = 104 Mscf/D, where P_{ioD1} = 1,484 psig.
11. Because P_{oD1} = 1,480 psig, ΔP_{ioc1} = 1,484 – 1,480 = 4 psi, which is less than the 20-psi minimum assigned surface pressure increase required to stroke the valve.
ΔP_{ioc1} < ΔP_{ioa}, ΔP_{io1} = ΔP_{ioa} = 20 psi and ΣΔP_{io1} = 20 psi for calculation of P_{oD1}.
Second valve depth calculations
12. D_{bv} = = 1,392 ft and D_{v2} = 2,778 + 1,392 = 4,170 ft.
7. For D_{v2} = 4,170 ft: P_{ptD2} = 1,095 psig, P_{ioD2} = 1,551 psig, and T_{vuD2} = 155°F.
8. P_{wfD2} = 1,951 psig at 6,000 ft and q_{lc} = 309 BPD. Because q_{lc} < q_{lu}, use q_{lu} = 1,000 BPD.
9. Refer to Table 2 with values of P_{pfD2} and q_{gi2} for assumed varying total-injection GLRs, R_{glt}. The P_{ptD2} of 1,095 psig intersects the tubing performance curve in Fig. 3 at q_{gi2} = 168 Mscf/D.
10. Refer to Table 2 with values of P_{ioD2} and q_{gi2} based on equations in Appendix A and the intersection of the gas lift valve performance curve in Figure 3 with q_{gi2} = 168 Mscf/D where P_{ioD2} = 1,518 psig.
11. Because P_{oD2} = 1,511 psig, ΔP_{ioc2} = 1,518 – 1,511 = 7 psi: ΔP_{ioc2} < ΔP_{ioa}, ΔP_{io2} = ΔP_{ioa} = 20 psi and ΣΔP_{io2} = 40 psi for calculation of P_{oD2}.
Third valve depth calculations
12. D_{bv} = = 1,392 ft and D_{v2} = 2,778 + 1,392 = 4,170 ft.
7. For D_{v3} = 5,064 ft: P_{ptD3} = 1,252 psig, P_{ioD3} = 1,583 psig, and T_{vuD3} = 162°F.
8. P_{wfd3} = 1,252 + 0.468 (6,000 – 5,064) = 1,690 psig at 6,000 ft and q_{lc} = 6.3 (2,000 – 1,690) = 1,953 B/D.
9. Refer to Table 3 with values of P_{pfD3} and q_{gi3} for varying assumed total-injection GLRs, R_{glt}. The P_{ptD3} of 1,252 psig intersects the tubing performance curve in Fig. 9 at q_{gi3} = 430 Mscf/D.
10. Refer to Table 3 with values of P_{ioD3} and q_{gi3} based on equations in Appendix A and the intersection of the gas lift valve performance curve in Fig. 9, with q_{gi3} = 430 Mscf/D where P_{ioD3} = 1,538 psig.
11. Because P_{oD3} = 1,523 psig, ΔP_{ioc3} = 1,538 – 1,523 = 15 psi: ΔP_{ioc3} < ΔP_{ioa}, ΔP_{io3} = ΔP_{ioa} = 20 psi and ΣΔP_{io3} = 60 psi for calculation of P_{oD3}.
Fourth valve depth calculations.
12. D_{bv} = = 558 ft and D_{v4} = 5,064 +558 = 5,622 ft.
7. For D_{v4} = 5,622 ft: The calculated D_{bv} for the fifth valve results in D_{v5} exceeding the maximum valve depth of 5,900 ft. Refer to the fifth valve depth calculations in Step 12 where the D_{bv} = 278 ft (5,900 – 5,622). The transfer P_{ptD4} is based on the actual D_{bv} of 278 ft and calculated with the following equation.
8. P_{wfd4} = 1,373 + 0.468 (6,000 – 5,622) = 1,550 psig at 6,000 ft. q_{lc4} = 6.3 (2,000 – 1,550) = 2,835 B/D for g_{ls}-traverse below D_{v4}.
