**3.1 Presentation of the steam boiler used for this study**

 The steam boiler used in this chapter is a water-tube, radiant type, and high power, with natural circulation from an ABB ALSTOM brand. It is installed in the natural gas liquefaction (NGL) complex which is operated by SONATRACH Company; is located at 5 km east side of Skikda, Algeria; and has been in production since 1970 [22]. The complex contains six units, each one equipped with a steam

boiler, to provide superheated steam primarily for driving a turbine, therefore making energy available to the unit [22].

This boiler operates at high heat flux density to produce 374 t/h of superheated steam at 73 bars and 487°C with a design thermal efficiency around 92% [2, 22]. It is composed of three main parts: the steam generator, the superheated steam line, and the feedwater line. A schematic representation of the steam boiler installation is illustrated by **Figure 6** [1, 2].

**Figure 6.**  *Steam boiler installation [1].* 

**Figure 7.**  *Longitudinal section of the steam generator [2].* 

The entire plant can be subdivided into three main parts, the feedwater line, which refers to the saturated liquid phase, the steam generator, and, finally, the main steam line and its transformations. The steam generator consists of one drum and two main parts; the first concerns the combustion chamber, and the second

*Numerical Simulation of the Accidental Transient of an Industrial Steam Boiler DOI: http://dx.doi.org/10.5772/intechopen.86129* 


#### **Table 2.**

*Steam boiler operating parameters.* 

 is the rear pass materialized by the water walls that form the evaporating tubes. The rear pass receives the superheaters at high and low temperatures at the top and the economizers below. The steam boiler is designed to operate by combination of automatic and manual operation. The main feedwater line includes the collection tank, two feed pumps, tree economizers, control and isolation valves, and feed piping. The main steam line is constituted by high and low superheaters, steam piping, pipeline of desuperheater, and control and safety valves. The steam generator shown in **Figure 7** [2] and the main operating characteristics of the steam boiler are given in **Table 2**.

 The heat transfer between the wall of the tubes and the combustion gases is generally done by two modes, radiative and convective [23]; in radiant steam boilers, as the name suggests, it receives almost the heat by radiation: convection and conduction represent only 5% [19, 20]. The heat received by the water walls is conducted through the membranes and walls of the tubes and transferred by forced convection to nucleate boiling to the water/vapor mixture in the vaporizer tubes.

The installation contains two control loops: water level control in the drum and superheated steam temperature control, in order to maintain the stable operation of the steam boiler. A detailed description of the steam boiler plant can be found in Ref. [1, 2].

#### **3.2 Adopted code and nodalization**

#### *3.2.1 RELAP5/Mod3.2 code presentation*

 The Reactor Excursion and Leak Analysis Program (RELAP5) is a best-estimate nuclear system code; it was developed at Idaho National Engineering Laboratory (INEL) at the request of the US Nuclear Regulatory Commission (NRC) [15]. It is mainly used for the transients' analysis of light-water reactor (LWR); however, the generalization of the RELAP5 code allowed its application to the nuclear and nonnuclear fields [1, 4, 11]. It has been designed to simulate the thermal-hydraulic behavior of installations during accidental or incidental transients. RELAP5 is based on a nonhomogeneous and nonequilibrium hydrodynamic model for the two-phase system. It solves the unstable and one-dimensional equation of mass, energy, and momentum for each phase using the semi-implicit finite difference numerical method [15, 24].

 The series of RELAP codes are started by Reactor Leak and Power Safety Excursion (RELAPSE). Previous versions of the RELAP code are RELAP2 and RELAP3, where the name RELAPSE has been changed to RELAP. All these versions are based on equilibrium homogeneous model for two-phase flow [15]. The development of a model of nonhomogeneous nonequilibrium was undertaken for RELAP4. In 1976, the last version (RELAP4/MOD7) of this series of codes has been released. It is clear that a complete rewrite of the code was required to effectively accomplish this goal. The result of this effort was the beginning of the RELAP5 project [15]. RELAP5/MOD3 is the third major release of the RELAP5 thermal-hydraulic system code which was realized in 1985. It is written in FORTRAN 77 for a variety of 64-bit and 32-bit computers. The latest version of the RELAP5 (RELAP-3D) code simulates three-dimensional thermal-hydraulic and neutron phenomena.

RELAP5 is designed in a modular way, using an ordered structure. The procedures and the models are separated into sub-programs and constitute the basis of thermal, hydraulic, and neutronic treatment. An option introduced makes it possible to perform the various calculations related to the steady state, by using the following algorithms:


Parameters such as pressure, flow rates, and densities would adjust quickly, but the thermal effects evolve more slowly. The accelerated transient technique is therefore used to reduce the transient computation time required to reach steady state. The transient calculation is characterized by the temporal variation of one or more variables related to the studied problem. Usually, the transient regime must be preceded by a well-established steady state in which the initial conditions of the simulated accident are completed. The introduction of the initial values is necessary for the execution of a problem either in the steady state or in the transient state. These values are provided by the user in the input for each component [15].

