1. Extrair e realizar uma análise cromatográfica da terceira fase formada em algumas regiões PVT, a fim de se conhecer a evolução composicional dessa fase.
2. Reproduzir esse estudo para outros tipos de óleos a fim de se obter um maior número de dados com o objetivo de gerar modelos de correlação.
3. Realizar a aquisição de um maior número de dados PVT com o objetivo de elaborar um equacionamento termodinâmico que represente sistemas de óleo com elevada concentração molar de CO2.
4. Realizar análises PVT em óleos com concentração molar crescente utilizando-se como gás de inchamento CO2 e uma mistura de gases que atuarão como gás de reciclo.
5. Realizar uma análise de propagação de erros que envolvam os ensaios de PVT para que se conheça mais a precisão dos resultados, além das precisões dos equipamentos, individualmente, fornecidas pelos fabricantes.
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BEGGS, H. D.; ROBINSON, J. R. Estimating the Viscosity of Crude Oil Systems. Journal of Petroleum Technology (ID: SPE-5434), 1975.
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CARNAHAN, N. F.; STARLING, K. E. “Intermolecular repulsions and the equation of state for fluids”. AIChE J., volume 18, novembro, 1972.
CHANDLER ENGINEERING, (06-06-2013), available in: http://www.chandlereng.com.
COATS, K. H. e SMART, G.T. “Application of a Regression-Based EOS PVT Program to Laboratory Data.” SPERE, Maio, 1986: 277.
DANESH, Ali. “PVT and Phase Behaviour of Petroleum Reservoir Fluids”, Elsevier Science B.V., Holanda, 1998.
DINDORUK, B.; CHRITMAN, P. G. PVT Properties and Viscosity Correlations for Gulf of Mexico Oils. Society of Petroleum Engineers (ID:SPE 71633), ATCE 2001.
DRANCHUK, P. M. e ABOU-KASSEM, J. H.”Calculation of Z Factors for Natural Gases Using Equations of State”. Journal of Canada Petroleum. Montreal. 1975.
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ELIAS JR, A. e TREVISAN, O. V. “Constant Composition Expansion Analysis to Calculate the Bubble Point through Adjustment of the Coefficient of Determination”, XV Congresso Colombiano de Petróleo, Bogotá, Novembro, 2013.
FEINBERG, Martin. “On Gibbs’ Phase Rule”, Archive for Rational Mechanics and Analysis, volume 70, Spring-Verlag, 1979.
GACIÑO, Félix M; REGUEIRA, Luis Lugo; COMUÑAS, Maria JP; FERNÁNDEZ, Josefa. "Influence of molecular structure on densities and viscosities of several ionic liquids." Journal of Chemical & Engineering Data, volume 56, 12 ed, pp 4984-4999, American Chemical Society.
GILLILAND, E. R., H. W. Scheeline. “High-pressure Vapor-Liquid Equilibrium”. Industrial & Engineering Chemistry, 1940.
GILLILAND, E. R., H. W. Scheeline. “Vapor-Liquid Equilibrium in the System Propane- Isobutylene”. Industrial & Engineering Chemistry, 1939.
GROB, ROBERT L. Modern Practice of Gas Chromatography. EUA: Editora John Wiley & Sons. 2004. 4ed. 28p
KAUFMAN R.L., Ahmed A.S., Elsinger R.J. 1990. Gas Chromatography as a development and production tool for fingerprinting oils from individual reservoirs: applications in the Gulf of Mexico, In: Schumaker D. & Perkins B.F. (eds.) Annual Research Conference of the Society of Economic Paleontologists and Mineralogists, 9th, New Orleans, USA, p. 263-282.
KESLER, M. G.; LEE, B. I. “Improve Predictions of Enthalpy of Fractions”. HydrocarbonProcessing, n.55, ed. 153, 1976.
LANÇAS, FERNANDO M. “Cromatografia em fase gasosa- 1.Teoria elementar”, Química Nova, Rio de Janeiro, 1983.
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LEE, B. I.; KESLER, M. G. “A generalized thermodynamic correlation based on three-parameter corresponding states”.AIChE J., n. 21, ed. 510, 1975.
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MARSH, K. N. “Thermodynamic Excess Functions of Mixtures of Simple Molecules according to several equations of state”. Transactions of Faraday Society, 1970, n° 66, pp 2453-2458.
McCAIN, W. D. Reservoir-Fluid Property Correlations. SPE Reservoir Engineering, pp 266-272, Maio, 1991.
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McGLASHAN, M. L. “Thermodynamic Excess Functions of Mixtures of Molecules of Different Sizes”. Transactions of Faraday Society, 1969, n° 66, pp 18-24.
