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A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydraulics and Hydrodynamics".

Deadline for manuscript submissions: closed (25 February 2024) | Viewed by 21093

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Special Issue Editors

Dr. Sanbai Li

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Guest Editor

School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen, China
Interests: multiphase flow; hydrology; multi-physics coupling; fractured porous media; numerical modeling; geomechanics

Dr. Qinzhuo Liao

E-Mail Website
Guest Editor

College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China
Interests: machine learning; surrogate model; reservoir simulation; flow and transport in porous media
Special Issues, Collections and Topics in MDPI journals

Dr. Shihao Wang

E-Mail Website
Guest Editor

Chevron Corp., Houston, TX, USA
Interests: reservoir engineering; geothermal engineering; multiphysical multiscale computing; machine learning and its applications；CO₂ sequestration and EOR

Special Issue Information

Dear Colleagues,

Modeling fluid flows through fractured and/or deformable porous media remains an interesting but challenging topic in the geo-energy field. Success in geo-energy resources extraction, energy storage, CO₂ geosequestration, and understanding ore-forming processes relies strongly upon the accurate modeling of single-/multi-phase fluid flow through porous media. The rapid advancement of physics-driven and data-driven approaches provides us with a rare opportunity to simulate and comprehend essential interplay between fluid flow, heat transfer, stress perturbation, chemical reaction, and pore/permeability evolution. The research in fluid dynamics modeling provides high support in the mitigation of greenhouse gas emissions and the efficient development and utilization of geo-energy resources.

This Special Issue titled “Fluid Dynamics Modeling in Porous Media” is intended to report innovative contributions to fluid dynamics modeling regarding numerical approaches, case studies, and data analytics, which may help advance our understanding of complex fluid flow behaviors underground. Our interests focus on, but are not limited to, the following topics:

Reactive fluid/heat flow in (deformable) porous media;
Development of geothermal energy and hydrocarbons;
Enhanced/engineered geothermal systems;
Fault slip in response to fluid injection;
Geo-sequestration of carbon dioxide;
Underground energy storage;
Ore-forming fluid evolution;
Proppant migration through fracture networks;
Data-driven modeling.

Dr. Sanbai Li
Dr. Qinzhuo Liao
Dr. Shihao Wang
Guest Editors

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Keywords

fluid flow
geomechanics
chemical reactions
simulation
greenhouse gas
hydrocarbons
geothermal energy
fault reactivation
ore-forming fluid
machine learning

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Published Papers (9 papers)

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Research

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19 pages, 15286 KiB

Open AccessArticle

Numerical Modeling and Simulation of Fractured-Vuggy Reservoirs Based on Field Outcrops

by Sanbai Li, Zhijiang Kang and Yun Zhang

Water 2023, 15(20), 3687; https://doi.org/10.3390/w15203687 - 21 Oct 2023

Cited by 2 | Viewed by 1855

Abstract

We propose a novel workflow to investigate the complex flow behaviors and remaining oil distribution related to the oil–gas–water three-phase system based on information from typical outcrops of fractured-vuggy reservoirs. A refined geological model is built to represent the size, geometry, and spatial distribution of the karst caves and fractures extracted from the field outcrop photographs. The combination of the perpendicular bisector (PEBI) grid technique and the control-volume finite difference method is adopted for space discretization. We have validated the numerical model against experimental data. Numerical simulations were performed to explore the impacts of the permeability of karst cave and natural fractures and the position of natural water bodies upon oil production performance. Numerical results indicate that (1) the cave permeability has few impacts on the oil production, yet the fracture permeability plays a significant role in determining the oil recovery; (2) a higher permeability of the fractures will lead to a longer period of time for no-water oil production and, thus, a higher oil recovery; (3) the position of natural water body shows significant impacts on oil recovery, e.g., a short distance between the natural water body and the production well tends to form preferential passages, causing severe reduction of water flooding range; and (4) the distribution of remaining oil is controlled by spatial patterns of the fractured-vuggy system and reservoir development schemes. We found that the remaining oil is mainly distributed along the model boundaries and at the corner of the caves with single or multiple connection/s to fractures. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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19 pages, 4842 KiB