 The RELAP5/MOD3.2 code includes many generic component models for the modeling of various systems and physical phenomena such as pipe, pump, turbines, separators, valves, accumulator, point kinetics of reactors, heat structure, control system component, etc. [25]. In addition, other special process models are introduced for the different form losses, flows in pipes with variable surfaces, branching and choked flow, and others. The programming of the various hydrodynamic calculations is based on a concept of volumes and junctions. System simulation consists to subdivide the plant into components connected by flow junctions. The main component models that are introduced in the RELAP5/MOD3.2 code are grouped in **Table 3**.

The code allows the calculation of the heat transfer through the solid walls, delimiting the hydrodynamic volume. Heat structures are solid elements that generate heat or not, put in contact with the fluid volume. Each heat structure is defined by the indices of the left and right control volumes, the solid volume, its thickness, and the type of the material. The heat transfer modeling of metal structures usually *Numerical Simulation of the Accidental Transient of an Industrial Steam Boiler DOI: http://dx.doi.org/10.5772/intechopen.86129* 


#### **Table 3.**

*Main thermal-hydraulic components of the RELAP5/Mod3.2 code [25].* 

includes fuel rods and plates (source of electrical heat or nuclear), heat transfer through the tubes of the steam generator, and the heat transfer to the walls of pipes and tanks in the case of a reactor. The temperature distribution in the heat structures is represented by one-dimensional heat conduction in spherical, rectangular, or cylindrical coordinates. The thermal conductivity and the heat capacity can be simulated by a series of tabulated values according to the temperature or a given function. The integral form of the heat conduction equation is given by expression (1), and finite differences are used for solving this equation [26].

$$\iiint\_{\overline{v}} \rho \, \mathcal{C}\_{\mathcal{P}}(T, \overline{\boldsymbol{x}}) \, \frac{\partial T}{\partial t}(\overline{\boldsymbol{x}}, t) \, dV = \iint\_{\overline{v}} \mathbb{k}(T, \overline{\boldsymbol{x}}) \, \overline{\nabla} \, T(\overline{\boldsymbol{x}}, t) \cdot d\overline{\boldsymbol{s}} + \iint\_{\overline{v}} \mathbb{S}(\overline{\boldsymbol{x}}, t) \, dV \tag{1}$$

The heat transfer model of the RELAP5 code divides the thermal transfer between the two phases—liquid and vapor (**Figure 8**). The total heat flux Q takes the following expression [26]:

$$\mathbf{Q} = \mathbf{h}\_{\mathbf{g}} \left( \mathbf{T}\_{\mathbf{w}} - \mathbf{T}\_{\text{ref}} \right) + \mathbf{h}\_{\mathbf{f}} \left( \mathbf{T}\_{\mathbf{w}} - \mathbf{T}\_{\text{ref}} \right) \tag{2}$$

where hg: coefficient of heat transfer to steam; hf: coefficient of heat transfer to liquid; Tw: wall temperature; Trefg: vapor reference temperature; Treff: liquid reference temperature.

**Figure 8.**  *Heat transfer process.* 

**Figure 9.**  *Discretization scheme.* 

The reference temperature can be the local temperature of liquid and vapor or the saturation temperature, all depending on the heat transfer correlation used. The wall

 temperature is calculated implicitly, and the reference temperature can be variable during the calculation. Wall-fluid heat transfer is subdivided into three regimes: condensation, convection, and boiling [26].

**Figure 9** illustrates the position of the different nodes (mesh points) for the temperatures' calculation. Each interval may contain different spacing between nodes, different materials, or both. The interval between nodes takes an axial direction for a rectangular structure and a radial direction for a cylindrical or spherical structure. Heat sources can be simulated by the kinetics of the reactor (nuclear source), a series of tabular values as a function of time, or by a control variable.

The code permits the introduction of different boundary conditions such as isolation conditions of tubes, surface temperature tables as a function of time, and atmospheric losses. These boundary conditions can be simulated in different ways: imposed heat flow, imposed temperature, and convection coefficient. A heat transfer correlation series is used to calculate the heat transfer between the circulating fluid and the metal structures connected to the hydrodynamic volumes. This series covers the different modes of heat transfer, convection, radiation, nucleate boiling, transient boiling, and boiling by film.

Boiling curves are used to select correlations of heat transfer. Modeled heat transfer regimes are classified as nucleate boiling, critical heat flow point (CHF), and dispersed flow regime. The heat transfer of condensation is also modeled. The pre-boiling regimes concern the liquid monophasic convection, subcooled nucleate boiling, and nucleate boiling at saturation [15].