PENG, Ding-Yu; ROBINSON, Donald B. “A new Two-Constant Equation of State”. IEChF, volume 15, n.1, 1976.
PRAUSNITZ, John M. “Molecular Thermodynamics of Fluid-Phase Equilibria”, Prentice Hall PTR, New Jersey, 1999.
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Site Petrobras Em: http://www.petrobras.com.br/pt/nossas-atividades/areas-de-
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APÊNDICE A - MÉTODO DE DETERMINAÇÃO DO PONTO DE
BOLHA (PAPER)
Constant Composition Expansion Analysis to Calculate the Bubble Point through Adjustment of the Coefficient of Determination
Antonio Elias Jr.a, Osvair Vidal Trevisanb
a. Phd Student, Department of Petroleum Engineering, University of Campinas, Brazil b. Professor , Department of Petroleum Engineering, University of Campinas, Brazil
Copyright 2013, Acipet
This paper was prepared for presentation at the ACIPET XV Congreso Colombiano del Petróleo held in Bogotá D.C., Colombia, 20-22 November 2013.
This paper was selected for presentation by an ACIPET Technical Committee following review of information contained in abstract submitted by the authors.
_________________________________________________________________________
Abstract
The traditional procedure for CCE tests conducted in PVT blind cells to determine the bubble point does not render precise results, and does not allow for automation. So, the implicit error in the procedure can conduce to erroneous bubble point values. This paper introduces and tests an improvement to the procedure for determining the bubble point from CCE experimental data. Example cases are run to validate the procedure.
1. Introduction
Besides all technical challenges that surround the pre-salt explotation, like the depth of reservoirs and the unique geological structure, there is the increase in the demand for laboratory tests altogether with the need for more precision on the results of these tests, given the huge volume of oil involved and the demanding conditions of its availability, so errors in the measurements have a significant impact.
One of the areas that present a increase of demand for tests is the miscibility methods. The primary production of the reservoir is made by depletion, in which the reservoir pressure declines as fluid are recovered. The thermodynamic behavior of the reservoir fluids according to variations of temperature and pressure is assessed by PVT (pressure – volume – temperature) tests and models.
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A PVT test is a collection of experiments that can categorized by, in order, constant composition expansion and compression (CCE), differential liberations (DL), flash liberation (FL), multistage- separator tests.
The PVT data are generated in the laboratory from surface or preserved samples taken during the well tests. These data are used to evaluate the integrity of collected samples and to perform the recombination process (EYTON, 1987).
The most common results that are obtained through the PVT tests are: gas-oil ratio, solubility ratio, bubble point, dew point and volume formation factor. In the present paper, we focus on the development of a technique to obtain with more precision the bubble point that is rendered by the data obtained from a CCE test.
The proposed technique is based on the known statistic parameter called coefficient of determination (R-square), and the split in two varying regions for the linear adjustment of such parameter the data points obtained from the CCE test. In order to automate the adjustment search, an optimization routine was developed with the objective function of maximizing the sum of the coefficients of determination obtained in each region adjustment.
2. Constant composition expansion (CCE)
The CCE test is a PVT experiment at which a mass of live oil is kept constant while the volume is expanded and the pressure is depleted. Usually this experiment is applied to determine bubble point, undersaturated oil density, isothermal oil compressibility and two-phase volumetric behavior at pressures below the bubble point. The test is used to obtain data for - Crude oil mixtures (WHITSON, 2000). There are two types of equipments used in the run of the CCE experiment, the “visual cell”(Figure A.1) and the “blind cell” (Figure A.2).
Figure A.1 - Schlumberger - DBR PVT Rig. [1] – thermal bath; [2] – high pressure visual cell; [3] – high pressure pump.
In Figure A.1 the equipment indicated by (1) is the bath heater and through which the high pressure pump is connected to the visual cell (2) where a sample fluid (live oil) is contained within a transparent glass tube surrounded by an annular see-through tube filled with an inert, transparent hydraulic fluid (Conosol), also responsible for communicating the pressure provided
131
by the DBR pump (3). Through the visual cell it is possible to determine the bubble point by the observation of the first bubble of gas liberated from the monophasic live oil.
The other equipment used to determine bubble point is the “no visual cell” or “blind cell”, illustrated in Figure A.2
Figure A.2 – Cylinder with floating piston that can be used as a blind cell. (Chandler, 2013).
The measurement of bubble point in a blind cell is defined by matching the point at which the data points (Figure A.3), obtained via an CCE experiment, change abruptly the trend in a PV graph.
