Simulation Of Fluid Flow Research Articles

A discontinuous Galerkin method for the Brinkman–Darcy-transport problem

In this paper, a weighted discontinuous Galerkin finite element method and an upwind format are presented to solve the coupled Brinkman–Darcy flow and transport model. The flow in a highly permeable region of the model is governed by the Brinkman equations, and the percolation in the porous media is controlled by the Darcy equations, which are coupled by three interface conditions. The permeability coefficients in this model are strongly nonhomogeneous, anisotropic, and discontinuous; the transport equation is a convection-dominated problem; and the velocity field in the porous media domain does not satisfy the divergence-free condition. A weighted discontinuous Galerkin finite element method is used to solve the complex permeability coefficient problem and an upwind scheme is used to solve the convection dominated problem. The interface conditions can be naturally incorporated into the discrete formulation without introducing additional variables. Optimal error estimates are obtained for the semi-discretization and the full discretization with the backward Euler scheme in suitable energy norm. A series of numerical experiments are provided to illustrate the proposed method, including testing the convergence and accuracy of various types of meshes; simulating fluid flow in complex porous media such as obstacles, layered media, and curved interfaces; and studying the coupled flow behavior of surface-subsurface flows with contaminant transport.

Two quantum algorithms for solving the one-dimensional advection–diffusion equation

Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection–diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithm (QLSA) based on the Harrow–Hassidim–Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to N=64 grid points on the unit interval. Both algorithms are hybrid in nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the accurate eigenvalue estimation with the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement noise. We reflect on the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.

Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.

Universal correlation for the critical diameter of deterministic lateral displacement devices with polygonal posts.

Deterministic lateral displacement (DLD) is a microfluidic technique that utilizes a specific array of micro-posts to separate cells or particles larger and smaller than a critical diameter. The critical diameter depends on the shape of the posts, the gap between the posts, and the relative shift between the adjacent rows of posts. Here, we present an experimental and numerical investigation to elucidate the functional dependence of the critical diameter of DLD arrays with polygonal posts on the geometric parameters. Based on simulations of fluid flow through DLD devices with varying geometric parameters, we first derived a correlation to predict the critical diameter of DLD arrays with polygonal post shapes having an arbitrary number of sides. We then used a novel experimental approach, wherein we coupled different DLD arrays with an upstream droplet generator to flow droplets of varying sizes and estimate the critical diameter. The critical diameter predicted by the correlation based on simulations compares well with our experimental data and with data available in the literature. The universal correlation for a critical diameter presented here can help design and optimize DLD devices with polygonal posts.

Deep learning accelerated numerical simulation for three-dimensional compressible fluids

Numerical simulation of fluid flow is a long-standing challenge across many physical application domains, including engineering, climate, and the physical science. There has been a surge of interest in high order schemes aimed at improving simulation accuracy on coarse grids. However, for high-dimensional fluids, the computational cost escalates with the number of dimensions involved. In this paper, we propose a deep learning-based approach to accelerate the numerical computation and further improve the accuracy in simulating three-dimensional (3D) compressible fluids which can be described by Eulerian equations. The proposed work utilizes 3D Euler transformer networks to learn the interpolation coefficients for cell boundaries, which are applied to approximate the boundary fluxes of fluid on coarser grids. Benefiting from learning features of high-resolution fluid flow, our learned interpolation method yields finer performance on coarse grids, thereby accelerating the fluid simulations and improving the numerical accuracy. The numerical experiments confirm that the proposed method improves performance in inference of coarse-grained dynamics.

Simulating flows in backward-facing step for various expansion ratios by finite element-lattice Boltzmann

The development of fluid flow in a channel with constant width and a backward-facing step was investigated through numerical simulation. For the first time, by employing the finite element lattice Boltzmann method, a series of numerical calculations were performed to explore the flow behavior across various Reynolds numbers and expansion ratios (the ratio of the outlet section width to the inlet section width). Analysis was conducted on the macroscopic flow parameters, including velocity fields, streamlines, and reattachment points, for different Reynolds numbers and expansion ratios. It was found that the reattachment length in flows over a backward-facing step is dependent on both the Reynolds number and the expansion ratio, rather than being a function of a singular variable. It was concluded, as the Reynolds number increases, the reattachment length also increases. For a Reynolds number range of 10≤ReD≤100, this increase can be described by an exponential relationship, with an expansion ratio of 1.94. The impact of the expansion ratio is less pronounced at lower Reynolds numbers when compared to that at higher ones. The minimum skin friction factor within the return zone is significantly influenced by the Reynolds number, emphasizing the dominant effects of viscosity in near-wall flows. The lattice Boltzmann method is a computationally efficient algorithm for simulating fluid flows through complex geometries, potentially offering significant processing time savings.