Open AccessArticle

An Analytical Model Coupled with Orthogonal Experimental Design Is Used to Analyze the Main Controlling Factors of Multi-Layer Commingled Gas Reservoirs

by Lei Wang, Yangyue Xiang, Hongyan Tao and Jiyang Kuang

Water 2023, 15(17), 3052; https://doi.org/10.3390/w15173052 - 25 Aug 2023

Cited by 1 | Viewed by 1262

Abstract

The majority of China’s multi-layer low permeability tight gas reservoirs are currently being extracted through the method of multi-layer co-production. However, due to the significant disparity in physical properties and varying degrees of pressure depletion among the production layers, elucidating the primary factors influencing the productivity contribution of each gas layer remains challenging. A multi-factor analytical model is proposed for commingled gas wells with multiple layers. An unstable model is established for the production of commingled layers, and the problem of flow distribution is addressed using the Duhamel convolution principle. The Laplace transform is subsequently employed to derive the solution in the Laplace domain, which can be inverted utilizing the Stehfest inversion algorithm to obtain a real-time domain solution. The influence of reservoir factors on the stratification contribution rate has been comprehensively analyzed, encompassing permeability, porosity, initial pressure, drainage radius, and layer thickness. The orthogonal test design was employed to conduct range analysis and variance analysis separately, yielding the primary and secondary order as well as influence weight of the five factors. The findings demonstrate that, within this gas reservoir, the discharge radius, thickness, and porosity are identified as the primary factors influencing gas well productivity. Furthermore, seven horizontal flow charts illustrating the double-layer gas reservoir and five horizontal flow charts depicting single-factor variations in the double-layer gas reservoir were constructed. These charts provide a clear visualization of the impact of each reservoir factor on stratification’s contribution rate. In contrast to previous studies, this novel approach presents a comprehensive optimization framework that ranks the influence weights of individual factors and identifies the most significant factors impacting multi-layer gas reservoirs. The presented method also serves as a foundation for the subsequent selection of multi-layer gas reservoirs, formulation of gas well stimulation measures, and efficient development. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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18 pages, 6140 KiB

Open AccessArticle

The Displacement of the Resident Wetting Fluid by the Invading Wetting Fluid in Porous Media Using Direct Numerical Simulation

by Yung-Li Wang, Qun-Zhan Huang and Shao-Yiu Hsu

Water 2023, 15(14), 2636; https://doi.org/10.3390/w15142636 - 20 Jul 2023

Viewed by 1410

Abstract

Understanding the displacement of the resident wetting fluid in porous media is crucial to the remediation strategy. When pollutants or nutrients are dissolved in the surface wetting fluid and enter the unsaturated zone, the resident wetting fluid in the porous system may remain or be easily flushed out and finally arrive in the groundwater. The fate and transport of the resident wetting fluid determine the policy priorities on soil or groundwater. In this study, the displacement of the resident wetting fluid by the invading wetting fluid in porous media was simulated using direct numerical simulation (DNS). Based on the simulations of the displacements in porous media, the effect of the non-wetting fluid on the displacement was evaluated by observation and quantification, which were difficult to achieve in laboratory experiments. The result can also explain the unknown phenomenon in previous column experiments, namely that the old water is continuously released from the unsaturated porous media even after a long period of flushing with the new water. The effects of the interfacial tension, contact angle, and injection rate, which affected the immiscible fluid–fluid flow pattern, were also evaluated. Since pollutants dissolved in the wetting fluid could change the physical properties of the wetting fluid, the interfacial tensions of the resident wetting fluid and the invading wetting fluid were set separately in the simulation. Moreover, our simulation demonstrated that the consecutive drainage–imbibition cycles could improve the displacement of the resident wetting fluid in porous media. The successful simulation in this study implied that this method can be applied to predict other immiscible fluid–fluid flow in natural or industrial processes. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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18 pages, 4742 KiB

Open AccessArticle

Digital Core Permeability Computation by Image Processing Techniques

by Qinzhuo Liao, Shaohua You, Maolei Cui, Xiaoxi Guo, Murtada Saleh Aljawad and Shirish Patil

Water 2023, 15(11), 1995; https://doi.org/10.3390/w15111995 - 24 May 2023

Cited by 4 | Viewed by 2041

Abstract

Calculation of REV (representative elementary volume) properties of geological porous media refers to the process of creating a 3D digital representation of a rock sample, typically obtained from imaging techniques such as X-ray microtomography. This technique allows for a detailed analysis of the internal structure and the properties of rocks, as well as precise calculation of various flow parameters. However, one major challenge with calculation of REV properties of geological porous media is the high computational cost required to generate accurate results, especially for large and complex samples. In this study, we constructed 3D digital cores of dune sand and fractured shale using CT scanning technology, and then used two image processing techniques, namely digital core image resampling and cutting, to reduce the computational cost of calculating digital core permeability. Next, a fast permeability calculation method is employed to reduce the complexity of permeability calculation. Finally, we summarized the applicability of different image processing methods to different rock samples, and provided prerequisites for high computational cost digital core permeability calculation. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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22 pages, 6116 KiB

