Petroleum Engineering Mathlab Code, for given inputs using petroleum emgineering formulas write a matlab code and find related graphs in questionIt is about petroleum engineering not just mathlabUsing matlab, and petroleum engineering formulas.Write a (Matlab) code to compute pseudo-pressure (psi²/cp) for a given gas. The gas is to be specified by the total gas gravity, and the mole fractions of the non-hydrocarbon gas component (CO2, H2S, N2). The code should ask or have input values of these parameters (that is, they can be read from a file, or specified values in the code as well). The code should draw pseudo-pressure vs. pressure curves at 60F, 150F and 300F for the pressure range of 0 to 10000 psi.Actually I need only a Z-factor determination method , not all question, since there is no given pressure and temperature initially I couldnt find Z-factor,

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GEO3020

Problem Set 4

Due on 20 November 2020

Crystallization in the System CaAl2Si2O8 – SiO2

      We often use simplified chemical systems to describe the melting and crystallization behavior of natural rocks and silicate magmas.  Because they contain fewer chemical components than real rocks, such model systems are easier to interpret and to study in the laboratory.  The model system CaAl2Si2O8-SiO2 contains the minerals anorthite and quartz.  The attached table summarizes the results of some hypothetical experiments on melting and crystallization in this system at a constant pressure, P = 1 bar.

      In experiments at one bar (~ one atmosphere), starting materials are placed in a container (such as a platinum crucible), heated at a known temperature for times from hours to weeks, and then cooled quickly (quenched in water).  If liquid were present at the temperature of the experiment, it would be preserved as a glass in the run products.  If crystals were present, they would also be preserved and can be identified by optical means or, if too fine-grained, by x-ray diffraction.

      In experimental work, the nature of the starting materials is important and it is important to “reverse” the directions of experiments.  Because the rates of reactions may be very sluggish, in a short experiment it is possible that crystals will persist above the melting temperature (the crystal is then metastable) or that they will fail to grow in the liquid until much below the freezing point (supercooling).  Consequently, it is important to show that the same result may be obtained using either crystals or glasses as a starting material.  The accompanying table indicates the nature of the starting materials and their composition.  Glasses are single homogeneous phases (a solution) of the specified weight per cent silica.  Crystalline starting materials in this binary system must be mixtures of anorthite and quartz having the indicated wt. per cent of quartz (SiO2) with the remainder being anorthite (CaAl2Si2O8).

      The products of the experiments may include glass quenched from high temperature liquids, anorthite, or one of several high temperature polymorphs of SiO2, such as cristobalite, tridymite, or -quartz.  In the attached table, all such polymorphs were simplified as “quartz.”

Table 1: Experimental Results at One bar in the  System CaAl2Si2O8 – SiO2

Start Material
wt.% SiO2
T(oC)
Products

Crystal
0
1360
An

Crystal
0
1400
An

Crystal
0
1540
An

Crystal
0
1560
gl

Glass
0
1550
An

Crystals
20
1350
An+Qtz

Crystals
20
1400
An+gl

Crystals
20
1480
An+gl

Crystals
20
1520
gl

Glass
20
1520
gl

Glass
20
1450
An+gl

Glass
20
1360
An+Qtz

Glass
40
1500
gl

Glass
40
1425
gl

Glass
40
1400
An+gl

Glass
40
1360
An+Qtz

Crystals
40
1380
An+gl

Crystals
50
1500
gl

Crystals
50
1400
gl

Crystals
50
1380
gl

Glass
50
1350
An+Qtz

Crystals
60
1500
gl

Glass
60
1400
Qtz+gl

Glass
60
1350
An+Qtz

Crystals
60
1380
Qtz+gl

Crystals
80
1625
gl

Crystals
80
1600
Qtz+gl

Glass
80
1500
Qtz+gl

Crystals
80
1400
Qtz+gl

Glass
80
1360
An+Qtz

Crystals
100
1720
gl

Glass
100
1700
Qtz

Phase Rule. 
For this part you don’t need, and you should not use, the experimental results.

a. Gives the phase rule necessary to describe equilibria at constant pressure. 

b. Does the phase rule predict that melting of pure An should occur at a specific temperature or a range of temperatures at one bar pressure.  Explain.  Indicate what you are counting as phases and components in this and all similar questions below.

c. Should mixtures of An + Qtz crystals begin to melt at a specific T or over a range of T according to the phase rule?  Explain.

d. How many components are necessary to describe the compositions of liquid in this system?

e. Use the phase rule to predict whether such liquids should coexist with anorthite at a single temperature or a range of temperatures.

f. What does the phase rule predict about the temperature at which An + Qtz + liq may coexist at equilibrium?

g. From your knowledge of the phase rule, can a range of liquid compositions coexist with An + Qtz? Explain.

Phase Diagram
a.  An excel version of table 1 is provided. Plot the results of the experiments summarized in Table 1 on a diagram of T versus wt. % SiO2.  Use EXCEL and write all your answer on your excel spreadsheet.

Instructions:

use a different symbol for each type of phase assemblage (e.g., series1 = glass, series2 = Glass + An, series 3 = Di+An,…) and make sure to show the legend (in excel: Tab:Chart tools –Design / Add chart element).  Remember that the presence of glass in quenched products implies the presence of liquid at the conditions of the experiments.
Make sure to label you axes legend (in excel: Tab:Chart tools –Design / Add chart element-> Axis title)
Setup your Y-axis (i.e., Temperature axis) between 1300 and 1750oC

b. Are the experimental results of the experiments consistent with your answer Ib? Why or why not?

c. Solidus:

      c.1 Draw a line on your phase diagram that separates the field of 100% crystalline phases from the fields in which a liquid is present (I encourage you to print your phase diagram and to draw you solidus on the printed version: USE A RULER. You can also do it on Excel, but drawing the liquidus curve on excel -question IId – will be more challenging).

      c.2 Estimate the uncertainty in your determination of the solidus temperature.

d. Draw the liquidus curve on your diagram that satisfy your experimental data and the predictions from the phase rule (this time, it will be much easier to do it manually on the printed version).

     III. Melting History

Write the history (I want sentences, not only number) of equilibrium melting of a rock containing 20 wt.% SiO2 and 70% CaAl2Si2O8.  Illustrate all critical stages of the melting on your phase diagram and include at least the following information: (1) Temperatures at which the first drop of melt appears and the last crystal disappears; (2) Compositions of the phases at 1450 oC and 1300 oC; (3) The proportions of phases at 1450 oC and at 1300 oC.

Bonus question: Illustrate the change of temperature with time during the crystallization process, assuming a constant input of heat (i.e, draw a Temperature – time diagram). (tip: don’t rush and take the time to think about it: What is more likely to change temperature faster when heat is applied? What happened at the eutectic? Ect…)

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