Compressibility Factor (z)
The Compressibility factor, Z is a dimensionless parameter less than 1.00 that represents the deviation of
a real gas from an ideal gas. Hence it is also referred to as the gas deviation factor. At low pressures and
temperatures Z is nearly equal to 1.00 whereas at higher pressures and temperatures it may range
between 0.75 and 0.90. The actual value of Z at any temperature and pressure must be calculated taking
into account the composition of the gas and its critical temperature and pressure. Several graphical and
analytical methods are available to calculate Z. Among these, the Standing-Katz, and CNGA (California
natural gas association) methods are quite popular. The critical temperature and the critical pressure of a
gas are important parameters that affect the compressibility factor and are defined as follows.
The critical temperature of a pure gas is that temperature above which the gas cannot be compressed
into a liquid, however much the pressure. The critical pressure is the minimum pressure required at the
critical temperature of the gas to compress it into a liquid.
As an example, consider pure methane gas with a critical temperature of 343 0R and critical pressure of
666 psia (Table 1-1).
The reduced temperature of a gas is defined as the ratio of the gas temperature to its critical temperature,
both being expressed in absolute units (0R). It is therefore a dimensionless number.
Similarly, the reduced pressure is a dimensionless number defined as the ratio of the absolute pressure
of gas to its critical pressure.
Therefore we can state the following:
Where
P = pressure of gas, psia
T = temperature of gas, 0R
Tr = reduced temperature, dimensionless
Pr = reduced pressure, dimensionless
Tc = critical temperature, 0R
Pc = critical pressure, psia
Example1-4: Using the preceding equations, the reduced temperature and reduced pressure of a sample
of methane gas at 70 0F and 1200 psia pressure can be calculated as follows
For natural gas mixtures, the terms pseudo-critical temperature and pseudo-critical pressure are used.
The calculation methodology will be explained shortly. Similarly we can calculate the pseudo-reduced
temperature and pseudo-reduced pressure of a natural gas mixture, knowing its pseudo-critical
temperature and pseudo-critical pressure.
The Standing-Katz chart, Fig. 1.3 can be used to determine the compressibility factor of a gas at any
temperature and pressure, once the reduced pressure and temperature are calculated knowing the
critical properties.
Pseudo-critical properties allow one to evaluate gas mixtures. Equations (1-13) and (1-14) can be used to
calculate the pseudo-critical properties for gas mixtures:
Example 1-5: Calculate the Compressibility factor for the following Gas mixture at 1000F and 800 psig:
Using Equation 1-11 and 1-12
T` r = (100+460)/464.5
=1.2
P`r = (800+14.7)/659.4 = 1.23
From fig.1-3. Compressibility factor is approximately, z= 0.72
Calculating the compressibility factor for example 1-4, of the gas at 70 0F and 1200 psia, using Standing-
Katz chart, fig. 1-3. Z = 0.83 approximately. For ) Tr = 1.5 , Pr = 1.8).
Another analytical method of calculating the compressibility factor of a gas is using the CNGA equation as
follows:
Where
Pavg = Gas pressure, psig. [psig = (psia – 14.7)]
Tf
= Gas temperature, 0R
G = Gas gravity (air = 1.00)
The CNGA equation for compressibility factor is valid when the average gas pressure Pavg is greater than
100 psig. For pressures less than 100 psig, compressibility factor is taken as 1.00. It must be noted that
the pressure used in the CNGA equation is the gauge pressure, not the absolute pressure.
Example 1-6: Calculate the compressibility factor of a sample of natural gas (gravity = 0.6) at 80 0F and
1000 psig using the CNGA equation.
Solution:
From the Eq. (1.15), the compressibility factor is
The CNGA method of calculating the compressibility, though approximate, is accurate enough for most
gas pipeline hydraulics work and process calculations.