Open AccessArticle

Optimization of Efficient Development Modes of Offshore Heavy Oil and Development Planning of Potential Reserves in China

by Taichao Wang, Fengming Liu and Xin Li

Water 2023, 15(10), 1897; https://doi.org/10.3390/w15101897 - 17 May 2023

Cited by 2 | Viewed by 1832

Abstract

Thermal recovery is still the most important means to increase heavy oil EOR. With the increase in the recovery factor and the difficulty of exploiting new exploration reserves, the efficient utilization of offshore heavy oil reserves has attracted much attention. However, due to the challenges of high development investments, high operating costs, platform safety factors, and high economic cumulative yield, the offshore heavy oil reserves of nearly 700 million tons have not been effectively utilized. In this paper, Chinese offshore heavy oil reserves were taken as the research object. The indoor one-dimensional experiments were carried out to optimize an applicable development method, and the superheated steam huff and puff was selected as the injection medium for high-speed and high-efficiency development of offshore heavy oil, which verified the great potential of the application of superheated steam in offshore heavy oil thermal recovery. A numerical simulation model for offshore heavy oil superheated steam injection development was established, and a dynamic model considering the thermal cracking of heavy oil was established through historical matching. Through the field numerical simulation models, the whole process development mode of a single sand body, thin interbedded reservoir superheated steam huff and puff turning to superheated steam flooding, and thick layer super heavy oil reservoir with bottom water sidetracking after superheated steam huff and puff for eight cycles was established. Through the numerical simulation method and grey correlation method, the main control factors of superheated steam development of different types of heavy oil reservoirs were determined, and the cumulative oil production charts of different types of reservoirs under the influence of the main control factors were built. The economic evaluation model of superheated steam development of offshore heavy oil was established. Combining multi-specialty of geological, reservoir engineering, drilling and completion, oceanographic engineering, economics, the economic limits of steam injection development under different reserve scales, and engineering conditions of offshore heavy oilfields were clarified. At last, we planned the economic production mode of undeveloped reserves and predicted the construction profile of superheated steam capacity of offshore heavy oil using the production charts and the economic charts. The research results clarify the great potential of thermal recovery development of offshore heavy oil, provide an important basis for the economic development of offshore heavy oil undeveloped reserves, and also provide an important decision for the sustainable and stable production of global heavy oil reservoirs. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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18 pages, 1254 KiB

Open AccessArticle

Status and Prospect of Improved Oil Recovery Technology of High Water Cut Reservoirs

by Liang Xue, Pengcheng Liu and Yun Zhang

Water 2023, 15(7), 1342; https://doi.org/10.3390/w15071342 - 30 Mar 2023

Cited by 16 | Viewed by 4623

Abstract

The high water cut stage is an important stage of the water injection development of oilfields because there are still more oil reserves available for recovery in this stage. Most oilfields have experienced decades of waterflooding development and adjustment. Although waterflooding reservoirs face the problems of the seriously watered-out and highly dispersed distribution of remaining oil, they remain dominant in waterflood development. This paper investigates the current situation of high-water content reservoirs and the methods available to improve oil recovery and elaborates on the fine reservoir description. Furthermore, it analyzes the main technical measures taken during the high water cut period, namely, secondary oil recovery waterflooding technology (including layer system subdivision, well pattern infilling, strengthening of water injection and liquid extraction, closure of high water cut wells, cyclic waterflooding technology, and water injection profile control) and tertiary oil recovery technology (represented by chemical flooding and gas flooding). In addition, this study reveals the mechanisms and effects of these methods on improving waterflooding development. Finally, this paper summarizes improved oil recovery technology and discusses the key directions and development prospects of this technology in enhancing the oil recovery rate. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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29 pages, 9095 KiB