A hybrid modeling approach: dynamic simulation of two-phase fluid flow in compacting gas condensate reservoirs using potential flow theory

Simulating the flow processes of complex hydrocarbon mixtures, such as gas condensate mixtures and volatile oils, in deep reservoirs is one of the most challenging problems in reservoir hydrodynamics. The challenge lies in meeting three requirements simultaneously when creating a simulator: high accuracy, low computational cost, and high reliability. These metrics determine the performance of the simulation. Meeting all these requirements at the same time necessitates a hybrid approach to solving the problem and optimizing the computational algorithm in terms of CPU time. A new technique has been developed for hybrid modeling of the development of deposits of complex hydrocarbon mixtures. This technique integrates the theory of potential flow, the Binary Flow Model (which accounts for rock compaction, PVT properties of reservoir fluids, phase transformation, and mass transfer between phases), and the material balance equations of the hydrocarbon system using time discretization. In this case, to linearize nonlinear differential equations for the flow of a gascondensate mixture, the method of averaging reservoir pressure along the radial coordinate was used. By introducing the Khrestianovich function, an algorithm was obtained to determine the rate of inflow of the gas-condensate mixture to the well. Using material balance equations for gas and condensate, it was possible to obtain differential equations that describe changes in reservoir pressure and condensate saturation over time. Based on this technique, a simulator for a gas condensate reservoir was created, enabling computer studies to be conducted. The results demonstrated the proposed technique's good accuracy compared with the results of the semi-analytical solution. Keywords: dynamic modeling; simulation; monitoring; streamline; hybrid modeling; binary model.

A five field formulation for flow simulations in porous media with fractures and barriers via an optimization based domain decomposition method

The present work deals with the numerical resolution of coupled 3D–2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model, fractures are represented as planar interfaces immersed in a 3D porous matrix and can behave as preferential flow paths, in the case of conductive fractures, or can actually be a barrier for the flow, when, instead, the permeability in the normal-to-fracture direction is small compared to the permeability of the matrix. Consequently, the pressure solution in a DFM can be discontinuous across a barrier, as a result of the geometrical dimensional reduction operated on the fracture. The present work is aimed at developing a numerical scheme suitable for the simulation of the flow in a DFM with fractures and barriers, using a mesh for the 3D matrix non conforming to the fractures and that is ready for domain decomposition. This is achieved starting from a PDE-constrained optimization method, currently available in literature only for conductive fractures in a DFM. First, a novel formulation of the optimization problem is defined to account for non permeable fractures. These are described by a filtration-like coupling at the interface with the surrounding porous matrix. Also the extended finite element method with discontinuous enrichment functions is used to reproduce the pressure solution in the matrix around a barrier. The method is presented here in its simplest form, for clarity of exposition, i.e. considering the case of a single fracture in a 3D domain, also providing a proof of the well posedness of the resulting discrete problem. Four validation examples are proposed to show the viability and the effectiveness of the method.

Enhancing CFD solver with Machine Learning techniques

This study addresses the computational challenges in fluid flow simulations arising from demanding computational grids, required to capture the temporal and length scales involved. Our approach focuses on the pressure solver, as this is a resource-intensive component in Computational Fluid Dynamics (CFD) solvers. We achieve this by integrating a Machine Learning (ML) surrogate model with an incompressible fluid flow solver. We created two variants of an ML-enhanced CFD solver which were able to reduce the number of iterations required by the CFD pressure solver during unsteady flow simulations. Consequently, the simulations yielded comparable drag coefficients and Strouhal numbers, accompanied by an eightfold decrease in execution time. The performance enhancements are attributed to reduced computational effort per temporal iteration and early-stage forcing on the simulation dynamical behavior when using the ML-based surrogate models. This research introduces an approach to enhance the computational efficiency of fluid flow analyses by incorporating surrogate models to aid the pressure solver in CFD simulations. We propose a Hybrid CFD solver, ie. a physics-informed solver enhanced with data-driven surrogate models.

