Guidelines for Sizing of Restriction Orifice for Single-phase Fluids

In our last article, we discussed restriction orifices in detail. The same article also lists the important factors on which the sizing of a restriction orifice depends. Click here to recapitulate those before proceeding with actual RO sizing steps.

Of many kinds of flow restriction devices, restriction orifices (RO) are frequently used, because they are simple and economical devices. RO is applied to regulate the flow rate or pressure. This article will provide the guidelines for the sizing of the Restriction Orifice. It should be noted that this standard practice is applicable to single-phase fluids only.

Inputs Required for Restriction Orifice Sizing

The following is a summary of input data to be prepared for the design of RO:

(1) Operating Conditions

• Flow rate
• Upstream & downstream pressure
• Temperature (for vapor)
• Line Size

(2) Physical properties

• For liquid service: density, vapor pressure
• For vapor service: molecular weight, Cp/Cv, Z-factor, viscosity

(3) Minimum allowable value of cavitation index for liquid service

Output from the Restriction Orifice Design

(1) Single orifice

• Orifice diameter
• The pressure at vena-contracta
• Velocity at orifice
• Calculated cavitation index (for liquid)
• Critical or non-critical (for vapor)

(2) Multi-stage orifice

• Required stage number
• Orifice diameter of each orifice
• Distance between adjacent orifice plates
• Inlet and outlet pressures of each orifice
• The pressure at vena-contracta of each orifice
• Velocity at each orifice
• Calculated cavitation index of each orifice

Principles of RO Sizing Calculation

Flow restriction orifice calculation for Gas Service

Critical Pressure Ratio:

The critical pressure ratio, r_c can be obtained from the following equation.

Orifice Diameter:

The equation for orifice diameter should be selected using equation (2), depending on whether the flow is critical or non-critical.

(A) Critical flow (sonic region)- When the ratio of downstream pressure to upstream pressure, r4, is smaller than or equal to the critical pressure ratio, r_c, the following equation of orifice diameter for a critical flow should be used.

(B) Non-critical flow (subsonic region)- The following equation of orifice diameter can be used for the non-critical flow region.

Restriction orifice calculation for Liquid Service:

Orifice Diameter:

Cavitation Index

In order to avoid the cavitation problem, the minimum allowable value of the cavitation index, K_d, should be selected based on the following:

(1) Cavitation index K_d=0.37 shall be used for the usual case. At this critical cavitation condition, the noise is steady but still light. No erosion will occur. (Once the orifice chokes and supercavitation occurs, no damage by erosion will exist near the orifice. This is because the damage is caused by the collapse of the cavities and the collapse occurs far downstream during supercavitation)

(2) On some occasions such as in the following cases, use K_d=0.93 as an incipient cavitation condition in order to avoid severe economical risk.

• Material is high grade such as stainless steel or higher and pipe size is larger than 12”.

Interval of Orifices

In the case of the multi-stage restriction orifice, the minimum distance, as shown below, should be provided between orifices, to avoid a reduction in RO performance.

• For concentric orifice: L ≥ 5.4*D*(1-β)
• For eccentric orifice: L ≥ D

Deflection Ratio of Eccentric Orifice

The deflection ratio of the eccentric orifice “e” is 0.75.

e = 2δ /(D − d₀ ) = 0.75 (14)

Where,

• δ: Pipe center to orifice center length (m)
• d₀: Orifice hole diameter (m)
• D: Pipe inside diameter (m)

Restriction Orifice Plate Sizing Calculation Procedure

A. Single RO system-

① Decide the minimum allowable value of the cavitation index to meet a given situation.

• K_d = 0.37: for the usual case
• K_d = 0.93: for the conservative case

② Assume d_O and calculate β by equation (8).

③ Incompressible coefficient of contraction CCi shall be calculated by equation (7).

④ Orifice diameter (d_O) shall be calculated by equation (13).

