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Recent Submissions

  • A Digital Twin for Unconventional Reservoirs: A Multiscale Modeling and Algorithm to Investigate Complex Mechanisms

    Zhang, Tao; Li, Yiteng; Cai, Jianchao; Meng, Qingbang; Sun, Shuyu; Li, Chenguang (Geofluids, Hindawi Limited, 2020-11-02) [Article]
    The special mechanisms underneath the flow and transport behaviors in unconventional reservoirs are still challenging an accurate and reliable production estimation. As an emerging approach in intelligent manufacturing, the concept of digital twin has attracted increasing attentions due to its capability of monitoring engineering processes based on modeling and simulation in digital space. The application potential is highly expected especially for problems with complex mechanisms and high data dimensions, because the utilized platform in the digital twin can be easily extended to cover more mechanisms and solve highly complicated problems with strong nonlinearity compared with experimental studies in physical space. In this paper, a digital twin is designed to numerically model the representative mechanisms that affect the production unconventional reservoirs, such as capillarity, dynamic sorption, and injection salinity, and it incorporates multiscale algorithms to simulate and illustrate the effect of these mechanisms on flow and transport phenomena. The preservation of physical laws among different scales is always the first priority, and simulation results are analyzed to verify the robustness of proposed multiscale algorithms.
  • Numerical investigation of carbonate acidizing with gelled acid using a coupled thermal–hydrologic–chemical model

    Liu, Piyang; Li, Jingfa; Sun, Shuyu; Yao, Jun; Zhang, Kai (International Journal of Thermal Sciences, Elsevier BV, 2020-10-23) [Article]
    In this work, an experiment-based rheological model that accounts for the influence of polymer concentration, shear-thinning behavior, and temperature variation on the in-situ viscosity of gelled acid is developed. On the basis of the rheological model, we present a thermal–hydrologic–chemical coupled model that describes the dissolution process of carbonate acidization with gelled acid. A sensitivity analysis of the dissolution dynamic regarding the temperature variation, polymer adsorption, and non-Newtonian behavior of the injected acid is carried out. The comparison of acidization curves and dissolution patterns obtained by injecting gelled acid and HCl is conducted. It is found that the optimal dissolution regime for gelled acid has a much wider range than neat HCl. It is observed from the numerical simulations that reservoir temperature and rheological parameters of the acid are key factors that affect acidizing efficiency, while the effect of polymer adsorption can be ignored. In addition, several recommendations for optimal stimulation of carbonates with gelled acids are provided.
  • Influence of fractal surface roughness on multiphase flow behavior: Lattice Boltzmann simulation

    Liu, Yang; Zou, Shuangmei; He, Ying; Sun, Shuyu; Ju, Yang; Meng, Qingbang; Cai, Jianchao (International Journal of Multiphase Flow, Elsevier BV, 2020-10-22) [Article]
    Accurate characterization of surface roughness and understanding its influence on multiphase flow behavior are important for industrial and environmental applications such as enhanced oil recovery, CO2 geological sequestration, and remediation of contaminated aquifers. Although some experimental and simulation studies have been conducted for investigating surface roughness in regular geometry structures, a more realistic description of roughness and its quantitative influence on multiphase flow need to be further explored. In this study, an optimized color-gradient lattice Boltzmann model is applied to simulate the steady-state two-phase flow in two-dimensional porous media modeled by a fourth-order Sierpinski carpet. The model is validated by comparing with the analytical solution and literature results, indicating reliability of our method. Then, rough surfaces with different roughness height and surface fractal dimension are characterized by a modified Weierstrass-Mandelbrot function and these effects on two-phase flow are investigated systematically by our model. The results show that the surface roughness has a negative effect on single-phase and two-phase fluid flow, which implies that the absolute and relative permeabilities for both wetting phase and nonwetting phase decreases with the increase of roughness height or surface fractal dimension. In addition, the surface roughness has influence on the two-phase distribution, velocity distribution and fluid-fluid/fluid-solid interface area, especially under the neutral wetting condition. Our study provides a pore-scale insight into the effect of surface roughness on two-phase flow, which is important for a fundamental understanding on macroscopic multiphase flow behaviors.
  • Bulk and Interfacial Properties of the Decane + Water System in the Presence of Methane, Carbon Dioxide, and Their Mixture