Pore‐Scale Modeling of Reactive Transport with Coupled Mineral Dissolution and Precipitation

AbstractWe present a new pore‐scale model for multicomponent advective‐diffusive transport with coupled mineral dissolution and precipitation. Both dissolution and precipitation are captured simultaneously by introducing a phase transformation vector field representing the direction and magnitude of the overall phase change. An effective viscosity model is adopted in simulating fluid flow during mineral dissolution‐precipitation that can accurately capture the velocity field without introducing any empirical parameters. The proposed approach is validated against analytical solutions and interface tracking simulations in simplified structures. After validation, the proposed approach is employed in modeling realistic rocks where mineral dissolution and precipitation are dominant at different locations. We have identified three regimes for mineral dissolution‐precipitation coupling: (a) compact dissolution‐precipitation where dissolution is dominant near the inlet and precipitation is dominant near the outlet, (b) wormhole dissolution with clustered precipitation where dissolution generates wormholes in the main flow paths and precipitation clogs the secondary flow paths, and (c) dissolution dominant where all solid grains are gradually dissolved. In the three regimes, the proposed approach provides reliable porosity‐permeability relationships that cannot be described well by traditional macroscale models. We find that the permeability can increase while the overall porosity decreases when the main flow paths are expanded by dissolution and adjacent pore spaces are clogged by precipitation.

Threshold pressure gradient in fractured reservoirs: Experimental simulation and mathematical modeling

Aiming to solve the problems of unclear fluid flow laws and controlling factors in fractured reservoirs, as well as the lack of a mathematical model of threshold pressure gradient (TPG) considering fracture structural parameters, research on the structural characterization of fractured reservoirs, physical simulation of fluid flow, and TPG prediction models has been carried out. Physical simulations demonstrate that fluid flow in fractured reservoirs under stress is nonlinear and exhibits TPG. The TPG displays a significant positive exponential relationship with confining pressure and water saturation. As the confining pressure or water saturation increases, the effective opening of fractures decreases. The TPG will increase dramatically when the fracture opening decreases to the critical thickness for the rapid increase in TPG. On the basis of the fluid flow law study, the TPG fractal prediction model is further developed based on fractal dimension of fracture length distribution (Df), fractal dimension of tortuosity (DT), water saturation (Sw), maximum fracture width (wmax), limit shear stress (η0), and sample characteristic length (L0). The results predicted by the model show good agreement with physical simulations (with average relative error of 7.56%). Experimental simulation and mathematical modeling of TPG in fractured reservoirs can reveal the fluid flow mechanism and improve the accurate evaluation of production capacity during different development processes.

Application of machine learning to model the pressure poisson equation for fluid flow on generic geometries

This study addresses the importance of enhancing traditional fluid-flow solvers by introducing a Machine Learning procedure to model pressure fields computed by standard fluid-flow solvers. The conventional approach involves enforcing pressure–velocity coupling through a Poisson equation, combining the Navier–Stokes and continuity equations. The solution to this Poisson equation constitutes a substantial percentage of the overall computational cost in fluid flow simulations, therefore improving its efficiency can yield significant gains in computational speed. The study aims to create a versatile method applicable to any geometry, ultimately providing a more efficient alternative to the conventional pressure solver. Machine Learning models were trained with flow fields generated by a Computational Fluid Dynamics solver applied to the confined flow over multiple geometries, namely wall-bounded cylinders with circular, rectangular, triangular, and plate cross-sections. To achieve applicability to any geometry, a method was developed to estimate pressure fields in fixed-shape blocks sampled from the flow domain and subsequently assemble them to reconstruct the entire physical domain. The model relies on multilayer perceptron neural networks combined with Principal Component Analysis transformations. The developed Machine Learning models achieved acceptable accuracy with errors of around 3%. Furthermore, the model demonstrated enhanced computational efficiency, outperforming the classical PISO algorithm by up to 30 times.

Optimized compact finite volume formulation with dispersion relation preserving characteristics in structured space discretizations

Computationally extensive fluid flow simulations usually require numerical schemes with a high degree of numerical precision, where high wavenumber and frequency capturing capability is desired in solutions with high physical fidelity. Numerical dispersion and diffusion errors must be reduced to a minimum in order to caputre low amplitude and high frequency flow aspects, such as flow induced sound waves and minor instabilities. Such schemes also must be capable of dealing with flow discontinuities, such as shockwaves and expansion waves in cases where the flow velocity stands near or above sound velocity. In this work the Dispersion Relation Preserving (DRP) optimization is formally extended to the compact Finite Volume (FV) framework where the error is minimized along a given spectral interval. This is done by equaling the resulting algebraic compact spectral optimized Finite Difference (FD) operators with the Finite Volume formulation with the desired numeric characteristics. Numerical tests are carried over linear and nonlinear governing equations models for one and three-dimensional cases, where the travelling Gaussian wave, the transient expansion wave and the smooth to nonsmooth step wave flows are considered. The proposed compact DRP FV schemes surpasses its counterparts in some numerical tests while maintaining comparable capabilities with other more basic schemes in the remaining numerical tests. Excellent broadband content capturing capability is observed, while possessing reduced numerical instabilities generation.

