Multiphase Flow Processes Research Articles

A comprehensive review on the flow behaviour in shale gas reservoirs: Multi‐scale, multi‐phase, and multi‐physics

AbstractAn accurate description of fluid flow is critical for the prediction of the productivity of shale gas reservoirs. In this paper, we present the current advances and a systematic summary on the fluid flow in shale gas reservoirs. First, shale pore structures, consisting of organic pores and inorganic pores ranging from nanoscale to micro‐scale, and reservoir fluids, including free gas, absorbed gas, and water, are systematically presented. Thereafter, multi‐physics flow phenomena motivated by scale effects, such as continuum flow, slip flow, transition flow, free molecular flow, and surface diffusion for gas, as well as the effective viscosity and slip boundary condition for water, are carefully summarized. Meanwhile, these flow mechanisms are discussed with molecular dynamics (MD) simulations and theoretical analysis. Subsequently, on the basis of upscaling approaches, including capillary bundle models, the lattice Boltzmann method (LBM), and pore network models (PNMs), fluid flow through heterogeneous shale matrix is reviewed and the influences of scale effects and pore structures are clarified. Additionally, shale gas well performance is discussed by combining the multiple transport mechanisms and a fracturing‐shut‐in‐flowback‐production process. Our review concluded that the fluid flow behaviour in shale gas reservoirs is a complex multi‐scale process accompanied by multi‐physical phenomena and multi‐fluid distributions. Keeping this in mind is helpful for predicting the shale gas production and recoverable gas resources. We expect this study can not only help by providing a better understanding of the fluid flow in shale reservoirs but also provide significant implications to address other multiphase flow processes.

Towards Tomography-Based Real-Time Control of Multiphase Flows: A Proof of Concept in Inline Fluid Separation.

The performance of multiphase flow processes is often determined by the distribution of phases inside the equipment. However, controllers in the field are typically implemented based on flow variables, which are simpler to measure, but indirectly connected to performance (e.g., pressure). Tomography has been used in the study of the distribution of phases of multiphase flows for decades, but only recently, the temporal resolution of the technique was sufficient for real-time reconstructions of the flow. Due to the strong connection between the performance and distribution of phases, it is expected that the introduction of tomography to the real-time control of multiphase flows will lead to substantial improvements in the system performance in relation to the current controllers in the field. This paper uses a gas–liquid inline swirl separator to analyze the possibilities and limitations of tomography-based real-time control of multiphase flow processes. Experiments were performed in the separator using a wire-mesh sensor (WMS) and a high-speed camera to show that multiphase flows have two components in their dynamics: one intrinsic to its nonlinear physics, occurring independent of external process disturbances, and one due to process disturbances (e.g., changes in the flow rates of the installation). Moreover, it is shown that the intrinsic dynamics propagate from upstream to inside the separator and can be used in predictive and feedforward control strategies. In addition to the WMS experiments, a proportional–integral feedback controller based on electrical resistance tomography (ERT) was implemented in the separator, with successful results in relation to the control of the distribution of phases and impact on the performance of the process: the capture of gas was increased from 76% to 93% of the total gas with the tomography-based controller. The results obtained with the inline swirl separator are extended in the perspective of the tomography-based control of quasi-1D multiphase flows.

Face failure analysis of a shield tunnel with slurry penetration into the ground

This paper focuses on the face stability analysis of a tunnel driven by a slurry shield machine in the water-bearing ground. A multifield model coupling seepage flow and face stability of the tunnel is developed. The slurry-soil interaction in the ground is considered as a multiphase flow process in porous media. The kinematic approach of limit analysis is used to assess the tunnel face failure. The pressure transfer mechanism of the bentonite suspension is time-dependent and shows good agreement with the field measurement. This model allows the consideration of the slurry support efficiency and its influence on the failure shape through the discretization technique. The results obtained indicate that the support effectiveness decreases with the slurry penetration into the ground, and the traditional membrane model leads to an overestimation of the face stability. Several charts are provided for parametric analysis to discuss the influence of the hydrogeological and slurry properties.

