The API states the following about tube rupture for a shell-and-tube heat exchangers:

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1 Tutorial This tutorial describes the theory and modeling process of a tube rupture event using the special element type Rupture element in BOSfluids. It covers the algorithm BOSfluids uses to model the rupture event and a worked out example of how to include a rupture element in a system.

2 1. INTRODUCTION This tutorial gives a basic introduction in using the element type, Rupture Element in BOSfluids. This element is used to simulate high pressure tube ruptures in heat exchangers. When a high pressure tube ruptures into a low pressure shell there will be an increase in pressure in the shell. The shell is usually protected by a pressure relief valve or rupture disk. The tube rupture and resulting pressure increase takes place in just a few milliseconds, the peak shell pressure is often attained in roughly 10 ms after a tube rupture. The pressure relief valve protecting the heat exchanger from overpressure needs some time to react; besides it also takes some time for the pressure wave to travel from the tube rupture location to the relief valve. In this time the pressure in the shell may further increase. As an alternative to a pressure relief valve, a rupture disk can be used. Rupture disks provide a faster response time to an increase in pressure. A rupture disk is commonly used as backup for pressure relief valves, in the scenario a pressure relief valve fails or does not relief the pressure fast enough. It is important that tube rupture events in heat exchangers are studied to choose an appropriate pressure relieve valve size and/or rupture disk. The API states the following about tube rupture for a shell-and-tube heat exchangers: In shell-and-tube heat exchangers, the tubes are subject to failure from a number of causes, including thermal shock, vibration, and corrosion. Whatever the cause, the result is the possibility that the highpressure stream will overpressure equipment on the low-pressure side of the exchanger. Economical design usually dictates that the higher-pressure stream flow through the tubes, since this can result in a thinner shell, but this is not always the case. The pressure relationships must be known to evaluate the results of tube failure properly. The ability of the low-pressure system to absorb this release should be determined. The possible pressure rise must be ascertained to determine whether additional pressure relief would be required if flow from the tube rupture were to discharge into the lowerpressure stream Low Pressure Tube Rupture The rupture element can also be used to describe a low pressure tube rupture into high pressure gas-filled shell. This tutorial describes such a problem. The basic principle of modelling a tube rupture in BOSfluids is outlined, including calculations that need to be performed to accurately model the tube bundle. The result of the simulation will be a pressure profile which can be used to size a safety relief valve. Copyright Dynaflow Research Group. Page 1 of 8

3 2. CONSTRUCTING THE MODEL A shell-and-tube heat exchanger is modeled in BOSfluids to simulate a shell side tube rupture. The heat exchanger consists of a shell containing methane at high pressure and a tube bundle containing low pressure water. The problem is schematically represented in Figure 1. Figure 1 Schematic of the heat exchanger 2.1. BOSfluids model Figure 2 Nodal description of the heat exchanger model in BOSfluids The heat exchanger will be modeled in BOSfluids as shown in Figure 2. The effective tube bundle is modeled from node 5 to 10, the channel cover from node 10 to 15 and the ruptured tube element from node 12 to 16. Rupture elements must be connected to two pipe elements. The high pressure influx will be applied to the system in between two pipe segments ends, with one of the pipe elements defined with a dead end. Before actually creating the BOSfluids model, the effective parameters for the equivalent tube bundle must be calculated. The effective internal area of the equivalent tube must be the same as the total area of the tube bundle: Tube OD Wall thickness Tube ID Page 2 of 8 Copyright Dynaflow Research Group.

4 Tube Area Total Tube Bundle Area The effective inner diameter is calculated as: ( ) Also an effective friction factor friction-to-diameter ratio of a single tube: needs to be determined. This is calculated from the The friction factor f of a single tube is calculated from the Colebrook-White friction factor expression, where the single tube roughness ε is taken as in: ( ) ( ) The effective friction factor is now calculated as: Again using the Colebrook-White expression the effective roughness is calculated as: To determine the thickness of the equivalent element, the speed of sound in the equivalent element must be equal to the speed of sound in a single tube: This means the diameter-to-thickness ratio of the effective tube needs to be equal to the diameter-to-thickness ratio of a single tube: Copyright Dynaflow Research Group. Page 3 of 8

5 The effective outer diameter is therefore: Having calculated the parameters for the equivalent tube, the BOSfluids model can be made Creating the BOSfluids model Create a new model and add the following elements. Table 1 Model Elements Element Length Element Type Parameters 5-10 Z-dim : -192 in Pipe OD = 9.19 in, t = 1.34 in, ε = 3.36 in X-dim : -24 in Pipe OD = 17.9 in, t = in, ε = in X-dim : -24 in Pipe OD = 17.9 in, t = in, ε = in Z-dim : 6 in Rupture element see Table 2 The rupture element is defined as: Table 2 Rupture Element parameters Tube diameter in Discharge coefficient 1 Rupture time sec Number of tubes 1 Gas temperature 300 F Gas Pressure 440 psig Specific Gas constant ft.lbf/lbm/r Cp/Cv 1.4 Pressure Exponent Boundary conditions The shell side pressure has been defined as part of the tube rupture element. The tube side pressure is defined in the model at node 5 as 50 psig. Page 4 of 8 Copyright Dynaflow Research Group.

6 Node 15 is specified as a dead end in the model. BOSfluids automatically defines dead ends on nodes that are connected to only one element and have no boundary condition defined. However the user is encouraged to explicitly specify dead ends when applicable. Table 3 Boundary conditions Node Boundary condition Value 5 Fixed Pressure 50 psig 15 Dead end - The completed model should look like Figure 3. Figure 3 The completed model of the heat exchanger Analysis Settings A transient analysis is performed using the fluid properties of water on the tube side. Given the short tube rupture time of seconds, the simulation time and output interval need to be appropriately defined to capture the transient phenomena of interest. Define the simulation time to be 0.25 seconds with an output interval seconds. All other options can remain as default, see Figure 4. Copyright Dynaflow Research Group. Page 5 of 8

7 Figure 4 The transient analysis settings Proceed to the Run tab and run the simulation. Page 6 of 8 Copyright Dynaflow Research Group.

8 3. RESULTS Figure 5 shows the pressure increase at node 10, the entrance of the equivalent tube bundle. Figure 5 The pressure at node 10 From Figure 5 it can be seen that the pressure peak reaches a maximum of 414 psig, 7 ms after the shell side tube rupture takes place. Once the pressure rise and time period of the pressure peak in the heat exchanger is known, an appropriate pressure relief valve or rupture disk can be chosen. The current BOSfluids model can be extended to include the pressure relief valve/rupture disk and adjoining piping to analyze the influence of relief valve size on the pressure peak and the forces on remainder of the piping. Figure 6 The pressure at 7 ms Copyright Dynaflow Research Group. Page 7 of 8

9 4. EXTENDING THE MODEL Extending the model to include the piping network of the heat exchanger allows for more advanced analyses to be performed. The model illustrated in Figure 7 shows a heat exchanger including piping network. Figure 7 Advanced tube rupture model of a heat exchanger In the extended model we can observe the pressure peaks within the shell/tube of the heat exchanger, but also the pressure wave propagating through the piping network and the unbalanced forces that result from the rupture. With this model the pressure relief valve and/or rupture disk in the system can be sized, but also a dynamic study can be performed. The unbalanced forces calculated in the transient solution of BOSfluids can be exported to a pipe stress software package (i.e. CAESAR II) to examine the impact of the unbalanced forces on the restraints of the piping system due to the tube rupture. Figure 8 3D visualization of the unbalanced forces on the piping network due to a tube rupture Page 8 of 8 Copyright Dynaflow Research Group.