Case Study :
The Importance of Bubble point,
Dew point, and Critical point for
Multicomponent System in a Crude Oil
Reservoir Behaviour and Production
Name : Sharon Wong
Student ID : 700024096 / 19412827
Unit Name : Hydrocarbon Phase Behaviour
Unit Code : PEEN3008
Lecturer : Dr. Hisham Khaled Ben Mahmud
Due Date : 5th June 2020
1
Table of content :
Executive Summary ------------------------------------------------------------------------------ Page 1
Introduction ----------------------------------------------------------------------------------- Page 1 – 2
General Phase Diagram -------------------------------------------------------------------------- Page 3
Multicomponent System --------------------------------------------------------------------- Page 4 – 5
Black Oils -------------------------------------------------------------------------------------- Page 5 – 7
Volatile Oils ----------------------------------------------------------------------------------- Page 7 – 9
The Importance of Bubble-Point, Dew-Point, and Critical Point --------------------- Page 9 – 11
Correlations of Bubble-Point ------------------------------------------------------------------ Page 11
Standing Correlation ---------------------------------------------------------------------- Page 11 – 12
Vasquez and Beggs Correlation --------------------------------------------------------- Page 12 – 13
Al-Marhoun Correlation ------------------------------------------------------------------------- Page14
Glasso Correlation ------------------------------------------------------------------------- Page 14 – 15
Petrosky Correlation ---------------------------------------------------------------------- Page 15 – 16
Conclusion ---------------------------------------------------------------------------------------- Page 16
References ---------------------------------------------------------------------------------- Page 17 – 18
2
Executive Summary :
This report is a case study about importance of bubble point, dew point, and critical point for
multicomponent system in a crude oil reservoir behaviour and production. This report includes
introduction of hydrocarbon phase behaviour mostly on multicomponent system. This report
will also study about the general phase diagram, multicomponent system, black oil reservoirs,
volatile oil reservoirs, and the importance of bubble point, dew point and critical point. Various
correlations of bubble point are also included such as the Standing Correlation, Vasquez and
Beggs Correlation, Al-Marhoun Correlation, Glasso Correlation, and Petrosky Correlation.
Lastly, a conclusion about the overall case study is included.
Introduction
Petroleum reservoir fluids are broadly classified as oil, gas, or gas condensate. Crude oil are
light, intermediate, and heavy which leads to classification of an oil reservoir. Crude oils exist
in a wide range of physical properties and chemical compositions because it is often important
to be able to group them into general classifications of related oils. Generally, crude oils are
usually classified into ordinary black oil, low-shrinkage crude oil, volatile (high-shrinkage
crude oil), and near-critical crude oil (Satter, Iqbal, and Buchwalter 2007).
Oil reservoirs consists of hundred of hydrocarbon components of different molecular weights
where gas samples are the fewer components and are mainly light hydrocarbons. Depending
on the initial reservoir pressure, oil reservoirs can be subclassified into undersaturated oil
reservoir and saturated oil reservoir. The reservoir is said to be an undersaturated oil reservoir
if the initial reservoir pressure is greater than the bubble-point pressure of the reservoir fluid.
However, if the initial reservoir pressure is equal to the bubble-point pressure of the reservoir
fluid, the reservoir is said to be saturated oil reservoir (Satter, Iqbal, and Buchwalter 2007).
3
In order to interpret a phase diagram, it is a must to understand the concepts of bubble
point and dew point for a mixture. Bubble point defines the point at which the first drop of a
liquid mixture begins to vaporize whereas dew point defines the point at which the first drop
of a gaseous mixture begins to condense. Critical point is defined as the state of pressure and
temperature where all properties of the gas and liquid phases are equal (Madhusha 2017).
Therefore, the main goal of this case study is to review the basic principles of reservoir oil
phase behaviours and illustrate the use of phase diagrams in characterizing the types of
reservoirs. Furthermore, the importance of bubble point, dew point and critical point will also
be covered in this case study as well as the different correlations for bubble point.
4
General Phase Diagram :
A general phase diagram is a graph that represents the physical states of substances under
different conditions of temperature and pressure in a closed container. As shown in the diagram
below (Figure 1), every point in the diagram shows a possible mixture of temperature and
pressure for the system. The y-axis represents pressure while the x-axis represents temperature.