Emergence of unstable invasion during imbibition in regular porous media

The unstable fluid–fluid displacement patterns in porous media with rough invasion fronts and trapping of the defending phase are often observed in drainage, i.e. when the solid is non-wetting to the invading phase. On the other hand, during imbibition, compact and faceted growth is expected in regular porous media with geometrically homogeneous pore structure. Here, we report the irregular growth of invading fluid during the imbibition process in two-dimensional regular porous media. The ramified invasion morphology associated with thin fingers is reminiscent of capillary fingering. Through examining the capillary pressure signals and the type of pore-scale invasion mechanisms, the fundamental differences between faceted growth and irregular invasion are revealed. By analysing the pore-scale invasion mechanisms, a phase diagram describing the dominance of different invasion events is proposed. Through conducting systematic quasi-static radial injection simulations across a wide range of porosity and wettability, excellent agreement is observed on the transition boundary from faceted and compact displacement patterns to irregular and dendritic invasion morphologies. This is reflected by the overlap of the transition boundaries from analytical prediction, type of pore-scale invasion events, and macroscopic morphology quantified by the fractal dimension. This work provides new insights on the role of geometrical features of solid structures during multiphase flow with emphasis on the porosity and wettability. The findings could assist in guiding the design of microfluidic devices to control deterministically the multiphase flow, transport and reaction processes.

Euler–Euler modeling of reactive bubbly flow in a bubble column

To clarify the mass transfer mechanism and reaction behavior in the multiphase flow process, numerical simulations were implemented in the process of NaOH absorbing CO2 by means of the Euler–Euler two-fluid model coupled with the net production rate model of species. Results show that the chemisorption process can be divided into three stages, which are dominated by different chemical reaction equations, and the influence of the water ionization cannot be neglected at pH <10. The concentration change of each species is slightly earlier than those in the literature, while the time-dependent pH value is in good agreement with the experimental results and the consistency between the simulation and the experiment of the hydrodynamic parameters such as the axial component of bubble velocity and the oscillation frequency of bubble flow can be achieved. Therefore, it can be concluded that the mathematical model proposed in this paper can better reproduce the detailed characteristics of the reactive bubbly flow. Furthermore, the effect of bubble induced turbulence on the interfacial reaction behavior is also discussed, and the influence of bubble induced turbulence can be negligible.

The Effect of Pore-Scale Two-Phase Flow on Mineral Reaction Rates

In various natural and engineered systems, mineral–fluid interactions take place in the presence of multiple fluid phases. While there is evidence that the interplay between multiphase flow processes and reactions controls the evolution of these systems, investigation of the dynamics that shape this interplay at the pore scale has received little attention. Specifically, continuum scale models rarely consider the effect of multiphase flow parameters on mineral reaction rates or apply simple corrections as a function of the reactive surface area or saturation of the aqueous phase, without developing a mechanistic understanding of the pore-scale dynamics. In this study, we developed a framework that couples the two-phase flow simulator of OpenFOAM (open field operation and manipulation) with the geochemical reaction capability of CrunchTope to examine pore-scale dynamics of two phase flow and their impacts on mineral reaction rates. For our investigations, flat 2D channels and single sine wave channels were used to represent smooth and rough geometries. Calcite dissolution in these channels was quantified with single phase flow and two phase flow at a range of velocities. We observed that the bulk calcite dissolution rates were not only affected by the loss of reactive surface area as it becomes occupied by the non-reactive non-aqueous phase, but also largely influenced by the changes in local velocity profiles, e.g., recirculation zones, due to the presence of the non-aqueous phase. The extent of the changes in reaction rates in the two-phase systems compared to the corresponding single phase system is dependent on the flow rate (i.e., capillary number) and channel geometry, and follows a non-monotonic relationship with respect to aqueous saturation. The pore-scale simulation results highlight the importance of interfacial dynamics in controlling mineral reactions and can be used to better constrain reaction rate descriptions in multiphase continuum scale models. These results also emphasize the need for experimental studies that underpin the development of mechanistic models for multiphase flow in reactive systems.

