Introduction
As a discipline, petroleum engineering seeks to assess prospective oil and gas reservoirs; supervise drilling undertakings; chose and implement extraction measures; and plan surface collection and treatment equipment (Bradley, 1987). But why petroleum engineering? The ever increasing energy needs and sustainable materials, necessitates developing new methods and practices to extracting hydrocarbons from oil shale and offshore oil and gas fields. Besides, petroleum engineering seeks to address complex challenges that arise from heavy fraction deposition in the extraction process that can sometime run into several millions dollars (Kinney, Lance, & Catherine, 2018).
Why phase behavior in petroleum engineering?
In a bid to model reservoirs, assess reserves; plan production, conveyance and utilization systems to eschew problems related to heavy organic deposition, there is need to develop models for foreseeing phase behavior of petroleum fluids (Jin, Zhehui, & Firoozabadi, 2016). Phase behavior is the study of pressure, composition and temperature properties of petroleum fluids in solid, liquid and gas states. If one increases temperature of a petroleum fluid in liquid state while keeping pressure constant, fluid reaches bubble point, upon further temperature increase it reaches dew point (Whitson et al., 2010). In another instance, if one reduces pressure of a petroleum fluid while keeping temperature constant, fluid reaches bubble point, upon further reduction it reaches the dew point (Mansoori 17). Phase behaviors influence the 1st order, 2nd order and infinite-order transitions of the fluids.
Advantage of EOS modeling over experiments
An Equation of State is an analytical expression relating pressure (p) to temperature (T) and volume (V). This relation is vital in assessing the volumetric and phase behavior of petroleum reservoir fluids and envisaging the performance of surface separation facilities (Pedersen et al., 2014). Most accepted EOSs in use today are the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) which are simple adjustment of the Van Der Waal’s equation in 1873. EOS model is more beneficial over fluid injection experiments in that an EOS model can be fine-tuned for any specific need by varying parameters to tell fluid properties (Vinet et al,. 2008).
What type of cubic EOS you would use in this report? Why?
All equations of state are developed for pure fluids first, then extended to mixtures by calculating mixture properties equivalent to those of pure substances. For this report, I would use PR EOS because it performs better by a small margin in predicting vapor-pressure and densities of fluids compared to SRK EOS and experimental methods (Abudour et al., 2017). PR EOS is also easy to use and more reliable (Ashour et-al., 2011).
What are CCE, CVD, and DV processes? Give some examples about these procedures in petroleum engineering.
Constant composition expansion (CCE) – is a property that illustrates pressure-volume behavior of a fluid without changes in fluid composition (Bi, Ran and Hadi, 2019).
Constant Volume Depletion (CVD) – these are processes done on gas condensates and volatile oils in order to simulate composition variation as well as reservoir depletion performance (Arabloo et al., 2014).
Differential Vaporization (DV) – it is the process that involves liberation of solution gas from the oil during pressure decline for example, differential liberation at the reservoir (separation process) (Umnahanant, 2019).
Report objective
The main objective of this report is to provide adept information about petroleum engineering and all that relate to phase behavior.
Methodologies
Key PR-EOS equations
–
Where a = 0.45724
b = 0.0778
= [1 + k (1 – )] 2
k = 0.37464 + 1.54226 – 0.2
Tr =
Equilibrium conditions of PR-EOS
At equilibrium, the given pressure and temperature are directly proportional. Temperature and pressure in PR-EOS are not independent quantities; they are linked to the general form of the EOS (Li et al., 2019).
Results and Discussions
Calculations Summary
Calculations of Constant Composition Expansion (CCE) of both upper and lower dewpoint, Constant Volume Depletion (CVD) for upper dewpoint, and Differential Vaporization (DV) bubblepoint.
