Calculate the Density of a solution of Formic acid in Water

Go to the Top

The density of a Formic acid is a difficult problem, due to association.  We can adjust the interaction between molecules (the dread kij factors) to account for this association

Setup

Note:  this is the path to the installed EOS packages

[Graphics:Images/index_gr_1.gif]
[Graphics:Images/index_gr_2.gif]

Last Run on:

[Graphics:Images/index_gr_3.gif]
[Graphics:Images/index_gr_4.gif]

Formic Acid Solution Density--Finding minimum errors using (an) adjustable Kij value(s)

Formic Acid (HCOOH) represents a very difficult calculation, since it is found mostly in dimers.  Hence, it represents  a 'worst case' scenario for EOS of associating species.  We handle it using interaction coefficients in the most accurate of the models, the Aasberg-Petersen

Functions

Lden is the density of the mixture z at temperature t, atomospheric pressure (.98 bar).

[Graphics:Images/index_gr_5.gif]
[Graphics:Images/index_gr_6.gif]
[Graphics:Images/index_gr_7.gif]
[Graphics:Images/index_gr_8.gif]
[Graphics:Images/index_gr_9.gif]
[Graphics:Images/index_gr_10.gif]
[Graphics:Images/index_gr_11.gif]
[Graphics:Images/index_gr_12.gif]
[Graphics:Images/index_gr_13.gif]

Next,the dtermining the sqr.error.LiquidDensityError takes a range of t's,a range of z's,and a list of real data,which should be of the form:

[Graphics:Images/index_gr_14.gif]
[Graphics:Images/index_gr_15.gif]
[Graphics:Images/index_gr_16.gif]

Data

Formic acid solution density {concentration__List:{__temperature}}, where concentration is mole percent HCOOH, temperature is 0, 15, 20, 30 ºC

[Graphics:Images/index_gr_17.gif]

Reform  data and sample at every 0.05 change in mole fraction

[Graphics:Images/index_gr_18.gif]

NOw, Examine graph of density of 4 temperatures

[Graphics:Images/index_gr_19.gif]
[Graphics:Images/index_gr_20.gif]

[Graphics:Images/index_gr_21.gif]

[Graphics:Images/index_gr_22.gif]

Using Equations of State to make Predictions

No kij adjustments
[Graphics:Images/index_gr_23.gif]

Plot the predictions along with the experimental

[Graphics:Images/index_gr_24.gif]

[Graphics:Images/index_gr_25.gif]

[Graphics:Images/index_gr_26.gif]
[Graphics:Images/index_gr_27.gif]
[Graphics:Images/index_gr_28.gif]

Store the MS error

[Graphics:Images/index_gr_29.gif]
[Graphics:Images/index_gr_30.gif]
Adapt the models to include one kij Adjustment

The following is a table of errors as a function of the k11 value

[Graphics:Images/index_gr_31.gif]
[Graphics:Images/index_gr_32.gif]
[Graphics:Images/index_gr_33.gif]
[Graphics:Images/index_gr_34.gif]
[Graphics:Images/index_gr_35.gif]

[Graphics:Images/index_gr_36.gif]

[Graphics:Images/index_gr_37.gif]
[Graphics:Images/index_gr_38.gif]
[Graphics:Images/index_gr_39.gif]
[Graphics:Images/index_gr_40.gif]
[Graphics:Images/index_gr_41.gif]

Now, replicate the data using the above 'best' k11 value for the water-formic acid mix

[Graphics:Images/index_gr_42.gif]
[Graphics:Images/index_gr_43.gif]
[Graphics:Images/index_gr_44.gif]
[Graphics:Images/index_gr_45.gif]
[Graphics:Images/index_gr_46.gif]

[Graphics:Images/index_gr_47.gif]

[Graphics:Images/index_gr_48.gif]
[Graphics:Images/index_gr_49.gif]
[Graphics:Images/index_gr_50.gif]

Though more kij adjustments slightly improve the guess, they do not SIGNIFICANTLY improve the guess (as shown below)

Two kij Adjustments
[Graphics:Images/index_gr_51.gif]
[Graphics:Images/index_gr_52.gif]
[Graphics:Images/index_gr_53.gif]

[Graphics:Images/index_gr_54.gif]

[Graphics:Images/index_gr_55.gif]
[Graphics:Images/index_gr_56.gif]
[Graphics:Images/index_gr_57.gif]
[Graphics:Images/index_gr_58.gif]
[Graphics:Images/index_gr_59.gif]
[Graphics:Images/index_gr_60.gif]
[Graphics:Images/index_gr_61.gif]
[Graphics:Images/index_gr_62.gif]

[Graphics:Images/index_gr_63.gif]

[Graphics:Images/index_gr_64.gif]
[Graphics:Images/index_gr_65.gif]
[Graphics:Images/index_gr_66.gif]
Three kij Adjustments
[Graphics:Images/index_gr_67.gif]
[Graphics:Images/index_gr_68.gif]
[Graphics:Images/index_gr_69.gif]
[Graphics:Images/index_gr_70.gif]
[Graphics:Images/index_gr_71.gif]
[Graphics:Images/index_gr_72.gif]
[Graphics:Images/index_gr_73.gif]

[Graphics:Images/index_gr_74.gif]

[Graphics:Images/index_gr_75.gif]
[Graphics:Images/index_gr_76.gif]
[Graphics:Images/index_gr_77.gif]
four kij Adjustments
[Graphics:Images/index_gr_78.gif]
[Graphics:Images/index_gr_79.gif]
[Graphics:Images/index_gr_80.gif]
[Graphics:Images/index_gr_81.gif]
[Graphics:Images/index_gr_82.gif]
[Graphics:Images/index_gr_83.gif]
[Graphics:Images/index_gr_84.gif]

[Graphics:Images/index_gr_85.gif]

[Graphics:Images/index_gr_86.gif]
[Graphics:Images/index_gr_87.gif]
[Graphics:Images/index_gr_88.gif]
[Graphics:Images/index_gr_89.gif]
[Graphics:Images/index_gr_90.gif]
[Graphics:Images/index_gr_91.gif]

[Graphics:Images/index_gr_92.gif]

[Graphics:Images/index_gr_93.gif]
[Graphics:Images/index_gr_94.gif]
[Graphics:Images/index_gr_95.gif]


Converted by Mathematica      May 6, 2002