Non-convex logarithm embedding subspace weighted graph approach to fault detection with missing measurements

In this work, we propose a robust fault detection method to address the problem of increase in missing and/or spurious alarms due to different degrees of loss or corruptions in data. Specifically, given historical data, our aim is to recover a clear low-space representation from corrupted data so that the detection control limits are updated, whenever required. To this end, a novel non-convex logarithm embedding subspace weighted graph detection method is presented. The method compensates the original missing nodes by embedding a non-convex logarithm regularizer, and then constructs an undirected graph model of the compensated nodes. Additionally, the dual constraints of l2,1-norm regularization and specific weights are introduced into the loss function of the graph model to further improve its robustness. Finally, the statistics and detectable criterion of the proposed method are given. Extensive simulations conducted on a real-world hot strip mill process and a multi-phase flow process demonstrate that the proposed method displays more robust detection than other state-of-the-art methods in the presence of outliers and missing measurements.

Вычислительная схема для расчета температурного поля при решении задач нефтедобычи

The paper presents an approach to coupled modeling of hydrodynamic and thermal processes occurring in the oil reservoir during field development using thermal methods of enhanced oil recovery. To simulate the processes of non-isothermal multiphase flow, an approach based on implicit calculation of pressure using the finite element method and an explicit calculation of phase saturations is used. A computational scheme for calculating the temperature field is considered. This scheme makes it possible to take into account both heat transfer between phases and heat transfer of a fluid mixture and matrix-rock. In order to take into account the effect of thermal conductivity, a coefficient characterizing the rate of heat transfer between the fluid mixture and the rock is used. The proposed scheme also takes into account the effect of the temperature field on the phases flow in the field reservoir and provides for the possibility of heat sources and sinks occured due to chemical reactions or thermodynamic processes in gaseous phases. Numerical experiments were carried out on a model of a real oil field obtained as a result of history matching of well data. The model contains a large number of wells and is characterized by a high heterogeneity of the porous medium. The applicability of the considered computational scheme is demonstrated on the example of modeling hot water injection into wells crossing a formation with super-viscous oil. The efficiency of thermal methods for the development of super-viscous oil fields is shown. When hot water was injected into the reservoir, the increase in oil production was about 25 % due to a significant decrease in oil viscosity. The time spent for calculating the temperature field while simulating a multiphase flow did not exceed 6 % of the total computational time.

Flow Balancing in Modeling of Multi-Phase Flow using Non-Conformal Finite Element Meshes

The method of balancing numerical finite element flows in modeling a process of multiphase flow using non-conformal hexagonal meshes is considered. Studies have been carried out for a simple reservoir configuration and on a more complex model of a real field of high-viscosity oil in the Tatarstan. The research results showed that the balancing method allows one to obtain a conservative solution when using non-conformal finite element meshes with sufficiently large cells. At the same time, this method is completely free of problems associated with grid orientation, even for complex models containing zones with highly variable permeability. The proposed algorithm for the adaptive choice of parameters allows to do the factorization of the SLAE matrix at sufficiently small number of time steps; therefore, the computational costs of the flow balancing procedure are an order of magnitude less than the costs associated with calculating the pressure field and phase transfer. The used non-conformal finite element meshes with an arbitrary number of docked hexagons can significantly reduce the number of degrees of freedom when modeling multiphase flows in reservoirs with much small local heterogeneity and in the presence of several perforated zones. As a result, computational costs are reduced by almost an order of magnitude, and, at the same time, the required approximation accuracy is maintained. With an increase in the scale of the model and the number of operating wells, this advantage increases even more.

Scalable active subspace low-rank graph representation for continuous system online security evaluation with input corruption

Continuous online system operation evaluation aims to monitor the occurrence of abnormal conditions. However, most of the currently popular monitoring methods are developed from the perspective of historical data integrity. In industrial processes, missing or corrupted entries generally exist due to improper recording or sensor drop-out, which brings difficulties to online monitoring evaluation. In this article, a scalable active subspace low-rank graph representation method is presented to deal with missing data in the offline phase of fault monitoring. The method realizes the reconstruction of a clean matrix by the linear combination of low-rank representation and scalable orthogonal matrix. Meanwhile, the low-rank representation and sparse error matrix with l2,1-norm are arranged in the loss function to improve the optimal feature selection and robustness of the model. Apart from that, to preserve the consistency of the adjacent structure between the reconstruction space and the original corrupted space, a Laplacian manifold regularization is designed to constrain the sparse error. Finally, we establish an optimal graph discriminant model of recovery data for online safety monitoring of continuous systems. Confirmatory simulations on benchmark TE process and actual multi-phase flow process illustrate that the proposed approach is superior to the state-of-the-art methods, fully verifying the robustness and detectability performance in the presence of specific corruption.

