Valve calculations

Functions to generate valve performance curves and valve pressure tables using current conditions.

PressureDrop.SageAndLacy_nitrogen_Zfactor
PressureDrop.ThornhillCraver_gaspassage
PressureDrop.ThornhillCraver_gaspassage_simplified
PressureDrop.domepressure_downhole
PressureDrop.estimate_valve_Rvalue
PressureDrop.valve_calcs
PressureDrop.valve_table

Example

using PressureDrop

MDs = [0,1813, 2375, 2885, 3395]
TVDs = [0,1800, 2350, 2850, 3350]
incs = [0,0,0,0,0]
id = 2.441

well = Wellbore(MDs, incs, TVDs, id)
valves = GasliftValves([1813,2375,2885,3395], #valve MDs
                       [1005,990,975,960], #valve PTROs (psig)
                       [0.073,0.073,0.073,0.073], #valve R-values
                       [16,16,16,16]) #valve port sizes in 64ths inches

tubing_pressures = [150,837,850,840,831] #pressures at depth
casing_pressures = 1070 .+ [0,53,70,85,100]
temps = [135,145,148,151,153] #temps at depth

vdata, inj_depth = valve_calcs(valves = valves, well = well, sg_gas = 0.72, tubing_pressures = tubing_pressures, casing_pressures = casing_pressures, tubing_temps = temps, casing_temps = temps)

valve_table(vdata, inj_depth)

╭─────┬──────┬──────┬──────┬──────┬───────┬───────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬───────┬───────┬───────╮
│ GLV │   MD │  TVD │  PSO │  PSC │  Port │     R │ PPEF │ PTRO │   TP │   CP │  PVO │  PVC │ T_td │ T_cd │   Q_o │ Q_1.5 │   Q_1 │
│     │   ft │   ft │ psig │ psig │ 64ths │       │    % │ psig │ psig │ psig │ psig │ psig │   °F │   °F │ mcf/d │ mcf/d │ mcf/d │
├─────┼──────┼──────┼──────┼──────┼───────┼───────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼───────┼───────┼───────┤
│   4 │ 1813 │ 1800 │ 1077 │ 1056 │    16 │ 0.073 │    8 │ 1005 │  837 │ 1123 │ 1130 │ 1109 │  145 │  145 │  1261 │   959 │   757 │
│   3 │ 2375 │ 2350 │ 1048 │ 1028 │    16 │ 0.073 │    8 │  990 │  850 │ 1140 │ 1118 │ 1098 │  148 │  148 │  1276 │   970 │   766 │
│   2 │ 2885 │ 2850 │ 1022 │ 1002 │    16 │ 0.073 │    8 │  975 │  840 │ 1155 │ 1107 │ 1087 │  151 │  151 │  1315 │   999 │   789 │
│   1 │ 3395 │ 3350 │  993 │  974 │    16 │ 0.073 │    8 │  960 │  831 │ 1170 │ 1093 │ 1074 │  153 │  153 │  1351 │  1027 │   811 │
╰─────┴──────┴──────┴──────┴──────┴───────┴───────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴───────┴───────┴───────╯

Functions

PressureDrop.estimate_valve_Rvalue — Function.

estimate_valve_Rvalue(port_size, valve_size, lapped_seat = true)

Estimates an R-value for your valve (not recommended) using sensible defaults, if you do not have a manufacturer-provided value specific to the valve (recommended).

Takes port size as a diameter in 64ths inches, a valve size in inches {1.0, 1.5}, and an indication of whether the seat is lapped as {true, false}.

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PressureDrop.valve_calcs — Method.

valve_calcs(<named args>)

Calculates a standard table of pressures and temperatures for anticipated valve operation at current (steady-state) conditions.

Note that all inputs and outputs are in psig for ease of interpretation.

Additionally, all forms are derived from the force balance for opening, Pt * Ap + Pc * (Ad - Ap) ≥ Pd * Ad and the force balance for closing, Pc ≤ P_d.

Further note that:

the valve closing pressures given are a theoretical minimum (casing pressure is assumed to act on the entire area of the bellows/dome until closing).
valve opening and closing pressures are recalculated from PTRO and current conditions, rather than the other way around common during design.
casing temperature is assumed to be 85% of tubing temperature if only a tubing temperature profile is provided. To force the use of identical temperature profiles, pass the wellbore temperature twice.

