MEASUREMENT AND MODELING METHODOLOGY FOR HEAVY OIL VAPOR PRESSURE. O. Castellanos-Díaz, W. Y. Svrcek, H. W. Yarranton, and M. A.

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1 MEASUREMENT AND MODELING METHODOLOGY FOR HEAVY OIL VAPOR PRESSURE O. Castellanos-Díaz, W. Y. Svrcek, H. W. Yarranton, and M. A. Satyro Department of Chemical and Petroleum Engineering, University of Calgary, AB, Canada Abstract: A new apparatus was designed and constructed for the measurement of the vapor pressures of heavy oils at pressures from atmospheric to 5x -7 kpa and temperatures in the range of 2 to 5ºC. A characterization methodology is developed based on the Gamma Molecular Distribution Function and the Peng Robinson equation of state. Given a particular set of established thermophysical property correlations for crude oil, the shape of the Gamma distribution is adjusted to fit vapor pressure data. Athabasca residue vapor pressure data was modeled using the proposed approach and fit the data to within ±3%. Keywords: Heavy Oil, Vapor Pressure, Static Apparatus, Modeling, Gamma Distribution Function. INTRODUCTION Both the refining of heavy oil and solvent-based recovery processes for heavy oils and bitumens require the prediction of phase behavior. A key part of modeling the phase behavior is to characterize the crude oil; that is, to divide the fluid into pseudo-components and assign meaningful properties to each, such as density, molar mass, and critical properties. Generally, petroleum fluids are characterized using distillation assays. However, when dealing with heavier fluids the residue is left undetermined because the components in this fraction have boiling points higher than their cracking temperatures even when high vacuum distillation assays are used. For heavy oils, up to 6% of the oil may be non-distillable (Nji et al, 28). To improve the characterization of heavy oils new nondestructive techniques are necessary. We propose that data in the form of total fluid and residue vapor pressures can provide an useful addition to the characterization methodology At present, few data of this type are available in the open literature. A novel methodology is proposed to extend the characterization from distillation using vapor pressures measured at high vacuum, Fig.. The residue fraction is represented by a Gamma Distribution Function to account its molecular distribution. The Gamma function has proved to provide meaningful representations of C7plus fractions of reservoir fluids (Whitson, 983) that can be readily fitted to a given set of physicochemical data such as vapor pressure. The distribution is divided into fractions and physical properties for the pseudo components are assigned using established property correlations (Whitson, 983). Vapor pressure is then predicted using the Advanced Peng- Robinson Equation of State (APR EoS) developed by Virtual Materials Group (24). The Gamma distribution parameters are adjusted until the calculated vapor pressure matches the experimental data using a minimization of the sum of the square error. Our intention is to combine the residue characterization with a similar type of characterization for the distillable fraction to obtain the total fluid true boiling point curve (TBP), Fig.. A high vacuum apparatus is proposed to measure vapor pressure for heavy oils. The measurement is based on the Constant Composition Expansion and Differential Liberation Expansion techniques widely used for reservoir fluid characterization (Whitson and Brule, 2). This paper presents the design of the apparatus and testing of the proposed experimental methodology on literature data for Athabasca residue vapor pressures.

2 Fig. Schematic Representation of the Methodology for Characterizing Heavy Oil using the Gamma distribution Function and an Equation of State to model. Vapor pressure data are used to adjust the molecular distribution. j is the objective function, MSE i is the mean square error of the i th vapor pressure data point, P exp i is the experimental vapor pressure data point, and P calc i is the vapor pressure point calculated based on the Gamma function and the chosen equation of state model.