DISCONTINUOUS GALERKIN FEM METHOD FOR THE COUPLING OF COMPRESSIBLE TWO-PHASE FLOW AND POROMECHANICS

Understanding the coupled multiphase flow and solid deformation processes in porous media is a significant issue in the area of developing and utilizing underground resources. This study first established the coupled modeling of compressible two-phase flow and deformation of porous media, which considers capillarity and gravity. Meanwhile, the strong form and the corresponding weak form of coupled multiphase flow and solid deformation model were presented. Then, the capacity of the proposed DG method for the coupled hydromechanical model was verified by comparison with analytical and numerical results of the one-dimensional Terzaghi consolidation problem. Subsequently, the two- and three-dimensional cases were performed to study the flow behaviors and deformation characteristics, respectively. In addition, the effects of the penalty factors \begin{document}$ {\delta }_{\rm{s}} $\end{document} and \begin{document}$ {\delta }_{\rm{f}} $\end{document} on the stability of the numerical results were analyzed. The simulation results show that gas saturation and pore pressure continually increase with the injection of gas. The increment of pore pressure reduces the effective stress, which results in deformation and expansion of the porous medium. The gas floats up and gathers at the top boundary due to gravity. The decrease of the penalty factors \begin{document}$ {\delta }_{\rm{s}} $\end{document} and \begin{document}$ {\delta }_{\rm{f}} $\end{document} trends to cause the fluctuation of saturation, pressure, effective stress, and displacement. The increases in penalty factors are beneficial to suppress the discontinuity of the finite element function crossing the elements.

Reduced-order modeling of near-field THMC coupled processes for nuclear waste repositories in shale

Performance assessment (PA) of geologic radioactive waste repositories requires three-dimensional simulation of highly nonlinear, thermo-hydro-mechanical-chemical (THMC), multiphase flow and transport processes across many kilometers and over tens to hundreds of thousands of years. Integrating the effects of a near-field geomechanical process (i.e. buffer swelling) into coupled THC simulations through reduced-order modeling, rather than through fully coupled geomechanics, can reduce the dimensionality of the problem and improve computational efficiency. In this study, PFLOTRAN simulations model a single waste package in a shale host rock repository, where re-saturation of a bentonite buffer causes the buffer to swell and exert stress on a highly fractured disturbed rock zone (DRZ). Three types of stress-dependent permeability functions (exponential, modified cubic, and Two-part Hooke’s law models) are implemented to describe mechanical characteristics of the system. Our modeling study suggests that compressing fractures reduces DRZ permeability, which could influence the rate of radionuclide transport and exchange with corrosive species in host rock groundwater that could accelerate waste package degradation. Less permeable shale host rock delays buffer swelling, consequently retarding DRZ permeability reduction as well as chemical transport within the barrier system.

Cellular fluidics.

The natural world provides many examples of multiphase transport and reaction processes that have been optimized by evolution. These phenomena take place at multiple length and time scales and typically include gas-liquid-solid interfaces and capillary phenomena in porous media1,2. Many biological and living systems have evolved to optimize fluidic transport. However, living things are exceptionally complex and very difficult to replicate3-5, and human-made microfluidic devices (which are typically planar and enclosed) are highly limited for multiphase process engineering6-8. Here we introduce the concept of cellular fluidics: a platform of unit-cell-based, three-dimensional structures-enabled by emerging 3D printing methods9,10-for the deterministic control of multiphase flow, transport and reaction processes. We show that flow in these structures can be 'programmed' through architected design of cell type, size and relative density. We demonstrate gas-liquid transport processes such as transpiration and absorption, using evaporative cooling and CO2 capture as examples. We design and demonstrate preferential liquid and gas transport pathways in three-dimensional cellular fluidic devices with capillary-driven and actively pumped liquid flow, and present examples of selective metallization of pre-programmed patterns. Our results show that the design and fabrication of architected cellular materials, coupled with analytical and numerical predictions of steady-state and dynamic behaviour of multiphase interfaces, provide deterministic control of fluidic transport in three dimensions. Cellular fluidics may transform the design space for spatial and temporal control of multiphase transport and reaction processes.

