### TOTAL LAG TIME

Single line Application

By Glenn Sheffield

Total lag time for a sample loop is the total internal volume of the transport tubing and conditioning devices divided by the flow rate in consistent units as follows:

T = V÷F

where T = time lag (minutes)

V = volume of components (cm³)

F = sample flow (cm³/min)

This equation should be modified to allow for first order lag and a compressibility factor for a gas sample. First order lag is the amount of time required to displace enough volume through a sample-conditioning device to ensure the sample is representative of a process change i.e., mixing time. This is generally a factor of 3 times the volume.

The compressibility factor for gas reflects the relative density of molecules in a given volume, which is proportional to the pressure of the sample. Taking the absolute pressure of the sample gas and dividing by 14.7 PSIA calculate the compressibility factor. Most gauges are read to the nearest psi, so 15 psi will be used in the examples. Thus the higher the pressure of a gas sample the greater the time required to transport it to the analyzer or to evacuate the sample from a conditioning device.

Temperature has a negligible effect on most field applications. This factor is omitted for simplicity.

The lag time equation for a liquid conditioning device is:

T = (3 x V) ÷ F

where 3 = factor for first order lag

The equation for a gas-conditioning device is:

T = (3 x V x Z) ÷ F

where Z = compressibility factor of gas

Z= (Absolute Pressure) / 15 psi

(Guage pressure psi + 15 psi) / 15 psi

Example: Compressibility factor for 15psig sample pressure would be:

(15 psi + 15 psi) ÷ 15 psi = 2

VOLUME CALCUATIONS

TRANSPORT LINE

Calculating the volume of transport tubing is simplified by using the known volumes of common tubing. The volumes of standard size tubes are as follows:

0.125 inch ( ⅛”) OD tube: 1cc/ft

0.25 inch (¼”) OD tube: 5cc/ft

0.50 inch (½”) OD tube: 30cc/ft

The calculation for the lag time of tubing is:

T = (v/l x L x Z) ÷ F

where T = time lag of transport tube (minutes)

v/l = volume of sample (cc/ft)

L = length of supply tubing (feet)

Z = compressibility factor for gas

F = sample flow (cc/min)

This formula works for liquid, but Z = 1 since liquids do not compress.

SAMPLE CONDITIONING DEVICE

The calculation for the volume of a sample-conditioning device is as follows:

V = π r²h

where π = 3.14

r² = radius of the device squared = (d/2)² = (diameter/2)²

h = the height or length of the device

WORKING EXAMPLE

An analyzer has a single line sample transport system with 100ft. of ¼” tubing from a regulator set at 15psig. Due to the relatively clean sample the only sample-conditioning device is a 3 inch high x 2.5inch wide filter. The flow to the analyzer and bypass rotometer is a total of 1000 cc/min.

What is the lag time of the transport system? What is the lag time of the filter housing? What is the total lag time? Is this considered excessive?

TRANSPORT LAG TIME

T = (V x L) ÷ F

For liquid sample,

T = 5cc/ft x 100ft.= 500cc ÷ 1000cc/min = 0.5 minutes (30 seconds)

For gas sample,

Z = (System pressure psig + 15 psia) / 15 psia.

= (15psig + 15psia) / 15psia = 2 (14.7 psi ≈ 15 psi)

so T = (5cc/min x 100 ft x 2) ÷ 1000cc/min = 1.0 minute (60 seconds for gas)

The transport lag time is 30 seconds for liquid and 1 minute for gas.

CONDITIONING DEVICE LAG TIME:

Dimension for filter: 3 inch high by 2.5 inch wide.

Area = πr² h

π= 3.14 ≈ 3

Converting to consistent volume units (cm),

r = D/2 = 2.5 inch ÷ 2 = 1.25 inch

= 1.25 in. x 2.5cm/inch = 3.1 cm ≈ 3cm

h = 3 inch x 2.5 cm/inch = 7.5 cm

Area - πr² h = 3 x 3² x 7.5 = 202.5 ≈ 200 cm³

200 cm³ x 3 (mixing factor) = 600 cm³

Z = (15 +15)/15 = 2

T = (3 x V x Z) / F

= 200 cm³ x 3 / 1200 cc/min = .50 minutes = 30 seconds for liquid

= 200 cm³ x 3 / 1200 cc/min x 2 (compressibility for gas) = 60 seconds

T (total) = sample transport + conditioning lag

For liquid = 30 seconds + 30 seconds = 1 min.

For gas = 60 seconds + 60 seconds = 2 min.

The rule of thumb is a maximum of 1 minute for transport and 30 second conditioning time.

The following is a comparison of the common filter used for the example above and the Sheffield kinetic separator. The same flow rates and pressures are assumed and thus only the dimensions are changed.

CONDITIONING DEVICE LAG TIME

SHEFFIELD SEPARATOR:

Area = πr² h

π= 3.14 ≈ 3

Total Volume of Sheffield Separator = 66 cm³

First Order Lag for the Sheffield Separator = 1

T = (1 x V x Z) / F

= (1 x 66 cm³ x 2) / 1200 cc/min = .11 x 60 = 6.6 seconds

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