Open AccessArticle

Real-Time Simulation of Hydraulic Fracturing Using a Combined Integrated Finite Difference and Discontinuous Displacement Method: Numerical Algorithm and Field Applications

by Shihao Wang, Xiangyu Yu, Philip H. Winterfeld and Yu-Shu Wu

Water 2023, 15(5), 938; https://doi.org/10.3390/w15050938 - 28 Feb 2023

Cited by 5 | Viewed by 2622

Abstract

Real-time simulation of hydraulic fracturing operations is of critical importance to the field-scale stimulation applications. In this paper, we present an efficient yet reasonably accurate program for the numerical modeling of dynamic fractures. Our program, named as FracCSM, is based on combined Integrated Finite Difference (IFD) method and Discontinuous Displacement Method (DDM). FracCSM simulates the initiation and propagation of hydraulic fractures with DDM and mass/heat transport inside fractures by IFD. The frictional loss within the wellbore is also taken into consideration. In this way, we are able to model the propped height and length of the fractures subject to the stress interference effect. Moreover, FracCSM captures the stress shadow effect of multi-stage fractures. To facilitate the monitoring and decision making during the hydraulic fracturing process, we have developed a general framework that supports real-time simulation of fracture propagation. Our developed program demonstrates sound accuracy in comparison with existing simulators. The novelty of this work is the combined simulation algorithm to simulate the multiphysical process during hydraulic fracturing operations. We will demonstrate the program structure as well as the field applications of FracCSM to the real-time simulation of hydraulic fracturing operations in Sulige tight sandstone reservoir. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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20 pages, 6620 KiB

Open AccessArticle

Experimental and Numerical Analysis of Forced Convection in a Horizontal Tube Partially Filled with a Porous Medium under Local Thermal Equilibrium Conditions

by Behzad Siavash Amoli, Seyed Soheil Mousavi Ajarostaghi, Majid Saffar-Avval, Reza Hosseini Abardeh and Nevzat Akkurt

Water 2022, 14(23), 3832; https://doi.org/10.3390/w14233832 - 24 Nov 2022

Cited by 7 | Viewed by 2385

Abstract

The objective of the present work is to analyze experimentally and numerically the laminar forced convection flow in a horizontal pipe partially filled with a porous medium under constant heat flux and to study the influence of the eccentricity of the porous medium on the results. In a numerical analysis, the governing equations are solved in three dimensions. To simplify the grid generation and the satisfaction of the boundary conditions, conformal mapping is applied to convert the cross-section of the tube in the fluid domain (space between two eccentric circles) into a rectangle, and the equations are solved in a computational domain in this domain. The Darcy–Brinkman–Forchheimer model is applied to simulate the hydrodynamic behavior of the flow in the porous region. Thermal equilibrium between solid and fluid is assumed for the energy equation. A FORTRAN program was developed to solve the equations using the finite volume method and the SIMPLE algorithm. Velocity profile, pressure drop and average Nusselt number are studied in a wide range of Darcy numbers, thickness of porous mediums and eccentricities. The results show that the eccentricity of the porous material reduces the heat transfer coefficient and the pressure drop simultaneously; of course, the reduction in the heat transfer coefficient is less noticeable when the thickness of the porous medium is smaller. For example, at R_P = 0.5, when the eccentricity of the porous medium increases up to E = 0.4, the average Nusselt number decreases by 66%, and this reduction for a smaller porous thickness decreases to 11%. The maximum pressure drop reduction for Da = 10⁻⁵ and E = 0.4 is 25%. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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Review

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18 pages, 4565 KiB

Open AccessReview

Flow Simulation in Fractures Using Non-Linear Flux Approximation Method

by Taichao Wang, Xin Li, Fengming Liu, Lijun Zhang, Haojun Xie and Yuting Bai

Water 2023, 15(24), 4281; https://doi.org/10.3390/w15244281 - 14 Dec 2023

Viewed by 1256

Abstract

The discrete fracture model (DFM) and the embedded discrete fracture model (EDFM) are both the most widely used methods to simulate fractured wells’ production. In general, DFM represents fractures using an unstructured grid, and EDFM represents fractures using 2D virtual polygon grids embedded into 3D corner point grids. However, both EDFM and DFM suffer from non-orthogonal grid effects. Based on the non-linear flux approximation, this work presents a new flux scheme for DFM and EDFM that is capable of simulating fractured reservoir production in second-order accuracy. Two test cases are set to verify the accuracy of this method. Finally, this work is used to simulate the production of one fractured horizontal well belonging to the Y-oil field. Orthogonal design is used to optimize the parameters. The results show that this method is capable of improving accuracy while keeping the solution effective. This method exhibits good practicability and has practical significance for fractured reservoir development. Full article

(This article belongs to the Special Issue Fluid Dynamics Modeling in Porous Media)

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