Saturation Pressure of a Binary
System Using PVT Simulator
Fathi PNGE 332
1
Motivation
In this experiment we will
generate a pressure composition
diagram at constant temperature
for a mixture of CO2 and C4H10
Observe the effect of changing
composition on a binary system
Composition will be expressed as
the mole fraction of CO2 in the
mixture
The pressures plotted are the
bubble point and dew point
pressures as a function of
composition
Fathi PNGE 332
2
3
1
Typical pressure composition diagram of two
component mixtures with one tie line, 123
2
Experiment 2: Pressure-Composition
Diagram
Initially visual cell contains 10 cc n-butane at 2000 psi at
constant T
Charging vessel #1 contains pure CO2 at 2000 psi but at room
temperature 71.6 oF
2
3
1
Typical pressure composition diagram of two
component mixtures with one tie line, 123
Fathi PNGE 332
3
Experiment 2: Pressure-Composition
Diagram (Cont.)
1.
2.
3.
4.
Find the bubble point and dew point of pure n-butane. This
corresponds to mole fraction of zero added CO2.
Restore system to its initial condition
At specific temperature the amount of added CO2 needed to
meet the required mole fractions (use Table 4)
The CO2 can be added in increments (Table 4b)or as a total
(Table 4a) which method is used depends on whether one use
the apparatus or the simulator
Fathi PNGE 332
4
Experiment 2: Using Apparatus
The only practical way is the incremental method
1. Add the amount of Co2 necessary for 0.1 mole fraction
2. let system reached the equilibrium
3. determine the saturation pressure
4. bring the cell back to 2000 psi
5. Then inject the incremental or additional amount of CO2
needed to make 0.2 mole fraction
6. Find the saturation pressures
7. Repeat from step 4
Fathi PNGE 332
5
Experiment 2: Using Apparatus
If we wanted to use the total amount method
1. add the amount of Co2 necessary for 0.1 mole fraction
2. let system reached the equilibrium
3. determine the saturation pressure
4. Purge the visual cell of the contents
5. Re-inject fresh butane
6. Allow the system to come to operating temperature (can take
several hours)
7. Add the Co2 needed for 0.2 mole fraction
8. Find the saturation pressures
9. Repeat from step 4
Fathi PNGE 332
6
Experiment 2: Using PVTLAB Simulator
Performing the Experiment using total amounts is much quicker all
you need to do is
1. Perform the experiment at 0.1 mol fraction
2. Exit then re-enter and perform, add the total amount needed
for 0.2 mole fraction
3. Collect the data exit, re-enter and continue
Performing the Experiment using incremental amounts is more
difficult since
1. After each increment you need to bring back the system to
initial pressure of 2000 psi (achieving that could be very
difficult)
2. If program crashes at any time you have to do all the steps
from begging
Fathi PNGE 332
7
Equations used to calculate Co2 volume
Fathi PNGE 332
8
Experiment 2: n-butane and Co2 Densities
Fathi PNGE 332
9
Khalid Alakeel
PNGE332
Lab#2
LAB 2
Saturation Pressure of a Binary System
Using PVT Simulator
2/26/2019
G1
Khalid Alakeel
PNGE332
Lab#2
Cover letter:
In this experiment, a mixture of two components were tested to define the bubble point
and dew point of the mixture at constant temperature. In our case, the two components were
carbon dioxide and n-butane, and the temperature was 71.6 oF.
This experiment was conducted on a PVT simulator because of the regulations of
mercury usage. Initially, the cell had 10cc of n-butane, then we started injecting CO2 gradually
from a different vessel starting from 0.1 mole until we reach 0.9 mole of CO2 and calculate the
bubble point at each time. The experiment was conducted 9 times since every time we had to
change the amount of CO2 inside the cell.
After recording the data, the graph of pressure vs mole fraction of CO2 will show the
regions of liquid, gas, and two phase are present. In addition, using table 5, we will be able to
calculate the density at the critical point which is 22oF. Finally, we will verify at least one of the
numbers in table 4.
Khalid Alakeel
PNGE332
Lab#2
Theory and objective:
This experiment will allow us to draw a saturation pressure diagram of a binary system
where we have 2 components. Using the PVT simulator, we will get accurate numbers and the
experiment will be done at a constant temperature of 71.6 F. And from the graph, we will be able
to observe the effect of changing the composition of the mixture and how it effects the bubble
and dew point.
As we know, the bubble point can be observed when the first gas bubble comes out of the
liquid. At this point, the PVT simulator allows us to record the values of liquid n-Butane, gas nButane, liquid CO2, gas CO2, as well as the pressure. Given the following data we can create the
pressure composition diagram.
By theory, as we increase the mole fraction, the bubble point and dew point increase.
However, they don’t have the same rate of change. For example, the bubble point pressure line is
linear, and the dew point pressure line in exponential (see figure 1).
Figure 1
Khalid Alakeel
PNGE332
Lab#2
Procedure:
This experiment was conducted 9 times due to the change of composition of CO2 each
time. The following procedure was done when opening the PVT simulator.
1- Withdrawing Hg from the cell by the same amount of CO2 that will be added to the cell to
make some space for it.
2- Adding the specified amount of CO2 from vessel 1 to the cell based on table 4a.