Constant Composition Expansion (CCE)
Pressure Calculation Sequence 2
P (bar) = 120.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -8.41734E-03 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.74898137 0.46563815 CH4
2 0.3000 0.25101863 0.53436185 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.82713 0.17287
VOLUME FRACTION: 0.87823 0.12177
ZFACTOR: 0.76673 0.50837
MW(g/mol): 33.64645 53.52014
MASS DEN(Kg/L): 0.14867 0.35647
MOLE DEN(mol/L): 4.41869 6.66043
VISCOSITY(cP): 0.01834 0.04226
SURFACE TENSION(dyne/cm): 0.17613
Iter (SSI) = 16
Iter (NR) = 2
Error flash = 3.31E-12
Tolerance flash = 1.00E-10
Pressure Calculation Sequence 3
P (bar) = 100.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -3.00633E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.76577924 0.37755794 CH4
2 0.3000 0.23422076 0.62244206 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.83056 0.16944
VOLUME FRACTION: 0.90184 0.09816
ZFACTOR: 0.79768 0.42722
MW(g/mol): 32.46824 59.69809
MASS DEN(Kg/L): 0.11492 0.39603
MOLE DEN(mol/L): 3.53938 6.63385
VISCOSITY(cP): 0.01686 0.04876
SURFACE TENSION(dyne/cm): 0.59546
Iter (SSI) = 11
Iter (NR) = 2
Error flash = 1.09E-11
Tolerance flash = 1.00E-10
Pressure Calculation Sequence 4
P (bar) = 80.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -5.96432E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.76653736 0.29556489 CH4
2 0.3000 0.23346264 0.70443511 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.85872 0.14128
VOLUME FRACTION: 0.93529 0.06471
ZFACTOR: 0.82167 0.34827
MW(g/mol): 32.41507 65.44908
MASS DEN(Kg/L): 0.08910 0.42778
MOLE DEN(mol/L): 2.74884 6.53608
VISCOSITY(cP): 0.01570 0.05491
SURFACE TENSION(dyne/cm): 1.26383
Iter (SSI) = 8
Iter (NR) = 2
Error flash = 4.11E-11
Tolerance flash = 1.00E-10
Pressure Calculation sequence 5
P (bar) = 60.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -6.94205E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.74902086 0.21505687 CH4
2 0.3000 0.25097914 0.78494313 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.90819 0.09181
VOLUME FRACTION: 0.96919 0.03081
ZFACTOR: 0.84135 0.26764
MW(g/mol): 33.64368 71.09591
MASS DEN(Kg/L): 0.06774 0.45520
MOLE DEN(mol/L): 2.01341 6.40260
VISCOSITY(cP): 0.01458 0.06113
SURFACE TENSION (dyne/cm): 2.17832
Iter (SSI) = 6
Iter (NR) = 2
Error flash = 4.22E-13
Tolerance flash = 1.00E-10
Constant Volume Depletion
Pressure Calculation Sequence 2
P (bar) = 120.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -8.41734E-03 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.74898137 0.46563815 CH4
2 0.3000 0.25101863 0.53436185 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.82713 0.17287
VOLUME FRACTION: 0.87823 0.12177
ZFACTOR: 0.76673 0.50837
MW(g/mol): 33.64645 53.52014
MASS DEN(Kg/L): 0.14867 0.35647
MOLE DEN(mol/L): 4.41869 6.66043
VISCOSITY(cP): 0.01834 0.04226
SURFACE TENSION(dyne/cm): 0.17613
Iter (SSI) = 16
Iter (NR) = 2
Error flash = 3.31E-12
Tolerance flash = 1.00E-10
Pressure Calculation Sequence 3
P (bar) = 100.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -3.00633E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.76577924 0.37755794 CH4
2 0.3000 0.23422076 0.62244206 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.83056 0.16944
VOLUME FRACTION: 0.90184 0.09816
ZFACTOR: 0.79768 0.42722
MW(g/mol): 32.46824 59.69809
MASS DEN(Kg/L): 0.11492 0.39603
MOLE DEN(mol/L): 3.53938 6.63385
