# Summary

For systems where liquid product may be trapped in a pipe section of an extended period of time thermal expansion can become a problem. Heating of the fluid in the pipe results in a rapid pressure rise as the fluid expands which can quickly exceed the design pressure of the pipeline. The damaging effects of the thermal expansion can be mitigated through the use of thermal relief valves and where there is several potential pipe blockages in series, it is often necessary to 'cascade' thermal relief valves back to a tank. This article describes how to design a cascading thermal relief system.

# Definitions

 $$a$$ : Allowable accumulation percentage $$P_{b}$$ : Back pressure on relief valve $$P_{d}$$ : Relief valve differential set pressure $$P_{p}$$ : Design pressure of pipe $$P_{s}$$ : Relief valve set pressure

# Introduction

Often there is a process requirement to shut-in a section of piping using check valves, isolation valves and control valves. If the piping is liquid filled at the time of shut in, subsequent heating of the fluid from sources such as the sun, ambient temperature, nearby process units or heat tracing will cause the fluid to expand, which due to the low compressibility of liquids, will result in a rapid increase in pressure. Thermal relief cascades reduce the pressure built up in an isolated system subject to heating by providing a means by which volume can be displaced as the liquid expands.

## Alternatives to Thermal Relief Cascades

Thermal relief cascades are complicated and require considered design. Before implementing a thermal relief cascade system it is often beneficial to assess the potential alternatives of which a selection is are summarised below.

• Do not shut-in liquid - this is often possible on process plants, a pipe system may be designed such that it is always open to a pressure vessel which will have its own pressure relief system.
• Relieve liquid to ground/sewer - applicable only to non-hazardous/non-polluting material, e.g. water
• Relieve liquid to a slops system - suitable for low value products or when a thermal relief cascade is not feasible.
• Control operationally - if a pipe is only isolated infrequently and deliberately a small amount of liquid may be drained from the line and air allowed to take it's place, the compressibility of the air will prevent pipe overpressure (typically not suitable for combustible or flammable products).

## When to use a Thermal Relief Cascade

The conditions which favour the use of thermal relief cascades over other protection methods are:

• The over-pressure can not be avoided by leaving the line open to a tank or pressure vessel or can not be handled operationally, and
• The product is environmentally sensitive, or hazardous to people and can not be released to the ground, or
• The value of the product is to high to allow thermal relief into a slops system, or
• It is desirable for the system to remain independent of the slops system to avoid down-time.

# Designing a thermal relief cascade

## Identification of Maximum Pressure

Often for a piping system the governing maximum pressure for a thermal relief cascade design will be the design pressure of the pipe itself, however this is not always the case. For some systems there will be other equipment, such as a control valve, flow meter, pump casing or hose which has a lower design pressure than the pipe class. In these cases the design pressure at the location of these 'weaker' pieces of equipment becomes the governing pressure for the thermal relief cascade.

## Set Pressure Margin and Allowable Overpressure

Typically the set pressure of a thermal relief valve will have a manufacturing margin (the uncertainty in the pressure at which the valve will actually open). When dealing with a thermal relief cascade where several valves are installed in series the error in the relief pressure of the system can be significantly increased.

Consider 5 valves in series where there is $$\pm 2 \%$$ error in the set pressure of the device. The potential total error in the series is $$5 \times 2\% = \pm 10\%$$, and therefore the opening pressure of the final thermal relief valves could be up to 10% greater than the desired set pressure.

This may become a factor where there are many relief valves, the set point is close to the design pressure of the system or the operating pressure of the system is close to the set pressure.

## Blowdown and Abnormal Pressures

The blowdown of a relief valve may be 20% below the set pressure. This means that a relief valve may not fully close until the process pressure is 20% lower than the pressure at which the valve begins to open. During the design process, the case in which a thermal relief valve is lifted by an abnormal process condition, such as pressure surge must be considered. There must be sufficient pressure differential between the set pressure and the normal process pressure to allow the valve to reseat after being lifted by abnormal conditions.

If the required differential pressure between the blow down and the normal process pressure is not available the relief valve will continue to pass after the event that causes it to lift. Which may lead to problems such as product contamination or tank overfill and loss of containment.

## Maximum Back Pressure

In an ideal situation a relief valve would be able to lift at the desired differential set pressure regardless of the back pressure on the valve. In practice there are realities of the valve design that prevent this, and it is primarily influenced by the ratio of areas exposed to the process above and below the disk. At low back pressures the resistance to opening is dominated by the spring force and the differential in the area of the valve disk are less significant. At high back pressures the force from fluid pressure is the dominant force, and the area differences may prevent the valve from opening until pressures are much greater than the desired set pressure. The upper limit for constant back pressure is typically 80% of the relief valve set point, however this can vary between vendors.

## Variable Back Pressure

Variable back pressure is the back pressure that builds up due to the flow of fluid through the valve. It is generally very important in the design of relief valves, however in the case of thermal relief the volume is relatively small, and the variable back pressure may be ignored.

## Flow Rate and Accumulated Pressure

When thermal relief valves are installed on short lengths of pipes with less volatile liquids and the pipe is not heated, the flow rate through the valve may be ignored, as it will be trivial and any standard orifice will be large enough to handle the capacity.

Cases where the flow rate becomes important are very long above ground pipelines, volatile liquids (e.g. LNG), and heated piping (e.g. Bitumen piping). In these systems the relief volume should be checked as it may exceed the capacity of smaller relief valves.

In most pressure vessel protection applications a relief valve is sized based on a allowable overpressure of 10% (i.e. valve reaches rated flow rate at 110% of the set pressure of the valve). This is not always acceptable for thermal relief cascade systems, because the set pressure of the valve includes both the differential set pressure of the valve and the superimposed back pressure. In thermal relief cascades the superimposed back pressure can be very high.

For the system shown above the flow rate and accumulation determines whether the system can be over pressured, despite having an identical thermal relief cascade. This will be explored in the following examples.

### Example 1: Low flow rate

Where the flow rate is low (e.g the pipe length is short and contains a liquid of low volatility) the accumulated pressure is not important because the relief valves will pass the liquid before any pressure accumulates. Only the set pressure of the valves and any constant back pressure needs to be considered.

• Pipe design pressure: $$P_{p} = 1000 \text{ kPa}$$
• Relief valve set pressure: $$P_{s} = 300 \text{ kPa}$$
$$\begin{split} P &= P_{s} + P_{s} + P_{s} \\ &= 300 + 300 + 300 \\ &= 900 \text{ kPa} \\ P &< P_{p} \end{split}$$

### Example 2: High flow rate

Where the valve is required to be full open to achieve the require flow rate, each valves set pressure is a function of the relieving pressure of the downstream valve.

$\displaystyle P = a \times \left( P_{s} + P_{b} \right)$

• Pipe design pressure: $$P_{p} = 1000 \text{ kPa}$$
• Relief valve set pressure: $$P_{s} = 300 \text{ kPa}$$
• Accumulation to reach full flow: $$a = 10\%$$ set pressure

For the valve closest to the tank:

$$\begin{split} P &= 110 \% \times \left( 300 + 0 \right) \\ &= 330 \text{ kPa} \\ P &< P_{p} \end{split}$$

For the second valve:

$$\begin{split} P &= 110 \% \times \left( 300 + 330 \right) \\ &= 693 \text{ kPa} \\ P &< P_{p} \end{split}$$

For the final valve:

$$\begin{split} P &= 110 \% \times \left( 300 + 693 \right) \\ &= 1092 \text{ kPa} \\ P &> P_{p} \end{split}$$

Due to the accumulation across the three valves the pipe is over pressured.