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
• A variation of the decreasing injection-gas pressure design that considers valve performance at each station.

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.

....................(1)

where

qgiu	=	maximum unloading injection-gas rate, Mscf/D,
qlt	=	total liquid (oil + water) daily production rate, B/D,
Rgl	=	maximum unloading GLR, scf/STB,
and
Rglu	=	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.

....................(2)

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.

....................(3)

where

ggio	=	static injection-gas pressure at depth gradient, psi/ft
Pio	=	injection-gas pressure at surface, psia,
PioD	=	injection-gas pressure at depth, psia,
Dd	=	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.

....................(4)

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.

....................(5)

....................(6)

or

....................(7)

where

Dv1	=	depth of top valve, ft,
Pko	=	surface kick-off or average field injection-gas pressure (optional), psig,
Pwhu	=	surface wellhead U-tubing (unloading) pressure, psig,
ΔPsD	=	assigned spacing pressure differential at valve depth, psi,
gls	=	static load (kill)-fluid pressure gradient, psi/ft,
and
ggio	=	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)

....................(9)

....................(10)

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:

....................(11)

Solve for D_bv.

....................(12)

and

....................(13)

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.

....................(14)

where

CgT	=	approximate gas gravity and temperature correction factor for choke charts, dimensionless,
TgD	=	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, P₁, 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 P₁ and the downstream flowing-production pressure, P₂, at the valve depth.

• 

  Fig. 2-Orifice or choke daily injection-gas throughput rates for 8 18/64-in.-ID orifices.

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,

....................(15)

where

PioD1	=	injection-gas pressure at valve depth, psig, and
PoD1	=	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.

....................(16)

....................(17)

or

....................(18)

where

CT	=	temperature correction factor for nitrogen from PbvD to Pb at 60°F, dimensionless,
PbvD	=	nitrogen-charged bellows pressure at valve temperature, psig,
(PpfD) min	=	minimum flowing-production pressure at valve depth, psig,
and
Pvo	=	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.

....................(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.

• 

  Fig. 3-Pressure/depth graphical determination of the additional production-pressure effect for the top gas lift valve in a continuous-flow gas lift installation designed with a constant decrease in operating injection-gas pressure between valves.

....................(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:

....................(21)

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, P₁ and P₂.

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.

• 

  Fig. 4-Flowing pressure at depth gradient curves for 800 B/D with a 50% water cut through 2 7/8 in. OD tubing.

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.

• 

  Fig. 5-Graphical representation of a continuous-flow gas lift installation design with nitrogen-charged gas lift valves based on a constant decrease in the operating injection-gas pressure for each successively deeper valve.

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, P₁ , is based on P_oD5 of the last unloading valve using Eq. 17 corrected to the orifice-check valve depth of 5,970 ft.

P₁ = 1,068 + 0.0257 (5,970 – 5,762) = 1,073 psig at 5,970 ft.

The downstream flowing-production pressure, P₂, is equal to the minimum flowing-production pressure at 5,970 ft with Eq. 6.

P₂ = 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.

• 

  Table 1

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 Pvo₁ 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.

• 

  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.

• 

  Fig. 7-Pressure/depth graphical design for a continuous-flow gas lift installation requiring high injection-gas rates for unloading and final gas lift operation.

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).

....................(22)

where

qgsc	=	gas-flow rate at standard conditions (14.7 psia and 60°F), Mscf/D,
Cd	=	discharge coefficient (determined experimentally), dimensionless,
A	=	area of orifice or choke open to gas flow, in.2,
P1	=	gas pressure upstream of an orifice or choke, psia,
P2	=	gas pressure downstream of an orifice or choke, psia,
g	=	acceleration because of gravity, ft/sec2,
k	=	ratio of specific heats (Cp/Cv), dimensionless,
T1	=	upstream gas temperature, °R,
Fdu	=	pressure ratio, P2/P1, 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.

....................(23)

Ape	=	valve port equivalent area open to gas flow, in.2
Patm	=	atmospheric pressure, psia
PioD	=	injection-gas pressure at valve depth, psig
Rdu	=	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.

....................(24)

where

Pio	=	injection-gas pressure at surface, psia,
PioD	=	injection-gas pressure at depth, psia,
e	=	Napierian logarithm base = 2.718...,
γg	=	gas specific gravity (air = 1.0), dimensionless,
D	=	true vertical depth of gas column, ft,
	=	average gas-column temperature, °R,
and
	=	compressibility factor based on gas-column average pressure and temperature , dimensionless.

....................(25)

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.

....................(26)

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.

....................(27)

....................(28)

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.

....................(29)

....................(30)

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.

....................(31)

....................(32)

or

....................(33)

where

Dv1	=	depth of top valve, ft,
Pko	=	surface kick-off or average field injection-gas pressure (optional), psig,
Pwhu	=	surface wellhead U-tubing (unloading) pressure, psig,
ΔPsD	=	assigned spacing pressure differential at valve depth, psi,
gls	=	static load (kill)-fluid pressure gradient, psi/ft,
and
ggio	=	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).

....................(34)

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).

....................(35)

If P_wfd(n) < P_wsd, calculate q_lc(n).

....................(36)

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.

....................(37)

....................(38)

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.

....................(39)

and

....................(40)

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

6. D_v1 = = 2,778 ft

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.

• 

  Table 1

• 

  Fig. 8-Tubing and gas lift valve performance at 2,778 ft with only load fluid and no formation production.

