A New Method of Continuous Thermodynamics Applied in an Equation of State
- T.P.J. Halpin (BP Research Centre) | Nick Quirke (BP Research Centre)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1990
- Document Type
- Journal Paper
- 617 - 622
- 1990. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 5.2.2 Fluid Modeling, Equations of State, 4.1.2 Separation and Treating, 5.5 Reservoir Simulation
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Continuous thermodynamics, in which a fluid's composition is regarded as a continuous function rather am as a set of discrete mole fractions, has been applied to petroleum fluids in a number of forms. The method provides a practical alternative to pseudocomponent methods in phase -equilibrium calculation with an equation of state (EOS). Current continuous-thermodynanuc methods are limited by the functional form assumed for the composition; they are unable to retain a continuous description of all phases in the calculation while preserving material balance. preserving material balance. A new functional representation of continuous mixtures based on an orthonormal expansion is proposed that preserves material balance between phases and provides a versatile composition description. With such a phases and provides a versatile composition description. With such a representation, the conditions for phase equilibrium are shown to be of a simple form. Because these conditions are similar to those for a discrete composition, phase equilibrium can be calculated in much the same way. The method's accuracy approaches that of a calculation in which the composition is fully represented by a large number of discrete components. The computer time requirement, however, is far less because only a small number of terms must be retained in the expansion series. Use of this new method is demonstrated for petroleum mixtures with a modified Soave EOS.
Modeling the composition of multicomponent mixtures is of considerable interest in reservoir and petroleum engineering. In the prediction of phase equilibrium with an EOS, the computer time prediction of phase equilibrium with an EOS, the computer time generally increases sharply with the number of components included in the calculation. For many applications, such as process design and reservoir simulation, computational speed is needed because phase equilibrium is calculated many times. The traditional way phase equilibrium is calculated many times. The traditional way to achieve more speed is to reduce the number of components through the pseudocomponent technique, in which components are grouped together. A number of empirical procedures for selecting these groupings have been suggested to make this reduced composition accurately mimic the phase behavior of the real system.
In recent years, a different approach, called continuous thermodynamics or the thermodynamics of polydisperse fluids, has been developed. In this approach, the set of discrete components (or part of it) is replaced by a continuous distribution of components. The mathematical treatment of the composition as a function rather than as a discrete set considerably simplifies the phase-Nuilibrium calculation. Use of this approach in the petroleum industry has a lon history, going back to the work of Bowman and Edmister on distillation. Much of the recent work on continuous systems has been from a more theoretical viewpoint. A number of workers in this field have provided the thermodynamic formalism for poly-disperse distributions. Most of the applications to the phase poly-disperse distributions. Most of the applications to the phase equilibria of such systems have been restricted to relatively simple thermodynamic models (for example, Raoult's law). Only recandy has this approach been recognized as potentially useful in more practical applications. Cotterman et al, Cotterman and Prausnitz, and Chou practical applications. Cotterman et al, Cotterman and Prausnitz, and Chou and Prasnitz developed continuous-thermodynamics techniques for general use in an. engineering EOS (see also Ref. 11).
Currently available methods of modeling real fluids through continuous thermodynamics suffer from a number of drawbacks, particularly the problem of material balance, as discussed later. We propose a new continuous representation of a fluid's composition propose a new continuous representation of a fluid's composition by use of an expansion in an orthonormal series. This technique removes a number of the disadvantages of continuous thermodynaics. Relations are derived that express the conditions for phase equilibrium for fluids described by this orthonormal series. The method is incorporated into the modified Soave EOS devised by Cotterman and Prausnitz for continuous mixtures. Example dewpoint and flash calculations made with this expansion method are pertonned and results are compared with those obtained by a pertonned and results are compared with those obtained by a normal discrete calculation.
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