# Homework Help: Process Eng: Water heating system

1. Nov 6, 2013

1. The problem statement, all variables and given/known data
You've been asked to draw a P&ID for a water heating system. 20 tonne/hr of water is to be pumped from the atmosphere into a heat exchanger at 1.6 MPa. Steam is being used to heat the water to 145 C. The heated fluid is then stored in a vessel, which is designed to hold 4 minutes of flow. Show all your calculations.

2. Relevant equations
Where $Q$ is the volumetric flow rate:
1)$Q = Av$ where $A$ is the cross sectional area of the pipe and $v$ is the velocity of the fluid through the pipe.

2)$Q = \frac{ \dot{m}}{\rho}$ where $\dot{m}$ is the mass flow rate and $\rho$ is the density of the fluid.

3)The speed of water through pipe can be approximated as 2 m/s.

3. The attempt at a solution
Well, 20 tonnes/hr is equal to 20(1000)/60(60) kg/s. Thus: $$\dot{m_{water}} = 5.55 kg/s$$
Dividing this by the density of water, the value of $Q_{water}$ was found to be 5.55 x $10^{-3}$ m^3/s.

Using this, the value of the pipe diameter can be calculated to be 0.059 metres by using equation (1). Now, I was wondering, does the heating by the steam affect the value of the flow rate out of the heat exchanger? If not, the capacity of the vessel can easily be calculated by multiplying the surge time (in seconds) by the flow rate.

Finally, how do I incorporate the values of temperature and pressure into my calculation? I'm not really sure what they're required for.

Also, how would I go about sizing the size of the pipe used to deliver the steam? Or is that even possible with the information required? Thanks in advance and if you need any clarification on the question, let me know.

Also, this is my first post, but I still know that I won't be told the answer. Just a help in the right direction would be handy. Thanks.

Last edited: Nov 6, 2013
2. Nov 7, 2013

Here's the exact question:
36 tonne per hour of water is to be pumped from atmosphere into a heat exchanger at 1.69MPa, and heated to 150°C using steam at 1.0MPa. The heated fluid is stored in a surge vessel designed to have a capacity equal to 5 minutes of flow.

• Draw a P&ID for this system, show all calculations.
• Consider very briefly the issues of pressure relief, recycle and isolation.
• Simple drawing (by hand if necessary) (Ignore this. Doesn't make much sense.)

I really just don't see how the values of pressure and the temperature factor into the problem.

3. Nov 7, 2013

### SteamKing

Staff Emeritus
It started out that 20 t/hr of water was being pumped; now it's 36 t/hr. Surge vessel 4 min. cap.; now 5 min. cap.
Are you sure this is the problem and the figures are correct?

4. Nov 7, 2013

Yes. They're correct now. This is the exact question. I changed them slightly myself initially just so that I'd have a little bit to do myself if somebody ended up giving me numerical answers. Can you make any sense of what I', required to do with those values? (The pressure and temp.)

5. Nov 7, 2013

### Staff: Mentor

Hi Undergrad1147. Welcome to Physics Forums.
The first thing you need to come to grips with is that this design is going to be an evolutionary process, with lots of alternative designs and concepts you would like to consider. All you know so far is that there is going to be a pump, a heat exchanger, and a surge tank. Before you start calculating pipe diameters and flows, you need to first focus on the thermo. What is the vapor pressure of water at 150C. This will tell you the minimum pressure needed in the heat exchanger to keep the water from boiling. How does the vapor pressure at 150 C compare with the inlet pressure to the heat exchanger. You now know the maximum pressure drop you can tolerate on the water flow side. What is the temperature of saturated steam at 1 MPa? Will this be high enough to heat the water to 150 C? These are some of the things you need to be looking at before you start designing. What is a reasonable value for the inlet temperature of the water from the environment? Should you consider a range of values?

Chet

6. Nov 8, 2013

Thanks for the reply. I found the vapour pressure of water at 150 C to be 475.72 kPa, which is 0.47572 MPa. This is less than the pressure in the HE, so the water doesn't begin to boil upon entry, yes? Is the maximum pressure drop then equal to (1.69 - 0.47572) MPa?

The temperature of the saturated steam is 179.88 C. Well, this is high enough to raise the temp of the water to 150 C, isn't it? I'm not too sure how I can judge this.

I suppose I could take room temperature to be the temperature of the water. Approximately 20 C or so.

7. Nov 8, 2013

### Staff: Mentor

The heat exchanger you design must have enough heat transfer area to allow the heat load to be transferred, and it must also have a low enough pressure drop to prevent the water from starting to boil. These are some constraints that you can use to help you design the heat exchanger.