3- Checking the amounts of n-Butane and CO2 in the cell to avoid any calculation errors.
4- Withdrawing Hg from the cell until we hit the bubble point and shaking the cell each time
we withdraw to mix the two substances together.
5- Record the amounts of liquid and gas of n-Butane and CO2 when reaching the bubble
point.
6- Repeating the same process for all CO2 composition.
Khalid Alakeel
PNGE332
Lab#2
Results:
Pressure
32.5
140.9
230.7
343.3
432.63
512.32
583.02
641.21
710.41
784.31
n-C4 (liquid)
1
0.9058
0.8104
0.714
0.6164
0.517
0.4161
0.3142
0.2109
0.1072
n-C4 (gas)
1
0.2501
0.152
0.1141
0.0945
0.0824
0.0738
0.0664
0.0577
0.0488
CO2 (liquid)
0
0.0942
0.1896
0.286
0.3836
0.483
0.5839
0.6858
0.7891
0.8928
CO2 (gas)
0
0.7499
0.848
0.8859
0.9055
0.9176
0.9262
0.9336
0.9423
0.9512
liquid
two phase region
Gas
Temprature
16.9
26.9
21.9
Density @
10 Mpa 15 Mpa
878.2 920.7
802.1 866.4
840.141 893.583
Khalid Alakeel
PNGE332
Temprature = 21.9 F
Pressure
Density
10
840.141
15
893.583
13.8
880.7544
Volume of CO2 = 𝑣 ∗ 𝑛
𝑘𝑔
𝑀 (𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠) 44.01 (𝑘𝑚𝑜𝑙𝑒) 103 𝑐𝑐
𝑐𝑐
𝑣=
=
∗
= 49.97
3
𝑘𝑔
𝜌 (𝑑𝑒𝑛𝑠𝑖𝑡𝑦)
𝑚
𝑚𝑜𝑙𝑒
880.7544 ( 3 )
𝑚
𝑛=
𝑍𝑐𝑜2 ∗ 𝑛𝐶4 0.6 ∗ 0.1025
=
= 0.1538 𝑚𝑜𝑙𝑒
1 − 𝑍𝑐𝑜2
1 − 0.6
Vco2 = 49.97*0.1538= 7.68 cc
Lab#2
Khalid Alakeel
PNGE332
Lab#2
Results analysis:
In the PVT simulator, the Peng-Robinson’s equation was used to calculate all the data
that we have. And as we can see, the equation shows that the bubble points show a linear
relationship and the dew points show an exponential relationship. However, since we are dealing
with a computer program, there are no external interference with the environment. Therefore,
there is limited sources of errors. However, due to the assumptions of the Peng-Robinson’s
equation, which neglects the volume of gas particles and assuming that gas particles collide
perfectly elastic, we can have some sort of error.
After creating the graph of the bubble point and the dew point, we can see that the bubble
point curve is not a perfect straight line where it is supposed to be a perfect straight line.
However, it was close enough to a straight line which makes it reliable. In addition, the
relationship of pressure and temperature is not linear in real gasses, but we assumed it is linear
due to the assumptions of Peng-Robinson.
Khalid Alakeel
PNGE332
Lab#2
Conclusion:
In this experiment, the mixture of carbon dioxide and n-Butane results were reasonable
even though they were treated as an ideal gas. The graphs were close enough to the theoretical
graphs which indicates that the experiment was conducted correctly.
West Virginia University
LAB 2
Saturation Pressure of a Binary
System Using PVT Simulator
Class No. W01
February 23, 2018
Groups:
G1
Cover letter:
First of all, the experiment was held on Feb 2nd, 2018 in G11. The
goal of the experiment was to define the bubble point and the dew point
of a binary system at a specific temperature. This binary system consists
of a mixture of carbon dioxide and normal butane. The specific
temperature is 22° F
In the beginning of the experiment the pressure was 2000 psia, and
10cc of normal butane, vessel number 1 contains pure CO2 at a pressure
of 2000 psia. Therefore, the students were asked to add specific amounts
of CO2 to the n-butane, these amounts of CO2 can vary between 0.1 mole
and 0.9 mole fraction in relation to the amount of normal butane.
Inserting carbon dioxide to the visual cell was done by removing mercury
from the visual cell to the hand pump. Then, the students connected and
disconnected some valves in order to move the amount of CO2 to the
visual cell. The experiment was done nine times because each time the
student inserted a specific amount of CO2 in terms of mole fraction.
Theory, concepts and objective of the experiment:
The objective was to find the bubble and dew point pressure at
71.6° F, C. temperature is the temperature above which the gas can't be
liquified. C. pressure is the pressure above which liquid and gas coexist.
The bubble point is the point where the first gas appears in the liquid. The
dew point is the point where the last drop of liquid converted to gas (The
Book).
The instructor showed the students how does the diagram of two
components looks like as shown in Figure1.
Figure1: Two component mixture phase
As illustrated there is a relationship between the mole fraction and
the pressure (bubble and dew points). As the mole fraction increases the
pressure increases. The simulator uses the equation PRE (Lab manual).
