Equations of State in Mathematical Models of Natural Gas Production and Transportation Systems
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tions of State in Mathematical Models of Natural Gas Production and Transportation Systems E. A. Bondarev†1 , A. F. Voevodin2* , K. K. Argunova1** , and I. I. Rozhin1*** 1
Institute of Oil and Gas Problems, Siberian Branch, Russian Academy of Sciences, ul. Oktyabr’skaya, Yakutsk, 677980 Russia 2 Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090 Russia Received March 2, 2018; in final form, February 25, 2019; accepted April 16, 2020
Abstract—For the Redlich–Kwong equation of state of real gas, which is widely used for description of behavior of hydrocarbon mixtures, the inversion curve, which determines the change in the throttling coefficient sign, is constructed. The reduced pressure and temperature variation ranges correspond to the characteristic values in natural gas production and transportation systems. DOI: 10.1134/S1995423920030052 Keywords: equation of state, throttling, inversion curve, natural gas, mathematical modeling.
1. INTRODUCTION In a recent publication [1] of the authors, the Redlich–Kwong equation [2] was analyzed and the possibility of using it in a mathematical model of non-stationary gas flow in gas pipelines was shown. In addition to providing sufficient accuracy of calculating the imperfection value and heat capacity of natural gas, the Redlich–Kwong equation also ensures that the system of equations for pipe hydraulics of compressible fluids is hyperbolic. This equation is considered to be “the most successful two-parameter equation of state” [2] and is most often used in calculating the behavior of hydrocarbon mixtures [3] and conditions of thermodynamic equilibrium of gas hydrates [4]. In this article, it is offered to expand the number of criteria for selection of equation of state for closure of mathematical models of natural gas production and transportation systems by introducing an important thermodynamic characteristic of inverse curve [5]. This addition is necessary to create a common approach to assessment of equations of state for the whole complex of gas production and transportation (gas reservoir, well, and gas pipeline). The fact is that phase transformations during natural gas production are described using methods of applied thermodynamics, including those for selection of equation of state of hydrocarbon mixtures [3]. This approach allows correct assessment of the processes of condensation and evaporation of reservoir fluids and estimation density of liquid and gas phases; it plays an important role in the choice of technological regimes of field exploitation. The inverse curve in the temperature–pressure coordinates corresponds to a change in the sign of the Joule–Thomson coefficient [5]
∂T ∂p
i
1 = cp
∂V −V , T ∂T p
which is determined using the equation of state †
Deceased. E-mail: [email protected] ** E-mail: [email protected] *** E-mail: [email protected] *
258
(1)
EQUATIONS OF STATE IN MATHEMATICAL MODELS
259
pV = zRT,
(2)
where p, T , and V are the pressure, temperature,
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