Saturated-Steam-Property Functional Correlations for Fully Implicit Thermal Reservoir Simulation
- W.S. Tortike (U. of Alberta) | S.M. Farouq Ali (U. of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1989
- Document Type
- Journal Paper
- 471 - 474
- 1989. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 5.2.1 Phase Behavior and PVT Measurements, 5.5 Reservoir Simulation, 4.2 Pipelines, Flowlines and Risers, 4.1.5 Processing Equipment
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Current methods for determining saturated-steam properties are to look them up in steam tables and interpolate and to use discontinuous polynomial approximations to the experimental data. The latter require heavy computation and are restricted to certain regions of the saturation envelope. This paper presents a complete suite of properties as functions of simple continuous polynomials throughout almost the entire saturation envelope.
Steam properties as a function of saturation pressure and temperature are essential for thermal reservoir simulation and other analyses. The properties are found with a computer either by interpolation of steam-table data or by using existing interpolation polynomials. The existing polynomials are of restricted range and generally discontinuous. This work offers a complete suite of steam properties as functions of continuous, simple polynomials throughout almost the entire saturation envelope-to within 7 K [13deg or 1.85 MPa [270 psi] of the critical point of water. Derivatives of the polynomials can be evaluated analytically.
Polynomial interpolation is necessary to use vector and parallel computers effectively because looking up and interpolating from tables, although quicker for single-point evaluation, is inefficient for many points. The most recent work on polynomial interpolation by Ejiogu and Fiori, presented new, mostly discontinuous interpolations over a wider range of pressure and temperature than were previously available and provided a literature survey of the preexisting interpolation. The polynomials of Ejiogu and Fiori provide a baseline for comparison with our correlations for the same properties. We also present three additional correlations for prop erties that Ejiogu and Fiori did not address. All the correlations are invalid outside the steam-saturation envelope.
Development of Correlations
The objective of the work was to develop polynomials that describe the behavior of the steam properties to a sufficient degree of accuracy with changing pressure and temperature within the entire saturation envelope. The polynomials should be continuous and should involve simple integer powers of the independent variable. Integer powers are efficient arithmetic operations, unlike the evaluation of transcendental functions that implicitly includes fractional exponents. Transcendental functions take an order of magnitude more effort to evaluate than basic arithmetic operations on a computer. This efficiency is particularly useful in microcomputers. Simple polynomials can be most effectively evaluated with the Homer expansion.
The data were tabulated in Perry and Green for saturated water substance. The property values were corroborated by the tables published by Cooper and Le Fevre. The correlations were developed by polynomial regression, using the correlation coefficient and the residuals to judge the suitability of each correlation. Two dental evaluations are required for the saturation temperature and for the vapor density, and the evaluation of a square root is required for the specific enthalpy of vaporization. The polynomials all have integer powers.
The correlations are presented jointly in SI metric and customary units, with version (a) in SI metric and version (b) in customary units. AH temperatures used as independent variables in the correlations are in kelvins [degrees Rankine), and pressures similarly used are in pascals [pia). The coefficients were developed separately for each unit system, so that the residuals are identical for each pair of approximations. Correlations are presented first for steam condensate, then for saturation steam. Note that the use of temperature as the correlations variable results in simpler expressions than in many previously published works. If pressure is required as the independent variable in these correlations, then the evaluation of temperature from Eq. 10 is very accurate and suitable for determining all other properties.
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