Numerical simulation of time-dependent viscous fluid flow with upward and downward fluctuation of spinning disk

The parametric approach towards time-dependent viscous fluid flow across a gyrating disk with upward and downward fluctuation. The major goal of this research is to assess fluid flow under the influence of magnetic fields and heat propagation processes. Because they provide a thorough description of electromagnetic interactions. Maxwell's equations are at the heart of all contemporary information and communication technologies. The governing equations comprising Navier Stokes equation, energy, concentration, and Maxwell equations have been represented appropriately for this purpose. The governing equations are turned down to the system of non-linear ODEs through a resemblance framework. The obtained system of differential equations has been resolved via numerical procedure Parametric Continuation Method (PCM). For the scale reliability purpose, the outcomes are compared to another numerical Matlab scheme boundary value solver. In the current analysis, the presence of convective boundary conditions correlated to mass and energy is of physical relevance. The numerical findings are provided in tabular and graphical forms. The consequences of suction and wall injection have been also highlighted. The upward motion of the spinning disc is thought to lead to comparable findings as in an injection scenario, whilst the downhill motion is thought to contribute to wall suction-like effects.

Permeability of needle-punched nonwoven geotextiles subjected to uniaxial tensile strains

During service life, needle-punched nonwoven geotextiles are frequently subjected to uniaxial tensile strains, which may impact their permeability behavior. The basic model of the permeability coefficient in nonwoven geotextiles is extended to the uniaxial tensile strain condition. The influence of the fiber orientation distribution was considered. The model is expressed as the functions of the tortuosity fractal dimension, pore size characteristics, fiber orientation, physical parameters, and tensile strain. To address the errors in the results of traditional permeability tests attributed to the inhomogeneity and multiple layers of specimens, in-situ X-ray computed tomography (CT) was employed to acquire three-dimensional images of the geotextile during stretching. The three-dimensional imaging technique was employed to extract the microstructure, facilitating fluid flow simulations for determining the permeability of two nonwoven geotextiles, thereby validating the theoretical method. It is shown that the simulated permeability coefficient decreases slightly and then increases with increasing uniaxial tensile strain and necking ratio. The permeability theoretical model exhibits a decreasing trend and then increases around 0.3% strain. The theoretical model can accurately predict the permeability values and rate of change of geotextiles subjected to specific uniaxial tensile strains, thereby offering valuable insights and tools for their effective utilization in various engineering applications.

A critical review of physics-informed machine learning applications in subsurface energy systems

Machine learning has emerged as a powerful tool in various fields, including computer vision, natural language processing, and speech recognition. It can unravel hidden patterns within large data sets and reveal unparalleled insights, revolutionizing many industries and disciplines. However, machine and deep learning models lack interpretability and limited domain-specific knowledge, especially in applications such as physics and engineering. Alternatively, physics-informed machine learning (PIML) techniques integrate physics principles into data-driven models. By combining deep learning with domain knowledge, PIML improves the generalization of the model, abidance by the governing physical laws, and interpretability. This paper comprehensively reviews PIML applications related to subsurface energy systems, mainly within the context of the oil and gas industry. The review highlights the successful utilization of PIML for tasks such as seismic applications, reservoir and fluid flow simulation, and hydrocarbons production forecasting. Additionally, it demonstrates PIML’s capabilities to revolutionize the oil and gas industry and other emerging areas of interest, such as carbon and hydrogen storage, by providing more accurate and reliable predictions for resource management and operational efficiency.

Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes

Finding the distribution of the velocities and pressures of a fluid by solving the Navier–Stokes equations is a principal task in the chemical, energy, and pharmaceutical industries, as well as in mechanical engineering and in design of pipeline systems. With existing solvers, such as OpenFOAM and Ansys, simulations of fluid dynamics in intricate geometries are computationally expensive and require re-simulation whenever the geometric parameters or the initial and boundary conditions are altered. Physics-informed neural networks (PINNs) are a promising tool for simulating fluid flows in complex geometries, as they can adapt to changes in the geometry and mesh definitions, allowing for generalization across fluid parameters and transfer learning across different shapes. We present a hybrid quantum PINN (HQPINN) that simulates laminar fluid flow in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a PINN, resulting in a 21% higher accuracy compared to a purely classical neural network. Our findings highlight the potential of machine learning approaches, and in particular HQPINN, for complex shape optimization tasks in computational fluid dynamics. By improving the accuracy of fluid simulations in complex geometries, our research using hybrid quantum models contributes to the development of more efficient and reliable fluid dynamics solvers.

