Any help appreciated...

[nhenslee]

I am hoping that this is the correct area, my math skills are limited to pre-algebra at this point.

I have an issue that I have been working on, it seems like it should be simple,but the deeper I go, the more complicated it seems. This has to do with asituation I am working with, it's not for school.

I will try to be as brief as possible.

I have 3 pumps, two have a capacity of 700 - 2000 gallons per minute, the thirdis 700-1500 GPM. All three have varying levels of two contaminants (arsenic and nitrate).

The issue I am working on is trying to balance the flowsbetween the three pumps to obtain the lowest contaminant levels.

For example say one is high in Arsenic, and low inNitrates, and the other is Low in arsenic and high in nitrates. If all things were equal, I could set each toan equal flow amount and via dilution get a lower level of both contaminants.

It seemed simple enough, but I have tried to create aformula where I could put in the desired total flow amount, and the contaminantlevels of each well, to calculate the appropriate amount from each well toachieve the lowest contaminant level, but it simply doesn’t work…

Right now I am just using an excel sheet and imputingdifferent amounts to try and get close to a good ratio, but it is inexact and timeconsuming as the total flow required changes several times a day.

I want to keep this short, hopefully I’ve been able todescribe what I am trying to do, help of ANY kind from the math ninjas would be appreciated beyond words.

 

[Quaid]

I think the scenario needs a bit of clarification.

Each of the three pumps move contaminated water from a different source to somewhere, and each of those three sources is contaminated with the same toxins but in differing ratios. Is this correct?

You mention three pumps, but your example involves two pumps.

Are you assuming that the toxins are evenly distributed, within each source?

Are you using the pumps to mix the three sources together?

Are you introducing any non-contaminated water to the system, at all?

Perhaps, a listing of a specific example (with ballpark estimates for the numbers involved) would help me to better understand the quantities and their relationships.

Cheers

 

[nhenslee]

I think the scenario needs a bit of clarification.

Each of the three pumps move contaminated water from a different source to somewhere, and each of those three sources is contaminated with the same toxins but in differing ratios. Is this correct?

You mention three pumps, but your example involves two pumps.

Are you assuming that the toxins are evenly distributed, within each source?

Are you using the pumps to mix the three sources together?

Are you introducing any non-contaminated water to the system, at all?

Perhaps, a listing of a specific example (with ballpark estimates for the numbers involved) would help me to better understand the quantities and their relationships.

Cheers

Thank you for the reply, I’d be glad to clarify, I just didn’twant to make the original thread unreadably long.

I used the two pump scenario for simplicity there are threedifferent pumps.

The toxins are not evenly distributed and the levels changemonth to month

The three sources are mixed

All water in the system contains some amount of the contaminants.

Here is the current scenario these are the actual current numbers I have, I will abbreviate Arsenic (Ar.) and Nitrate (Ni) theconcentrations of toxins are in parts per million, flow amounts are in US gallons per minute.

Total flow request = 4,000.00 GPM

Pump 1

Ar = 9.41
Ni = 6.61
Flow = 800

Pump 2

Ar = 18.8
Ni = 2.6
Flow = 1200

Pump 3

Ar = 3.73
Ni = 14.7
Flow = 2000

Calculated final concentrations:Ar = 9.387Ni=9.452

The aim is to stay below 10 PPM concentration (this is the regulated limit) The above is just an example, the final concentration varies based on how much I send out of each pump, I have figured out how to calculate the output, it is a fairly simple dilution ratio.

What I am trying to find out is if there is another way, besides trial and error, to findout what the optimum flow for each pump would be to get the lowest amount ofeach contaminant without exceeding ten?

I feel like I should be able to figure this out but I have been vexed for months.

 

[Deleted member 4993]

Thank you for the reply, I’d be glad to clarify, I just didn’twant to make the original thread unreadably long.

I used the two pump scenario for simplicity there are threedifferent pumps.

The toxins are not evenly distributed and the levels changemonth to month

The three sources are mixed

All water in the system contains some amount of the contaminants.