Experimental Procedure:
In the beginning of the experiment we opened the PVT simulator
program, then we typed:
Copylab2\G1.la2 setup.par
The lab
Then press F2 in order to open two valves (8 and 9), so we can have a
communication between the visual cell and the hand pump. Then, we also
opened valves 4 and 11, there will be no change in pressure so it will
remain 2000 psia. Then, then start withdrawing mercury from the visual
cell until we have a 0.1 mole fraction using F5 bottom. Then we close
valve 8 in order to isolate the cell from the hand pump. After that, we
open valve 1 to start injecting amount of mercury to the charging vessel
as the amount of mercury withdrawn. Now we have CO2 in the cell, then
we close valves 1, 4, and 11, and open valve 8. Since we have a mixture
in this experiment we will need to use F6 in order to mix the content and
to let the system in equilibrium. Now, using F5 we will start withdrawing
mercury until the bubble point which is 0.002 cc (you must use F6 after
each withdrawing). Then record the analysis in an excel sheet. Also, press
F10 to record a chromatographic analysis. Then repeat this experiment
with the same temperature, but different mole fractions, each time record
the data.
Results and calculations:
P
Xco2
32.569
140.9
342.66
433.11
512.54
581.13
641.19
700.11
773.31
0
0.0942
0.2855
0.3842
0.4833
0.5839
0.6858
0.7891
0.8938
yco2
xc4
0
0.7699
0.8857
0.9056
0.9177
0.9262
0.9336
0.9423
0.9585
yc4
1
0.9058
0.7145
0.6158
0.5167
0.4161
0.3142
0.2109
0.11062
1
0.2501
0.1143
0.0944
0.0823
0.0738
0.0664
0.0577
0.0415
Volume
Mole
of CO2
Fraction Added
0.1
0.57
0.2
1.282
0.3
2.197
0.4
3.418
0.5
5.126
0.6
7.69
0.7
11.962
0.8
20.505
0.9
46.137
900
800
700
Liquid
600
500
400
two phase region
300
200
100
Gas
0
0
0.2
0.4
0.6
0.8
Bubble Point
1
1.2
Dew Point
Figure 2: Pressure, mole fraction of CO2
Since the temperature of 22° C is not found in table 5 in the lab manual,
we have to use an average between 16.9and 26.9 same thing for the
density.
D
T
10 Mpa
15 Mpa
16.9
878.2
920.7
26.9
802.1
866.4
21.9
840.15
893.55
940
920.7
920
Density
900
878.2
880
866.4
860
840
820
802.1
800
780
0
5
10
15
20
25
30
Temperature C
Figure 3: Temp. Vs. Density
So, the density at a 13.8 Mpa is 880.169 Kg/M3.
Pressure Vs. Density
900
890
Density
880
870
860
850
840
830
0
2
4
6
8
10
12
14
16
Pressure MPa
The volume of carbon dioxide is not calculated yet so, the equation given
has to be used in order to find the volume.
Molecular weight of carbon dioxide = 44.010 kg/kmole
Density of carbon dioxide = 880.169 kg/m3
Volume of carbon dioxide = (44.010/880.169)*103 = 50.002cc/mole =
50.002*(0.6*0.1025/0.4) = 7.69 cc
Analysis and Discussion:
PVT simulator uses PR equation (lab manual) this simulator is an old
program and it is not well updated (the book), so there might be some
minor errors.
P = (RT)/(V-b) – a/(V2+2Vb-b2)
This equation is not correct because of some reasons (the book):
1- the tubing in the system which is the lines leading between the
valves, has no volume.
2- Pressure changes happen isothermally
3- Joule-Thomson impacts are ignored.
4- Mercury is considered as non-compressible substance.
5- Equilibrium in thermodynamic is instantaneous
Conclusion:
A mixture of carbon dioxide and normal butane was examined for
the bubble point and dew point at a specific temperature using PVT
simulator. There is a relationship between the pressure and the mole
fraction "as the pressure increases the mole fraction increases". The
interpolations (table 5 in the lab) was used to determine the density at a
given temperature. On the graph the highest point indicates the critical
point.
References:
1- McCain, William D. The Properties of Petroleum Fluids. PennWell Books, 1990.
2- Lab manual, EXP 2: Saturation Pressure of a Binary System Using PVT
Simulator
Lab #2:
Saturation Pressure of a Binary System Using PVT
Simulator
1/12/2016
Table of Contents
Pages
Cover Letter……………………………………………………………3-4
1
Theory, concepts, and objective……………………………..5-6
Experimental Procedure………………………………………….7-9
Results and calculations………………………………………….10-11
Analysis and discussion…………………………………………..12-14
Conclusions……………………………………………………………….15
References…………………………………………………..……………16
Cover Letter
Dear Dr. Fathi,
In Experiment # 2, the main objective was to generate a pressure composition diagram
at a constant temperature for a mixture of CO2 and C4H10. This diagram is used to display how
2
changing the composition of a binary system effects the system as a whole. Once this diagram
was constructed, a tie-line could be created from the data points. The pressures plotted in the
diagram are bubble point (PB) and the dew point (PD) pressures of the binary system as a
function of composition, expressed as the mole fraction of CO2.