It is also divided into three sections which are representing the solid, liquid and gaseous states
of substance. As we cross the lines on the phase diagram, a phase change occurs and also two
states of the substance exist side-by-side in equilibrium on the lines.
By looking at the diagram in Figure 1, the triple point on the phase diagram represents the point
where the three states of matter exist which are solid, liquid and gas. The critical point on the
phase diagram represents the point where the substance is indistinguishable between liquid and
gaseous states. The curve which represents the transition between liquid and solid states is
known as the fusion. The curve which represents the transition between gaseous and liquid
states is known as vaporization. The curve which represents the transition between gaseous and
solid states is known as sublimation (Chemistry LibreText 2020).
Figure 1 : General Phase Diagram (Chemistry LibreText 2020)
5
Multicomponent system :
A multicomponent mixture system shows an envelope for liquid/vapor phase change in the
pressure/temperature diagram. The envelope contains a bubble-point line and a dew-point line,
compared with only a phase change line for a pure component. There are several reservoir types
of oil and gas systems based on the phase behaviour of hydrocarbons in the reservoir which are
black oils, volatile oils, condensate, wet gas, and dry gas (Oilfield Wiki 2016). However, in
this case study, only oil phase behaviours will be studied.
Compared to a pure compound phase diagram, a multicomponent system is more detailed and
elaborate as it consists of components with different structure and molecular sizes in the system.
As shown in the Figure 2 below, a transition zone exists between the liquid phase and the
vapour phase, which means when the pressure is decreasing at a fixed temperature, the phase
changes from liquid to vapour on a line. Thus, there are two phases at equilibrium (PERM Inc
2003).
Figure 2 : Typical Multicomponent System Phase Diagram (Petroblogger 2013)
6
The use of a multicomponent pressure-temperature diagram is to help classify the types of
reservoir, naturally occurring hydrocarbon systems, and to describe phase behaviour of a
reservoir fluid (Petroblogger 2013). There are some key points in the diagram which are
important and necessary to understand. The Cricondentherm is defined as the maximum
temperature at which liquid and vapour may co-exist. The Cricondenbar is defined as the
maximum pressure at which liquid and vapour may co-exist. The Critical Point is defined as
the state of pressure and temperature where all properties of the gas and liquid phases are equal.
The temperature and pressure at this point are known as the critical temperature (Tc) and the
critical pressure (Pc). The Two-Phase Region also known as the phase envelope, is the region
bounded by the bubble-point curve and the dew-point curve where liquid and gas coexist in
equilibrium phase. The Bubble-Point curve is the line separating the liquid phase region from
the two-phase region which represents the true vapour pressure of a liquid. The bubble-point
for a liquid is the first appearance (bubble) of a gas phase on reaching the two-phase
equilibrium line. The Dew-Point curve represents the line separating the vapor phase region
from the two-phase region. The dew-point for a gas indicates the first appearance of liquid
(dew) at the two-phase line. The dashed lines within the phase diagram are known as Quality
Lines. These lines indicate the pressure and temperature conditions for equal volumes of
liquids. They intersect at the critical point (Cp) and are roughly parallel to the bubble-point and
dew-point curves. The bubble-point curve represents 0 % vapour and the dew-point curve 100 %
vapour (Zhang and Gao 2016).
Black Oils :
Black oil or also known as low-shrinkage crude oil, is a single-phase liquid system that resides
in reservoirs with temperature below the critical temperature of a hydrocarbon mixture. Black
oil consists of a wide variety of chemical species including large, heavy, and non-volatile
hydrocarbons. Black oils are transported in the liquid phase throughout the transport process
in transport pipelines. However, the produced hydrocarbon mixtures are usually in thermodynamical equilibrium with gas in the production flowlines (King 2018). Black oils that are
dark in colour indicates that heavy hydrocarbons are in present. Nonetheless, black oils are not
always dark or black in colour. The critical temperature of black oil is greater than the reservoir
7
temperature. The producing gas oil ratio (GOR) of black oil reservoir is less than 170 (<1000
scf/STB) and will increase during production when reservoir drops below bubble point pressure.
The specific gravity of black oil is >0.802 (<45° API). Its formation volume factor is <2.0 and
its composition of C7+ are normally >20%.
