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Hassan Hassanzadeh - One of the best experts on this subject based on the ideXlab platform.
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semi analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded Dual Porosity reservoir
Journal of Hydrology, 2018Co-Authors: Morteza Dejam, Hassan Hassanzadeh, Zhangxin ChenAbstract:Abstract We study the role of a hydraulic fracture on the pressure transient behavior of a vertical well producing from a bounded (or finite) Dual-Porosity formation. A combination of Laplace transform (LT) and the finite Fourier cosine transform (FFCT) are used to solve the diffusivity equation. The presented analysis allows identification of five flow regimes, including: 1) early linear flow, 2) volumetric depletion of natural fractures, 3) natural-fracture radial flow, 4) transition from natural-fracture radial flow to total (natural fractures and matrix) radial flow, and 5) pseudo-steady state flow. The results reveal that the interPorosity flow coefficient, storativity ratio, natural-fracture permeability anisotropy, and reservoir size play significant roles on the identified flow regimes compared to the hydraulically fractured well location and reservoir shape. The developed solution can be useful for well test analysis by generating a new set of type curves or can be applicable to a forward model for estimating parameters of reservoir. This study presents a new semi-analytical solution which finds application in well testing of hydraulically fractured wells in Dual-Porosity formations.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
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matrix fracture transfer shape factor for modeling flow of a compressible fluid in Dual Porosity media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan HassanzadehAbstract:Abstract The matrix–fracture transfer shape factor is one of the important parameters in the modeling of fluid flow in fractured porous media using a Dual-Porosity concept. Warren and Root [36] introduced the Dual-Porosity concept and suggested a relation for the shape factor. There is no general relationship for determining the shape factor for a single-phase flow of slightly compressible fluids. Therefore, different studies reported different values for this parameter, as an input into the flow models. Several investigations have been reported on the shape factor for slightly compressible fluids. However, the case of compressible fluids has not been investigated in the past. The focus of this study is, therefore, to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media. In this study, a model for the determination of the shape factor for compressible fluids is presented; and, the solution of nonlinear gas diffusivity equation is used to derive the shape factor. The integral method and the method of moments are used to solve the nonlinear governing equation by considering the pressure dependency of the viscosity and isothermal compressibility of the fluid. The approximate semi-analytical model for the shape factor presented in this study is verified using single-Porosity, fine-grid, numerical simulations. The dependency of the shape factor on the gas specific gravity, pressure and temperature are also investigated. The theoretical analysis presented improves our understanding of fluid flow in fractured porous media. In addition, the developed matrix–fracture transfer shape factor can be used as an input for modeling flow of compressible fluids in Dual-Porosity systems, such as naturally fractured gas reservoirs, coalbed methane reservoirs and fractured tight gas reservoirs.
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Shape factor in the drawdown solution for well testing of Dual-Porosity systems
Advances in Water Resources, 2009Co-Authors: Hassan Hassanzadeh, Mehran Pooladi-darvish, Shahram AtabayAbstract:Abstract One of the important parameters in existing commercial Dual-Porosity reservoir simulators is matrix–fracture shape factor, which is customarily obtained by assuming a constant pressure at the matrix–fracture boundary. In his work, Chang [1] , [2] addressed the impact of boundary conditions at the matrix–fracture interface and presented analytical solutions for the transient shape factor and showed that for a slab-shaped matrix block a constant pressure boundary condition leads to an asymptotic (long-time) shape factor of π2/L2, and that a constant volumetric flux leads to an asymptotic shape factor of 12/L2. In a recent paper [3] , we reconfirmed Chang’s [1] , [2] results using a Laplace transform approach. In this study, we extend our previous analysis and use infinite-acting radial and linear Dual-Porosity models, where the boundary condition is chosen at the wellbore, as opposed to at the matrix boundary. The coupled equations for fracture and matrix are solved analytically, taking into account the transient exchange between matrix and fracture. The analytical solution that invokes the time dependency of fracture boundary condition under constant rate is then used to calculate the transient shape factors. It is shown that, for a well producing at constant rate from a naturally fractured reservoir, the appropriate value of stabilized shape factor is 12/L2. This contrasts with the commonly used shape factor for a slab-shaped matrix block that is subject to a constant pressure boundary condition, which is π2/L2. The errors in the matrix–fracture exchange term in a Dual-Porosity model associated with the use of a shape factor derived based on constant pressure boundary condition at the matrix boundary are then evaluated.
Zhangxin Chen - One of the best experts on this subject based on the ideXlab platform.