The procedure to generate this pressure composition diagram was carried out using the
PVT simulator. The initial conditions for this lab were that the visual cell contained 10 cc. of
normal butane at 2000 psia at room temperature, 71.6°F. A charging vessel containing pure
CO2, initially at 2000 psia and room temperature, was used to add specific volumes of CO2 to
the mixture in order to make 10 different mole fractions of CO2. Each individual mole amount
of CO2 added to the butane generated different bubble point pressures due to the variation of
the composition of the binary mixture. The PVT simulator allowed the user to pump the
amount of mercury needed to make 0 – 0.9 mole fraction of CO2 into the charging cell which in
turn transferred that exact amount of CO2 to the visual cell. The components then reached
chemical equilibrium and the bubble points were found by removing arbitrary amounts of
mercury from the visual cell until 0.002 cc or less of gas was displayed. This process was
repeated for 0 to 0.9 mole fraction of CO2. To find the dew point pressure, one of the 9 mole
fractions of CO2 was used but with 1 cc of butane instead of 10 cc in order to allow for more
room in the visual cell to expand the liquid to the gas phase. Since one-tenth of the original
volume of butane was used, one-tenth the amount of CO2 added to find the bubble points was
used to find the dew point.
Using this procedure for each of the mole fractions of CO2, several different bubble
point pressures were found that were used to generate the pressure composition diagram. The
liquid and gas compositions, Xi and Yi respectively, for both the CO2 and C4H10 were displayed by
the chromatograph once each bubble point was found. The experiment was started by first
finding the bubble point of the system with 0 mole fraction of CO2 which was found to have a
bubble point of 32.569 psia. For 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 mole fraction of CO 2
initially in the visual cell, the bubble point pressures were 140.9 psia, 245.18 psia, 343.30 psia,
433.11 psia, 512.54 psia, 581.14 psia, 640.58 psia, 700.38 psia, and 773.25 psia, respectively. It
is a clear trend that as the mole fraction of CO2 was increased, the bubble point pressures
3
increased as well. The dew point was found using one-tenth the amount of CO2 added for 0.4
mole fraction of CO2. After repeating the procedure for finding the bubble point, the dew point
pressure was found to be 68.323 psia. It is necessary to understand that the accuracy of the
simulator regarding the pressure was (+ or – 0.001 psia). The accuracy of the composition of the
liquid and gas of CO2 and C4H10 was (+ or – 0.0001 %).
The theory behind this experiment involves two-component mixtures and the pressurecomposition diagrams that are generated using the data found in the experiment. It is
necessary to notice that in a pressure- volume diagram for a two-component mixture, the line
from the bubble point to the dew point isn’t straight like it was in the diagram for the pure
component. This is due to the changes in composition of the liquid and gas in the two-phase
region (McCain). Regarding the attributes of the pressure-composition diagram, a bubble point
line and dew point line are created using the data from the experiment which together form
the saturation envelope of the two-component mixture. If the pressure and composition
combinations occur above the envelope, the mixture is completely liquid. Likewise, if the
combination occurs below the envelope, the mixture is completely liquid (McCain). If the
composition and pressure occur within the envelope, the mixture is in two-phases. The bubble
point line is the center of the compositions of liquid when two-phases are present and the dew
point line is the center of the compositions of gas when the mixture is in two phases. A tie line
is the line that connects the bubble point line to the dew point line. Ratios of moles of gas and
liquid to the total moles of the mixture can be calculated by using these tie lines. Establishing
the bubble point line, dew point line, and tie line is the premise of this experiment. Finding this
criteria allows for easy computation of percent gas and percent liquid at specific pressures and
compositions.
Sincerely, Cole Bertol
Theory, concepts, and objective
4
The objective of this experiment was to create a pressure-composition diagram using
the bubble point pressures of a mixture of CO2 (carbon dioxide) and C4H10 (butane) as a function
of composition of CO2 in mole fraction. Ten different increments of mole fraction of CO2 were
used (0-0.9) and the corresponding bubble points were found. These bubble points found were
used to generate the bubble-point line of the pressure composition diagram which corresponds
to the compositions of liquid present when two-phases exist. A single dew-point pressure was
calculated using a similar procedure that was used in finding the bubble-point pressure. Having
this dew point pressure, the dew-point line of the pressure-composition diagram could be
generated. The combination of the dew-point line and bubble-point line creates the saturation
envelope for the two-component mixture. If a plotted point with a certain pressure and
composition occurs within this envelope, it is in a two-phase. It is interesting to note that the
bubble point pressure and dew point pressure of a binary system are not identical because of
the changing composition of the mixture.
Drawing a line through this point from the
bubble-point line to the dew-point line, the
compositions of equilibrium gas and liquid
can be found. This line is referred to as a tie
line. A tie line must be horizontal, and it can
also determine the quantities of liquid and
gas at that specific point in the form of
ratios (McCain). Dividing the section of the
Figure 1
tie-line from the bubble-point line to the specific plotted point by the entire tie-line gives the
ratio of moles of gas to the total moles of the mixture. Inversely, dividing the section of the tieline connecting the plotted point to the dew-point line by the entire tie-line gives the ratio of
moles of liquid to the total moles of the mixture (McCain). This is logical because the bubblepoint line is the center of the liquid compositions at the two phase region and the dew-point
line is the center of the compositions of gas at the two phase region. Dividing the sections of
the tie-line by the entire tie-line will then give the corresponding ratios of gas or liquid to the
5
total moles of the mixture. An example of a pressure-compostion diagram is displayed in
Figure 1.