Geometric Criteria for the Snap‐Off of a Non‐Wetting Droplet in Pore‐Throat Channels With Rectangular Cross‐Sections

AbstractSnap‐off is a phenomenon that occurs when a non‐wetting fluid is displaced by wetting fluid in pore‐throat channels, leading to the breakup of droplets at the throat. Snap‐off plays a key role in many industrial processes involving immiscible multiphase flows, such as aquifer remediation, carbon capture and geological storage, recovery of hydrocarbons. Here we derive geometric criteria for the capillary snap‐off at the pore‐throat junctions in 2D microchannels with rectangular cross‐sections. The criteria are theoretically presented in three categories according to the range of the throat depth, h. We find that if h is smaller than the throat width, snap‐off will be inhibited, if h is larger than the pore width, snap‐off may occur but it is independent of h, and if h is in between the throat width and the pore width, a critical depth exists for the occurrence of snap‐off. These criteria are verified using numerical CFD simulations and validated using microfluidic experiments. These results indicate the conditions for snap‐off in the pore‐throat channel with rectangular cross‐sections, which clarify previous debates in the literature. One application of this work is for micromodels, which are porous microfluidic chips used as tools to observe multiphase flow in porous media at the pore‐scale. Most micromodels are two‐dimensional (2D), which have rectangular cross‐sections with uniform depth. The geometric criteria derived here provide guidelines for the design of micromodels used in the study of multiphase flow processes in porous media.

Study on the Influence of Sand Production on Seepage Capacity in Natural Gas Hydrate Reservoirs

Sand production has become a common phenomenon in the exploitation of unconsolidated natural gas hydrate reservoirs, which will hinder the long-term production of natural gas hydrate reservoirs. However, there are few literatures reported on the influences in reservoir physical properties such as permeability and porosity, and production laws caused by sand production. This paper provides a numerical model, coupled with reservoir sand-gas-water multiphase flow processes, which is capable to simulate the process of sand production in natural gas hydrate reservoirs. The simulation results indicate that sand settlement is mainly concentrated near the wellbore due to the high concentration of migrated sand. The decrease in reservoir porosity and permeability caused by sand settlement has a significant impact on production. The impact of sand production on reservoir fluid fluidity shows that fluid flow is inhibited near the wellbore, while fluid flow performance increases far away from the wellbore. The numerical model and analysis presented here could provide useful insight into changes in reservoir physical properties and production laws caused by sand production in the natural gas hydrate-bearing marine sediments using depressurization method.

Investigation of Complex Permittivity/Conductivity Distribution by Electrical Tomography

The electrical tomography technology is a multi-phase flow detection technology. This technology has the advantages of non-radiation, non-invasive and visualization, can be widely used in traditional energy field and new energy field. The permittivity and conductivity, as the basic electrical parameters of material, are closely related to the distribution of material in multiphase flow. However, in the actual multiphase flow, due to the non-uniform distribution of permittivity and conductivity in time and space, the accuracy and validity of measuring instruments are challenged. The main target of this research is to investigate the application of electrical capacitance tomography (ECT), electrical resistance tomography with voltage excitation (ERTv) and electrical resistance tomography with current excitation (ERTc) on the multiphase flow with complex permittivity and conductivity distribution. The final objective based on the above research is to provide suitable tomography modual for different multiphase flow process. The experimental results show that ECT is suitable for measuring dry gas-solid fluids. ERTv is better for measuring high water content gas-solid fluids and low conductivity gas-liquid fluids, while ERTc is better for measuring continuous phase conductivity gas-liquid fluids.

