# Sampling System Design: Managing System Variables

By Randy Rieken |

*Understanding the effect of flowrate, velocity, density, viscosity, pressure drop, friction, components and sample line sizes will help you design a sampling system*

The primary goal when designing an analytical sampling system is to ensure timely, accurate measurements. The sooner you can discover anomalies in a process stream, the sooner you can react to correct them. To meet this goal, your sampling system should minimize time delay, or the total time elapsed from tapping the process stream to completing sample analysis. It should also ensure that the sample is not contaminated and accurately represents true process-stream conditions. This may require some form of conditioning, such as maintaining sample temperature, as the sample moves from the process tap to the analyzer.

An additional consideration is to minimize the amount of material sampled to reduce waste and not disrupt the process stream. If the sampling system is a single-line setup that disposes of sample material via a vent, flare, or drain (Figures 1a and 1b), you should minimize the flowrate to avoid wasting an excessive amount of process fluid. If it’s a fast-loop system that returns the sample to process (Figures 1c and 1d), make sure the flowrate isn’t so high that it interferes with the process stream.

To achieve the above guidelines, you’ll need to experiment with and refine multiple variables related to your system layout and performance, including the following:

** Type of flow.** Turbulent flow is typically preferred over laminar flow in a sampling system to ensure the sample is properly mixed. A parameter known as the Reynolds number (Re) will help you determine whether the flow is laminar or turbulent and to what degree.

** Fluid properties.** The fluid’s velocity, density, and viscosity are all variables that are included in the Re equation. These variables can be manipulated in some manner in an effort to achieve turbulent flow.

** Pressure differential.** The pressure drop between the process tap and the return point in a fast-loop system must be sufficient to drive the desired flow through the lines. The Darcy equation will help you determine the pressure loss and whether you need to adjust flow velocity or line diameter.

** Friction factor.** Sampling lines with a lower friction factor help to reduce pressure drop. System operating conditions influence the friction factor, and it will need to be recalculated with any system changes.

** Bends, fittings and components.** Longer sampling systems experience lower velocities and greater pressure drops. Simply reducing their overall length, including the number of bends, could yield the desired performance for a system. When determining a system’s actual length, include the sampling lines, as well as the equivalent lengths of all the components. Equivalent lengths represent the internal flow paths of elbows, tees, valves, returns and more converted into the length of a straight tube or pipe to account for the resistance of the entire flow path.

** Diameter of sampling lines.** The right sampling line size depends on your target response time and the available source pressure. Sometimes adjusting both supply line and return line sizes will help; other times changing just one line will be the right choice.

Based on the above variables, your system design process will take some trial and error. First, gather all known information about the system, and then try manipulating different variables to determine if you can achieve your desired performance.

Note that these variables are highly interrelated. A single adjustment may require complete reworking of your calculations. This article will help give you a better understanding of how these variables are correlated. In addition, it includes a comprehensive design example for a fast-loop sampling system (see sidebar below), which demonstrates how modifying just one variable can help you achieve the desired time delay, accuracy, and flowrate for your sampling system.

## Fluid velocity in the line

Start by deciding the velocity you need. This is a fundamental design objective. Usually, it’s sufficient to simply divide the sample line length in meters by the transport time desired, *t*.

*u* = *L*/ *t* (**1**)

Where:

*u* = Fluid velocity, m/s

*L* = Line length, m

*t* = Desired transport time, s

For example, if the sample line is 100 m long and you want to limit the delay to one minute, the required velocity is *u* = *L*/ *t* =100 m/60 s = 1.7 m/s.

If possible, ensure that the velocity is greater than 1 m/s, as this will help to keep the lines clean. A velocity of 1–3 m/s is recommended for liquids and 2–5 m/s for gases.

## Turbulent or laminar flow

The flow within the lines of your analytical sampling system will have one of two types of patterns — laminar or turbulent (Figure 2). Each type is highly dependent on the velocity of the sample fluid, as well as the density and viscosity of the fluid.

Turbulent flow is typically preferred, as it enables faster analyzer responses and minimizes the settling of solids in sample lines to avoid contamination and clogging. However, turbulent flow isn’t always achievable. Sometimes you’ll have to accept the inherent deficiencies of laminar flow, including slower analysis.

Evaluating the Reynolds number (Re) is an easy way to determine the type of flow. This value provides a relative marker of the flow type and the degree to which it is laminar or turbulent. An Re value less than 2,000 typically indicates laminar flow. And an Re value of 4,000 or more indicates turbulence. However, turbulence usually begins before the Re reaches 4,000, but only to a degree. Therefore, you can’t accurately define the type of flow if your Re is in the critical zone between 2,000 and 4,000.

The Reynolds number (Re) can be calculated using Equation (2):

(**2**)

Where:

*D*’ = Line internal diameter, mm

ρ = Fluid density, kg/m^{3}

*u* = Fluid velocity, m/s

η’ = Fluid viscosity, cP

To achieve a suitable turbulent flow, you may need to adjust some system variables, including the internal diameter of sample lines and the fluid velocity. Table 1 demonstrates how the Re value increases as line size increases. In addition, you can sometimes manipulate the density and viscosity of the fluid by adjusting the pressure and temperature of the sample lines.

It helps to know the density-to-viscosity ratio (ρ/η) of the sample fluid. Generally, a higher ρ/η ratio favors turbulence (see Tables 1 and 2). Application conditions may have an effect on the ρ/η ratio, so it’s good to know how pressure and temperature influence the ratio — and therefore turbulence — for both liquids and gases.