6
Experimental Procedure
This experiment was performed using the PVT simulator (Figure 2) since a PVT
apparatus is unavailable for use. The bubble points for the two-component mixture had to be
found for each mole fraction of CO2. The procedure was carried out using the Function Keys
(F2-F10) to operate the PVT simulator. For this experiment, however, only F2, F5, F6, and F10
were used to generate the proper results. The initial step was to find the bubble point of
normal butane with no mole fraction of CO2 added. This was done by using F2 to open the
valves connecting the visual cell to the hand pump. After the valves were open, F5 was used to
pump incremental amounts of mercury out of the visual cell, therefore increasing the volume in
the cell and decreasing the pressure. This process was repeated until 0.002 cc or less of gas was
visible in the visual, indicating the bubble point. Continuing with the process, the dew point was
found by the presence of 0.002 cc or less of liquid left in the visual cell. This is the same process
used for a single-component experiment since no moles of CO2 were added at this time.
Figure 2
7
After finding the bubble point and dew points for the mixture with no CO 2 present, the
two-component procedure was carried out. This involved using F2 to open the valves
connecting the visual cell to the hand pump and the top valves connecting the charging cells to
the visual cell. Once valves were open, F5 was used to withdraw the amount of mercury from
the visual cell to make each mole fraction of CO2. Each mole fraction of CO2 had a
corresponding volume of CO2 at a specific temperature that needed to be added to the mixture
in order for that mole fraction to be valid. The pressure of the system was reduced from 2000
psia at this point. For 0.1 mole fraction of CO2 at room temperature (71.6°F), 0.570 cc of CO2
had to be added to the mixture. This volume of CO2 was added to the mixture by removing that
same amount of mercury from the visual cell and pumping it into the charging cells. Doing so
replaced the amount of mercury removed with the same amount of CO2 added. This was done
by using F2 again to close the valve from the visual cell to the hand pump and open the valve
connecting the hand pump to the bottom of the charging cell. Once these valves were open, F5
was used to pump the amount of mercury originally taken from the visual cell into the charging
cell. That amount of mercury pumped into the charging cell was the same amount of CO 2
transferred to the visual cell. Pumping the equivalent amount of CO2 into the visual cell as
amount of mercury removed from the visual cell allows the system to return to its original
pressure of 2000 psia. Since the pressure was brought back to its original condition, the
procedure for finding the bubble point and dew point could then be carried out. The valves
connecting the charging cell and visual cell were closed and the valve connecting the visual cell
with the hand pump was opened using F2. The F6 key (LC pump) was used to mix the contents
in the visual cell and bring them to equilibrium. In order to check the composition of the
mixture the chromatograph needed to be viewed using F10. The procedure was the same as
that used when no CO2 was added to the system. Mercury was removed in arbitrary amounts
from the visual cell until 0.002 cc or less of gas was visible, indicating the bubble point. It was
essential that the LC pump be used every time mercury was removed, as it is necessary to bring
the mixture to chemical and thermal equilibrium before accurate results can be recorded. Once
the bubble point was found, the pressure was recorded as well as the liquid and gas
8
composition of CO2 and C4H10 from the chromatograph. This process was repeated for each of
the mole fractions of CO2 (up to 0.9).
Once the bubble point pressures and compositions of carbon dioxide and butane at the
pressures were recorded, at least one dew point pressure and corresponding composition had
to be found. I used the values related to 0.5 mole fraction of CO2 since it is relatively in the
middle. This was done by the same method used to find the bubble point, but instead of 10 cc
of butane to start, only 1 cc of butane was used in the visual cell. This was necessary in order to
give enough room for the liquid to expand to gas in the visual cell. The same procedure was
followed to find the dew point with the exception that the volume of mercury removed (equal
to the volume of CO2 added to give the specific mole fraction) was one-tenth the value used
when finding the bubble point since it was one-tenth the original volume of butane.