⑤ Compare the assumed d0 with the calculated d_O in step ④.

⑥ Calculated d_O shall be replaced with the previous d_O and repeat step ② to step ⑤ until the dO agrees with the calculated d_O.

Calculate the cavitation index, K_d by equation (15), and compare it with the minimum allowable value.

If the cavitation index ≥ 0.37 (or 0.93), then the orifice diameter is acceptable.

If the cavitation index < 0.37 (or 0.93), then a single orifice is unable to accommodate the required pressure drop. In that case, a multi-stage orifice system should be applied.

B. Multistage Restriction Orifice Calculation

① Decide the minimum allowable value of the cavitation index to meet a given situation.

• Kd = 0.37: for the usual case
• Kd = 0.93: for the conservative case

First stage orifice: located at the outlet

② Assume upstream pressure of the first stage orifice.

③ Assume d_O and calculate β by equation (8) for the first stage orifice.

④ Incompressible coefficient of contraction CCi shall be calculated by equation (7).

⑤ Orifice diameter (d_O) shall be calculated by equation (13) using assumed upstream pressure.

⑥ Compare the assumed d₀ with the calculated d_O in step ⑤.

⑦ Calculated d_O shall be replaced with the previous d_O and repeat step ③ to step ⑥ until the dO agrees with the calculated d_O.

⑧ Calculate cavitation index, K_d, using Equation (15), and compare with minimum allowable value.

If the cavitation index > 0.37 (or 0.93), increase the upstream pressure and repeat the steps from ③ to  ⑧.

If the cavitation index < 0.37 (or 0.93), decrease the upstream pressure and repeat the steps from ③ to ⑧.

If the cavitation index equals or slightly bigger than 0.37 (or 0.93), the design of the first stage RO is completed and go to step ⑨.

n-th stage orifice

⑨ Set the upstream pressure of (n-1)-th stage orifice for the downstream pressure of the n-th stage orifice.

⑩ Assume the upstream pressure of the n-th stage orifice.

⑪ Repeat the steps from ③ to ⑧, until the cavitation index is equivalent to the minimum allowable value.

Special Consideration of RO Design:

(1) The minimum hole diameter of RO-

To prevent the plugging problem with RO caused by debris, the hole diameter should be greater than the following values:

• For the clean liquid service: 2mm
• For the clean Gas service: 1mm

When a diameter smaller than the above values is required, the strainer or filter to remove debris should be provided upstream of RO.

(2) The necessity of minimum straight run length-

Basically, the objective of RO is rough control of the flow rate and should not be used for strict control of the flow rate. Therefore, it should not be necessary to take a straight run of piping both upstream and downstream of RO to keep performance. However, for erosional services such as slurry or flush services, countermeasures for erosion shall be considered.

(3) The calculated hole diameter of RO should be rounded to the conservative size for easy manufacturing.

Restriction Orifice Sizing Spreadsheet

A restriction orifice sizing spreadsheet is an electronic tool or software program that helps in calculating the size of a restriction orifice based on various parameters such as flow rate, fluid properties, pressure drop, and pipe dimensions. Often they may come in the form of restriction orifice calculation excel.

Restriction orifices are used in piping systems to control the flow rate of a fluid, and their proper sizing is crucial for the system’s safe and efficient operation. A restriction orifice sizing spreadsheet typically uses industry-standard equations and formulas to calculate the required orifice diameter and other necessary parameters.

The input parameters required for the calculation typically include fluid density, viscosity, pressure, temperature, pipe diameter, and the desired pressure drop across the restriction orifice. The spreadsheet then calculates the required orifice diameter and other related parameters such as Reynolds number, velocity, and flow rate.

The use of a restriction orifice sizing spreadsheet can simplify the orifice sizing process and reduce errors associated with manual calculations. However, it is essential to use reliable and accurate spreadsheet templates or software programs and to validate the results obtained from the spreadsheet against industry standards and guidelines.

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