** Liquids.** For liquid samples, pressure changes will barely affect density or viscosity, and therefore system turbulence. However, temperature changes can influence the ρ/η ratio, as higher temperatures reduce viscosity, which increases flow and potentially turbulence.

** Gases.** For gas samples, increased line pressure has no effect on viscosity, but it compresses the gas, thereby increasing its density and the ρ/η ratio, favoring turbulence. And while increased temperature reduces the density of gas samples and increases their viscosity, the net effect is relatively small. Line temperature is usually set to avoid condensation without worrying about its effect on turbulence.

## Calculating pressure drop

A sampling system must have enough of a pressure differential between the process tap and the return point to drive the desired flow through the lines to achieve the desired response time. If not, you’ll have to modify the design, perhaps by using a larger return line.

Pressure will drop naturally within the sampling system due to a variety of factors, including line length and diameter, the number of bends in a system, elevation changes, friction, sample fluid density, and flow velocity. The system must be designed so it performs as desired when operating with the pressure differential actually available in the plant. To ensure this happy result, compute the expected pressure loss in your system design using the Darcy equation.

(**3**)

Where:

Δ *P* = Change in pressure, Pa

*f* = Friction factor

*L =* Line length, m

ρ = Fluid density, kg/m^{3}

*u =* Flow velocity, m/s

*D* = Line internal diameter, m

Entering all values in coherent SI units yields a Δ *P* value in Pascals. Alternatively, you can use millimeters for the line diameter (*D*’) to determine the pressure drop (Δ *P*’) in kiloPascals:

(**4**)

When making any adjustments to your system, your design work will focus on the flow velocity (*u*) and the line diameter (*D*), as application conditions fix the other variables.

## The friction factor

When using the Darcy equation (Equation (3)), remember that the friction factor (*f*) is not a constant. This measure of the effect of friction on the walls of the sample lines varies with operating conditions.

As a resource, Table 3 provides friction factors for the limited range of tube and pipe sizes commonly used for sample lines. For tubes and pipes not shown, you can retrieve a friction factor from the Moody chart shown in Figure 3. To look up a value, you need to know the Re of the system and the relative roughness (ε’/*D*’) of the inside walls of the sample lines. Notice that the friction factor decreases as the Re increases, indicating that there’s less resistance to flow — and therefore less pressure drop — at higher Re values, assuming other variables remain constant.

The relative roughness of the tube or pipe is the ratio of absolute roughness (ε) to its internal diameter (*D*):

(**5**)

It is convenient to enter the values of ε and *D* in millimeters.

The absolute roughness is the actual wall irregularity of the tube or pipe, and it doesn’t change much with diameter — typically 0.0015 mm for tubing and 0.05 mm for pipe.

Once you determine the Re and the relative roughness, estimate the friction factor from the Moody chart. The pressure drop is directly dependent on this value. Insert your number into the Darcy equation and figure the pressure loss in your line.

## Allowing for bends

The number of bends in a sampling system contributes to pressure drop. Each sharp bend adds length ( *L*), causing some additional pressure loss that you’ll need to account for in your calculations. When possible, install lines with gradual bends, as the minimal additional length will barely affect the pressure drop. If this is impractical and you must use elbows — whether fittings or bent tubing — assign an equivalent length to each bend to account for the pressure drop it causes.

Table 4 lists some typical equivalent lengths expressed as multiples of the internal diameter. Multiply the appropriate length-to-diameter (*L*/*D*) value by your line bore to get the equivalent length of each tube bend or fitting.

For example,½-in. tube has a bore of about 10 mm, and a 90-deg tubing elbow has an *L*/ *D* ratio of 60. Therefore, each elbow tube fitting adds an extra 0.6 m to the length of the line (0.01 m × 60 = 0.6 m).

Add those figures to the actual line length, and use the total value for *L* in the Darcy equation to calculate the pressure drop. If you don’t have enough Δ *P*, you may need to reduce the number of bends.

## Sound designs

Mastering the art of manipulating numerous variables and understanding the effect of flowrate, velocity, density, viscosity, pressure drop, friction, components, and sample line sizes will help you achieve sophisticated sampling-system designs that provide timely and efficient analyses. But there’s more to consider.

Even seemingly trivial details can impact the performance of the system, such as where to locate the tap for the sampling system; how to orient the tap nozzle; whether to use a probe and, if so, what style probe and how to orient it; if the system uses filters; and numerous other variables. Although not addressed above, these variables should also be considered in your design.

When designing your sampling system, above all else, recognize that you’ll need to be patient. Achieving a proper design takes time. But the rewards of accurate, efficient analysis will certainly pay off for years to come.

## Reference

1. This article was adapted from: Waters, Tony,“Industrial Sampling Systems: Reliable Design and Maintenance for Process Analyzers,” Swagelok Company, 2013. For more information, go to www.industrial-sampling-systems.com.

## Author

Randy Rieken is market manager for chemical and refining at Swagelok Company (29,500 Solon Road, Solon, Ohio 44139; Phone: 1-440-248-4600; Email: randy.rieken@swagelok.com). He is responsible for the development and implementation of chemical and refining market-driven strategies. Rieken joined Swagelok in November 2014 and has over 25 years of global business development experience providing engineered fluid-control components, subsystems, and instrumentation solutions for the most critical applications in the oil-and-gas, chemical, semiconductor, power, and life sciences markets.

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