High-Pressure Saturated-Steam Correlations

Summary During steam-assisted oil recovery processes, the thermal properties of saturated steam are required in the computation of heat losses and quality changes in steam distribution networks and wellbores. These properties can be evaluated either by interpolation of steam table data or by empirical correlations. Most correlations available in the literature are designed for steam pressures below 500 psia [3.4 MPa] and no single reference covers all the properties needed for the computations previously mentioned. This paper presents a new and complete set of saturated-steam properties correlations for pressures between 500 and 2,500 psia [3.4 and 17.2 MPa] and compares their accuracies to those in other works. These correlations do not apply to supercooled water or superheated steam. Introduction The Wolf Lake Project developed by BP Resources Canada Ltd. and Petro-Canada Inc. uses cyclic steam stimulation to recover bitumen from the Clearwater formation. The project is located 55 miles [90 km] north of Bonnyville, Alta., in the Cold Lake oil sands developments area. Reservoir injectivity is low and high-pressure steam injection is required to induce formation parting. As part of the development of a high-pressure wet-steam-network computer model for the project, correlations currently found in the literature for steam temperature, specific volume of vapor and condensate, enthalpy of vaporization and of vapor and condensate, and viscosities of the same were examined for accuracy and for possible use. When existing correlations proved to be satisfactory, a new set was developed, focusing on high-pressure applications. This paper will briefly review literature correlations and compare other predictions with steam-table values. The approach used in developing the new correlations will be presented. The resultant equation for each steam property will then be presented and discussed separately. Advantages of these correlations will be highlighted. Accuracy of all correlations below 500 psia [3.4 MPa] will be compared, in view of recommending the best set for low-pressure applications. Literature Review Literature correlations were obtained from three sources, the best known being perhaps the work of Farouq Ali.1 The other two sources were a steamdrive model by Jones,2 and the work of Cox and Chesnut.3 All these authors presented their correlations in customary units, and thus this work was performed in the same unit system for ease of comparison. A set of corresponding metric correlations is given in Table 1. Literature correlations were found to lose their accuracy very rapidly for pressures above 500 psia [3.4 MPa]. Minimum and maximum errors were documented for each correlation in Tables 2 through 4 for Refs. 1 through 3, respectively. Correlations with acceptable accuracy (Ref. 3) failed to use steam pressure as the independent variable and did not constitute a complete set. Method of Development As a first step, correlations of the same form as those found in the literature were tried. Constants in these correlations were calculated by regression analysis. Predicted values were compared with steam-table values from the ASME Steam Table.4 In total, 105 data points in the pressure range were used to assess the accuracy of the new correlations. For the viscosity of vapor and condensate, the ASME steam tables provided 75 data points to test the correlations. When the form of the correlation proved inadequate, new forms were tried. As before, the coefficients were calculated by regression analysis. For a given steam property, the standard deviation of each correlation was calculated, the correlation with the smallest deviation was selected and reported in this paper. When two correlations were required to describe a property adequately, discrepancy between predictions at the junction pressure (1,500 psia [10.3 MPa]) was kept well below 1%. Note that even though discontinuity of the values was minimal, discontinuity of the mathematical derivatives will be large. For greater accuracy, derivatives should be calculated according to the fundamental expressionEquation 1 New Correlations Summaries of the new correlations are given in Tables 5 through 7. Temperature. Steam temperature was generally well predicted. The correlation was further improved (Fig. 1) by using the form given by Farouq Ali and calculating new coefficients. Thus,T=116.79 p0.2229, (2) where 500 p 2,500 psia [3.4 p 17.2 MPa]. Eq. 2 can also predict steam temperature for pressures between 300 and 500 psia [2.1 and 3.4 MPa] with a maximum error of 0.2%. Enthalpy Condensate. To achieve high accuracy over the entire pressure range, two correlations were developed:Hss=77.036p0.28302 (3) where 500 p 1,500 psia [3.4 p 10.3 MPa], andHsc=0.12038p+430.984 (4) where 1,500 p 2,500 psia [10.3 p 17.2 MPa]. At 1,500 psia [10.3 MPa], the difference in predicted value was calculated to be no more than 0.2% (Fig. 2). Temperature. Steam temperature was generally well predicted. The correlation was further improved (Fig. 1) by using the form given by Farouq Ali and calculating new coefficients. Thus,T=116.79p0.2229, (2) where 500 p 2,500 psia [3.4 p 17.2 MPa]. Eq. 2 can also predict steam temperature for pressures between 300 and 500 psia [2.1 and 3.4 MPa] with a maximum error of 0.2%. Enthalpy Condensate. To achieve high accuracy over the entire pressure range, two correlations were developed:Hss=77.036p0.28302 (3) where 500 p 1,500 psia [3.4 p 10.3 MPa], andHsc=0.12038p+430.984 (4) where 1,500 p 2,500 psia [10.3 p 17.2 MPa]. At 1,500 psia [10.3 MPa], the difference in predicted value was calculated to be no more than 0.2% (Fig. 2).