Asymptotic Solutions of the Diffusivity Equation and Their Applications

2016 ◽  
Author(s):  
Michael J. King ◽  
Zhenzhen Wang ◽  
Akhil Datta-Gupta
Keyword(s):  
Asymptotic Solutions ◽  
Diffusivity Equation

Effects of Langmuirian adsorption on the potentiostatic response at spherical and planar electrodes

1991 ◽  
Vol 56 (1) ◽  
pp. 42-59 ◽  
Author(s):  
María-Luisa Alcaraz ◽  
Jesús Gálvez
Keyword(s):  
Power Law ◽  
Adsorption Process ◽  
Asymptotic Solutions ◽  
Planar Electrodes ◽  
Comparison Of The Results

Equations for a potentiostatic reaction with an adsorption process following Langmuir’s isotherm have been derived for the expanding sphere with any power law electrode model. This model is very general and includes, among others, the following ones: (a) stationary plane; (b) stationary sphere; (c) expanding plane; and (d) expanding sphere. Characteristics of these solutions and the behavior of the corresponding asymptotic solutions are discussed. A comparison of the results obtained for plane and spherical electrodes has also been performed.

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

Asymptotic solutions for a symmetric plasma under ionization nonequilibrium

1999 ◽  
Vol 86 (9) ◽  
pp. 4792-4798 ◽  
Author(s):  
Lindsey D. Thornhill ◽  
Prateen V. Desai
Keyword(s):  
Asymptotic Solutions ◽  
Ionization Nonequilibrium
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