Below in Figure 3 shows a typical P-T phase diagram of an ordinary black oil. The quality lines
which are approximately equally spaced followed by the pressure reduction path in the phase
diagram characterizes this black oil phase diagram. At point 1  2, it indicates undersaturated
oil which mean the oil is able to dissolve more gases present if there were more. At point 2
where the oil is at its the bubble-point, indicates saturated oil which contains the maximum
amount of dissolved gas and the oil cannot absorb more gas if more gases are present. Whereas
at point 2  3 (surface separator condition), more gas will evolve out of the oil into the
reservoir, meaning that the reservoir pressure can no longer force the fluids to the surface under
its current state. Thus, a large percentage of the oil phase is recovered at this surface which
indicates that the gases are released. When the pressure is below to the surface pressure at
separator, the black oil will present (IHS Markit 2014).
Figure 3 : Typical Black Oil Phase Diagram (Lecture 3 notes)
8
Figure 4 : Typical Low-Shrinkage Crude Oil Phase Diagram (Petroblogger 2013)
Volatile Oils :
Volatile oil, also known as high shrinkage crude oil or near-critical crude oil, contains lesser
heavy molecules than black oils but more ethane through hexane. They are very close to the
critical temperature and pressure at reservoir conditions where the more the pressure decrease,
the more the amount of gas will be released. Volatile oil reservoir begins similarly like a black
oil reservoir with the initial reservoir pressure lying above the bubble point line. However, the
initial pressure is much closer to the bubble point pressure because a volatile oil reservoir
consists of more lighter hydrocarbon components compared to a black oil reservoir (Tolbert
2020). The critical temperature of a volatile oil is greater than the reservoir temperature. Its
colour at stock tank is lighter than black oil and are usually green, orange, or brown. The gas
oil ratio (GOR) is in the range of 170 – 580 (1000 – 3300 scf/STB). The specific gravity of
volatile oil is <0.825 (>40° API). Its formation volume factor is >2.0 and its composition of
C7+ is around 12.5% − 20%.
9
Below in Figure 5 shows a typical P-T phase diagram of a volatile oil. As we can see, the
quality lines are closer to each other which indicates that a small reduction of pressure below
the bubble point line will release a huge quantity of gas. More gas will be produced at the
surface because more solution gas evolves out of the oil which leads to a less liquid recovery.
Thus, it is clearly shown that volatile oil produces a higher quantity of gas than black oils. At
point 1  2, it indicates undersaturated oil which means the oil is able to dissolve more gases
present if there were more. At point 2 where the oil is at its the bubble-point, indicates saturated
oil whereas at point 2  3, indicates a small pressure change resulting in a large amount of gas
released. A volatile oil may become as much as 50% gas in the reservoir at only a couple of
MPa below the bubble-point pressure. At separator condition, the percent of liquid is lower
than gas at reservoir conditions (IHS Markit 2014).
Figure 5 : Typical Volatile Oil Phase Diagram (Lecture 3 notes)
10
Figure 6 : Typical Near-Critical Crude Oil Phase Diagram (Petroblogger 2013)
The Importance of Bubble-Point, Dew-Point, and Critical Point :
Bubble point of reservoir oil is an important fluid property which defines the pressure where
the volatile components in the oil begin to “bubble up.” The pressure at which these bubbles
of light hydrocarbons first appear is known as the bubble point for the fluid system. The
performance of a reservoir changes significantly when the reservoir produces below the bubble
point, including oil and gas rates at the wells. In the case of volatile oil which contains more
light hydrocarbon components, it has a higher bubble point pressure where the gas phase begins
to evolve early during depletion. However, for heavy oils, the bubble point appears to be lower.
The bubble point pressure in typical oil reservoirs ranges between 1800 psi and 2600 psi (Satter
and M. Iqbal 2016).
Dew point of a reservoir defines the point at which the first drop of a gaseous mixture begins
to condense. It is not an easy parameter to measure due to several factors including gas
composition, contaminants, high pressures, and the presence of corrosive compounds. Hence,
a higher dew point indicates a higher amount of heavy hydrocarbon components. The dew point
11
line separates the two-phase gas and liquid region and the single-phase gas region. Two dew
point temperatures are possible at a given pressure and two dew point pressures are possible at
a given temperature (Michell Instruments n.d.).