Figure A.3 – Graph after data rendered by a CCE experiment executed in a blind cell.
According to the procedure, in Figure A.3 the dot in red corresponds to the bubble point and the cartoon along the data points illustrates what happens inside the blind cell during the CCE run.
Depending on the temperature and/or the gas-oil ratio, the variation in the PxV data points, does not change abruptly as in the previous graph, but presents a monotonic and smooth decline curve (Figure 4).
Pressure
Volume
blind cell
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Figure A.4 – Graph obtained by CCE experiment executed in a blind cell for a light oil (high OGR).
In Figure A.4 any of the red dot can be the pinpointed as the bubble point, according to the procedure and depending on the analyst judgement. So, it is necessary to elaborate or to have a new procedure for determining the point at which the properties changes more significantly, to mean the appearance of a new phase in the system.
3. Determination: Bubble Point
In the usual procedure for bubble point determination, as illustrated by the line sin Figure 4, the bubble point is defined as the intersection of two lines obtained by the user to fit the data points. One to fit the data which are expected to be in the high range, above the region (yellow points) estimated to house the bubble point, and the other to cover the low range, below the estimated region (RUTLEDGE, 2007).
Figure A.5 – Determination the bubble point by line drawing.
Figure A.5 illustrates the procedure and what occurs very commonly to the fit and to the interpretation of the results. According to the practice the red dot in the graph is the bubble point. As the figure shows, the line fittings disregard some intermediate points (yellow points), although those data hold information about the behavior of the oil-gas system. The bubble point is also
133
picked out of the CCE data curve. One can argue that the chosen point is a “fictional point”, once it does not belong to the determined CCE data curve.
4. Adjustment: Coefficient of Determination (CD)
In order to improve the procedure, the present study explores ways of automation of the line fitting technique.
The proposed route is to calculate all possible pairs of complementary lines that fit the data provided by a CCE test and demonstrate that the pair of lines whose sum of CDs is the highest. This way it would eliminate dependence on users perceptions to obtain the intersection of possible lines which ultimately lead to the bubble point.
In a dispersion of n points, two lines R and S are complementary if the sum of the points used to fit them, by a linear regression, is equal to n. The procedure is set to select the pair of complementary lines whose sum of CD is the highest.
Let´s assume two complementary lines R and S with corresponding CDs (Eq. 1) and (Eq. 2), respectively. (1) (2)
Where, and represents the points of functions that describe, respectively, the fitted lines R and S. The variable and represents the ordinate values of the dispersions points (units of pressure in a CCE graph). and are the means of the dispersion and .
The denominators of the fractions in Equations 1 and 2 do not vary, so they behave as weight functions that vary depending on how the data points are off from the mean. For simplicity, these weights are defined:
(3) (4)
134 (5)
Functions, and , that describe respectively the lines R and S can be represent as.
(6)
(7)
In Equations (6) and (7), and represent the slope of the fitted line, and represents the abscissa variable, volume in a CCE graph, and are the linear coefficient.
In order to maximize the sum , the differences and shall bear minimum values.
Replacing Equations (6) and (7) into equation (5), and manipulating its sum one obtains the linear coefficients. - (8) - (9)
Atypical CCE plot (Figure A.6) illustrates the relation between the fitted lines, its slope and the geometry of its disposition.
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Figure A.6 – CCE graph with adjusted curves, R and S, to the data points.
From basic analytical geometry, , β, α and θ can be correlated as:.
(10)
(11)
(12)
Replacing Equations (10) and (11) in (12):
(13)
Angle will be maximum when is maximum and minimum. Considering the physical CCE system will be maximum when the variation of pressure is of major value for a low variation in volume (according to equation 8).Such would occur in a monophasic region. On the other hand, is minimum when the variation of pressure is of minor value for a great variation in volume (according to equation 9).This would be the case in the biphasic region, due the liberation of gas.
The maximum for the sum of CDs in the determination of two lines with the highest value for the angle separating them, which ultimately implies in one line fitting the monophasic region and other the biphasic region, defining, by the intersection, the bubble point.
5. Application and Results
Three examples of application of the proposed procedure are presented.
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Using the Perdersen data and applying the procedure on the data, the results are summarized in the graph of Figure A.7.
Figure A.7 – Pedersen CCE experiment with enlargement of bubble point region.
The bubble point pressure value encountered using the proposed procedure is 3389 psi and the original reported value is 3466 psi, the difference between them was 77 psi or 2%.