3 Pressure (reference units) 2. EXPERIMENTAL 2. Methodology Vapor pressure is determined from the change in the isothermal compressibility that occurs at a liquid-vapor phase transition. Pressure and volume are measured as a fluid sample, initially in the liquid state, is expanded at constant temperature into the vapor-liquid region. The pressure at which vapor forms is determined from the change of slope on a plot of pressure versus volume, Fig Vapor Pressure Volume (reference units) Pure Component Fig. 2. Schematic representation of the pressure-volume data used to determine vapor pressure. When used for reservoir fluid characterization, this assay is known as a Constant Composition Expansion (CCE) (Whitson and Brule, 2) and it is performed at high pressure and high temperature conditions to obtain physical data for the fluid at reservoir conditions. However, for residue fractions, very low pressures are expected at temperatures below the beginning of cracking. 2.2 Apparatus The apparatus is a small PVT cell designed to operate at vacuum pressures as low as -7 kpa, Fig. 3. It consists of a 6 ml stainless steel piston chamber which can be expanded at a rate of.6443 ml/turn. The pressure in the chamber is measured by a full range combined Cold Cathode and Pirani gauge by Pfeiffer Vacuum, capable of measuring pressures in the range of to 5x -7 kpa at temperatures below 6 ºC with a precision better than 3%. The gauge is backed up by a MKS Baratron capacitance gauge, capable of measuring pressures in the range of to 5x -4 kpa stabilized at 5 ºC and a precision better than.5%. The data is read out using a digital display suitable for each type of gauge. A cold finger condenser traps the vapor generated by the expansion. It creates enough residence time to ensure that the oil is trapped in the device. It is made of Pyrex glass and is modified to fit a Swagelok Ultra-Torr fitting that connects it to the system. The different sections of the apparatus are connected using stainless steel NW25 KF flanges, tees, and elbows, and are sealed with Viton o-rings which are good to hold pressures down to x -7 kpa. VAT Viton-sealed bellows valves are used for isolation. The system is regularly tested for leaks using a Varian 979 Helium Leak Detector and has proved to have a leak rate of less than.x -5 kpa.ml/s. The system is pumped out by a Pfeiffer Turbopump station that consists of a Turbomolecular pump and a dry diaphragm backing pump. The available pressure is measured by a second combined Cold Cathode-Pirani gauge also by Pfeiffer. The pump is protected from possible condensates that escape the cold finger condenser by a dry ice stainless steel cold trap. PID controllers by Watlow technologies and J-Type thermocouples are used for controlling the temperature throughout the equipment. A Glas-Col heat jacket and heat tapes are utilized to provide the heat to the system, as shown in Fig. 3. Finally, a RTD provides accurate measurement of the piston chamber temperature; it was calibrated against a certified high precision thermometer with accuracy better than.5 ºC. Oil

4 Fig. 3. Vapor Measurement Apparatus schematic: a. Sample piston chamber; b. Pfeiffer combined Cold Cathode- Pirani pressure gauge; c. MKS Baratron capacitance gauge; d. VAT Viton-seal bellows valve; e. Cold-finger condenser; f. Dry-ice cold trap; g. Pfeiffer turbomolecular pump; h. Pfeiffer diaphragm dry backing pump; i. RTD; j. j-type thermocouple; k. TPD gauge display; l. PTR-4 gauge display; m. Glas-Col electrical heat jacket; n. Heat tape; o. Watlow temperature display-pid controller. 2.3 Procedure Heavy oil samples often have light impurities, such as water as well as solvents used in processing the oils samples such as naphtha, toluene, or paraffinic solvents. These impurities affect the vapor pressure measurement since their partial pressure is significant in comparison with the expected vapor pressure of the sample. Therefore, the sample needs to be degassed. The apparatus shown in Fig. 3 allows for the degassing of the sample based on the Differential Liberation Extraction (DLE) method (Whitson and Brule, 2). A liquid sample is placed in the piston vessel and brought to the desired temperature. The cell is expanded until vapor forms. The vapor is released from the piston vessel into the rest of the vessel and the piston vessel is again isolated. The cell is again expanded and the procedure is repeated. A series of expansions are performed and a step wise series of pressure-volume measurements are obtained. Fig. 4 shows the composition of the gas and the liquid phase per step for a simulated degassing process of Athabasca residue (Schwartz et al. 987) at 5 ºC, using VMGSim. 4 wt% of a 5/5 mass ratio mixture of heptane and toluene was added to the oil. The mixture was simulated with the Gamma Molecular Distribution Function (GMDF) using 9 pseudo-components, as will be explained later. For the sake of simplicity only three cuts are shown: a light cut (NBP 62 ºF -327ºC), a medium cut (NBP 932 ºF -5ºC) and a heavy cut (NBP 44 ºF -782ºC). As can be seen from Fig. 4a, the solvent is removed from the liquid phase after 4 to 5 steps. Further steps act to fractionate the oil, indicated by the depletion of the lightest cuts in the liquid phase, Fig 3a, and the enrichment of the light cuts in the gas phase, Fig. 4b. The ideal degassing process would be one in which all the solvent is vaporized from the sample. However, before this occurs, some fractionation is expected, in this example, between Step 4 and Step 5. In order to measure an accurate vapor pressure curve for the heavy sample, some fractionation is recommended as part of the degassing process. Once the sample is degassed, the piston is cranked down and the pressure and volume are recorded. A PV curve such as the one shown in Fig. 2 is obtained as a result of the expansion. The inflection point is reported as the vapor pressure or bubble point of the sample at the working temperature.

