# Modeling of a boiler

hello,
I have dynamically modelled a drum boiler, but when i am solving the equation i am getting an negative rate of change of enthalpythe reason i find is the enthalpy of the steam is very higher than the enthalpy of water. can someone please verify the model and help me with this.
$$\rho_w\cdot V_w\cdot \frac{\mathrm{d} h_w}{\mathrm{d} t} = Q+\dot{m}\cdot (h_w-h_s)-M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t}$$
where $$M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t} = Q-(n\cdot \pi \cdot D\cdot L\cdot \alpha \cdot (T_m-T_s))$$
ρw = density of water
Vw = volume of water
m. = massflow rate of water
hs = enthalpy of steam
M = mass of metal
Cp = specific heat of metal
Tm = temperature of metal
n = number of tubes
D = Dia of tube
L = length of tube
∝ = heat transfer coefficient

BvU
Homework Helper
Hello again,

A lot of heat is needed to evaporate water (look it up). What is ##Q## ?

BvU
Homework Helper
As a start, you can find a steady state value for ##Q## ...

thank you so much now it works but it requires a high Q. Sounds very silly to you but can u tell me this, i am using a electrical power source can you tell me how cani convert input power in watts to Q?

BvU
Homework Helper
Perhaps ##Q = ## input power ?

Re post #1:
$$M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t} = Q-(n\cdot \pi \cdot D\cdot L\cdot \alpha \cdot (T_m-T_s))$$

What is ##T_s## ?

$$\rho_w\cdot V_w\cdot \frac{\mathrm{d} h_w}{\mathrm{d} t} = Q+\dot{m}\cdot (h_w-h_s)-M\cdot C_p\cdot \frac{\mathrm{d} T_m}{\mathrm{d} t}$$ Boiling usually occurs at a fixed temperature, so how come you have ##dh_w\over dt## as accumulation variable ? Or are you modeling the heating up of water instead of the boiling ?

Ts is the saturated temperature of the steam.
I have gone through many papers and
ρw⋅Vw⋅dhwdt=Q+˙m⋅(hw−hs)−M⋅Cp⋅dTmdt
is the equation for dynamic modelling of boiler

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BvU
Homework Helper
Ts is the saturated temperature of the steam.
I thought you had an electric heater ?

The equation may be appropriate in some (other?) context. But I don't think you have that context. A diagram of your setup ?

To be clear, I dont have any diagram of the setup. I need to model a boiler where the water is boiled to get steam using an electric source as heat input and the output steam is to be collected and will be sent through a superheater.

BvU
Homework Helper
To avoid errors for yourself and in communication you should draw a diagram, showing all the relevant variables. Look in a textbook for examples.
The way you work now is confusing for yourself and hinders your understanding of what goes where and which parts are important and which can be ignored (definitely or temporarily)

anorlunda
Staff Emeritus
I'm with you. I don't like links to PDF files in posts.

sorry for the link, i have deleted it and will upload the clear view of the boiler

Chestermiller
Mentor
You are leaving out details of how this boiler is operated. Is the pressure constant? Are you just looking at transients from the steady state operation, or are you looking at startup? Do you really think the mass holdup of water in the system is constant?

yes I am looking for transient steady state operation. I am modelling the basic boiler in simulink, where the pressure is constant, and the volume is also constant. What I need is when i use an electric power as input source, the water has to boil and the outlet steam is collected. I just basically need to show in the equation that the water is boiled and steam is being produced. All the other designing parameters and physical parameters such as pressure and volume are neglected.

anorlunda
Staff Emeritus
I need to model a boiler where the water is boiled to get steam using an electric source as heat input and the output steam is to be collected and will be sent through a superheater.
That sounds like a drum type boiler, because if it was a once through boiler there is no defined boundary between the boiling region and the superheating region. Double down if it is a supercritical once through. Nor do you provide hints at the size scale. Is this boiler small enough to hold in your hand, or is it bigger than a football stadium?

I would not attempt such a modelling job without first having drawings. Can you post drawings and dimensions?

Chestermiller
Mentor
yes I am looking for transient steady state operation.
Steady state and transient are mutually exclusive concepts. So, which is it, transient or steady state that you are interested in?

i am looking for a transient state model.

BvU
Homework Helper
Please make an attempt to make clear to us what you are trying to do -- a complete description, with a drawing of the setup. You really are constantly overestimating other people's capabilities for telepathy

Chestermiller
Mentor
i am looking for a transient state model.
Then you need to include a mass balance equation.

At what pressure is this system being operated? Is air being purged from the system during the startup of the system, and are you interested in the startup? Is so, then the exit stream is not at the equilibrium vapor pressure of the liquid water.