9
Results and calculations
Using the procedure described, ten different bubble point pressures were
calculated, each one differing from the other based upon the mole fraction of CO 2 added to the
system. For each increment of mole fraction of CO2 added (0-0.9) the bubble point pressures
were 32.569 psia, 140.9 psia, 245.18 psia, 343.3 psia, 433.11 psia, 512.54 psia, 581.14 psia,
640.58 psia, 700.38 psia, and 773.25 psia, respectively. A trend is visible that as the mole
fraction of CO2 was increased, the corresponding bubble points increased as well. The results to
this experiment were calculated using an accuracy of (+ or – 0.001 psia) for the bubble point
pressures and dew point pressure. It is interesting to note that the sum of Xi and Yi values for
each mole fraction of CO2 add up to 1. The liquid and gas composition data for CO2 and C4H10
used an accuracy of (+ or – 0.0001). Common errors, such as human error, also have to be
taken into consideration when viewing the results to this experiment. The following tables and
pressure-composition diagram display the results found from this experiment:
CO_2
P_B
mol/frac. psia
0
32.569
0.1
140.9
0.2
245.18
0.3
343.3
0.4
433.11
0.5
512.54
0.6
581.14
0.7
640.58
0.8
700.38
0.9
773.25
CO_2
X_i
liquid
0
0.0942
0.1896
0.2862
0.3842
0.4833
0.5839
0.6847
0.7891
0.8938
Y_i
gas
0
0.7499
0.848
0.8859
0.9056
0.9177
0.9262
0.9335
0.9423
0.9585
C_4H_10
X_i
Y_i
liquid
gas
1
0
0.9058
0.2501
0.8104
0.152
0.7138
0.1141
0.6158
0.0944
0.5167
0.0823
0.4161
0.0738
0.3153
0.0665
0.2109
0.0577
0.1062
0.0415
10
CO_2
C_4H_10
CO_2
P_D
X_i
Y_i
X_i
Y_i
mol/frac. psia
liquid
gas
liquid
gas
0.5
68.323
0.0302
0.5967
0.9693
0.4933
PRESSURE-COMPOSITION DIAGRAM
Bubble-point line
Dew-point line
900
800
700
PRESSURE
(PSIA)
600
500
400
300
200
100
0
0
0.2
0.4
0.6
0.8
1
1.2
FRACTION CO_2
11
Analysis and discussion
The results found in the experiment clearly indicate that changing the composition of a
binary system drastically affects the bubble point pressures. One of the assumptions used in
this lab was that density is a linear function of pressure when in reality density is NOT a linear
function of pressure. This is assumed for this experiment in order to verify the values in Table
4a which were calculated from Appendix A. In this experiment Table 4a was used for the mole
fraction of CO2 which uses the total CO2 volume at the pressure of the system. It is much
quicker and easier to use the total volume amounts when using the PVT simulator because the
user can find the bubble point at 0.1 mole fraction of CO2, exit the program, and then restart
using the value for 0.2 mole fraction of CO2 and so on. If the incremental volume amounts of
CO2 were used it would be much more difficult because after the bubble point was found at
each incremental value, the simulator requires the system to be brought back to 2000 psia
which can be difficult. Also, if the program were to crash at any point during the experiment,
the experiment would have to be restarted from the beginning, which would be frustrating. On
the other hand, when using the PVT apparatus, the incremental method is the only practical
way to perform the experiment. If the total amount method were used on the apparatus, the
user would have to add the volume of CO2 necessary for 0.1 mole fraction of CO2, find the
bubble point pressure, dump out all the contents in the visual cell, and add fresh butane to the
visual cell and allow the system to come to the appropriate temperature before the next
volume of CO2 needed for 0.2 mole fraction of CO2 could be added. This would take much
longer than necessary. Therefore, the incremental method is practical for the PVT apparatus
and the total method is used for the PVT simulator.
Errors that could occur that affect the results of the experiment include those from the
user and from the program. As with any experiment, human error is a factor that can easily
affect the accuracy of the results obtained. Misusing the program by not following the lab
procedure correctly can drastically affect the results. Other errors such as recording incorrect
values from the program or not recording the values to the appropriate decimal place can
cause deviations from accurate results. The program itself can be a cause of error as well. The
12
user can only perform the experiment within the boundaries of the simulator. The simulator
may have a malfunction or display incorrect results. The results obtained from the simulator
may be different from the results obtained using the PVT apparatus since the simulator is using
a software program for the experiment which may not be as accurate as the real PVT
apparatus.
The values displayed in Table 4a were calculated using the equations in Appendix 1. To
verify one of these values the equations in Appendix 1 can be used to check that the values in
Table 4a are correct. The density of CO2 in the mixture had to evaluated using linear
approximation of the densities on Table 5 and converted to kg/cc. Below is the verification:
Solution Method:
MCO2 = 44.10 (molecular weight of CO2)
MC4H10 = 58.123 (molecular weight of butane)
Molar volume (m3/kmol) v = M/ ρ (kg kmol3/kg m-3)
Volume V = v*n number of moles
Binary system: zCO2 = nCO2/(nCO2 + nC4H10) = mole fraction
ZCO2(nCO2 + nC4H10) = nCO2
NCO2(1 – zCO2) = zCO2nC4H10
NCO2 = (zCO2nC4H10/1 – zCO2) = no. of moles of CO2 in the system
NC4H10 = no. moles of butane at temp. and pressure, column 2 of tables 1a, 1b
VCO2 = vCO2 * nCO2 = vCO2(zCO2nC4H10/1 – zCO2)
13
Results:
Verifying mole fraction of 0.1 CO2 is correct:
vCO2 = M/ ρ = 44.010(kg/kmol)/8.40*10-4(kg/cc) = 52383.5 (cc/kmol)
zCO2 = 0.1 mole fraction required
nC4H10 = 0.1025 from Table 4a
nCO2 = (0.1 * 0.1025/1 – 0.1) = 0.011389 = 1.1389 *10-5 kmol of CO2 in system
VCO2 = vCO2 * nCO2 = 52383.5 (cc/kmol) * 1.1389 *10-5 kmol of CO2 = 0.596 cc
14
Conclusions
Experiment 2 involved finding the saturation pressure of a binary system using the PVT
simulator. The objective was to generate a pressure-composition diagram by finding the bubble
points of different mole fractions of CO2 in a mixture with butane. Each mole fraction CO2 had a
corresponding volume amount of CO2 that needed to be added to the mixture in order for that
specific mole fraction to exist in the mixture. From the experiment, it was easily noticeable how
the changing of composition of the mixture – different mole fractions of CO2 in the mixture –
caused the bubble point to differ. The trend was that the higher mole fraction of CO 2 in the
mixture, the higher the bubble point was. The pressure-composition diagram was generated by
plotting the bubble points found at 10 different mole fractions of CO2 against the composition
of the CO2 at that pressure. The fraction of liquid CO2 at the various bubble point pressures
generated the bubble point line, and the fraction of the gaseous CO2 generated the dew point
line. The combination of these two lines of a graph created the saturation envelope where two
phases exist. From this envelope, a horizontal line connecting the bubble point line with the
dew point line, the tie-line, can be drawn which is used to compute the ratios of liquid and gas
to the entire mixture. The pressure-composition diagram is a very useful tool when computing
ratios of liquid and gas at certain pressures. Using the PVT simulator allowed for this diagram to
be created for a useful purpose, all while demonstrating how the change of composition of a
mixture effects the system.