#### *3.2.2 Steam boiler nodalization*

Knowledge of all the components and parts of the installation as well as all the physical phenomena that may occur in the system is essential for the modeling of any thermal installation. Preparing data to access this type of work using the RELAP5 code requires considerable effort because of the large amount of

*Numerical Simulation of the Accidental Transient of an Industrial Steam Boiler DOI: http://dx.doi.org/10.5772/intechopen.86129* 

**Figure 10.**  *Nodalization of the steam boiler installation.* 

information required for the entire installation and its associated components. The information and data of the modeling of the steam boiler plant were obtained from the installation documentation and staff [22], that is, the RELAP5 steam boiler model is based on geometrical and technical data.

The philosophy of using the RELAP5 code is to subdivide the hydrodynamic system into control volumes connected by flow junctions. The thermal behavior of the metal wall of the boiler tubes, such as heat transfer with the fluid, is modeled by heat structures that are connected to vaporizer tubes and heat exchangers. The heat densities between the combustion gases and the external surfaces of the vaporizer tubes are calculated from the energy balance performed on the fumes at each exchanger.

The thermal-hydraulic conditions at the inlet and outlet of the installation represent the condensed feedwater that enters the collection tank and the superheated steam flowing to the turbine. Regulation plays a very important role in the operation of the steam boiler; the RELAP5 code includes the possibility to model the regulation system by components specific to the code. The installation of the entire steam boiler is modeled in 582 control volumes, 589 junctions, and 142 heat structures. The thermodynamic conditions at the system boundaries are imposed by "time-dependent volumes" component **Figure 10** shows the nodalization diagram of the entire installation. More details on the steam boiler nodalization are given in Ref. [1, 2]. The modeling of the steam boiler using the RELAP5 code will be followed by a qualification at the steady-state level.

#### **3.3 Validation at steady-state level**

Numerical simulation allows a better understanding of thermal-hydraulic phenomena that could take place in industrial installations; they are of a capital contribution especially in accident situations. The RELAP5 code allows the prediction of the thermal-hydraulic behavior and response of the steam boiler during normal and accidental operations. Prior to the transient accident analysis, it is essential to check the establishment of the steady state in different points of the steam boiler installation. The steady state is reached after running the RELAP5/Mod3.2 code for 5000 seconds in our case study. To demonstrate the establishment of the steady

**Figure 11.**  *Main steam boiler parameters during steady state.* 


#### **Table 4.**

*Comparison between operating and calculated data at steady state.* 

*Numerical Simulation of the Accidental Transient of an Industrial Steam Boiler DOI: http://dx.doi.org/10.5772/intechopen.86129* 

state, we selected some steam boiler operating parameters (**Figure 11**). The analysis of the curves representing the evolution of these parameters showed that the regime is stationary and well established, and the set-point values of the regulation system were reached.

The qualification of the steam boiler RELAP5 model is based on available operating data, and it aims to verify that the steady state is well reproduced. In order to validate the plant nodalization under steady-state condition, the simulation results are compared with the experimental data; it provides precious information on the quality of the nodalization, the selection of the appropriate code options, and the appropriate choice of the boundary and initial conditions (1). The comparison between the RELAP5/Mod3.2 results and operating data at steady state is summarized in **Table 4**. As it could be seen, the simulation results are in good agreement with the operating data of the steam boiler, proving the adequacy of the model and expressing the capacity and reliability of the RELAP5/Mod3.2 code in simulating thermal-hydraulic behavior of industrial installations. At this level, it should be noted that the present model could potentially be used for further transient analysis.

#### **3.4 Transient calculation**

 For a steam boiler, loss of feedwater is the most severe incident that can occur and that may potentially end with serious consequences because water flow rate decreases suddenly leading to a decrease in drum water level and the walls of the tubes are overheated. Various factors can produce this accident; it can be caused by pump power loss, failure of the feedwater pump, ruptures and leakages from pipes located in the main feedwater line, feedwater control valve closing, or failure of the water level regulation [27].

In this chapter, the numerical simulation of the steam boiler thermal-hydraulic behavior and response during loss of feedwater accident caused by the pump power loss is discussed. The transient was performed including protected and unprotected scenarios. In the first one (protected scenario), it is assumed that all control systems are functioning properly to mitigate the sequences of the accident; in the second one (unprotected scenario), it is assumed that there is a failure in the security and control system. Prior to the accident, the steam boiler was operating under steadystate condition. The accidental transient is initiated when the feedwater pump costs down accidentally leading to a sudden decrease in feedwater flow rate. The burners' shutdown is actuated immediately following the triggering of the pump stopping alarm signal. **Table 5** groups the main events describing the accidental scenario as a function of time.


#### **Table 5.**

*Main accidental sequences of the transient.* 
