# Density and pressure drop relationship quotes

### Basics of Air Velocity, Pressure and Flow Air velocity is a function of air density and differential pressure, but determining air flow requires that the geometry of the piping be taken into account. The pitot. Average velocity of the fluids in the pipes and pressure drop list of fluids ( fluids liquids and gases are near to be used with their density and viscosity data). When ordering, please quote the EUR number and the title, which are indicated on the cover of . system, A theoretical relation has been derived by means of which the Already with a pressure difference of 1 atm over the leak, leak flow- rates of .. v/here ρ is the vapour pressure in atm, and p-, the density of the liquid in.

Since flow is proportional to the square root of density at the vena contracta, the decrease in density causes the flow to be less than it would be if gas were not compressible, accounting for flow graph starting to round off instead of following the straight line.

Density change and vena contracta enlargement are responsible for the shape of the flow graph. As we continue to increase the pressure drop ratio, the velocity at the vena contracta becomes greater and the pressure becomes less, resulting in an even lower density. Now the flow deviates even more from the straight line that assumes a constant density at the vena contracta as would be the case for a liquid.

At some point, as the pressure drop ratio is increased and the flow rate increases, the velocity at the vena contracta becomes sonic. Because the vena contracta is downstream of the physical restriction and has a smaller cross sectional area than that of the physical restriction, even though the velocity has reached the maximum velocity that is possible at a restriction, it is still possible for the flow rate to increase.

As the pressure drop ratio is increased further, the vena contracta starts backing up toward the physical restriction and the cross sectional area of the vena contracta increases, so even though flow is sonic there is still some increase in flow because the area is larger. Finally, when the vena contracta backs up to the physical restriction, it can get no larger, and since flow is already sonic, no increase in flow is possible, and flow becomes fully choked.

Summarizing how the gas flow graph gets its shape: At vena contracta velocities below sonic, the deviation of the flow curve from a straight line is caused by the density at the vena contracta decreasing. Once sonic velocity is reached, the velocity, pressure and density at the vena contracta remain constant, but the vena contracta backs up toward the physical restriction, becoming larger and thus allowing flow to increase. When the vena contracta finally reaches its maximum size and since the velocity is already at the maximum possible flow chokes. With p1 at psia and starting with delta p at zero and gradually increasing it we would find that flow would choke when the pressure drop was 70 psi.

Knowing that the terminal pressure drop ratio for this particular model globe valve is 0. In order to properly size control valves for gas service, it is necessary to know at what pressure drop flow will choke.

Different valve styles have different values of xTand for each valve type, xT also varies with valve opening. Typical values of xT and how they affect the flow through control valves. Valve manufacturers test their valves for xT and then publish the results, making it possible to predict the point at which flow will choke and therefore properly size control valves. The blue line on the left hand graph represents the flow through a globe control valve, where xT is 0.

### Pressure Loss Calculations

Although both valves have the same flow capacity CVthe graph of flow through the butterfly valve red line on the left hand graph looks quite different than the graph of flow through the globe valve. That is because it has an xT of 0. At low pressure drop ratios, the flow is the same through both valves, but as the pressure drop ratio increases, the flow in the butterfly valve starts aiming toward choked flow before the flow in the globe valve does.

Understanding this will help you understand why a sizing calculation may show that, with all the flow conditions the same, one style of valve will need a larger Cv than is required of a different style of valve. Most tables of gas properties include values of the Ratio of Specific Heats. In other words, the friction factor depends on the fluid properties and flowing conditions in the system. Blasius was the first to present a correlation between the Reynolds number and the friction factor for a very limited range of applications.

Nikuradse experimentally identified a relationship between the flow regimes using the Reynolds numberthe pipe roughness, and friction.

Nikuradse found that pressure losses were higher for rougher pipes than for smooth ones due to frictional effects. He also observed that for small Reynolds numbers in the laminar flow regimethe friction factor was the same for rough and smooth pipes.

Several authors have since tried to relate the Reynolds number and the absolute roughness of the pipe to estimate the friction factor. Hydrostatic Component This component is of importance only when there are differences in elevation from the inlet end to the outlet end of a pipe segment.

In horizontal pipes this component is zero. A generalized form accounting for pipe inclination using the angle with respect to the horizontal can be written as: To use the angle with respect to the vertical for example, in well deviation surveyschange the trigonometric function to cosine. For gases, density varies with pressure. Note that this is equivalent to a Multi-Step Cullender and Smith calculation. Flow Correlations Many single-phase correlations exist that were derived for different operating conditions or from laboratory experiments. Generally speaking, these only account for the friction component, i.