The second example is based on a CCE experiment data published by Whitson (WHITSON, 2000). Figure A.8 shows the results obtained via the proposed procedure for the bubble points pressure, compared with the experimental value determined via visual cell, as well the overall behavior of the data and fitting lines.
Figure A.8 – Whitson CCE experiment with enlargement of bubble point region.
Results ended in a difference of 14 psi or 0,5% between the bubble pressure found by the experimental measurement and the one calculated by the procedure.
The third example (illustrated in Figure A.9) is a typical CCE experiment for high GOR oil where it is evidently inadequate to determine the bubble point pressure by the classic procedure of fitting two lines,. The test was carried out in visual cell, so the experimental bubble point was defined with high precision.
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Figure A.9 – Unicamp CCE experiment with enlargement of bubble point region.
The Figure A.9 shows that the difference between the experimental values and the determined by the procedure for the bubble point pressures was 80 psi or 1,5%.
The calculation of bubble point by the coefficient of determination procedure does not rely on any thermodynamic theory to adjust or validate them. It only explores to the best the data provided by the test runs. So, the acquisition of precise data from a CCE stable system via a proven and tested methodology it remains crucial.
6. Conclusion
The paper present a new procedure for the determination of bubble point pressure from PVT data obtained from blind cells. The procedure uses automated fitting of the data by variable lines applied to variable regions of the data points.
The procedure when applied to CCE experiment is consistent in terms of mathematics and physics, and the results provided by CCE data proved that this application is valid and provide results that are not only reliable but very close to the values obtained when using much more sophisticated equipments, like the visual cell.
The weight functions are independent of and , but are variable dependent of the experimental data, so they are not constant, according the variation of pressure. So, those functions can be more strictly studied and may further be used as a parameter of adjustment in the fit.
Acknowledgments.
The authors would like to acknowledge ANP – Brazil for providing the oil for PVT test, Petrobras, for research support, and the Laboratory of Miscible Recovery Methods of CEPETRO.
References
Eyton, D. G. et al.: “Practical Limitations in Obtaining PVT Data for Gas Condensate Systems” , SPE 15765 presented at the Middle East Oil Show, 7-10 March 1987, Bahrain.
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Danesh, Ali: PVT Phase Behaviour of Petroleum Reservoir Fluids, first edition, Elsevier, Netherlands (1998).
Whitson, Curtis H. and Brulé, Michael R.: “Phase Behaviour”, Monograph, vol. 20, pp 93 - 94, SPE (2000).
Chandler engineering, (06-06-2013), available in: http://www.chandlereng.com.
Rutledge, L. A. Medeiros: “Determinação de pontos de bolha de um óleo vivo a partir de dados PVT”, 4° PDPETRO (2007), Campinas, SP.
Pedersen, K. S. and Fredenslund & Thomassen: Properties of Oils and Natural Gases, Gulf Publishing Company, (1989), pp 133.
Miklós, D. et al., Thermodynamic consistency of data bank, Fluid Phase Equilibria (1995), 110, pp 89 – 113.
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APÊNDICE B - VARIÁVEIS DO WINPROP (LISTA DE
PARÂMETROS)
******************************************************************************** * * * WINPROP 2014.10 ** EOS Phase Property Program *
* General Release for Win x64 * * 2014-Sep-19 11:36:05 * * * * (c) Copyright 1977 - 2014 *
* Computer Modelling Group Ltd., Calgary, Canada *
* All Rights Reserved * * * ******************************************************************************** Command-line Arguments: -dd
-f Empty Cromo 2009 v10 com visco.dat Maximum Dimensions:
Component = 200
SCN Group in + Fractions = 200; Lab. Calculation points = 200 Streams in Process = 200; Units in Process = 20 Regression variables = 150; Regression data points = 10000
**FILE NAME: EMPTY CROMO 2009 V10 COM VISCO.DAT
*FILENAMES *OUTPUT *SRFOUT *REGLUMPSPLIT *GEMOUT *NONE *STARSKV *NONE *GEMZDEPTH *NONE *IMEXPVT *NONE
*WINPROP '2010.10' **=-=-= TITLES/EOS/UNITS **REM *TITLE1 ' ' *TITLE2 ' ' *TITLE3 ' ' *UNIT *FIELD *MODEL *PR *1978 **=-=-= COMPONENT SELECTION/PROPERTIES **REM *NC 24 24 *COMPNAME 'CO2' 'N2' 'C1' 'C2' 'C3' 'IC4' 'NC4' 'IC5' 'NC5' 'FC6' 'FC7' 'FC8' 'FC9' 'FC10' 'FC11' 'FC12' 'FC13' 'FC14' 'FC15' 'FC16'