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nh3simman
03-04-2007, 07:29 AM
We talk theory about optimization, so let's see how it works in practice.


In South Africa, we have a power supply problem. A pumped storage scheme was proposed some time ago to pump water to a dam in the Drakensberg mountains. This saves water and produces hydro-electric power during off-peak times. It is apparently a very successful project.


An ideal (and relatively simple) target for optimization is the stage pipe diameter.


The total cost of the stage can be simplified to (1) installed pipe and (2) the pumping cost as follows:

Installed cost of the pipe = 800 x diameter
Pumping cost = 100x10^12 / (diameter)^5

What diameter would give the least cost?

Ravi
03-04-2007, 12:44 PM
92.4655 (what ever units). Just did the basic minima calc. Set up a spreadsheet and check the data for yourself.

nh3simman
04-04-2007, 01:00 PM
92.4655 (what ever units). Just did the basic minima calc. Set up a spreadsheet and check the data for yourself.

This answer is not correct.

Firstly, the minimum can be found by setting the 1st derivative to zero.
dC/dd = 800 - 100x10^12/d^6 = 0
gives d = 95.3mm

But, the answer is wrong for a much more important reason.

As engineers, we tend to dive in and solve any equation we see without thinking about the significance. Even worse, we use a spreadsheet and fudge a local minima.

In optimizarion, the problem is much broarder. We need to understand the relationship of this sub-system with the complete system. What I was hoping for was that someone would question the distance between pump stations, the flow rate, the head, and so on.


Solving a single equation is easy (or maybe not so easy as Ravi has discovered), but finding a system optimization is much more complex.

Ravi
05-04-2007, 04:22 AM
Curiosity kills the cat and this happens quite often in forums. I mistook the post as a question and not as a quiz. I tought your second equation (for pumping) was based on an existing setup and you deduced it from pump power equation. Never mind it.

However, the first derivative (or the slope) is 800-5x100x10^12/d^6 and that gives d as 100x(500/800)^(1/6) = 92.4655

Your answer is based on first derivative of 800-6x100x10^12/d^6, which is wrong.

nh3simman
06-04-2007, 08:53 PM
Oops, Ravi is right about my slope calculation.

nh3simman
07-04-2007, 05:17 AM
Hi Ravi,

In my rush to prove a point, I made a mistake.

But I think that the point is valid and it doesn't matter that I'm not actually busy with the installation. Sometimes we can play with ideas to find real solutions to problems.

USIceman has raised the topic of optimization that has got me thinking. what I have tried here is to give an isolated example where optimisation can be done (as you did), but is not necessarily the solution for the system.

Maybe a better example would be the suction line of a single stage vapor compression cycle. Similar to the above approach, I could optimize the line diameter with no reference to the cycle.

From basic optimisation theory
Penalty = Cost of tube + Cost of frictional pressure drop
subject to some constraints
1. Velocity for oil return.
2. Max saturated temperature drop.

But, would this give me an optimised system. Maybe, I don't know?

What do you think?

US Iceman
07-04-2007, 05:39 AM
From basic optimisation theory
Penalty = Cost of tube + Cost of frictional pressure drop
subject to some constraints
1. Velocity for oil return.
2. Max saturated temperature drop.

But, would this give me an optimised system. Maybe, I don't know?


That's an interesting idea. But there are two competing criteria.

In one you are optimising for the oil return velocity at part load conditions at the sacrifice to full load pressure/temperature loss.

Conversely, if sized for the full load condition to minimize pressure /temperature loss then the part load oil return velocity suffers.

Which one should we optimise for? This is one of the predicaments of optimization and overall system design. In some cases, it is a lesser of two evils.:o

lana
07-04-2007, 05:47 AM
In one you are optimising for the oil return velocity at part load conditions at the sacrifice to full load pressure/temperature loss.
Conversely, if sized for the full load condition to minimize pressure /temperature loss then the part load oil return velocity suffers.


Hi guys,

In refrigerant pipe sizing, both full load and min. load must be taken into account. For horizontal pipes it is relatively easier, but for vertical pipes ....:eek: you have to be carefully for min. load. This is where the double-riser comes into picture, if necessary.
My point is, if pipe sizing is done according to the standard procedures then it must be optimized, otherwise there will be a huge problem.
Cheers:)

nh3simman
07-04-2007, 05:54 AM
That's an interesting idea. But there are two competing criteria.

I don't think that the competing criteria is a problem.

When you select a tube diameter, you have to satisfy these conditions anyway. If the tube is too big, the velocity will be low and the min velocity criteria kicks in. If the tube is too small, the pressure drop is too high and the pressure drop criteria kicks in. All these two criteria do is give upper and lower limits to the size.

The ideal tube size could be anywhere between these limits, depending on the first cost + friction loss cost.

You have to choose some size, so why not the one with minimum cost.

I think that I'm begining to agree with you about optimizing the sub-system. After all, if this component is at its best then is must contribute to the system accordingly.

US Iceman
07-04-2007, 03:55 PM
You have to choose some size, so why not the one with minimum cost.


Unfortunately, that tends to happen more often for that specific reason. It saves money, but I often find these attempts are at odds with overall good system design practices.

This subject is also sometimes confused with value added engineering. The whole thrust of this always seems to be the desire to make something cheaper under the disguise of cost-effective.

I am not taking issue with your comment, but only offering an additional viewpoint for consideration.

I believe what you started off with was similar to economic pipe sizing where you can include the cost of utilities and other crtieria to determine the minimum required pipe size.

Isn't this fun?

Ravi
09-04-2007, 11:06 AM
. In some cases, it is a lesser of two evils.:o

That is what most of we engineers follow, IMHO. My experience has been in Pharma for 12 years and sometimes I don't feel like justigying my job. Every time you make a conservative estimate, there are distractions interms of bosses and future uncertainities. You will have expansion coming up before you finish a project.

With pumping and HVAC systems, I heavily bank on variable capacity systems, not for variable loads but to take care of design redundancies. When money is not a criterion, saving your sking should be:(

As far as piping is concerned, the biggest drawback in optimization can be commercial availability of different sizes. If we want to optimize then manufacturers may lose. Take bigger sizes, go for VSDs, show some savings and everybody is happy.

However, I feel the discussions in these technical forums can throw light from many directions and can give us good confidence while trying system optimization.