Apparent Molecular Weight of Gas Mixture
For compounds, the term molecular weight is used, while, for hydrocarbon mixture the term apparent
molecular weight is commonly used. Apparent molecular weight is defined as the sum of the products of
the mole fractions of each component times the molecular weight of that component. As shown in Eq. 1-4
Example 1.2: Determine the apparent molecular weight for the gas mixture in Table 1-2:
Molecular Weight and Apparent Molecular Weight
The molecular weight of a compound is the sum of the atomic weight of the various atoms making up that
compound. The Mole is the unit of measurements for the amount of substance, the number of moles is
defined as follows:
Example 1.1: Methane molecule consists of one carbon atom with atomic weight =12 and 4 hydrogen atoms with atomic weight = 1 each. Molecular weight for Methane (CH 4) = (1 × 12) + (4 × 1) = 16 lb/lb-mole. Similarly, Ethane (C2H6) molecular weight = (2 × 12) + (6 × 1) = 30 lb/lb-mole.
Hydrocarbon up to four carbon atoms are gases at room temperature and atmospheric pressure. Reducing the gas temperature and/or increasing the pressure will condense the hydrocarbon gas to a liquid phase. By the increase of carbon atoms in hydrocarbon molecules, consequently the increase in molecular weight, the boiling point increases and a solid hydrocarbon is found at high molecular weight.
Physical constants of light hydrocarbon and some inorganic gases are listed in Table 1-1.
Hydrocarbon Gases
Most of compounds in crude oil and natural gas consist of molecules made up of hydrogen and carbon, therefore these types of compounds are called hydrocarbon.
The smallest hydrocarbon molecule is Methane (CH4) which consists of one atom of Carbon and four atoms of hydrogen. It may be abbreviated as C1 since it consisted from only one carbon atom. Next compound is Ethane (C2H6) abbreviated as C2, and so on Propane (C3H8), Butane (C4H10)…etc. Hydrocarbon gases are C1:C4), with the increase of carbon number, liquid volatile hydrocarbon is found (e.g. Pentane C5 is the first liquid hydrocarbon at standard conditions).
Hydrocarbon Preparation
The goal is to produce oil that meets the purchaser’s specifications that define the maximum allowable amounts of water, salt, and sulfur. In addition to the maximum allowable value of Reid vapor pressure and maximum allowable pour point temperature.
Similarly, the gas must be processed to meet purchaser’s water vapor maximum allowable content (Water dew point), hydrocarbon dew point specifications to limit condensation during transportation, in addition to the maximum allowable content of CO2, H2S, O2, Total Sulfur, Mercaptan, Mercury, and maximum gross heating value.
The produced water must meet the regulatory requirements for disposal in the ocean if the wells are offshore, or to meet reservoir requirements for injection into an underground reservoir to avoid plugging the reservoir.
The specifications for the above requirements may include maximum oil in water content, total suspended solids to avoid formation plugging, bacteria counts, toxicity in case of offshore disposal, and oxygen content. Before discussing the industry or the technology of oil and gas processing it is best to define the characteristic, physical properties and main chemical composition of oil and gas produced.
Figures 1-1 and 1-2, illustrates gas-oil separation plant, and oil flow diagram.
Separator may be a slug catcher, free water knock out drum, two phase separator, or gun barrel. A dehydrator may be a heater treater, separator, or settling tank. Heat is added upstream or downstream separator depending on crude oil temperature and gas oil ratio. Crude oil stabilization is usually performed in separation step or during heat addition. Crude oil sweetening is usually performed upstream or downstream heater treater. Gas and water are separated and undergoes further treatment processes not in the scope of this book.
Fig.1-2. Crude oil flow Diagram
Pressure Relieving Systems – Procedures for Sizing
Modifications to API RP 520
API Effective Area and Effective Coefficient of Discharge
1) The minimum size of PR valves shall be as follows:
a) 1 in. NPS (25 mm) inlet size with flanged inlet and outlet connections.
b) 3/4 in. NPS (20 mm) when used only for protection against liquid thermal expansion. This size may be used with threaded inlet and outlet connections.
2) The use of smaller sizes shall be approved by Owner’s Engineer. Vessels fabricated from pipe less than 24 in. NPS (600 mm), which are not ASME Code stamped, may not require PR devices for protection against fire.