VISCOSITY(cP): 0.01686 0.04876
SURFACE TENSION(dyne/cm): 0.59546
Iter (SSI) = 11
Iter (NR) = 2
Error flash = 1.09E-11
Tolerance flash = 1.00E-10
Pressure Calculation Sequence 4
P (bar) = 80.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -5.96432E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.76653736 0.29556489 CH4
2 0.3000 0.23346264 0.70443511 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.85872 0.14128
VOLUME FRACTION: 0.93529 0.06471
ZFACTOR: 0.82167 0.34827
MW(g/mol): 32.41507 65.44908
MASS DEN(Kg/L): 0.08910 0.42778
MOLE DEN(mol/L): 2.74884 6.53608
VISCOSITY(cP): 0.01570 0.05491
SURFACE TENSION(dyne/cm): 1.26383
Iter (SSI) = 8
Iter (NR) = 2
Error flash = 4.11E-11
Tolerance flash = 1.00E-10
Pressure Calculation sequence 5
P (bar) = 60.000000
T (K) = 426.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -6.94205E-02 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.74902086 0.21505687 CH4
2 0.3000 0.25097914 0.78494313 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.90819 0.09181
VOLUME FRACTION: 0.96919 0.03081
ZFACTOR: 0.84135 0.26764
MW(g/mol): 33.64368 71.09591
MASS DEN(Kg/L): 0.06774 0.45520
MOLE DEN(mol/L): 2.01341 6.40260
VISCOSITY(cP): 0.01458 0.06113
SURFACE TENSION (dyne/cm): 2.17832
Iter (SSI) = 6
Iter (NR) = 2
Error flash = 4.22E-13
Tolerance flash = 1.00E-10
Differential Vaporization (DV)
Pressure Calculation sequence 2
P (bar) = 160.000000
T (K) = 400.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -6.30686E-04 -3.98676E-04
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.79042681 0.61227622 CH4
2 0.3000 0.20957319 0.38772378 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.49241 0.50759
VOLUME FRACTION: 0.54167 0.45833
ZFACTOR: 0.75595 0.61477
MW(g/mol): 30.73946 43.23495
MASS DEN(Kg/L): 0.19563 0.33520
MOLE DEN(mol/L): 6.36406 7.75298
VISCOSITY(cP): 0.02063 0.03964
SURFACE TENSION (dyne/cm): 0.03460
Iter (SSI) = 39
Iter (NR) = 4
Error flash = 2.09E-14
Tolerance flash = 1.00E-10
Pressure Calculation sequence 3
P (bar) = 130.000000
T (K) = 400.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -1.52545E-02 -3.30254E-03
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.83656193 0.48169813 CH4
2 0.3000 0.16343807 0.51830187 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.61517 0.38483
VOLUME FRACTION: 0.71778 0.28222
ZFACTOR: 0.80525 0.50530
MW(g/mol): 27.50355 52.39369
MASS DEN(Kg/L): 0.13351 0.40465
MOLE DEN(mol/L): 4.85418 7.72325
VISCOSITY(cP): 0.01774 0.05142
SURFACE TENSION(dyne/cm): 0.50615
Iter (SSI) = 16
Iter (NR) = 2
Error flash = 1.69E-13
Tolerance flash = 1.00E-10
Pressure Calculation sequence 4
P (bar) = 100.000000
T (K) = 400.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -8.21593E-02 -2.11102E-03
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.85330992 0.36947400 CH4
2 0.3000 0.14669008 0.63052600 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.68314 0.31686
VOLUME FRACTION: 0.81859 0.18141
ZFACTOR: 0.83964 0.40310
MW(g/mol): 26.32884 60.26509
MASS DEN(Kg/L): 0.09429 0.45168
MOLE DEN(mol/L): 3.58106 7.49497
VISCOSITY(cP): 0.01606 0.06226
SURFACE TENSION (dyne/cm): 1.55209
Iter (SSI) = 11
Iter (NR) = 2
Error flash = 4.44E-15
Tolerance flash = 1.00E-10
Pressure Calculation sequence 5
P (bar) = 70.000000
T (K) = 400.000000
STABILITY ANALYSIS
ONE-PHASE TPD = -2.37955E-01 0.00000E+00
Mixture is in “TWO-PHASE”
TWO-PHASE Flash computation
idx feed vapor liquid comp.