Critical point or also known as critical states defines the point at which two phases of a
substance initially become indistinguishable from one another where all properties of the gas
and liquid phases are equal. For each substance, the conditions defining the critical point are
the critical temperature, the critical pressure, and the critical volume. To understand this better,
we take a simple experiment as an example. In a closed vessel filled with pure substance, partly
liquid and partly vapour, the average density equals to the critical density. Hence, the critical
conditions can be achieved. As the temperature is increasing, the vapour pressure will increase
as well causing the gas phase to be denser. The liquid expands and becomes less dense till it
reaches the critical point. Then, the densities of liquid and vapour becomes equal, eliminating
the boundary between the two phases (Helmenstine 2018). Critical point is important as it helps
in identifying compound. If the temperature is higher than the critical temperature, the
substance cannot exist as a liquid no matter what the pressure is. However, if the temperature
and pressure is higher than the critical point, the substance is considered a fluid. If the pressure
is below the critical pressure (but at higher temperature), the substance is considered a gas.
Knowing the dew point and bubble point of solutions helps to determine what phases exist at
certain temperatures. Hence, bubble point pressure is an important characteristic of
the reservoir fluid that is used to forecast a reservoir’s performance. The bubble point pressure
is handled as a function of solution gas oil ratio, gas gravity, oil gravity, and temperature.
Knowing the bubble point pressure is very crucial while planning a field development strategy
as it helps to determine the gas oil ratio (GOR) and control the forming of secondary Gas Cap.
For example, the initial pressure of reservoir is 1050 psi and the bubble point pressure for the
crude in the reservoir is 700 psi. In this case, the effort is to be aware that the reservoir pressure
should not be lowered below 700 psi. This way, you will obtain a better well placement and
exploitation rate from each well. If the reservoir pressure moves below 700 psi (assume gas
cap is absent), this will lead to a high GOR meaning a low ultimate recovery and formation of
secondary gas cap (Ahmed 2019).
12
The importance of dew point pressure will vary from different reservoirs, but in most situations
accurate dew point determination is not important. In the context of compositional variation
with pressure accurate determination of the thermodynamic dew point pressure is not of
particularly important. In fact, knowledge of the specific dew point is important as long as the
variation of composition (C7+ content) with pressure is clearly defined “near” the
thermodynamic dew point. Moreover, when the bottom-hole flowing pressure shrinks below
the dew point and two phases start flowing near the wellbore, gas relative permeability drops
which causes the well productivity to drop too. Next, dew point pressure is also essential to
determine whether an underlying saturated oil zone may exist, and a PVT model is used to
predict the existence and location of the gas oil contact (GOC). Thus, the PVT model dew point
must be adjusted precisely to an accurately measured dew point pressure. An accurate
description of the dew point pressure plays an important role in the prediction of initial oil and
gas in place, placement of delineation wells, and potential field development strategy. In this
situation, an accurate dew point measurement and equally accurate modelling of the measured
dew point should be highly taken note of (Ghosh 2016).
Correlations of Bubble-Point :
Bubble point is an essential characteristic as it helps to forecast a reservoir’s performance.
Bubble point is known as highest pressure at which the gas bubbles co-exist with oil. Without
experimentally measured properties of reservoir fluids, it is compulsory for the field engineers
to estimate the fluid properties based on the usually measured producing parameters. To help
in these estimations, various correlations can be used to estimate the bubble point pressure for
crude oil. These includes Standing Correlation, Vasquez and Beggs Correlation, AlMarhoun Correlation, Glaso Correlation, and Petrosky Correlation (Lasater 1958).