API Effective Area and Effective Coefficient of Discharge
1) Unless otherwise specified, pressure relief valves with Q, R, and T size orifices shall not be used where the temperature exceeds 350?F (177?C) and the molecular weight is less than 10 without Owner Engineer’s approval. Pressure relief valves with orifice sizes larger than T (16,775 mm2 or 26.0 in2) or with inlet flanges larger than NPS 8 in. (200 mm) shall not be used without Owner Engineer’s approval.
: Balanced Pressure Relief Valves
1) In new designs, the total back pressure (built-up plus superimposed) shall be limited to 50 percent of the set pressure for balanced bellows type PR valves for either operating or fire contingencies. In retrofits, the maximum backpressure published by the valve manufacturer for correction factors, Kb may be allowed with approval by the Owner’s Engineer. The built up backpressure shall be calculated based on the frictional plus kinetic pressure changes.
2) When total backpressure for balanced bellows relief valves exceeds 30 percent of the set pressure, the valve manufacturer shall be consulted. The capacity of the valve and the maximum allowable backpressure on the bellows shall be verified with the manufacturer.
Effect of Back Pressure and Header Design on PRV Sizing and Selection
- The maximum superimposed backpressure for non-discharging PR valves during a maximum system release (from either single or multiple valve releases under a design contingency) shall be as follows:
For spring-loaded, conventional PR valves:
For balanced bellows and pilot operated valves:
| Where: | ||
| Psi (max) | = | Maximum superimposed back pressure |
| Pset | = | Pressure relief valve set pressure |
| Pd | = | Differential spring pressure |
| C | = | Multiplier applied to design pressure to obtain hydrostatic test pressure per GP 05-03-01, dimensionless |
Operating Contingencies
1) Where not prohibited by local legislation and in accordance with the requirements of the ASME Code, Section VIII, Division 1 (ASME SEC VIII D1), accumulated pressure can be increased when multiple PRVs are installed as follows:
a) 116% of the maximum allowable working pressure for operating contingencies,
b) 121% of the maximum allowable working pressure when fire is the only contingency requiring a PRV,
c) 106% of the maximum allowable working pressure for boilers.
Pressure Relieving Systems – Rupture Disks
Modifications to API RP 520
Applications of Rupture Disks
1. Soft seated PR valves may be considered as an alternative to rupture disk (RD)/PR valve combinations for services operating below 450?F (232?C) when control of fugitive emissions is required to meet environmental regulations. The use of soft seated PR valves shall be approved by the Owner’s Engineer.
2. If installed upstream of a PR valve, rupture disks (RD) shall be installed as shown in Figure A–5.
3. The rated temperature at which the RDs are specified to function is the minimum temperature of the disk itself before it relieves. This may be lower than the normal process temperature due to ambient cooling of the non-flowing piping, RD, and disk holder, and is strongly affected by the geometry of the inlet piping.
The inlet piping must be designed and evaluated before the rated rupture temperature of the RDs is finalized.
Rupture Disk Selection and Specification
1) Rupture disks (RD) may be used in conjunction with or as a substitute for PR valves only with the approval of the Owner’s Engineer. Acceptable types of RDs are:
a) Pre-scored tension loaded conventional (forward acting) for both liquid and gas/two-phase service.
b) Pre-scored (cross-scored) reverse buckling for gas/two-phase only service.
c) Pre-scored (semi-circular) reverse buckling for gas/two-phase or liquid service. Pre-scored (semi-circular) may not be used under PRVs due to possible fragmentation.
2) The manufacturing range for all RDs shall be the lowest available from the manufacturer. The manufacturing range shall be applied below the design pressure of the equipment. Use of other types of RDs with larger manufacturing ranges shall be approved by the Owner’s Engineer.
Baleen Filters 131 sq. ft. Pool Filter Replaces Unicel C-7494, P
Figure 7.2 shows a once-through thermosyphon reboiler. The driving force to promote flow through this reboiler is the density difference between the reboiler feed line and the froth filled reboiler return line. For example:
• The specific gravity of the liquid in the reboiler feed line is 0.600.