Chet

8. Nov 9, 2013

Well, this particular module that I'm taking is more of an intro into process and chemical engineering. We haven't actually covered the design or theory of HEs whatsoever. Although, whenever we've needed to include a HE in a flow diagram of any sort, it's usually a shell and tube heat exchanger. So, I really don't know enough of the relevant theory to go and design a HE in proper detail.

That being said, I think I have seen some equation that relates the area of HE to the heat load or temperature difference, something along those lines. Does such an equation exist?

a) Well, the head load will be the difference in rate of energy in, i.e. from the steam and cool water streams, and the hot water stream out. Is this correct?

b)You can calculate the amount of energy per second required to heat the water from 20 C to 150 C using Q = $\dot{m}$ * c * (T2 - T1), yes? Then using this values and dividing it by the enthalpy of condensation of the steam, you can calculate the amount of steam flow required. Does that sound correct?

c), d) and e) I'm not sure what you mean by all of those temp. differences really. The temperature between the water and steam?

Thanks for the help so far.

9. Nov 9, 2013

### Staff: Mentor

Good. You're doing very well so far. Shell and tube looks like a good choice. We'll put the water through the tubes, and the steam through the shell.
Yes. We can get to that shortly.
Yes. Very good.
Excellent. So, what numbers do you get in MJ/hr and kg/hr?
The difference between the steam temperature and the water temperature at the water inlet is 160 C. The difference between the steam temperature and the water temperature at the water outlet is 30 C. These are the temperature driving forces for heat transfer to take place. Locally, the rate of heat transfer per unit heat exchange area is equal to the overall heat transfer coefficient times the local temperature driving force. Have you learned about heat transfer coefficients yet? In order to find the heat transfer area, you are going to need to determine the heat transfer coefficient. Knowing the required heat transfer area will help you determine the length of the tubes, the diameter of the tubes, and the number of tubes. So please bring us up to date on your understanding of heat transfer coefficients.

10. Nov 9, 2013

I'll post my numerical workings up here later on, in a little while.

I have a vague understanding of the heat transfer coefficient. Actually, not so much an understanding of the theory behind it, but an idea how to compute it. $$h = \frac{Q}{A\Delta T}$$

Will Q be the heat load across the HE?

Now, for h. Is h intrinsic to the material of construction of the HE? Something like that? I honestly have very little idea of the background theory of what the heat transfer coefficient is.

Rearranging the above formula for A, once we know the value of h, what formula then relates the area to the number of tubes, their diameter and length? $A = N * l * d$ possibly?

Last edited: Nov 9, 2013
11. Nov 9, 2013

$\dot{Q} = 4200(150 - 20) =$ 0.546 MJ/hr.

$h_{fg}$ = 2014.6 kJ/kg

Thus $\dot{m}_{steam}$ = 0.271 kg/hr.

12. Nov 9, 2013

### Staff: Mentor

That's not what I get. I get $\dot{Q} = (20000)4.186(150 - 20) = 10.9 × 10^6kJ/hr=10.9 gJ/hr$
Thus $\dot{m}_{steam}$ = 5400 kg/hr.

13. Nov 9, 2013

### Staff: Mentor

Yes. This is the definition of the heat transfer coefficient. If you know the heat transfer coefficient, you can calculate the heat transfer area A.

There are actually three resistances to heat transfer in series: The resistance through the tube wall, the resistance on the steam side, and the resistance on the water side. These three resistances determine the overall heat transfer coefficient. In your application, the resistance on the water side is the one that is likely to dominate.

This venue is not appropriate for a tutorial on how to design heat exchangers. If you need to educate yourself on this, please read Chapter 14 in Transport Phenomena by Bird, Stewart, and Lightfoot. Are you familiar with this book?

Is it your understanding that you have to provide a design for the heat exchanger, or is it sufficient to just provide the material and energy balances? My guess is that you do need to design it.

You need to include a factor of pi in this equation.

14. Nov 9, 2013

My apologies, I completely left out the mass flow rate of the water. Also, the mass flow rate of the water is 36000 kg/s, not 20000 kg/s. If you remember, I actually changed this when I restated the question earlier.

15. Nov 9, 2013

Thanks for that. I'm not familiar with that book actually. I'll see if I can find it online tomorrow.

To be honest, we haven't covered HEs in this course really. We have our first module on HEs next term and most of the theory of calculating the length and diameter of the tubes is completely alien to me. I'd honestly say it's enough for us to calculate the heat loads and flow rates. Possibly, including the heat exchange area would be a bonus seeing as it was mentioned once, VERY briefly. So, I'm sure our lecturer doesn't expect too much detail with respect to the HE at all.

