Exact solution of a key equation in a finite planetary atmosphere by the method of laplace transform and linear singular operators

1980 ◽  
Vol 67 (2) ◽  
pp. 343-347 ◽  
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Planetary Atmosphere ◽  
Singular Operators ◽  
Key Equation

Flow Mathematic Model and Exact Solution of Swabbing Wells’ Fluid Level Build up

2012 ◽  
Vol 524-527 ◽  
pp. 1418-1422
Author(s):  
Yan Chen ◽  
Xin Hai Wang ◽  
Feng Yang ◽  
Hai Min Xu ◽  
Bo Tao Liu
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Bessel Function ◽  
Mathematic Model ◽  
Well Bore ◽  
Fluid Level ◽  
Type Curve ◽  
Skin Factor ◽  
Reservoir Flow

The fluid level of swabbing wells with packers or without packers is different from other wells’ when the swabbing wells are stopped swabbing, because the effect of gravity differentiation is obvious, which is used to calculate the sand face pressure. In the homogeny reservoir, flow mathematic model of build-up of fluid swabbing well in circular sealed stratum is built up under considering the well bore effect and skin factor. Then, the non-homogeneous equation’s exact solution in Laplace space of the model are acquired by using theory of Laplace transform and Bessel function ,then the chart of type curve and the matching of type curve are analyzed. Finally, the software of swabbing well’s fluid level build-up is developed which is used to calculate the formation parameters that are fitted the formation parameters calculated with other methods.

scholarly journals Exact Solution of Linear and Nonlinear Wave Equations by Double Laplace and Iterative Method

2019 ◽  
Vol 11 (5) ◽  
pp. 33
Author(s):  
Adesina K. Adio ◽  
Wumi S. Ajayi ◽  
Olabode O. Bamisile ◽  
Babatunde T. Akanbi
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Iteration Process ◽  
Nonlinear Wave Equations ◽  
Double Laplace Transform ◽  
Linear And Nonlinear

A coupling of double Laplace transform with Iterative method is used to solve linear and nonlinear wave equations subject to initial and boundary conditions. The iteration process leads to disappearance of noise terms and exact solution is obtained at first iteration. Through several examples, the convenience and efficiency of the method is demonstrated, showing its usefulness to overcome difficulties associated with some existing techniques.

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