13
Standing Correlation :
Standing (1947) introduced a correlation for bubble point pressure with 105 experimental data
from California crude oil fields. It was introduced as a two-step flash liberation test to gather
experimental data and it was reported that the average error in this method is about 4.8%
(Mahdavi, Suleymani, and Rahmanian 2017). The Standing correlation was initially presented
in graphical form, and later a mathematical form was introduced as below in Equation 1 and
Equation 2 :
𝑅
0.83
𝑃𝑏 = 18.2 [ (𝛾 𝑠 )
𝑔
10𝑎 − 1.4 ] -------------------- (Equation 1)
Where,
𝑃𝑏 = Bubble Point pressure (psi)
Rs = Solution gas and ratio (SCF/STB)
𝛾𝑔 = Gas specific gravity
𝑎 = 0.00091 (𝑇 − 460) − 0.0125 𝐴𝑃𝐼 -------------------- (Equation 2)
Where,
T = Temperature (°R)
14
Vasquez and Beggs Correlation :
Vasquez and Beggs (1980) used an extensive set of data from different oil fields for their
correlation. This correlation is applicable as it contains equations for solution GOR, oil FVF,
and oil compressibility. The subsequent formula is the result of data obtained from over 600
laboratory PVT analyses collected from fields around the world and regression over more than
5000 data points. The data was divided into two groups which is the oil gravity above 30°API
and below 30°API (Mahdavi, Suleymani, and Rahmanian 2017). The authors introduced the
following expression in Equation 3 and Equation 4 below, followed by the data coefficient data
in Table 1 :
𝑅
𝑃𝑏 = [ (𝐶1 𝛾 𝑠 ) 10𝑎 ]
𝐶2
𝑔𝑛
-------------------- (Equation 3)
Where,
𝑃𝑏 = Bubble Point pressure (psi)
Rs = Solution gas and ratio (SCF/STB)
𝛾𝑔𝑛 = Normalized gas specific gravity at reference separator condition
a=
−𝐶3 𝐴𝑃𝐼
𝑇
-------------------- (Equation 4)
Where,
T = Temperature (°R)
15
Table 1 : Coefficient of Vasquez and Beggs Correlation
Al-Marhoun Correlation :
Al-Marhoun correlation was based on experimental PVT data from Middle East oil mixtures
which includes equations to estimate bubble point pressure, solution gas oil ratio, and oil
formation volume factor for Saudi Arabian oils. As claimed by the author, the correlations
should be valid for all types of gas-oil mixtures that have the same properties as those used in
the derivation. The average absolute error was said to be 3.66% which is lower than the
Standing and Glaso correlations for Saudi Arabian crude oils (Mahdavi, Suleymani, and
Rahmanian 2017). The equation below was introduced by Al-Marhoun (1988) :
𝑃𝑏 = 𝑎 𝑅𝑠𝑏 𝛾𝑔𝑐 𝛾𝑜𝑑 𝑇 𝑒 -------------------- (Equation 5)
Where,
𝑃𝑏 = Bubble Point pressure (psi)
a = 5.38088 × 10-3
T = Temperature (°R)
b = 0.715082
Rs = Gas oil ratio (SCF/STB)
c = −1.87784
𝛾𝑔 = Gas specific gravity
d = 3.1437
𝛾𝑜 = Oil specific gravity
e = 1.32657
16
Glaso Correlation :
Glaso (1980) introduced a correlation for bubble point prediction based on experimental data
obtained mostly from North Sea reservoirs which includes equations for estimating bubble
point pressure, solution gas oil ratio, and oil formation volume factor for North Sea oils. As
claimed by the author, the correlation is valid for a wide range of oil and gas mixtures after
correcting for non-hydrocarbons in the surface gases and the paraffinicity of the oil. The
correlation can also accurately predict the oil properties of North Sea oils than the Standing
correlation. The average error is 1.28% whereas the standard deviation is 6.98%. Thus, the
Glaso correlation is more accurate than the Standing correlation (Mahdavi, Suleymani, and
Rahmanian 2017). The correlation introduced by Glaso is as below :
log 𝑃𝑏 = 1.7669 + 1.7447 log(𝐴) − 0.30218 [log(𝐴)] 2 -------------------- (Equation 6)
𝑅
A = (𝛾 𝑠 ) 0.816
(𝑇−460) 0.172
𝑔
𝐴𝑃𝐼 0.989
-------------------- (Equation 7)
Where,
𝑃𝑏 = Bubble Point pressure (psi)
T = Temperature (°R)
Rs = Solution gas and ratio (SCF/STB)
𝛾𝑔 = Gas specific gravity
17
Petrosky Correlation :
Petrosky (Petrosky and Farshad, 1993) introduces a correlation for Gulf of Mexico oil which
includes equations for estimating bubble point pressure, solution gas oil ratio, oil formation
volume factor, and oil compressibility. It was introduced using fluid samples obtained from
offshore regions located in Texas and Louisiana. As claimed by the author, these correlations
produce improved results compared to other correlations for the Gulf of Mexico which are the
Standing, Vasquez and Beggs, Glaso, and Al-Marhoun correlation. An analysis of a set of 128
PVT data of oil mixtures has been utilized to develop a nonlinear regression model. The
average error is 3.28% relative to the database (Mahdavi, Suleymani, and Rahmanian 2017).
