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# Newton Raphson Convergence Problem For Multicomponent Flash

8 replies to this topic
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### #1 smuk

smuk

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Posted 19 April 2020 - 10:14 AM

Dear all,

I am facing a convergence problem for a multicomponent flash. By conventional method the root of the Newton Raphson terns ie. V/F, (developed using Rachford Rice equation) converges. However, with Newton Raphson method, convergence is not obtained. The attached xcel sheet gives the necessary details. I want to know where I am going wrong. Can someone help? Thanks for your time.

smuk

### #2 breizh

breizh

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Posted 19 April 2020 - 11:26 PM

Hi,

To me it's unclear ! what is the problem , convergence or code ?

Anyway if it's a convergence issue it may come from a wrong initialization or because the number of equations to solve  .

You should start with a smaller set of equations to test your code .Consider the example shared with you to test your code and initialize the Newton Raphson method .

Good luck

Breizh

#### Attached Files

Edited by breizh, 20 April 2020 - 01:25 AM.

### #3 smuk

smuk

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Posted 19 April 2020 - 11:50 PM

Hello

Thanks for the response. I will go through the test code and see about the convergence. As stated, the problem is that of convergence and not of code. The equations for f () and f'() are given in the excel sheet. I have tried with many initial values of , but convergence was not obtained. But when done with conventional trial and error method, the Rachford Rice equation (from where the Newton Raphson equations are derived) has a solution at  = 0.97. I hope this explains the problem.

smuk

### #4 breizh

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Posted 20 April 2020 - 01:49 AM

Hi,

I found that your Ki1 was not correct , to me K methane is 2.6 @ 600 psi  ,-20F .

Consider to check all .

Good luck

Breizh

### #5 breizh

breizh

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Posted 20 April 2020 - 02:16 AM

hi,

I did a run of the software mentioned in my first answer , the result is 0.9679 for the vapor phase .

a copy is attached .

I believe the problem is coming from the number of components and some values are very small .

You should be able to combine some of them to ease the calculation.

Breizh

### #6 breizh

breizh

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Posted 20 April 2020 - 05:29 AM

Hi ,

Sorry for the typos, I needed to review the document , even the results for V/F  was correct 0.96.

Cheers

Breizh

### #7 smuk

smuk

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Posted 21 April 2020 - 09:19 AM

Hello

Thanks for the effort you put in to clarify the solution. The problem is taken from Engineering Data Book of Natural Gas Processor Supplier Association under chapter Equilibrium Ratio Data. The problem is solved using the conventional trial and error method. K values are estimated from convergence pressure, as given in the problem statement. The same values have been used. I have attempted to solve the problem using Rachford Rice equation and Newton Raphson method. I will redo the problem to see where the bug lies. Thanks for your time.

Regards

smuk

### #8 breizh

breizh

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Posted 22 April 2020 - 07:28 AM

hi ,

let you and other consider this link , it's a wonderful resource .

Good luck

Breizh

Edited by breizh, 22 April 2020 - 07:30 AM.

### #9 smuk

smuk

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Posted 22 April 2020 - 08:50 AM

Regards

smuk