    Yang, Yafan; Nair, Arun Kumar Narayanan; Anwari Che Ruslan, Mohd Fuad; Sun, Shuyu (The Journal of Physical Chemistry B, American Chemical Society (ACS), 2020-10-16) [Article]
    Molecular dynamics simulations are carried out to study the two-phase behavior of the n-decane + water system in the presence of methane, carbon dioxide, and their mixture under reservoir conditions. The simulation studies were complemented by theoretical modeling using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) and density gradient theory. Our results show that the presence of methane and carbon dioxide decreases the interfacial tension (IFT) of the decane + water system. In general, the IFT increases with increasing pressure and decreasing temperature for the methane + decane + water and carbon dioxide + decane + water systems, similar to what has been found for the corresponding decane + water system. The most important finding of this study is that the presence of carbon dioxide decreases the IFT of the methane + decane + water system. The atomic density profiles provide evidence of the local accumulation of methane and carbon dioxide at the interface, in most of the studied systems. The results of this study show the preferential dissolution in the water-rich phase and enrichment at the interface for carbon dioxide in the methane + carbon dioxide + decane + water system. This indicates the preferential interaction of water with carbon dioxide relative to methane and decane. Notably, there is an enrichment of the interface by decane at high mole fractions of methane in the methane/decane-rich or methane/carbon dioxide/decane-rich phase. Overall, the solubility of methane and carbon dioxide in the water-rich phase increases with increasing pressure and temperature. Additionally, we find that the overall performance of the PC-SAFT EoS and the cubic-plus-association EoS is similar with respect to the calculation of bulk and interfacial properties of these systems.
  • Stability theory of nano-fluid over an exponentially stretching cylindrical surface containing microorganisms.

    Ferdows, M; Hossan, Amran; Bangalee, M Z I; Sun, Shuyu; Alzahrani, Faris (Scientific reports, Springer Science and Business Media LLC, 2020-10-12) [Article]
    This research is emphasized to describe the stability analysis in the form of dual solution of the flow and heat analysis on nanofluid over an exponential stretching cylindrical surface containing microorganisms. The research is also implemented to manifest the dual profiles of velocity, temperature and nanoparticle concentration in the effect of velocity ratio parameter ([Formula: see text]). Living microorganisms' cell are mixed into the nanofluid to neglect the unstable condition of nano type particles. The governing equations are transformed to non-linear ordinary differential equations with respect to pertinent boundary conditions by using similarity transformation. The significant differential equations are solved using build in function bvp4c in MATLAB. It is seen that the solution is not unique for vertical stretching sheet. This research is reached to excellent argument when found results are compared with available result. It is noticed that dual results are obtained demanding on critical value ([Formula: see text]), the meanings are indicated at these critical values both solutions are connected and behind these critical value boundary layer separates thus the solution are not stable.
  • An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

    Li, Jing Fa; Yu, Bo; Wang, Dao Bing; Sun, Shuyu; Sun, Dong Liang (Petroleum Science, Springer Science and Business Media LLC, 2020-09-28) [Article]
    In this paper, an efficient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible flow in porous media. The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of flow equation in original full-order space, and the discrete empirical interpolation method (DEIM) is applied to speed up the solution of Peng–Robinson equation of state in reduced-order subspace. The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reduced-order subspace, which not only preserves good prediction accuracy of full-order model, but also gains dramatic computational acceleration by multigrid and DEIM. Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method. In addition, the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng–Robinson equation of state is demonstrated and carried out in detail. Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors. The general acceleration is up to 50–60 times faster than that of standard semi-implicit method in two-dimensional simulations, but the average relative errors of numerical results between these two methods only have the order of magnitude 10−4–10−6%.
  • Accelerating flash calculations in unconventional reservoirs considering capillary pressure using an optimized deep learning algorithm