9. Refer to Table 4 with values of P_{pfD4} and q_{gi4} for varying assumed total-injection GLRs, R_{glt}, and to the intersection of P_{ptD4} = 1,373 psig with the tubing performance curve in Fig. 10, where q_{gi4} = 730 Mscf/D.
10. Refer to Table 4 with values of P_{ioD4} and q_{gi4} based on equations in Appendix A and the intersection of the gas lift valve performance curve in Fig. 5 with q_{gi4} = 730 Mscf/D where P_{ioD4} = 1,543 psig.
11. Because P_{oD4} = 1,513 psig, ΔP_{ioc4} = 1,543 – 1,513 = 30 psi ΔP_{ioc4} > ΔP_{io}, ΔP_{io4} = ΔP_{ioc4} = 30 psi and ΣΔP_{io4} = 90 psi for calculation of P_{oD4}.
Fifth valve depth calculations
12. D_{bv} = = 308 ft, and D_{v5} = 5,622 + 308 = 5,930 ft exceeds given maximum valve depth of 5,900 ft; therefore, D_{v5} = D_{v(max)} = 5,900 ft and D_{bv} = 278 ft (5,900 – 5,622).
and D_{v5} = 5,622 + 308 = 5,930 ft exceeds given maximum valve depth of 5,900 ft; therefore, D_{v5} = D_{v(max)} = 5,900 ft and D_{bv} = 278 ft (5,900 – 5,622).
7. T_{vuD5} = 120 + 0.008333 (5,900) = 169°F at 5,900 ft for injection-gas rate calculations. An orifice-check valve with a 5∕16-in.-ID port is installed in the bottom wireline-retrievable gas lift valve mandrel at 5,900 ft. An orifice-check valve is fully open at all times. The three-parameter graphical solution in Fig. 11 includes two curves that are a function of P_{pfD5}.
The daily liquid production rates curve is based on the well PI, P_{wfd}, and P_{wsd}(P_{wfd} = P_{pfD5} + 34 psi for the approximate increase in pressure between 5,900 and 6,000 ft). An increase in the q_{gi} (higher R_{glt}) decreases the P_{pfD5} and increases the calculated q_{lc} for the given PI and P_{wsd}. For a constant assigned q_{gia}, different values of q_{l} are assumed and the R_{glt} and corresponding P_{pfD5} are calculated (or P_{pfD5} is determined from gradient curves) for each q_{l}. The assumed q_{l} is compared to the calculated q_{lc} based on the PI and P_{wsd}. This procedure is repeated until the calculated q_{lc} is equal to the assumed q_{l} for the total assigned q_{gia}. Refer to Table 5.
In the above calculations, a P_{pfD5} is calculated for each assumed q_{gia} that is less than and a q_{gia} equal to the assigned maximum of 2,000 Mscf/D. The injection-gas requirements curve is a plot of the assumed q_{gia} vs. the calculated P_{pfD5}.
The maximum assigned q_{gia} of 2,000 Mscf/D intersects the injection-gas requirements curve at P_{pfD5} = 1,190 psig. The calculated P_{ioD5} is 1,393 psig at 5,900 ft (upstream pressure) for the maximum assigned q_{gia} of 2,000 Mscf/D through a 5 ∕16-in.-ID orifice with a P_{pfD5} of 1,190 psig downstream pressure and an upstream T_{gD5} of 169°F. The P_{io5} at the surface is 1,180 psig for a P_{ioD5} of 1,393 psig at 5,900 ft. The upstream surface injection-gas pressure for 2,000 Mscf/D should not exceed a surface injection-gas pressure that would reopen any of the upper unloading valves. The calculated minimum P_{io} to reopen the deepest unloading valve is 1,310 psig at the surface (injection-gas available line pressure, P_{io} – ΣΔP_{io} = 1,400 – 90) and is 1,523 psig at 5,900 ft. Because the calculated upstream choke pressure of 1,393 psig is considerably less than 1,523 psig, there will be no unloading valve interference when the orifice-check valve becomes the operating valve, and the change in surface injection-gas pressure will be readily apparent after the depth of gas injection has transferred to the orifice-check valve.