5 Mole Fraction Pressure [kpa] Mole Fraction Pressure [kpa]..8 (a).6.5 (b) Step Step. Heptane Toluene NBP 62 NBP 932 NBP 44 Pressure Heptane Toluene NBP 62 NBP 932 NBP 44 Pressure Fig. 4 Compositions of the liquid phase (a) and the gas phase (b) of a step wise degassing process of a heavy oil simulated using VMGSim. 3. MODELING OF THE VAPOR PRESSURE DATA The overall purpose of this work is to use high vacuum vapor pressure data to extend the characterization of a heavy oil obtained from a distillation. The connection between the two different types of data is made through the molar mass distribution. The Gamma Molecular Distribution Function, Eq., is used to model the entire oil as a continuous distribution in molecular weight. From this distribution a TBP can be estimated and pseudo-component physical properties defined using normal refinery oil characterization techniques: P M M exp M () where P(M) is the probability function of the variable M, M is the molecular weight, β is average molecular weight of the distribution, η is lowest molecular weight in the distribution, and α is a parameter setting the shape of the distribution. Equation provides a molecular distribution for the heavy oil based on initially estimated parameters, α and η, and the average molecular weight. The distribution is then divided to generate the pseudo-components. These fractions are also characterized with a specific gravity value using the average specific gravity of the oil and a combinatory rule such as the Søreide s equation (Whitson and Brule, 2). Subsequently, a boiling point curve can be generated from equations that relate this property with the specific gravity and the molecular weight. Furthermore, the TBP curve is divided to obtain boiling-point based pseudo-components, which are more related to a distillation characterization than the mole-based pseudo-components. Pseudo-components determined in this manner are characterized by a mole fraction, normal boiling point, molecular weight and specific gravity. Critical properties are calculated and an equation of state, such as the APR EoS, can be utilized to predict the vapor pressure curve for the heavy oil. Finally, the parameters α and η are adjusted to fit the vapor pressure data (Whitson and Brule, 2). The fitting is performed using a minimization procedure on the sum of the logarithm of the errors squared. The logarithm is used as a weighting factor in order to account for the shape of the vapor pressure curve. A SIMPLEX optimization method is used since the objective function shows a global optimum with no local optima.

6 Pressure [kpa] Mole Fraction Pressure [kpa] Mole Fraction The approach to fit vapor pressure data using the Gamma function was tested on data obtained from Schwartz et al. (987) and from Rodgers et al. (987) for Athabasca residue. 2 (a)..8 (b) Temperature [C] GMDF Approach Schwarz et al Data 2 3 Molecular Weight Fig. 5a shows the fit to the vapor pressure data and Fig 4b shows the molecular weight distribution used to fit the data. The vapor pressures were fit to within a maximum error of ±3%. When the methodology is complete, the characterization obtained for the residue can be combined with the characterization of the distillable fraction the fluid obtained from a conventional distillation data. 2 (a)..8 (b) Temperature [C] GMDF Approach Schwarz et al Data 2 3 Molecular Weight Fig. 5 a). Schwartz et al. data modeled using the Gamma Distribution Function for Athabasca residue. b). Molecular distribution for the Athabasca residue sample. α=.4 and η= CONCLUSIONS The static apparatus has been designed, constructed, leak tested, and degassed. It has been shown to hold a pressure of 5x -7 kpa, which is within the expected range of vapor pressure based on a simulation of vapor pressure data of an Athabasca residue. A characterization methodology has been developed to integrate the characterizations obtained from conventional distillation and high vacuum pressure data. The characterization approach provided a good fit to data for an Athabasca residue. It remains to collect high vacuum pressure data and distillation data for a heavy oil to validate the proposed methodology. ACKNOWLEDGEMENTS

7 The authors are grateful to all the people involved in the design and construction of the apparatus, especially: Florian Schoeggl, Asphaltene and Emulsion Research Group, University of Calgary, AB; Bernie Then and Mike Grigg, Chemical and Petroleum Department Staff, University of Calgary, AB; Colin Branner, Science Department Staff, University of Calgary, AB; Michal Fulem, Institute of Chemical Technology, Prague, Czech Republic; the Consortium for Asphaltene and Emulsion Research at the University of Calgary for the funding provided and Virtual Materials Group, Inc. REFERENCES Nji, G. N.; Svrcek, W. Y.; Yarranton, H. Y.; and Satyro, M. A. (28). Characterization of Heavy Oil and Bitumens.. Vapor Pressure and Critical Constant Prediction Method for Heavy Hydrocarbons. Energy and Fuels. 22 () Rodgers, P, Creagh, L., Prange, M., and Prausnitz, J. M. (987). Molecular Weight Distributions for Heavy Oil Fossil Fuels from Gel Permeation Chromatography and Characterization Data. Ind. and Eng. Chem. Res Schwarz, B. J., Wilhelm, J. A., and Prausnitz, J. M. (987). Vapor Pressures and Saturated-Liquid Densities of Heavy Fossil-Fuel Fractions. Ind. and Eng. Chem. Res Virtual Materials Group Inc. (24). APR for Natural Gas Validation Documentation. Calgary, Alberta, Canada. Whitson, C. H. (983). Characterizing Hydrocarbon Plus Fractions. Trans. AIChE Whitson, C. H.; and Brule, M. R. (2). Phase Behavior. In: Henry L. Doherty Series. Monograph Volume 2. Society of Petroleum Engineers Inc.