    Zhang, Tao; Li, Yiteng; Sun, Shuyu; Bai, Hua (Journal of Petroleum Science and Engineering, Elsevier BV, 2020-09-15) [Article]
    An increasing focus was placed in the past few decades on accelerating flash calculations and a variety of acceleration strategies have been developed to improve its efficiency without serious compromise in accuracy and reliability. Recently, as machine learning becomes a powerful tool to handle complicated and time-consuming problems, it is increasingly appealing to replace the iterative flash algorithm, due to the strong nonlinearity of flash problem, by a neural network model. In this study, an NVT flash calculation scheme is established with a thermodynamically stable evolution algorithm to generate training and testing data for the proposed deep neural network. With a modified network structure, the deep learning algorithm is optimized by carefully tuning neural network hyperparameters. Numerical tests indicate that the trained model is capable of accurately estimating phase compositions and states for complex reservoir fluids under a wide range of environmental conditions, while the effect of capillary pressure can be captured well. Thermodynamic rules are preserved well through our algorithm, and the trained model can be used for various fluid mixtures, which significantly accelerates flash calculations in unconventional reservoirs.
  • A Comprehensive Experimental Study on Mechanical Behavior, Microstructure and Transport Properties of 3D-printed Rock Analogs

    Song, Rui; Wang, Yao; Ishutov, Sergey; Zambrano-Narvaez, Gonzalo; Hodder, Kevin J.; Chalaturnyk, Rick J.; Sun, Shuyu; Liu, Jianjun; Gamage, Ranjith P. (Rock Mechanics and Rock Engineering, Springer Science and Business Media LLC, 2020-09-08) [Article]
    3D-printed (3DP) analogs of natural rocks have been used in laboratory tests concerning geomechanical and transport properties. Rock analogs manufactured by 3D printing can be used to manufacture batch of the samples with specified heterogeneity compared to natural rocks. Rock analogs were manufactured with silica sand (SS) and gypsum powder (GP) using binder jetting as well as with coated silica beads (CSB) using selective laser curing. The uniaxial and triaxial compressive tests were conducted to investigate the strength and deformation characteristics of 3DP rocks that were quantitatively compared with natural rocks. CSB and SS specimens experienced tensile failure, while the GP specimen has shown shear failure and shear-expansion behavior. The microstructural characteristics (e.g. grain shape, pore type, and bonding form) of the SS specimen were similar to a natural sandstone (Berea sandstone reported in the literature) with a relatively loose texture. In addition, 3DP rocks were more permeable than Berea sandstone (permeability of SS, CSB, and Berea sandstone was 12580.5 mD, 9840.5 mD, and 3950 mD, respectively). The effect of microscopic mechanical behavior on macroscopic strength and failure characteristics was investigated using scanning electronic microscopy. CSB and SS specimens could be suitable to simulate the transport behavior of the highly permeable sedimentary rocks. The GP specimen could be used to study the large deformation characteristics and creep failure mode of highly stressed soft rocks. Despite the early stage of 3DP rock analog studies, the potential applications could be expanded by controlling the physical properties (e.g. wettability and surface roughness).
  • Construction of a minimum energy path for the VT flash model by an exponential time differencing scheme with the string method

    Zhang, Yuze; Li, Yiteng; Zhang, Lei; Sun, Shuyu (arXiv, 2020-08-07) [Preprint]
    Phase equilibrium calculation, also known as flash calculation, plays significant roles in various aspects of petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development, the current research interest on flash calculation has been shifted from accuracy to efficiency, but the ultimate goal remains the same focusing on estimation of the equilibrium phase amounts and phase compositions under the given variable specification. However, finding the transition route and its related saddle points are very often helpful to study the evolution of phase change and partition. Motivated by this, in this study we apply the string method to find the minimum energy paths and saddle points information of a single-component VT flash model with the Peng-Robinson equation of state. As the system has strong stiffness, common ordinary differential equation solvers have their limitations. To overcome these issues, a Rosenbrock-type exponential time differencing scheme is employed to reduce the computational difficulty caused by the high stiffness of the investigated system. In comparison with the published results and experimental data, the proposed numerical algorithm not only shows good feasibility and accuracy on phase equilibrium calculation, but also successfully calculates the minimum energy path and and saddle point of the single-component VT flash model with strong stiffness.
  • Thermodynamically Consistent Darcy-Brinkman-Forchheimer Framework in Matrix Acidization