Calculation of test-rack opening pressures of the gas lift valves The following calculations apply to injection-pressure-operated, unbalanced, single-element, nitrogen-charged bellows gas lift valves with a square, sharp-edged seat.
1. Calculate the injection-gas initial valve opening pressure at valve depth, P_{oD(n)}, on the basis of the available installation design injection-gas pressure at depth, P_{ioD(n)}.
2. The nitrogen-charged bellows pressure is calculated at the unloading valve temperature at depth, T_{vuD}, in the well using Eq. 40.
3. Calculate the temperature correction factor for nitrogen, C_{T}, using Eq. 43 or determine C_{T} from Table 6.
where
P | = | P_{b} + P_{atm} and T = T_{vD} - 60 |
If P_{b} is less than 1,250 psia:
A | = | 3.054E – 07 ( T ), B = 1 + 0.001934(T) and C = – 0.00226 (T – P). |
If P_{b} is greater than 1,250 psia:
A | = | 1.84E – 07 (T), B = 1 + 0.002298 (T) and C = –0.267 (T – P). |
4. Calculate the nitrogen-charged bellows pressure at a test-rack setting temperature of 60°F.
5. Calculate the test-rack opening pressure at 60°F using Eq. 45 or Eq. 46.
C_{T} | = | temperature correction factor for nitrogen from P_{bvD} to P_{b} at 60°F, dimensionless, |
P_{bvD} | = | nitrogen-charged bellows pressure at valve temperature, psig, |
Solution – Calculation of Test-Rack Opening Pressures
Top Valve Calculations 1/4-in.–ID Port) 1. P_{oD1} = P_{ioD1} -∑ΔP_{io1} = 1,500 – 20 = 1,480 psig at 2,778 ft. 2. and 3. P_{bvD1} = 0.936 (1,480) + (0.064)849 = 1,440 psig at 143°F, and C_{T1} = 0.8378 (calculated). 4. and 5. P_{b1} = 0.8378 (1,440) = 1,206 psig at 60°F, and
Second Valve Calculations (1/4-in.-ID Port) 1. P_{oD2} = 1,551 – 40 = 1,511 psig at 4,170 ft. 2. and 3. P_{bvD2} = (0.936) 1,511 + (0.064) 1,095 = 1,484 psig at 155°F, and C_{T2} = 0.8184 (calculated). 4. and 5. P_{b2} = (0.8184) 1,484 = 1,215 psig at 60°F, and
Third Valve Calculations (3/8-in.-ID Port) 1. P_{oD3} = 1,583 – 60 = 1,523 psig at 5,064 ft. 2. and 3. P_{bvD3} = 0.857 (1,523) + 0.143 (1,252) = 1,484 psig at 162°F, and C_{T3} = 0.8079 (calculated). 4. and 5. P_{b3} = 0.8079 (1,484) = 1,199 psig at 60°F, and
Fourth Valve Calculations (1/2-in.-ID Port) 1. P_{oD4} = 1,603 – 90 = 1,513 psig at 5,622 ft. 2. and 3. P_{bvD4} = 0.745 (1,513) + 0.255 (1,373) = 1,477 psig at 167°F, and C_{T4} = 0.8007 (calculated). 4. and 5. P_{b4} = 0.8007 (1,477) = 1,183 psig at 60°F, and
A summary of the installation design calculations is shown in Table 7. The significant increase in P_{vo(n)} with depth is the result of the larger-ID port sizes required for the unloading gas lift valve Numbers 3 and 4.
Casing-annulus-flow installation design
The design calculations for an annular-flow installation are similar to those for a continuous-flow installation through the tubing. Intermittent gas lift is not recommended for annular flow. Because the gross liquid production is generally thousands of barrels per day, selecting valve port inside diameter (ID) sizes for adequate gas passage is very important for annular-flow installations. Actual gas lift valve performance, based on port ID, maximum linear stem travel, and bellows-assembly load rate, is an important factor in the design calculations for annular-flow installations because of the high injection-gas requirements. The increase in the injection-gas pressure to overcome the bellows-assembly load rate and to attain the needed equivalent port area for a required injection-gas throughput should be considered.