If the method of choosing a heat coefficient isn't overly involved, I'll go ahead and calculate the heat exchange area. How would I go about choosing a suitable value for h?

16. Nov 9, 2013

### Staff: Mentor

Bird has dimensionless correlations for calculating h as a function of the reynolds number and the prantdl number. The book also has typical ranges for h for condensing vapors, and for convective heat transfer of water flow in tubes. You might start out by using a mid-range value from the typical range to get you started.

What would you consider a reasonable length for the heat exchanger: 0.1 - 1 meters, 1 -10 meters, 10 - 100 meters? I know what range I would choose to start with.

17. Nov 9, 2013

### Staff: Mentor

Oh yes. That's right. I forgot. So what numbers do you get now?

18. Nov 10, 2013

Q = 16.3254 GJ/hr and $\dot{m}$ = 8104 kg/hr.

Last edited: Nov 10, 2013
19. Nov 10, 2013

I think determining the heat transfer coefficient is a little too involved for the purpose of the current module that I'm taking. I'm not so sure that our lecturer would expect us to be able to design a HE in great detail seeing as haven't covered that yet. I'll ask him though just to be sure.

I'd go ahead and choose a length between 10 and 100 m just because it's the widest range really. Purely a guess.

So far, I've calculated the steam flow rate and the heat load across (well, I've stated how to do this), if I was the leave the HE be for now (and get back to it once I get some clarification from my lecturer), which part of the process should I consider next? The pump? The line sizes and surge vessel capacity is fairly easy, so designing the pump is the last part really, I would think.

Also, would it be possible for me to recycle the water produced by the condensing steam in the shell of the HE?

Last edited: Nov 10, 2013
20. Nov 10, 2013

Actually, I just got my hands on Transport Phenomena an had a quick look at chapter 14. While most of it is quite out of context, as I haven't studied Transport Phenomena before, I found the table of heat transfer coefficients. Is what we have in this case, Forced Convection? (Seeing as there's a pump involved.)

If this is the case, for water, the value of h ranges between 500 and 10000 W/m^2.K. This is a fairly large range. How would I go about choosing a good estimate for h? From engineeringtoolbox.com, 680 seems to be a good choice if the material of construction is SS.

21. Nov 10, 2013

### Staff: Mentor

I'm not sure about your question about using the water from the condensing steam. The problem statement doesn't say anything about this. It all depends on what this plant is being used for. Since your instructor made up this problem, it doesn't correspond to any real situation. But, if the water being heated was really a process stream that contained dissolved chemicals that are being processed, you wouldn't normally mix the steam with the process stream (since the steam might not be as pure as you would like it).

22. Nov 10, 2013

### Staff: Mentor

Well, I would have chosen a value close to the low end also, so the 680 is fine with me. Don't despair. Nothing is carved in granite yet. We just need something to get us in the ballpark. Then we will be refining the design gradually until we arrive at something that we are comfortable with. Like I said in my first post, design of a heat exchanger is an evolutionary process. So, for the first crude approximation to the heat exchanger design, you will be using the 680. As you refine the design, you will be using Eqn. 14.3-16 of BSL to estimate the heat transfer coefficient on the liquid water side more accurately.

To calculate the heat transfer area using the 680, you're going to need to use the average temperature driving force in your overall heat transfer equation. As we said, the driving force at the water inlet end is 160 C, and the driving force at the outlet end is 30 C. If you used the arithmetic average driving force, you would use (160 + 30)/2 = 95 C. However, the solution to the differential equations for a heat exchanger tell us that we should be using the so-called logarithmic mean driving force: (160 - 30)/ln(160/30) = 78 C. So that's what you should consider using. With these values, what do you get for your starting estimate of the heat transfer area in your heat exchanger?

23. Nov 10, 2013

The only reason I bring it up, is because in the problem statement it states 'Consider briefly the issues of pressure relief, recycle and isolation'. I though that this was a good opportunity to think about recycle. It was just a thought really. Though, I was more so thinking that the water produced during the steam condensation could be recycled to the heater where the steam was initially produced.

Does this make any sense at all? This way, the way the water could be put to good use and at the same time, not interfere with the process water. This could all be nonsense though.

24. Nov 10, 2013

That equation is completely alien to me, but I assume I'll cover it some time over the next year.

$A = \frac{Q}{h\Delta T}$
Just edited this post as I made a mistake with the LMTD. I had thought you made a mistake using 160C and 30C as your temps but it was actually just me not fully understanding what the LMTD equation was. I'll post the value for A in the morning. Although, I think it'll be far too large judging by how big Q was, yes?

Last edited: Nov 10, 2013
25. Nov 10, 2013

### Staff: Mentor

You also forgot to divide by 3600 sec/hr.