1 0.7000 0.85160535 0.25853311 CH4
2 0.3000 0.14839465 0.74146689 nC6
VAPOR LIQUID
MOLAR FRACTION: 0.74437 0.25563
VOLUME FRACTION: 0.89663 0.10337
ZFACTOR: 0.87029 0.29529
MW(g/mol): 26.44840 68.04649
MASS DEN(Kg/L): 0.06396 0.49018
MOLE DEN(mol/L): 2.41846 7.20361
VISCOSITY(cP): 0.01468 0.07396
SURFACE TENSION (dyne/cm): 3.17602
Iter (SSI) = 6
Iter (NR) = 2
Error flash = 1.88E-15
Tolerance flash = 1.00E-10
Comparisons among CCE, CVD, and DV
According to the above findings, it can be shown that the expected results such as feed composition, compressibility factors, and compositions in gas and liquid phases, for constant composition expansion (CCE) and constant volume depletion (CVD) have similar computation values. With the same properties, the values of differential vaporization (DV) are different from those of CCE and CVD.
Conclusions
From the thermodynamic point of view, phase transitions happen when the free energy of a system is non-analytic for some choice of thermodynamic variables. The distinguishing characteristic of a phase transition is an abrupt change in one or more physical properties, with a small or no change in the intensive thermodynamic variables such as the temperature and pressure. Phase transitions are generally categorized in the first order transitions, the second order transitions and the infinite-order phase-transitions
Works Cited.
Abudour, Agelia M., et al. “Predicting PR EOS binary interaction parameter using readily available molecular properties.” Fluid Phase Equilibria 434, 2017: 130-140.
Arabloo, Milad, and Shahin Rafiee-Taghanaki. “SVM modeling of the constant volume depletion (CVD) behavior of gas condensate reservoirs.” Journal of Natural Gas Science and Engineering 21, 2014: 1148-1155.
Ashour, I., Al-Rawahi, N., Fatemi, A. & Vakili-Nezhaad, G. Applications of Equations of State in the Oil and Gas Industry. Thermodynamics – Kinetics of Dynamic Systems, 2011. DOI: 10.5772/23668.
Bi, Ran, and Hadi Nasrabadi. “Molecular simulation of the constant composition expansion experiment in shale multi-scale systems.” Fluid Phase Equilibria 495, 2019: 59-68.
Bradley, Howard B. “Petroleum engineering handbook.“, 1987.
Jin, Zhehui, and Abbas Firoozabadi. “Thermodynamic modeling of phase behavior in shale media.” Spe Journal 21.01, 2016: 190-207.
Kinney, Lance, and Catherine Norwood. “Review of Professional Engineering in Petroleum Engineering.” SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2018.
Li, Chuanyan, et al. “Calculation of the Phase Equilibrium of CO 2–Hydrocarbon Binary Mixtures by PR-BM EOS and PR EOS.” Transactions of Tianjin University 25.5, 2019: 540-548.
Pedersen, Karen Schou, Peter Lindskou Christensen, and Jawad Azeem Shaikh. Phase behavior of petroleum reservoir fluids. CRC press, 2014.
Umnahanant, Patamaporn. “An examination of vaporization, fusion and sublimation enthalpies of tolazoline using correlation gas chromatography and differential scanning calorimetry.” “Journal of Thermal Analysis and Calorimetry”, 138.1, 2019: 443-450. To
Vinet, P. J. J. R., et al. “A universal equation of state for solids.” Journal of Physics C: Solid State Physics 19.20, 2008: L467.
Whitson, Curtis H., and Michael R. Brulé. Phase behavior. Vol. 20. Richardson, TX: Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, 2010.