Here is the current scenario these are the actual current numbers I have, I will abbreviate Arsenic (Ar.) and Nitrate (Ni) theconcentrations of toxins are in parts per million, flow amounts are in US gallons per minute.

Total flow request = 4,000.00 GPM

Pump 1

Ar = 9.41
Ni = 6.61
Flow = 800

Pump 2

Ar = 18.8
Ni = 2.6
Flow = 1200

Pump 3

Ar = 3.73
Ni = 14.7
Flow = 2000

Calculated final concentrations:Ar = 9.387Ni=9.452

The aim is to stay below 10 PPM concentration (this is the regulated limit) The above is just an example, the final concentration varies based on how much I send out of each pump, I have figured out how to calculate the output, it is a fairly simple dilution ratio.

What I am trying to find out is if there is another way, besides trial and error, to findout what the optimum flow for each pump would be to get the lowest amount ofeach contaminant without exceeding ten?

I feel like I should be able to figure this out but I have been vexed for months.

Do you have access to MS_Xcel?

It has a function called - SOLVER - ideally suited for this type of problem.

 

[nhenslee]

MS_Xcel

Hopefully this is not a completely ignorant response, but if the term is short for Microsoft Excel, then yes, I have access, but I'm unfamiliar with that function, if it's another program, then no I don't have access, but maybe I could find it somewhere?

 

[Deleted member 4993]

Hopefully this is not a completely ignorant response, but if the term is short for Microsoft Excel, then yes, I have access, but I'm unfamiliar with that function, if it's another program, then no I don't have access, but maybe I could find it somewhere?

Yes it is Microsoft Excel. You will need to add-in the SOLVER unit. Go through HELP to add this in to your Excel.

 

[nhenslee]

Found it but...

Yes it is Microsoft Excel. You will need to add-in the SOLVER unit. Go through HELP to add this in to your Excel.

Thank you, I did end up finding it a bit ago, I've been doing some homework on the program, I think it's a bit beyond my skills, it seems like there may be too many variables that are related to each other, and the solver seems to be set up to put out a single answer, but I would need it to put out all three pump speeds, I'm sure it's possible in this thing, but I think the programming languages may be over my head... I'll keep at it, but if anyone can point me in the right direction as to setting it up, I'd be grateful.

 

[nhenslee]

I know it's probably not linear, I was hoping that there was a fairly straight forward differential equation that I could graph or something or plug in values and solve etc... I do genuinely appreciate everyone's time and input, getting this figured out would definitely make my life easier and help me produce better water for the public.

 

[Quaid]

The toxins are not evenly distributed

Pump 1

Ar = 9.41
Ni = 6.61

Just to be sure (because it's important), I asked about distribution within each source. For example, you list the current level of Ar at source1 as 9.41ppm. Would that number remain constant, during the pumping time-interval under consideration? I'm concerned about heavier concentrations at lower water levels, and we don't know anything about the depth at which the water is captured. If toxin concentration is not evenly distributed throughout the source, then ppm could vary with time, and the optimization becomes more complicated.

 

[nhenslee]

I didn't catch that one the first time through, yes the contamination levels remain constant for each source independent of the speed that the water is removed. For instance, source 1 would read 9 parts per million of arsenic whether it was running at minimum (700 gpm) or max (2100 gpm)

All three sources would be the same way.

The only caveat to the above would be that, due to soil characteristics, the contamination levels do change over time, so it would be nice to be able to adjust those variables, however those changes are very small, usually less than 1% over a span of months, which is small enough to be negated if need be.

So hopefully I'm on the same page here, for the purpose of calculating optimal flow rates between the sources, the contamination levels can be treated as constants.

Hope that helps...

Also, I'm not sure if there is a way here, but, if possible, when I get to work tomorrow I'm going to try to upload or attach a copy of the excel sheet I currently use to manually calculate all this stuff, it works and is real life accurate, I just have try a bunch of combinations until I get one that works...


- Nick