    Wu, Yuanqing; Kou, Jisheng; Sun, Shuyu; Wu, Yu-Shu (arXiv, 2020-07-23) [Preprint]
    Matrix acidization is an important technique to enhance oil production at the tertiary recovery stage, and its numerical simulation is never concluded. From one of the earliest models, i.e. the two-scale model (Darcy framework), the Darcy-Brinkman-Forchheimer (DBF) framework is developed by adding Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is put outside of the time derivation term, which cannot describe the change of porosity well. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton's second law. The modified framework is called improved DBF framework. Furthermore, based on the improved DBF framework, the thermal DBF framework is given by introducing the energy balance equation to the improved DBF framework. Both of the frameworks are verified by the former works through numerical experiments and chemical experiments in labs. Parallelization to the codes of the complicated frameworks is also realized, and good scalability can be achieved.
  • Dual solution of boundary-layer flow driven by variable plate and streaming-free velocity

    Ferdows, M.; Alzahrani, Faris; Sun, Shuyu (Advances in Mechanical Engineering, SAGE Publications, 2020-07-22) [Article]
    This article presents a numerical study to investigate boundary-layer heat transfer fluid associated with a moving flat body in cooperation of variable plate and streaming-free velocity along the boundary surface in the laminar flow. The thermal conductivity is supposed to vary linearly with temperature. Similarity transformations are applied to render the governing partial differential equations for mass, momentum and energy into a system of ordinary differential equations to reveal the possible existence of dual solutions. MATLAB package has been used to solve the boundary value problem numerically. We present the effects of various parameters such as velocity ratio, thermal conductivity and variable viscosity on velocity and temperature distribution. The analysis of the results concerning Skin friction and Nusselt number near the wall is also presented. It is focused on the detection and description of the dual solutions. The study reveals that the undertaken problem admits dual solutions in particular range of values of different physical parameters. It can be seen that for the first branch solution, the fluid velocity decreases near the sheet, but it increases far away from the sheet for velocity ratio parameter, whereas the opposite effect is induced for second branch solution. Skin friction coefficient and rate of heat transfer increase due to increase in thermal conductivity parameter.
  • Effect of salinity on oil production: review on low salinity waterflooding mechanisms and exploratory study on pipeline scaling

    Zhang, Tao; Li, Yiteng; LI, CHENGUANG; Sun, Shuyu (Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, EDP Sciences, 2020-07-21) [Article]
    The past decades have witnessed a rapid development of enhanced oil recovery techniques, among which the effect of salinity has become a very attractive topic due to its significant advantages on environmental protection and economical benefits. Numerous studies have been reported focusing on analysis of the mechanisms behind low salinity waterflooding in order to better design the injected salinity under various working conditions and reservoir properties. However, the effect of injection salinity on pipeline scaling has not been widely studied, but this mechanism is important to gathering, transportation and storage for petroleum industry. In this paper, an exhaustive literature review is conducted to summarize several well-recognized and widely accepted mechanisms, including fine migration, wettability alteration, double layer expansion, and multicomponent ion exchange. These mechanisms can be correlated with each other, and certain combined effects may be defined as other mechanisms. In order to mathematically model and numerically describe the fluid behaviors in injection pipelines considering injection salinity, an exploratory phase-field model is presented to simulate the multiphase flow in injection pipeline where scale formation may take place. The effect of injection salinity is represented by the scaling tendency to describe the possibility of scale formation when the scaling species are attached to the scaled structure. It can be easily referred from the simulation result that flow and scaling conditions are significantly affected if a salinity-dependent scaling tendency is considered. Thus, this mechanism should be taken into account in the design of injection process if a sustainable exploitation technique is applied by using purified production water as injection fluid. Finally, remarks and suggestions are provided based on our extensive review and preliminary investigation, to help inspire the future discussions.
  • Base level changes based on Basin Filling Modelling: a case study from the Paleocene Lishui Sag, East China Sea Basin