15
References
William D. McCain, The Properties of Petroleum Fluids, 1990, Volume 2, Pages 67-70
PNGE 332 Lab Manual
http://people.cst.cmich.edu/teckl1mm/PChemI/Chm351Ch8aF01.htm
16
PNGE 332_W01
Lab 2
Saturation pressure of a binary system using PVT simulator
November 3, 2019
Dear Dr. Fathi,
Nasser Alghamdi
November 3, 2019
During Petroleum Properties and Phase Behavior Lab class in the computer Lab in ESP
room G3, the experiment performed was about the saturation pressure of a binary system
between two components which were (Co2 and C4h10), using the PVT simulator at constant
temperature. The system contained 10cc of pure n-Butane C4h10 at 2000 psi with accuracy of
(±0.1). The temperature was kept at 71.6℉ and it was kept constant during the whole
experiment.
The mixture of carbon dioxide and n-Butane was generated by removing mercury and adding
same amount carbon dioxide to the cell. The volume of carbon dioxide which had to be added in
the mixture is given in the lab manual (Table 4a). A diagram of pressure vs composition of
carbon dioxide is attached which shows the bubble points and dew points pressure of different
mole fractions of carbon dioxide. These pressures of the mixture change due to the change in
composition of carbon dioxide in the mixture.
Moreover, after removing the mercury volume and injecting the same amount of carbon dioxide
in the cell, the pressure of the mixture was increased, whereas when the mercury was removed
from the mixture to find the bubble point, the pressure was decreased. To find the bubble point,
the volume of the gas was kept at (0.001-0.002) cc. However, we were unable to find the dew
point of the mixture.
At the initial condition, the bubble point equal 32.569psi (±0.001). At 0.1 of Co2, the bubble
point equal 140.9psi (±0.001). At 0.2 of Co2, the bubble point equal 245.18psi (±0.001). At 0.3
of Co2, the bubble point equal 343.3psi (±0.001). At 0.4 of Co2, the bubble point equal 433.11psi
(±0.001). At 0.5 of Co2, the bubble point equal 512.54psi (±0.001). At 0.6 of Co2, the bubble
point equal 518.13psi (±0.001). At 0.7 of Co2, the bubble point equal 614.19psi (±0.001). At 0.8
of Co2, the bubble point equal 700.41psi (±0.001). At 0.9 of Co2, the bubble point equal
773.31psi (±0.001). it is clear to see that for a higher mole fraction there are higher bubble point
pressure.
Sincerely,
Nasser Alghamdi
1
Nasser Alghamdi
November 3, 2019
Theory, Concept and Objective of the Experiment
The experiment was performed using the PVT simulator. The simulator uses the Peng-Robinson
equation of state to calculate phase behavior.
(
𝑅𝑇
𝑎
)( 2
)=𝑃
(𝑉𝑀 − 𝑏) 𝑉𝑀 + 2𝑉𝑀 𝑏 − 𝑏 2
The simulator has some assumptions in order to make the calculations needed:
•
•
•
•
Mercury is incompressible.
The tubing in the system has no value.
The thermodynamic equilibrium is instantaneous.
Joule Thomson effects are neglected.
The objective of this is experiment was to find the bubble and dew point of the tow components
carbon dioxide and n-butane in different compositions of carbon dioxide and constant
temperature. The generating the pressure composition diagram of two components mixtures is as
follows:
Figure 1
In figure 1 you can see that the combination of compositions and pressure above the bubble point
line is liquid and below the dew point line is gas. The bubble point line is the locus of
composition of the liquid when two phases are present. The dew point line is the locus of
compositions of gas when gas and liquid are in equilibrium. The equilibrium tie line is a
2
Nasser Alghamdi
November 3, 2019
horizontal line that connects the composition of liquid with the composition of gas at
equilibrium.
Experimental Procedure
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Start recoding the initial condition of pressure, volume and temperature.
Open valve 8 to read initial condition temperature i.e. 2000psi.
Open valve 9 to connect the hand pump to the cell.
Find bubble point of pure n-Butane.
Use the hand pump to remove an amount of mercury volume that corresponds to the mole
fraction of carbon dioxide.