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.

• 

  Table 2

• 

  Fig. 3-Tubing and gas lift valve performance at 4,170 ft with only load fluid and no formation production.

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.

• 

  Table 3

• 

  Fig. 9-Tubing and gas lift valve performance at 5,064 ft with load fluid and no formation gas production.

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.

• 

  Table 4

• 

  Fig. 10-Tubing and gas lift valve performance at 5,622 ft with load fluid and no formation gas production.

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.

• 

  Fig. 11-Predicted daily production rate for a 5/16-in.-ID orifice in a 1.5-in.-OD orifice-check valve at 5,900 ft.

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.

• 

  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).

....................(41)

2. The nitrogen-charged bellows pressure is calculated at the unloading valve temperature at depth, T_vuD, in the well using Eq. 40.

....................(42)

3. Calculate the temperature correction factor for nitrogen, C_T, using Eq. 43 or determine C_T from Table 6.

....................(43)

where

P

=

Pb + Patm and T = TvD - 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).

• 

  Table 6

4. Calculate the nitrogen-charged bellows pressure at a test-rack setting temperature of 60°F.

....................(44)

5. Calculate the test-rack opening pressure at 60°F using Eq. 45 or Eq. 46.

....................(45)

CT	=	temperature correction factor for nitrogen from PbvD to Pb at 60°F, dimensionless,
PbvD	=	nitrogen-charged bellows pressure at valve temperature, psig,

....................(46)

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.

• 

  Table 7

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 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.

• 

  Fig. 14-The mandrel pocket configuration differs for annular flow because injection gas enters the pocket from the tubing rather than 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

Ab	=	total effective bellows area, in.2
Ap	=	valve port area (ball/seat-line contact area for sharp-edged seat), in.2
CT	=	temperature correction factor for nitrogen from PbvD at TvuD to Pb at 60°F, dimensionless
D	=	true vertical depth of gas column, ft
Dbv	=	distance between gas lift valves, ft
Dbv(min)	=	minimum distance between gas lift valves, ft
Dd	=	reference datum depth (usually lower end of production conduit) for bottomhole temperature and pressures, ft
Dv	=	valve depth, ft
Dv1	=	depth of top valve, ft
Dv(max)	=	maximum depth for bottom (deepest) valve, ft
fo	=	oil cut, fraction
fw	=	water cut, fraction
Fp	=	production-pressure factor, dimensionless
gpfa	=	flowing pressure at depth gradient (traverse) above the depth of gas injection, psi/ft
gpfb	=	flowing pressure at depth gradient (traverse) below the depth of gas injection, psi/ft
ggio	=	static injection-gas pressure at depth gradient, psi/ft
glc	=	average pressure gradient for liquid production in chamber, psi/ft
gls	=	static load (kill)-fluid pressure gradient, psi/ft
gTv	=	unloading gas lift valve temperature at valve depth gradient, °F/ft
PbvD	=	nitrogen-charged bellows pressure at valve temperature, psig
Pio	=	injection-gas pressure at surface, psig or psia
Piod	=	static injection-gas pressure at Dd, psig or psia
PioD	=	injection-gas pressure at depth (usually valve depth), psig or psia
Pko	=	surface kick-off or average field injection-gas pressure (optional), psig
Po	=	surface injection-gas initial valve opening pressure of gas lift valve, psig
PoD	=	injection-gas initial opening pressure of gas lift valve at valve depth, psig
Pot	=	tester pressure upstream of gas lift valve port, psig
Ppfd	=	flowing-production pressure at Dd based on design qlt and Rglu, psig
PpfD	=	flowing-production pressure at valve depth, psig
(PpfD1)max	=	maximum flowing-production pressure opposite an unloading valve immediately after the point of gas injection has transferred to the next lower valve, psig
(PpfD)min	=	minimum flowing-production pressure at valve depth, psig
Ppft	=	tester pressure downstream of gas lift valve port, psig
Ppt	=	surface valve-spacing transfer production pressure, psig
Pptd	=	valve spacing transfer production pressure at Dd, psig
PptD	=	flowing-production transfer (spacing) pressure at valve depth, psig
Pwh	=	surface wellhead pressure, psig
Pwhu	=	wellhead U-tubing unloading pressure, psig
Pwsd	=	static bottomhole well pressure at depth Dd, psig
ΔPsD	=	assigned spacing pressure differential at valve depth, psi
qga	=	actual daily volumetric gas rate, Mscf/D
qgc	=	chart daily volumetric gas rate, Mscf/D
qgi	=	daily injection-gas rate, Mscf/D
qgiu	=	maximum unloading daily injection-gas rate, Mscf/D
qlt	=	total liquid (oil + water) daily production rate, B/D
Rglf	=	formation-gas/liquid ratio, scf/STB
Rglu	=	maximum unloading injection-gas/liquid ratio, scf/STB
Tgio	=	wellhead injection-gas temperature, °F
Twh	=	surface wellhead temperature, °F
Twhf	=	flowing surface wellhead temperature, °F
Twhu	=	assigned unloading flowing surface wellhead temperature, °F
Twsd	=	bottomhole well temperature at Dd, °F

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See also

Gas lift system design

Gas lift installation design

Simplified mathematical gas lift performance model

Intermittent-flow gas lift installation design

Gas lift for unusual environments

Gas lift

PEH:Gas_Lift