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numerical simulation of two phase flow in naturally fractured reservoirs using Dual Porosity method on parallel computers numerical simulation of two phase flow in naturally fractured reservoirs
IEEE International Conference on High Performance Computing Data and Analytics, 2019Co-Authors: Lihua Shen, Zhangxin Chen, Tao Cui, Hui Liu, Zhouyuan Zhu, He Zhong, Bo Yang, Huaqing LiuAbstract:The two-phase oil-water flow in naturally fractured reservoirs and its numerical methods are introduced in this paper, where the fractured reservoirs are modeled by the Dual Porosity method. An efficient numerical scheme, including the finite difference (volume) method, CPR-FPF preconditioners for linear systems and effective decoupling methods, is presented. Parallel computing techniques employed in simulation of the two-phase flow are also presented. Using these numerical scheme and parallel techniques, a parallel reservoir simulator is developed, which is capable of simulating large-scale reservoir models. The numerical results show that this simulator is accurate and scalable compared to the commercial software and the numerical scheme is also effective.
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semi analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded Dual Porosity reservoir
Journal of Hydrology, 2018Co-Authors: Morteza Dejam, Hassan Hassanzadeh, Zhangxin ChenAbstract:Abstract We study the role of a hydraulic fracture on the pressure transient behavior of a vertical well producing from a bounded (or finite) Dual-Porosity formation. A combination of Laplace transform (LT) and the finite Fourier cosine transform (FFCT) are used to solve the diffusivity equation. The presented analysis allows identification of five flow regimes, including: 1) early linear flow, 2) volumetric depletion of natural fractures, 3) natural-fracture radial flow, 4) transition from natural-fracture radial flow to total (natural fractures and matrix) radial flow, and 5) pseudo-steady state flow. The results reveal that the interPorosity flow coefficient, storativity ratio, natural-fracture permeability anisotropy, and reservoir size play significant roles on the identified flow regimes compared to the hydraulically fractured well location and reservoir shape. The developed solution can be useful for well test analysis by generating a new set of type curves or can be applicable to a forward model for estimating parameters of reservoir. This study presents a new semi-analytical solution which finds application in well testing of hydraulically fractured wells in Dual-Porosity formations.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
Ehsan Ranjbar - One of the best experts on this subject based on the ideXlab platform.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
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effect of fracture pressure depletion regimes on the Dual Porosity shape factor for flow of compressible fluids in fractured porous media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a Dual-Porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in Dual-Porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.
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matrix fracture transfer shape factor for modeling flow of a compressible fluid in Dual Porosity media
Advances in Water Resources, 2011Co-Authors: Ehsan Ranjbar, Hassan HassanzadehAbstract:Abstract The matrix–fracture transfer shape factor is one of the important parameters in the modeling of fluid flow in fractured porous media using a Dual-Porosity concept. Warren and Root [36] introduced the Dual-Porosity concept and suggested a relation for the shape factor. There is no general relationship for determining the shape factor for a single-phase flow of slightly compressible fluids. Therefore, different studies reported different values for this parameter, as an input into the flow models. Several investigations have been reported on the shape factor for slightly compressible fluids. However, the case of compressible fluids has not been investigated in the past. The focus of this study is, therefore, to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media. In this study, a model for the determination of the shape factor for compressible fluids is presented; and, the solution of nonlinear gas diffusivity equation is used to derive the shape factor. The integral method and the method of moments are used to solve the nonlinear governing equation by considering the pressure dependency of the viscosity and isothermal compressibility of the fluid. The approximate semi-analytical model for the shape factor presented in this study is verified using single-Porosity, fine-grid, numerical simulations. The dependency of the shape factor on the gas specific gravity, pressure and temperature are also investigated. The theoretical analysis presented improves our understanding of fluid flow in fractured porous media. In addition, the developed matrix–fracture transfer shape factor can be used as an input for modeling flow of compressible fluids in Dual-Porosity systems, such as naturally fractured gas reservoirs, coalbed methane reservoirs and fractured tight gas reservoirs.
Samo Mahnickalamiza - One of the best experts on this subject based on the ideXlab platform.
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Dual Porosity model of liquid extraction by pressing from biological tissue modified by electroporation
Journal of Food Engineering, 2014Co-Authors: Samo Mahnickalamiza, Eugene VorobievAbstract:The objective of this study is to provide insight into the phenomena related with juice expression from electroporated tissue. We propose an analytical model and study consolidation behaviour of a block of tissue during pressing; before and after electroporation. By the Dual-Porosity approach, we treat compressibility and hydraulic permeability of intracellular and extracellular space separately. Initial parameter estimations are based on previously published studies (for hydraulic permeability), or analysis of modelled data (for compressibility moduli). Good agreement between simulations and experiments performed is then obtained by optimization (i.e. fitting). Impact of electroporation on membrane permeability is theoretically estimated and elucidated via the extraction–consolidation model; results are compared with experimental kinetics for validation and evaluation of model performance. Permeability coefficient estimates from literature proved valuable as initial approximations, and the model results were able to fit experimental data with high accuracy, clearly demonstrating the power of the proposed approach.
