Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper is concerned with the study of stability analysis to a complicated recovered frac- turing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction- diffusion equation with Neumann boundary conditions.
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Key Findings & Data:Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation.
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Conclusion & Impact:Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Recovered fracturing fluid model · stability analysis · hemivariational inequality
Abstract
This paper is concerned with the study of stability analysis to a complicated recovered frac- turing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction- diffusion equation with Neumann boundary conditions. Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation. Then, we prove that the existence of weak solutions to perturbated problems and the solution sequence to perturbated problems are uniformly bounded. Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.
CEN, J., COSTEA, N., MİN, C., YAO, J. (2023). Stability analysis for a recovered fracturing fluid model in the wellbore of shale gas reservoir. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1533–1549. https://ajindex.com/articles/971784
M. A. Abbasi, D. O. Ezulike, H. Dehghanpour and R. V. Hawkes, A comparative study of flowback rate and pressure transient behavior in multifractured horizontal wells completed in tight gas and oil reservoirs, J. Nat. Gas Sci. Eng. 17, 82–93, 2014
M. Asadi, R. A. Woodroof and R.E. Himes, Comparative study of flowback analysis using polymer concentrations and fracturing-fluid tracer methods: a field study, SPE Prod. & Oper. 23 (2), 147–157, 2008
Y. R. Bai, N. S. Papageorgiou and S. D. Zeng, A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian, Math. Z. 300, 325–345, 2022
J. X. Cen, A. A. Khan, D. Motreanu and S. D. Zeng, Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems, Inverse Problems, 38, 065006, 28 pp, 2022
J. X. Cen, S. Migórski, C. Min and J. C. Yao, Hemivariational inequality for contaminant reaction-diffusion model of recovered fracturing fluid in the wellbore of shale gas reservoir, Commun. Nonlinear Sci. Numer. Simulat. 118, 107020, 2023
F. H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205, 247–262, 1975
F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, Interscience, New York, 1983
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory, Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003
Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications, Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003
X. X. Dong, W. J. Li, Q. Liu and H. H. Wang, Research on convection-reaction- diffusion model of contaminants in fracturing flowback fluid in non-equidistant frac- tures with arbitrary inclination of shale gas development, J. Petrol. Sci. Eng. 208, 109479, 2022
C. J. Fang and W. M. Han, Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow, Discrete Contin. Dyn. Syst. 36 (10), 5369-5386, 2016
C. J. Fang and W. M. Han, Stability analysis and optimal control of a stationary Stokes hemivariational inequality, Evol. Equ. Control The. 9 (4), 995-1008, 2020
E. Ghanbari, M.A. Abbasi, H. Dehghanpour and D. Bearinger, Flowback volumetric and chemical analysis for evaluating load recovery and its impact on early-time production, Presented at the SPE Unconventional Resource Conference Canada, Calgary