Pore-scale numerical study of multiphase reactive transport processes in cathode catalyst layers of proton exchange membrane fuel cells

understanding interactions between multiphase flow and reactive transport processes in catalyst layers (CL) of proton exchange membrane fuel cells is crucial for obtaining better performance and lower cost. In this study, a pore-scale model is developed to simulate coupled processes occurring in CLs, including oxygen diffusion, electrochemical reaction, and air-liquid two phase flow. Simulation conducted in an idealized local CL structures shows that the pore-scale model successfully captures dynamic behaviors of liquid water including generation, growth and subsequent migration, as well as the interaction between multiphase flow and reactive transport. Pore-scale simulation is then conducted in hydrophobic CLs with complicated structures where carbon, platinum, ionomer and pores are resolved. It is found that filling modes of the liquid water in the CLs are different. Before forming the continuous flow paths in CLs, liquid water presents as tiny droplets in pores surrounding relative large pores. After the continuous flow paths are formed, liquid water dynamic behaviors follow the capillary fingering mechanism. The multiphase flow and reactive transport processes are closely coupled with each other, and as liquid water saturation increases the reaction rate decreases. Increasing the hydrophobicity can alleviate the water flooding, accelerate the water breakthrough, and facilitate the water evaporation.

Flow Regimes Identification-based Multidomain Features for Gas–Liquid Two-Phase Flow in Horizontal Pipe

Accurate flow regimes identification is of great significance for the deep understanding of the flow structure and ensuring the safe and economic operation of actual production in the multiphase flow process. For the flow regimes identification of the gas-liquid two-phase flow in the horizontal pipe, a multidomain features processing scheme is proposed. The water holdup data are acquired by conductance rings sensor, and processed by the improved empirical wavelet transform (EWT) to obtain the Fourier spectrum in the frequency domain and decomposition components in the multiscale domain. The obtained multidomain feature information is quantified to get the high-dimensional feature vectors of different flow regimes. To make the features more representative and realize the visualization of the structural relationship between the flow regime samples, the isometric feature mapping (Isomap) method in manifold learning is used to synthesize the feature structure relationships and map them to low-dimensional space. The obtained low-dimensional feature vectors of training samples are input into the support vector machine (SVM) to acquire the flow regimes identification model. Compared with other flow regimes identification schemes that feature reduction uses different manifold learning methods, or feature extraction is not in multidomain, or data preprocessing uses traditional wavelet transform, the proposed scheme can better retain the global structural relationship of the flow regimes, has the characteristics of strong stability, and the identification rate of the gas-liquid two-phase flow regimes in the horizontal pipe is over 95%.

Novel dynamic enhanced robust principal subspace discriminant analysis for high-dimensional process fault diagnosis with industrial applications

Since the data are often polluted by numerous measured noise or outliers, traditional subspace discriminant analysis is difficult to extract optimal diagnostic information. To alleviate the impact of the problem, a robust principal subspace discriminant analysis algorithm for fault diagnosis is designed. On the premise of decreasing the impact of redundant information, the optimal latent features can be calculated. Specifically, in the algorithm, dual constraints of the weighted principal subspace center and l2,1-norm are introduced into the objective function to suppress outliers and noise. Besides, considering that the current changes of the data in a dynamic process rely on past observations, merely analyzing the current data may lead to an incorrect interpretation of the mechanism model, especially in the presence of similar variable data under the two different conditions. Therefore, based on the robust principal subspace discriminant analysis, we further develop its dynamic enhanced version. The dynamic enhanced method utilizes the dynamic augmented matrix to enhance the latent features of historical data into current shifted features, so as to enlarge the difference between similar modes. Finally, the experimental results arranged on the Tennessee Eastman process and a commercial multi-phase flow process demonstrate that the proposed method has advanced diagnostic performance and satisfactory convergence speed.

Actively Exploring Informative Data for Smart Modeling of Industrial Multiphase Flow Processes

Accurate depiction of the process characteristics of dynamic multiphase flows using a data-driven model is a challenge in industrial practices. Collection of sufficient data is costly and cumbersome, and it is difficult to identify representative data efficiently. This article develops an active learning method to explore information from multiphase flow process data, thus facilitating smart process modeling and prediction. An index is proposed to describe the process dynamics and nonlinearity using a probabilistic model, facilitating determination of informative data. The subsequent absorption of these data into the training set enhances the model quality gradually. This is relevant especially for transitional regions exhibiting dynamic information. In addition, a simple and efficient criterion to judge the learning termination has been designed. Consequently, new representative data are explored and learned in a sequential manner. The experimental results of two industrial multiphase flows demonstrate the advantages of the proposed method.