An Improved Computational Method for the Calculation of Mixture Liquid–Vapor Critical Points

Dimitrakopoulos, Panagiotis; Jia, Wenlong; Li, Changjun

doi:10.1007/s10765-014-1680-7

Cited by 10 publications

(18 citation statements)

References 26 publications

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“…The final results obtained by the numerical inversion of this function are presented in Table 2, which also shows a comparison between these results and the ones produced by the methodology proposed by Dimitrakopoulos et al (2014), that uses a damped Newton's method for temperature, volume and the numbers of moles vector ∆n. The results are fully compatible, indicating that the methodology is capable to produce accurate results.…”

Section: Resultsmentioning

confidence: 99%

“…A huge quantity of numerical procedures can be applied in the solution of this kind of system. Among these, we can mention Newton-type methods (Dimitrakopoulos et al, 2014), homotopy-continuation procedures (Sidky et al, 2016;Wang et al, 1999) and interval methods (Stradi et al, 2001). Here, we employ the methodology of numerical inversion of functions from the plane to the plane, proposed by Malta et al (1993).…”

Section: Numerical Methodologymentioning

confidence: 99%

“…According to Heidemann and Khalil (1980), Stockfleth and Dohrn (1998) and Dimitrakopoulos et al (2014), the derivatives of Helmholtz free energies A can be substituted using standard thermodynamic relations, by expressions involving the derivatives of the fugacities fi of the components in the mixture:…”

Section: Problem Formulationmentioning

confidence: 99%

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Critical Point Calculations by Numerical Inversion of Functions

Parajara,

Platt,

Neto

et al. 2020

Preprint

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In this work, we propose a new approach to the problem of critical point calculation, based on the formulation of Heidemann and Khalil (1980). This leads to a 2 × 2 system of nonlinear algebraic equations in temperature and molar volume, which makes possible the prediction of critical points of the mixture through an adaptation of the technique of inversion of functions from the plane to the plane, proposed by Malta, Saldanha, and Tomei (1993). The results are compared to those obtained by three methodologies: (i) the classical method of Heidemann and Khalil (1980), which uses a double-loop structure, also in terms of temperature and molar volume;(ii) the algorithm of Dimitrakopoulos, Jia, and Li (2014), which employs a damped Newton algorithm and (iii) the methodology proposed by Nichita and Gomez (2010), based on a stochastic algorithm. The proposed methodology proves to be robust and accurate in the prediction of critical points, as well as provides a global view of the nonlinear problem.

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Section: Resultsmentioning

confidence: 99%

Section: Numerical Methodologymentioning

confidence: 99%

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Critical Point Calculations by Numerical Inversion of Functions

Parajara,

Platt,

Neto

et al. 2020

Preprint

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“…Fluid Phase Simulation. The PVTsim software by the Calsep Company specializes in the calculation of fluid properties, employing several different equations of state (EOS); it is widely used in oil and gas reservoir studies [20]. The input data for the PVTsim software include well fluid components (C 1 -C 30+ , molecular weight), constant mass expansion experimental data, and constant volume depletion experimental data; these were all derived from the PVT analysis report for Well ZG7-5 (inner report of the Tarim Oil Company, 2016) (Tables 1 and 2).…”

Section: Methodsmentioning

confidence: 99%

Fluid Phase Simulation and Evolution of a Condensate Gas Reservoir in the Tazhong Uplift, Tarim Basin

et al. 2019

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The fluid phase and the evolution of the condensate gas reservoir in the Lianglitage Formation (O3), Well ZG7-5, Tazhong Uplift, were studied by integrating the PVTsim and the PetroMod software. The fluid phase was successfully simulated, and the burial, temperature, pressure, and pressure coefficient histories were reconstructed. The evolution of the fluid phase and its properties (density, viscosity, and gas-oil ratio) under the ideal and gas washing conditions was also explored. The simulated pressure-temperature (P‐T) phase diagram confirms that the reservoir fluid is in the condensate gas phase at present, with an order of critical point-cricondenbar-cricondentherm (CP‐Pm‐Tm). The temperature and pressure show an overall increasing trend considering the entirety of geological evolution. Under ideal conditions, fluid transition from coexisting gas and liquid phases to a single condensate gas phase occurred during the Late Cretaceous (80 Ma, T=135.7°C, and P=58.19 MPa). The density and viscosity of the liquid phase decreased gradually while the density and viscosity of the gas phase and the solution gas-oil ratio increased during geological processes. With the consideration of gas washing, the critical phase transition time points for 100% and 50% gas washing fluid are 394 Ma, 383 Ma, 331 Ma, and 23 Ma, as well as 266 Ma and 23 Ma, respectively. The average liquid phase density, gas phase density, and liquid phase viscosity under 100% gas washing are larger than those under 50% gas washing before 23 Ma (Miocene), while the gas phase viscosity values are similar for both cases. This study visually suggests that the temperature and pressure histories, which are controlled by the burial history and heat flow evolution, and gas washing have significant impacts on the formation of the condensate gas reservoirs and evolution of the fluid phase and its features in the Tazhong Uplift.

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“…Such limitations are true of all nonlinear solvers that are local in nature. Nevertheless, a significant amount of effort has been dedicated toward improving the convergence properties and overall efficiency of local solver implementations. These techniques are typically well suited for large‐scale reservoir and multiphase flow simulations where critical point calculations may be performed

O (10^{6})

or more times each time‐step.…”

Section: Introductionmentioning

confidence: 99%

Reliable mixture critical point computation using polynomial homotopy continuation

2016

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The numerical computation of multicomponent mixture critical points has been the subject of much study due to their theoretical and practical importance. Both deterministic and stochastic methods have been applied with varying degrees of reliability and robustness. In this work, we utilize numerical polynomial homotopy continuation (NPHC) to reliably identify all mixture critical points. This method is unique due to its robustness, initialization‐free nature and ease of parallelization. For a given system of equations, all complex solutions are found. Computational times are also found to be invariant to mixture composition. We validate this technique against previous work and extend the method to mixtures of up to eight components. NPHC is shown to be a modern and powerful technique which offers mathematical reliability at a moderate computational cost. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4497–4507, 2016

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An Improved Computational Method for the Calculation of Mixture Liquid–Vapor Critical Points

Cited by 10 publications

References 26 publications

Critical Point Calculations by Numerical Inversion of Functions

Critical Point Calculations by Numerical Inversion of Functions

Fluid Phase Simulation and Evolution of a Condensate Gas Reservoir in the Tazhong Uplift, Tarim Basin

Reliable mixture critical point computation using polynomial homotopy continuation

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