### Gas Flow in Control Valves | Valin

For example, if the Gray correlation was selected but there was only gas in the system, the Fanning gas correlation is used. Single-phase correlations can be used for vertical or inclined flow provided that the hydrostatic pressure drop is accounted for in addition to the friction component. Even though a particular correlation may have been developed for flow in a horizontal pipe, incorporation of the hydrostatic pressure drop allows that correlation to be used for flow in a vertical pipe. Multiphase Flow Multiphase pressure loss calculations parallel single-phase pressure loss calculations. Essentially, each multiphase correlation makes its own particular modifications to the hydrostatic pressure difference and the friction pressure loss calculations, in order to make them applicable to multiphase situations.

The presence of multiple phases greatly complicates pressure drop calculations. This is due to the fact that the properties of each fluid present must be taken into account. Also, the interactions between each phase must be considered. Mixture properties must be used, and therefore the gas and liquid in-situ volume fractions throughout the pipe need to be determined. In general, multiphase correlations are essentially two-phase and not three-phase.

Accordingly, the oil and water phases are combined, and treated as a pseudo single-liquid phase, while gas is considered a separate phase. The hydrostatic pressure difference calculation is modified by defining a mixture density.

This is determined by a calculation of in-situ liquid holdup amount of liquid in the pipe section. Some correlations determine holdup based on defined flow patterns. They can be grouped as follows: Do not account for flow patterns: Gray — Developed using data from gas and condensate wells.

Hagedorn and Brown — Derived using a test well running different oils and air Consider flow patterns: Beggs and Brill — Correlation derived from experimental data for vertical, horizontal, inclined uphill and downhill flow of gas-water mixtures Petalas and Aziz — Mechanistic model combined with empirical correlations.

This multi-purpose correlation is applicable for all pipe geometries, inclinations and fluid properties.

These models can be used for gas-liquid multiphase flow, single-phase gas or single-phase liquid, because in single-phase mode, they revert back to the Fanning equation, which is equally applicable to either gas or liquid.

The Gray and Hagedorn and Brown correlations were derived for vertical wells and may not apply to horizontal pipes. Flow Fluid Properties Superficial Velocities The superficial velocity of each phase is defined as the volumetric flow rate of the phase divided by the cross-sectional area of the pipe as though that phase alone was flowing through the pipe.

Since the liquid phase accounts for both oil and water: The oil, water, and gas formation volume factors BO, BW, and Bg are used to convert the flow rates from standard or stock tank conditions to the prevailing pressure and temperature conditions in the pipe. Since the actual cross-sectional area occupied by each phase is less than the cross-sectional area of the entire pipe, the superficial velocity is always less than the true in-situ velocity of each phase.

Mixture Velocity Mixture velocity is another parameter often used in multiphase flow correlations. The mixture velocity is given by: These in-situ velocities depend on the density and viscosity of each phase.

Typically the phase that is less dense flows faster than the other. This causes a "slip" effect between the phases. As a consequence, the in-situ volume fractions of each phase under flowing conditions will differ from the input volume fractions of the pipe.

If the slip condition is omitted, the in-situ volume fraction of each phase is equal to the input volume fraction. Because of slippage between phases, the liquid holdup EL can be significantly different from the input liquid fraction CL. In other words, the liquid slip holdup EL is the fraction of the pipe that is filled with liquid when the phases are flowing at different velocities. It can be defined as follows: We can also write them in function of the superficial velocities as: QL is the liquid rate at the prevailing pressure and temperature.

Similarly, QGBg is the gas rate at the prevailing pressure and temperature. The input volume fractions, CL and EL, are known quantities, and are often used as correlating variables in empirical multiphase correlations.

Actual Velocities Once the liquid holdup has been determined, the actual velocities for each phase can be determined as follows: Note that this is in contrast to the way density is calculated for friction pressure loss. Mixture Density Mixture density is a measure of the in-situ density of the mixture, and is defined as follows: Mixture density is defined in terms of in-situ volume fractions ELwhereas no-slip density is defined in terms of input volume fractions CL.

## Gas Flow in Control Valves

No-Slip Density "No-slip" density is the density that is calculated with the assumption that both phases are moving at the same in-situ velocity. No-slip density is therefore defined as follows: No-slip density is defined in terms of input volume fractions CLwhereas the mixture density is defined in terms of in-situ volume fractions EL.

Mixture Viscosity Mixture viscosity is a measure of the in-situ viscosity of the mixture and can be defined in several different ways. In general, unless otherwise specified, is defined as follows: Mixture viscosity is defined in terms of in-situ volume fractions ELwhereas no-slip viscosity is defined in terms of input volume fractions CL. No-Slip Viscosity "No-slip" viscosity is the viscosity that is calculated with the assumption that both phases are moving at the same in-situ velocity.

There are several definitions of "no-slip" viscosity. However, a value is required for use in calculating certain dimensionless numbers used in some of the pressure drop correlations. For intermediate temperatures, linear interpolation is used.