• The height of liquid above the reboiler inlet is 20 ft.
• The mixed-phase specific gravity of the froth leaving the reboiler is 0.061.
• The height of the return line is 15 ft.
• Feet of water per psi =2.31.
The differential pressure driving force is then
What happens to this differential pressure of 4.7 psig? It is consumed in overcoming the frictional losses, due to the flow in the
• Reboiler
• Inlet line
• Outlet line
• Nozzles
If these frictional losses are less than the 4.7 psig given above, then the inlet line does not run liquid full. If the frictional losses are more than the 4.7 psig, the reboiler draw-off pan overflows, and flow to the reboiler is reduced until such time as the frictional losses drop to the available thermosyphon driving force.
The once-through thermosyphon reboiler, shown in Fig. 7.2,
operates as follows:
• All the liquid from the bottom tray flows to the reboiler.
• None of the liquid from the bottom of the tower flows to the reboiler.
• All the bottoms product comes from the liquid portion of the reboiler effluent.
• None of the liquid from the bottom tray flows to the bottom of the tower.
This means that when the once-through thermosyphon reboiler is working correctly, the reboiler outlet temperature and the towerbottom temperature are identical. If the tower-bottom temperature is cooler than the reboiler outlet temperature, something has gone wrong with the thermosyphon circulation.
Circulating vs. Once-Through Thermosyphon Reboilers
We said before that it was wrong to return the effluent from a oncethrough reboiler with a vertical baffle to the cold side of the tower’s bottom. Doing so would actually make the once-through thermosyphon reboiler work more like a circulating reboiler. But if this is bad, then the once-through reboiler must be better than the circulating reboiler. But why?
• The once-through reboiler functions as the bottom theoretical separation stage of the tower. The circulating reboiler does not, because a portion of its effluent back mixes to its feed inlet. This back mixing ruins the separation that can otherwise be achieved in reboilers.
• Regardless of the type of reboiler used, the tower-bottom product temperature has to be the same, so as to make product specifications. This is shown in Fig. 7.5. However, the reboiler outlet temperature must always be higher in the circulating reboiler than in the once-through reboiler. This means that it is more difficult to transfer heat in the former than in the latter.
• Because the liquid from the bottom tray of a tower with a circulating thermosyphon reboiler is of a composition similar to that of the bottoms product, we can say that the circulating thermosyphon reboiler does not act as a theoretical separation stage. However, the liquid from the bottom tray of a tower with a once-through thermosyphon reboiler can be quite a bit lighter in composition (and hence cooler) than the bottoms product composition, and thus we say that the once-through thermosyphon reboiler does act as a theoretical separation stage. The cooler the liquid flow from the bottom tray of a tower, the less the vapor flow through that tray. This is because the hot vapor flowing up through a tray heats up the downflowing liquid. This means that there is a greater vapor flow through the bottom tray of a tower with a circulating thermosyphon reboiler than there would be through the bottom tray of a tower with a once-through thermosyphon reboiler. Everything else being equal, then, the tower served by the circulating reboiler is going to flood before the tower served by the once-through reboiler.
Tower Final Inspection
At a Gulf Coast refinery, the reboiler thermosyphon circulation could not be reestablished after a turnaround. The tower was reopened and a lessthan-alive contract employee was found stuck in the reboiler draw-off nozzle. At the Good Hope Refinery (when I was the technical manager), we once left a complete scaffold (poles, boards, everything) in the bottom of a debutanizer tower. Rags, hard hats, plywood, and especially plastic bags left in packed columns should be removed from inside draw sumps and downcomers. I know it’s rough on the knees, but crawl across every tray and look into each downcomer. One lost flashlight in a small downcomer may flood every tray in the tower. A rag caught on a vortex breaker in a jet fuel draw box has caused a complete refinery shutdown.
Check the tray clips, tray panels, and downcomer bolting bars. At least the nuts and bolts should be finger-tight. If you find a single loose nut, insist that every nut on that tray be retightened. I will check the tray clips and 10 percent of the downcomer bolting bar nuts for finger-tight.