A simple method of determination of the degree of gas mixing by numerical Laplace inversion and Maple®

• Autorzy: Wójcik M. , Szukiewicz M.

Identyfikatory

DOI

10.24425/bpas.2019.128484

• Języki publikacji: EN

Abstrakty

EN

This article presents a new efficient method of determining values of gas flow parameters (e.g. axial dispersion coefficient, DL and Pèclet number, Pe). A simple and very fast technique based on the pulse tracer response is proposed. It is a method which combines the benefits of a transfer function, numerical inversion of the Laplace transform and optimization allows estimation of missing coefficients. The study focuses on the simplicity and flexibility of the method. Calculations were performed with the use of the CAS-type program (Maple®). The correctness of the results obtained is confirmed by good agreement between the theory and experimental data for different pressures and temperature. The CAS-type program is very helpful both for mathematical manipulations as a symbolic computing environment (mathematical formulas of Laplace-domain model are rather sophisticated) and for numerical calculations. The method of investigations of gas flow motion is original. The method is competitive with earlier methods.

Słowa kluczowe

EN

inverse boundary value problem; Gaver-Stehfest algorithm; axial gas dispersion coefficient; Peclet number; CAS program

PL

algorytm Gavera-Stehfesta; dyspersja gazu; liczba Pecleta; program CAS; Maple

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 2
• Strony: 235--240
• Opis fizyczny: Bibliogr. 16 poz., rys., tab., wykr.

Twórcy

autor

Wójcik M.

• The Faculty of Chemistry, Department of Chemical and Process Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 6, 35-959 Rzeszow, Poland

autor

Szukiewicz M.

• The Faculty of Chemistry, Department of Chemical and Process Engineering, Rzeszow University of Technology, al. Powstancow Warszawy 6, 35-959 Rzeszow, Poland

Bibliografia

• [1] F. Yang, X. Wang, and H. Liu, “Application of Laplace transform in well test interpretation-an example of the field cavity-fractured reservoirs in tarim basin”, 2011 International Conference on Multimedia Technology, IEEE, Hangzhou, China, 1988‒1991, 2011.
• [2] C. Montella, “LSV modelling of electrochemical systems through numerical inversion of Laplace transforms, I: The GSLSV algorithm”, J. Electroanal. Chem., 614(1‒2), 121‒130 (2008).
• [3] R.M. Endah and S.D. Surjanto, “Performance of Gaver-Stehfest numerical Laplace inversion method on option pricing formulas”, Int. J. Appl. Math. Comput. Sci., 3(2), 71‒76 (2017).
• [4] J.H.Knight and A.P. Raiche, “Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method”, Geophysics, 47(1), 47‒50 (1982).
• [5] N.Smith and L. Brančik, “Comparative study on one-dimensional numerical inverse Laplace transform methods for electrical engineering”, Elektrorevue, 18(1), 1‒6 (2016).
• [6] I. Kocabas, “Application of iterated Laplace transformation to tracer transients in heterogeneous porous media”, J. Franklin. Inst., 348(7), 1339‒1362 (2011).
• [7] Q. Wang and H. Zhan, “On different numerical inverse Laplace methods for solute transport problems”, Adv Water Resour, 75, 80‒92 (2015).
• [8] L.-W. Chiang, “The application of numerical Laplace inversion methods to groundwater flow and solute transport problems”, New Mexico Institute of Mining and Technology, Socorro, New Mexico, 1989.
• [9] F.H. Escobar, F.A. Leguizamo, and J.H. Cantillo, “Comparison of Stehfest’s and Iseger’s algorithms for Laplacian inversion in pressure well tests”, J. Eng. Appl. Sci., 9(6), 919‒922 (2014).
• [10] J.S. Chen, C.W. Liu, C.S. Chenb, and H.D. Yehc, “A Laplace transform solution for tracer tests in a radially convergent flow field with upstream dispersion”, J. Hydrol., 183(3‒4), 263‒275 (1996).
• [11] K. Boupha, J.M. Jacobs, and K. Hartfield, “MDL Groundwater software: Laplace transforms and the De Hoog algorithm to solve contaminant transport equation”, Computers & Geosciences, 30(5), 445‒453 (2004).
• [12] O. Taiwo, J. Schultz, and V. Krebs, “A comparison of two methods for the numerical inversion of Laplace transforms”, Computers Chem. Eng., 19(3), 303‒308 (1995).
• [13] O. Taiwo and R. King, “Determination of kinetic parameters for the adsorption of a protein on porous beads using symbolic computation and numerical Laplace inversion”, Chem Eng. Proc., 42(7), 561‒568 (2003).
• [14] P. Wyns, D.P. Foty, and K.E. Oughstun, “Numerical analysis of the precursor fields in linear dispersive pulse propagation”, J. Opt. Soc. Am., 6(9), 1421‒1429 (1989).
• [15] M. Wójcik, M. Szukiewicz, P. Kowalik, and W. Próchniak, “The efficiency of the Gaver-Stehfest method to solve one-dimensional gas flow model”, Adv. Sci. Technol. Res. J., 11(1), 246‒252 (2017).
• [16] M. Wójcik, M. Szukiewicz, and P. Kowalik, “Application of numerical Laplace inversion methods in chemical engineering with Maple®”, J. Appl. Comput. Sci. Meth., 7(1), 5‒15 (2015).

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).