Installation design
Selection of the proper size of gas-injection tubing string that will deliver the required daily injection-gas requirement for unloading and operating is absolutely essential. An initial assumption can be an injection-gas tubing size that will deliver the maximum daily injection-gas requirement with no pressure loss (i.e., the increase in the injection-gas pressure with depth, as a result of gas-column density, is offset by the flowing frictional pressure loss). This should be the smallest nominal tubing size considered for the injection-gas string. Charts for static injection-gas pressure at depth cannot be used for the valve spacing calculations.
The Cullender and Smith^{[1]} correlation is recommended for calculating the pressure loss in the injection-gas tubing string. This method for calculating the flowing injection-gas pressure at depth was derived for a producing gas well and not for gas injection. The only difference in the calculations is the friction term for gas being injected rather than being produced. The sign for the friction term changes (i.e., the friction term becomes negative in the Cullender and Smith equation for gas injection).
Wireline-retrievable gas lift valve mandrels that accommodate standard injection-pressure-operated valves for annular flow are available (Fig. 1). When these mandrels are used, the valves are run and set in the pocket in exactly the same manner as for tubular flow. However, the mandrel configuration is such that the injection gas enters the side of the pocket from inside the tubing. This allows injection gas to pass through the valve and exit the pocket into the casing annulus rather than into the tubing. Annular-flow mandrels should be used for annular flow wherever possible because they allow full gas passage through the valve without the restriction imposed by cross-over seats. Also, gas is injected from the bottom rather than the side of the mandrel. This provides a much safer installation from an erosion standpoint than the installation using valves with crossover seats in which gas is injected from the side of the pocket into the wall of the casing.
Where mandrels for tubing flow are already installed and are not feasible to replace, valves with crossover seats must be installed. In such installations, the check disk in the reverse-flow checks valve seats in the opposite direction for casing flow as compared to a tubing flow installation and allows gas passage from the injection-gas tubing to the casing annulus. In the wireline-retrievable valve tubing flow series mandrel, the valve for casing flow is similar to a production-pressure-operated valve, except the integral check valve is reversed for injection-gas flow from tubing to casing.
Because nitrogen-charged bellows gas lift valves have a lower bellows-assembly load rate than a spring-loaded valve, bellows-charged valves are recommended for high injection-gas volumetric throughput, as required for most annular-flow installations. Fortunately, the valve temperature at depth is not difficult to predict accurately in high-volume wells. The flowing surface temperature is near the bottomhole flowing temperature; therefore, the operating temperature of all valves in a high-volume, annular-flow gas lift installation is approximately the same. An important caution is to never use the surface injection-gas temperature to estimate the valve temperature at depth. The injection gas will begin to approach the flowing-fluid temperature within a few hundred feet of the surface. The flowing wellhead temperature of the fluid production should be used to establish the unloading valve temperatures at depth. This same consideration is applicable to the Cullender and Smith injection-gas pressure-at-depth calculations.