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Dual Porosity model of solute diffusion in biological tissue modified by electroporation
Biochimica et Biophysica Acta, 2014Co-Authors: Samo Mahnickalamiza, Damijan Miklavcic, Eugene VorobievAbstract:In many electroporation applications mass transport in biological tissue is of primary concern. This paper presents a theoretical advancement in the field and gives some examples of model use in electroporation applications. The study focuses on post-treatment solute diffusion. We use a Dual-Porosity approach to describe solute diffusion in electroporated biological tissue. The cellular membrane presents a hindrance to solute transport into the extracellular space and is modeled as electroporation-dependent Porosity, assigned to the intracellular space (the finite rate of mass transfer within an indiviDual cell is not accounted for, for reasons that we elaborate on). The second Porosity is that of the extracellular space, through which solute vacates a block of tissue. The model can be used to study extraction out of or introduction of solutes into tissue, and we give three examples of application, a full account of model construction, validation with experiments, and a parametrical analysis. To facilitate easy implementation and experimentation by the reader, the complete derivation of the analytical solution for a simplified example is presented. Validation is done by comparing model results to experimentally-obtained data; we modeled kinetics of sucrose extraction by diffusion from sugar beet tissue in laboratory-scale experiments. The parametrical analysis demonstrates the importance of selected physicochemical and geometrical properties of the system, illustrating possible outcomes of applying the model to different electroporation applications. The proposed model is a new platform that supports rapid extension by state-of-the-art models of electroporation phenomena, developed as latest achievements in the field of electroporation.
Eugene Vorobiev - One of the best experts on this subject based on the ideXlab platform.
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Dual Porosity model of liquid extraction by pressing from biological tissue modified by electroporation
Journal of Food Engineering, 2014Co-Authors: Samo Mahnickalamiza, Eugene VorobievAbstract:The objective of this study is to provide insight into the phenomena related with juice expression from electroporated tissue. We propose an analytical model and study consolidation behaviour of a block of tissue during pressing; before and after electroporation. By the Dual-Porosity approach, we treat compressibility and hydraulic permeability of intracellular and extracellular space separately. Initial parameter estimations are based on previously published studies (for hydraulic permeability), or analysis of modelled data (for compressibility moduli). Good agreement between simulations and experiments performed is then obtained by optimization (i.e. fitting). Impact of electroporation on membrane permeability is theoretically estimated and elucidated via the extraction–consolidation model; results are compared with experimental kinetics for validation and evaluation of model performance. Permeability coefficient estimates from literature proved valuable as initial approximations, and the model results were able to fit experimental data with high accuracy, clearly demonstrating the power of the proposed approach.
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Dual Porosity model of solute diffusion in biological tissue modified by electroporation
Biochimica et Biophysica Acta, 2014Co-Authors: Samo Mahnickalamiza, Damijan Miklavcic, Eugene VorobievAbstract:In many electroporation applications mass transport in biological tissue is of primary concern. This paper presents a theoretical advancement in the field and gives some examples of model use in electroporation applications. The study focuses on post-treatment solute diffusion. We use a Dual-Porosity approach to describe solute diffusion in electroporated biological tissue. The cellular membrane presents a hindrance to solute transport into the extracellular space and is modeled as electroporation-dependent Porosity, assigned to the intracellular space (the finite rate of mass transfer within an indiviDual cell is not accounted for, for reasons that we elaborate on). The second Porosity is that of the extracellular space, through which solute vacates a block of tissue. The model can be used to study extraction out of or introduction of solutes into tissue, and we give three examples of application, a full account of model construction, validation with experiments, and a parametrical analysis. To facilitate easy implementation and experimentation by the reader, the complete derivation of the analytical solution for a simplified example is presented. Validation is done by comparing model results to experimentally-obtained data; we modeled kinetics of sucrose extraction by diffusion from sugar beet tissue in laboratory-scale experiments. The parametrical analysis demonstrates the importance of selected physicochemical and geometrical properties of the system, illustrating possible outcomes of applying the model to different electroporation applications. The proposed model is a new platform that supports rapid extension by state-of-the-art models of electroporation phenomena, developed as latest achievements in the field of electroporation.