The Evaluation of Explicit Parameters on Eulerian-Lagrangian Simulation of Wave Impact on Coastal Bridges

Simply supported bridges along the United States Gulf Coast are highly vulnerable to extreme wave conditions and water elevations. A better understanding of the loading demands on the bridges under these extreme events will lead to improved designs and enhanced resiliency. Nonetheless, analyses through numerical models pose difficulties in terms of reliability and computational burden. On the other hand, experimental models for large-scale bridge superstructures are subject to limited space allocation and related scaling challenges. Hence, optimized Finite Element (FE) models that can simulate Wave-Superstructure Interaction (WSI) are a preferred viable solution to estimate loads experienced by these bridge superstructures. Nonetheless, the results of the FE simulations are highly dependent on the numerical parameters and configurations implemented in the model; thus, the implications of parameter selection must be assessed to help scholars and engineers develop reliable FE models. In this paper, an experimental scaled model was used to calibrate numerical models following the Coupled Eulerian-Lagrangian (CEL) technique in ABAQUS. This explicit approach solves the Navier-Stokes (NS) equations to simulate fluid flow, and the dynamics response of the structure depends on analysis parameters (mass scaling factor, damping hourglass control, displacement hourglass scaling factor, and bulk viscosity scaling factors) and configurations (mesh size). The results provide a platform to compare numerical outputs and find the best parameters that suit WSI models. Moreover, the force signals applied to the superstructure experience high oscillations due to WSI. Different digital filter designs have been used to remove unwanted oscillations and provide researchers with recommendations on generating models that deliver optimal results.

Numerical simulation for MHD Oldroyd-B fluid flow with melting and slip effect

This investigation reflects an examination of Oldroyd-B fluid flow over a permeable surface subjected to the effects of melting, slip effect, inclined magnetic field and chemical reactions. The governing equations are resolved using the bvp4c inbuilt MATLAB tool, the arithmetic computation for the momentum, thermal and concentration equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted by aid of velocity, concentration, temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The results obtained indicated that Deborah number β1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta_{1}$$\\end{document} reduces the momentum boundary layer thickness whereas Deborah number β2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta_{2}$$\\end{document} enhances the adjacent momentum boundary layer. Furthermore, temperature profile declined for melting parameter Me\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Me$$\\end{document}. The application of this study transcends various engineering disciplines, offering practical solutions and optimization opportunities in polymer processing, coating technologies, cooling systems, materials processing, biomedical and environmental engineering.

A Practical probabilistic history matching framework for characterizing fracture network parameters of shale gas reservoirs

Simulating fluid flow in complex fracture systems encountered in subsurface systems, such as those encountered in tight or shale gas reservoirs, presents considerable challenges. Sophisticated numerical techniques and characterization approaches are required to integrate static and dynamic data from multiple sources to account for the intricate interplay between fractures and the surrounding rock matrix. A novel workflow using an indicator-based probability perturbation method (PPM) is applied to characterize uncertain discrete fracture network parameters. The posterior probability distributions of primary and secondary fracture transmissivity, aperture, length, height, and intensity of the secondary fracture are estimated according to the production (flow) histories. A case study based on the Horn River shale gas reservoir is presented. A pilot point scheme is formulated to update the distributions of P32L. The forward modelling entails upscaling each fracture model into a dual-porosity dual-permeability model and performing multiphase flow simulation. This approach produces an ensemble of history-matched discrete fracture and upscaled models by incorporating static and dynamic data. The results demonstrate the utility of the developed method for estimating secondary fracture parameters, which are not inferrable from other static information alone. The inference of both primary and secondary fractures offers a more comprehensive characterization of the fracture networks in tight or shale gas reservoirs. Integrating a pilot point parameterization technique and a sequential simulation approach into the PPM framework presents significant novelties in contributing to a comprehensive and effective method of simulating fluid flow in complex fracture systems, addressing the challenges associated with non-linear relationships between fracture model parameters and the corresponding flow response.