Nomenclature
A_{b} | = | total effective bellows area, in.^{2} |
A_{p} | = | valve port area (ball/seat-line contact area for sharp-edged seat), in.^{2} |
C_{T} | = | temperature correction factor for nitrogen from P_{bvD} at T_{vuD} to P_{b} at 60°F, dimensionless |
D | = | true vertical depth of gas column, ft |
D_{bv} | = | distance between gas lift valves, ft |
D_{bv(min)} | = | minimum distance between gas lift valves, ft |
D_{d} | = | reference datum depth (usually lower end of production conduit) for bottomhole temperature and pressures, ft |
D_{v} | = | valve depth, ft |
D_{v1} | = | depth of top valve, ft |
D_{v(max)} | = | maximum depth for bottom (deepest) valve, ft |
f_{o} | = | oil cut, fraction |
f_{w} | = | water cut, fraction |
F_{p} | = | production-pressure factor, dimensionless |
g_{pfa} | = | flowing pressure at depth gradient (traverse) above the depth of gas injection, psi/ft |
g_{pfb} | = | flowing pressure at depth gradient (traverse) below the depth of gas injection, psi/ft |
g_{gio} | = | static injection-gas pressure at depth gradient, psi/ft |
g_{lc} | = | average pressure gradient for liquid production in chamber, psi/ft |
g_{ls} | = | static load (kill)-fluid pressure gradient, psi/ft |
g_{Tv} | = | unloading gas lift valve temperature at valve depth gradient, °F/ft |
P_{bvD} | = | nitrogen-charged bellows pressure at valve temperature, psig |
P_{io} | = | injection-gas pressure at surface, psig or psia |
P_{iod} | = | static injection-gas pressure at D_{d}, psig or psia |
P_{ioD} | = | injection-gas pressure at depth (usually valve depth), psig or psia |
P_{ko} | = | surface kick-off or average field injection-gas pressure (optional), psig |
P_{o} | = | surface injection-gas initial valve opening pressure of gas lift valve, psig |
P_{oD} | = | injection-gas initial opening pressure of gas lift valve at valve depth, psig |
P_{ot} | = | tester pressure upstream of gas lift valve port, psig |
P_{pfd} | = | flowing-production pressure at D_{d} based on design q_{lt} and R_{glu}, psig |
P_{pfD} | = | flowing-production pressure at valve depth, psig |
(P_{pfD1})_{max} | = | maximum flowing-production pressure opposite an unloading valve immediately after the point of gas injection has transferred to the next lower valve, psig |
(P_{pfD})_{min} | = | minimum flowing-production pressure at valve depth, psig |
P_{pft} | = | tester pressure downstream of gas lift valve port, psig |
P_{pt} | = | surface valve-spacing transfer production pressure, psig |
P_{ptd} | = | valve spacing transfer production pressure at D_{d}, psig |
P_{ptD} | = | flowing-production transfer (spacing) pressure at valve depth, psig |
P_{wh} | = | surface wellhead pressure, psig |
P_{whu} | = | wellhead U-tubing unloading pressure, psig |
P_{wsd} | = | static bottomhole well pressure at depth D_{d}, psig |
ΔP_{sD} | = | assigned spacing pressure differential at valve depth, psi |
q_{ga} | = | actual daily volumetric gas rate, Mscf/D |
q_{gc} | = | chart daily volumetric gas rate, Mscf/D |
q_{gi} | = | daily injection-gas rate, Mscf/D |
q_{giu} | = | maximum unloading daily injection-gas rate, Mscf/D |
q_{lt} | = | total liquid (oil + water) daily production rate, B/D |
R_{glf} | = | formation-gas/liquid ratio, scf/STB |
R_{glu} | = | maximum unloading injection-gas/liquid ratio, scf/STB |
T_{gio} | = | wellhead injection-gas temperature, °F |
T_{wh} | = | surface wellhead temperature, °F |
T_{whf} | = | flowing surface wellhead temperature, °F |
T_{whu} | = | assigned unloading flowing surface wellhead temperature, °F |
T_{wsd} | = | bottomhole well temperature at D_{d}, °F |
References
- ↑ ^{1.0} ^{1.1} API RP 11V6, Recommended Practice for Design of Continuous Flow Gas Lift Installations Using Injection Pressure Operated Valves, second edition. 1999. Washington, DC: API.
- ↑ Winkler, H.W. and Eads, P.T. 1993. Applying the Basic Performance Concepts of Single-Element, Unbalanced Gas-Lift Valves for Installation Design. SPE Prod & Oper 8 (3): 211-216. SPE-21636-PA. http://dx.doi.org/10.2118/21636-PA.
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See also
Simplified mathematical gas lift performance model
Intermittent-flow gas lift installation design
Gas lift for unusual environments