Arguments

valves::GasliftValves: a GasliftValves object defining the valve string
well::Wellbore: a Wellbore object defining the survey/segmentation points, deviation survey, and tubing
sg_gas: injection gas specific gravity
tubing_pressures::Array{T, 1} where T <: Real: precalculated tubing pressures in psig
casing_pressures::Array{T, 1} where T <: Real: precalculated casing pressures in psig
tubing_temps::Array{T, 1} where T <: Real: precalculated tubing temperature profile in °F
casing_temps::Array{T, 1} where T <: Real = tubing_temps .* 0.85: precalculated casing temperature profile in °F
dp_min = 100: minimum differential pressure (CP - TP) in psi for calculating an assumed injection point
one_inch_coefficient = 0.76: coefficient of discharge for Thornhill-Craver gas passage calculations for 1" valves
one_pt_five_inch_coefficient = 0.6: coefficient of discharge for Thornhill-Craver gas passage calculations for 1.5" valves

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PressureDrop.valve_table — Function.

valve_table(valvedata, injection_depth = nothing)

Pretty prints the data returned by valve_calcs for interpretation.

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PressureDrop.SageAndLacy_nitrogen_Zfactor — Method.

SageAndLacy_nitrogen_Zfactor(p, T)

Sage and Lacy experimental Z-factor correlation.

Takes pressure in psia and temperature in °F.

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PressureDrop.ThornhillCraver_gaspassage — Function.

ThornhillCraver_gaspassage(<args>)

Thornhill-Craver gas throughput for square-edged orifice.

See section 8.1 of Fundamentals of Gas Lift Engineering by Ali Hernandez, as well as published work by Ken Decker, for an in-depth discussion of the application of Thornhill-Craver to gas lift valve performance.

In general, T-C will be optimistic, but should be expected to have an effective error of up to +/- 30%.

Arguments

P_td: tubing pressure at depth, psig
P_cd: casing pressure at depth, psig
T_cd: gas (casing fluid) temperature at depth, °F
portsize_64ths: valve port size in 64ths inch
sg_gas: gas specific gravity relative to air
molFracCO2 = 0.0, molFracH2S = 0.0: produced gas fractions of hydrogen sulfide and CO2, [0,1]
C_d = 0.827: discharge coefficient–uses 0.827 by defaul to match original T-C
Z_correlation::Function = KareemEtAlZFactor: natural gas compressibility/Z-factor correlation to use
pseudocrit_pressure_correlation::Function = HankinsonWithWichertPseudoCriticalPressure: psuedocritical pressure function to use
pseudocrit_temp_correlation::Function = HankinsonWithWichertPseudoCriticalTemp: pseudocritical temperature function to use

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PressureDrop.ThornhillCraver_gaspassage_simplified — Method.

ThornhillCraver_gaspassage_simplified(P_td, P_cd, T_cd, portsize_64ths)

Thornhill-Craver gas throughput for square-edged orifice (optimistic since it assumes a fully open valve where the stem does not interfere with flow).

This simplified version assumes gas specific gravity at 0.65.

Arguments

P_td: tubing pressure at depth, psig
P_cd: casing pressure at depth, psig
T_cd: gas (casing fluid) temperature at depth, °F
portsize_64ths: valve port size in 64ths inch

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PressureDrop.domepressure_downhole — Function.

domepressure_downhole(p_d_set, T_v, error_tolerance = 0.1, p_d_est = p_d_set/0.9, T_set = 60, Zfactor::Function = SageAndLacy_nitrogen_Zfactor)

Iteratively calculates the dome pressure in psia of the valve downhole using gas equation of state, assuming that the change in dome volume is negligible.

Arguments

PTRO: test rack opening pressure of valve in psig
R: R-value of the valve (nominally, area of port divided by area of bellows/dome, but adjusted for lapped seats, etc)
T_v: valve temperature at depth
error_tolerance = 0.1: error tolerance in psi
delta_est: initial estimate for downhole dome pressure as a percentage of surface set pressure
T_set = 60: setting temperature in °F
Zfactor::Function = SageAndLacy_nitrogen_Zfactor: Z-factor function parameterized by target conditions as pressure in psia and temperature in °F

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