The equation of the correlation is as follows :
𝑃𝑏 = [
112.727 𝑅𝑠0.577421
𝛾𝑔0.8439 10𝑎
] − 1391.051 -------------------- (Equation 8)
a = 7.916 × 10−4 × (𝐴𝑃𝐼)1.5410 − 4.561 × 10−5 × (𝑇 − 460)1.3911 --------------- (Equation 9)
Where,
𝑃𝑏 = Bubble Point pressure (psi)
T = Temperature (°R)
Rs = Solution gas and ratio (SCF/STB)
𝛾𝑔 = Gas specific gravity
18
Conclusion :
To conclude this case study, oil with a higher bubble point pressure produces better than the
case where the bubble point of oil is lesser. This is because the reservoir pressure rejects early
below the bubble point which leads the way for solution gas drive to produce oil. However, if
the bubble point of the reservoir fluid is low, the reservoir tends to produce above the bubble
point by mechanism of fluid expansion. Besides that, lighter crudes have higher production
rates as lighter hydrocarbons have higher ultimate recovery. Thus, bubble point, dew point and
critical point are essential characteristics to identify and forecast a reservoir’s performance as
well as to classify the types of reservoir. Lastly, to achieve better results of ultimate oil recovery,
early pressure maintenance operation by gas/water injection needs to be done to ensure that the
reservoirs will produce above the bubble point.
References :
Chemistry LibreText. 2020. “Phase Diagrams”. LibreText.
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbo
ok_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_P
roperties_of_Matter/States_of_Matter/Phase_Transitions/Phase_Diagrams
Ghosh, Aninda. 2016. “What is the importance of knowing the value of bubble point and
what is its effect on the production from the reservoir?”. Oges G Pte. Ltd.
https://oges.info/question/140082/importance-knowing-value-bubble-effectproduction-reservoir
Helmentine, Anne Marie. 2018. “Critical Point Definition”. ThoughtCo.
https://www.thoughtco.com/definition-of-critical-point-605853
IHS Markit. 2014. “Reservoir Fluid Types”. Fekete.
19
http://www.fekete.com/SAN/WebHelp/FeketeHarmony/Harmony_WebHelp/Content/
HTML_Files/Reference_Material/General_Concepts/Reservoir_Fluid_Types.htm
King, Gregory. 2018. “2.8: Undersaturated Black Oil (Low Shrinkage Oil) Reservoirs”. The
Pennsylvania State University.
https://www.eeducation.psu.edu/png301/node/829#:~:text=Undersaturated%20black%20oils%2C%
20sometimes%20referred,than%20critical%20temperature%2C%20TC.&text=The%2
0phase%20diagram%20for%20the,composition%20of%20the%20crude%20oil.
Lasater, J.A. 1958. “Bubble Point Pressure Correlation”. OnePetro.
https://www.onepetro.org/journal-paper/SPE-957-G
Mahdavi, Suleymani, and N. Rahmanian. 2017. “Oil and Gas Properties and Correlations”.
Knovel.
https://app.knovel.com/web/view/khtml/show.v/rcid:kpT6OXK115/cid:kt00CRMKB
1/viewerType:khtml//root_slug:1-oil-and-gas-properties-and-correlations/url_slug:oilgas-properties-correlations?kpromoter=federation&b-toc-cid=kpT6OXK115&b-tocroot-slug=&b-toc-url-slug=oil-gas-properties-correlations&b-toctitle=Fluid%20Phase%20Behavior%20for%20Conventional%20and%20Unconventio
nal%20Oil%20and%20Gas%20Reservoirs&page=17&view=collapsed&zoom=1
Michell Instruments. n.d. “What is Hydrocarbon Dew Point?”. Michell Instruments.
http://www.michell.com/us/documents/whtpapers/What_is_Hydrocarbon_DewPoint.p
df
OilField Wiki. 2016. “Phase Diagram”. OilField Wiki.
http://www.oilfieldwiki.com/wiki/Phase_Behavior#Black_Oils
PERM Inc. 2003. “Fluid Phase Behavior: Pressure-Temperature Diagram (P-T Diagram)”.
PERM Inc.
https://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter5-miscible-displacement/fluid-phase-behavior/pressure-temperature-diagram-p-tdiagram/
Satter and M. Iqbal. 2016. “Bubblepoint”. ScienceDirect.
20
https://www.sciencedirect.com/topics/engineering/bubblepoint
Zhong and Gao. 2016. “Multicomponent System”. ScienceDirect.
https://www.sciencedirect.com/topics/engineering/multicomponent-system
21