Close valve 8 to isolate the cell from the hand pump.
Open valves 1, 4 and 11 to connect the cell to the charge vessel and be able to inject.
Inject into the vessel the volume of mercury required which can be obtained from table
4a. This volume is equal to the volume of carbon dioxide that will be pushed.
Close valve 1, 4 and 11 to disconnect the charge vessel from the cell.
Open valve 8 to connect the pressure gage.
Shake the cell using F6. As the system contains a mixture carbon dioxide and n-butane,
so it has to be shaken in order to achieve equilibrium in the cell.
Find the bubble point of the mixture by using the hand pump to remove an amount of
mercury volume from the cell until the first drops of gas are formed in the cell (0.001cc)
of gas.
Repeat the steps for each mole fraction.
When the mole fraction is 9% the volume of carbon dioxide that needs to be added is
large, so this volume can be injected by separating it into two parts.
Continue removing the volume of mercury until reaching the dew point. However, the
dew points in this experiment could not be found because the cell volume was small
compared to the liquid volume, which couldn’t allow the liquid to convert to gas.
Figure 2
3
Nasser Alghamdi
November 3, 2019
Results and Calculations
mole
fraciton
P
xC02
y C02
xC4
yC4
Volume of
C02 added
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
32.569
140.9
245.18
343.3
433.11
512.54
581.13
641.19
700.41
773.31
0
0.0942
0.1896
0.2862
0.3842
0.4833
0.5839
0.6858
0.7891
0.8938
0
0.7499
0.848
0.8859
0.9056
0.9177
0.9262
0.9336
0.9432
0.9585
1
0.9058
0.8104
0.7138
0.6158
0.5167
0.4161
0.3142
0.2109
0.11062
1
0.2501
0.152
0.1141
0.0944
0.0828
0.0738
0.0664
0.0577
0.0415
0
0.57
1.282
2.197
3.418
5.126
7.69
11.962
20.505
46.137
Chart Title
900
800
700
600
500
400
300
200
100
0
0
0.2
0.4
0.6
xC02
0.8
1
1.2
yCo2
Figure 3
Calculations of Carbon dioxide volume of mole friction
Z=0.1
4
Nasser Alghamdi
November 3, 2019
At first, the density of carbon dioxide was found at initial pressure which was 2000psi. Table 5
was used as shown:
density (kg/m3)
Density vs temperature
940
920
900
880
860
840
820
800
780
y = -5.43x + 1012.5
y = -7.61x + 1006.8
15
17
19
21
23
25
27
Temperature (C)
10 MPa
15 MPa
Figure 4
Density of Co2 at
Temperature
C
P=10 Mpa
P=15 Mpa
16.9
878..2
920.7
26.9
802.1
866.4
22
839.4
893.0
5
29
Nasser Alghamdi
November 3, 2019
Density(kg/m3)
Pressure vs denisty
900.00
880.00
860.00
y = 10.652x + 732.82
840.00
820.00
9
10
11
12
13
14
15
Pressure (MPa)
Pressure
(Mpa)
Density
(Kg/m^3)
10
839.34
15
879.10
13.79
669.31
Calculating the Volume of Co2
Volume of CO2 was calculated using the following equation:
V CO2= v CO2 * n CO2 = v CO2 * (Z CO2 *nC4/ 1-Z CO2)
Where,
n = number of moles (lb. mole)
V = volume (cc)
v = molar volume(cc/kmole)
Z= mole fraction
6
16
Nasser Alghamdi
November 3, 2019
molecular weight of CO2 = 44.01 (kg/kmol)
𝜌 = 880.1 (Kg/m^3)
So:
v = 44.01/880.1= 0.05 (m^3/kmol) *(106)= 50000 (cc/kmole)
V = 50000 (cc/kmole) * 1 kmole/1000 mole * 0.1*0.0984/(1-0.1) (lb. mole)= 7.38 cc
Analysis and Discussion
There are possible errors that might be faced. For examples, errors in copying the data from the
PVT simulator. There is some possible source of errors. In the experiment we uses PengRobinson equation to calculate the values in obtained and it is not necessary to obtain a 100%
accurate values from the equation.
(
𝑅𝑇
𝑎
)( 2
)=𝑃
(𝑉𝑀 − 𝑏) 𝑉𝑀 + 2𝑉𝑀 𝑏 − 𝑏 2
1. Thermodynamic equilibrium is instantaneous
2. Joule-Thomson effects are neglected.
3. Mercury is incompressible
4. The tubing in the system has no value
Considering other source of errors, when calculating the density by the interpolation, assumption
of linear relationship was made.
Conclusion
In this experiment, the bubble point pressure was found using the PVT simulator.
However, due to the large volume of liquid the dew point was hard to be obtained so we had to
obtain it by plotting the pressure vs the mole fraction diagram. And we get to see that for
7
Nasser Alghamdi
November 3, 2019
different mole fractions, higher mole fraction of carbon dioxide gives higher initial pressure and
higher bubble point pressure. And the density was calculated by drawing the trend lines.
References
•
•
McCain, William D. The Properties of Petroleum Fluids. 2nd ed. Tulsa, OK: PennWell,
1990. Print.
Phase Behavior Lab Manual.
8
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