    Li, Jing Zhe; Liu, Pi Yang; Zhang, Jin Liang; Sun, Shuyu; Sun, Zhi Feng; Du, Dong Xing; Zhang, Ming (Petroleum Science, Springer Science and Business Media LLC, 2020-07-17) [Article]
    Estimation of base level changes in geological records is an important topic for petroleum geologists. Taking the Paleocene Upper Lingfeng Member of Lishui Sag as an example, this paper conducted a base level reconstruction based on Basin Filling Modelling (BFM). The reconstruction was processed on the ground of a previously interpreted seismic stratigraphic framework with several assumptions and simplification. The BFM is implemented with a nonlinear diffusion equation solver written in R coding that excels in shallow marine stratigraphic simulation. The modeled results fit the original stratigraphy very well. The BFM is a powerful tool for reconstructing the base level, and is an effective way to check the reasonableness of previous interpretations. Although simulation solutions may not be unique, the BFM still provides us a chance to gain some insights into the mechanism and dynamic details of the stratigraphy of sedimentary basins.
  • Adsorption and Diffusion of Carbon Dioxide, Methane, and Their Mixture in Carbon Nanotubes in the Presence of Water

    Yang, Yafan; Nair, Arun Kumar Narayanan; Sun, Shuyu (The Journal of Physical Chemistry C, American Chemical Society (ACS), 2020-07-09) [Article]
    Molecular simulations were performed to investigate the adsorption and diffusion properties of methane and carbon dioxide in carbon nanotubes (CNTs) with preadsorbed water at 300 K and pressures up to 40 bar. Our results show that, at low pressures, a high uptake of methane and carbon dioxide is obtained in relatively small pores, and the presence of water enhances the adsorption of carbon dioxide in CNTs with large diameters. The effect of the preadsorbed water is more pronounced on the mobility of methane than that of carbon dioxide. Importantly, at high water contents, we see that the mobility of methane is a nonmonotonic function of the nanotube diameter. This is probably due to the splitting of the water clusters in the small pores which may lead to a faster diffusion process. Simulations were also performed for the methane/carbon dioxide mixture in CNTs with preadsorbed water. Here, the overall adsorption and diffusion properties are similar to those observed for the methane/water and carbon dioxide/water mixtures in CNTs. The adsorption selectivity of carbon dioxide over methane increases with water content which may be because of the relatively stronger water-carbon dioxide interactions. A significant result is that the mobility of methane in the CNTs decreases with decreasing bulk mole fraction of methane. In general, this decrease is more pronounced at higher loadings of methane and lower water contents. However, the presence of methane has less effect on the diffusion properties of carbon dioxide in the CNTs. These results may be explained by the preferential adsorption of carbon dioxide over methane in the CNTs. Furthermore, these simulated adsorption isotherms and diffusivity results are in reasonable agreement with the theoretical predictions based on the ideal adsorbed solution theory and the Krishna and Paschek approach, respectively.
  • Numerical Study of CH4 Generation and Transport in XLPE-Insulated Cables in Continuous Vulcanization

    Ruslan, Mohd Fuad Anwari Che; Youn, Dong Joon; Aarons, Roshan; Sun, Yabin; Sun, Shuyu (Materials, MDPI AG, 2020-07-03) [Article]
    In this work, we apply a computational diffusion model based on Fick’s laws to study the generation and transport of methane (CH 4 ) during the production of a cross-linked polyethylene (XLPE) insulated cable. The model takes into account the heating process in a curing tube where most of the cross-linking reaction occurs and the subsequent two-stage cooling process, with water and air as the cooling media. For the calculation of CH 4 generation, the model considers the effect of temperature on the cross-linking reaction selectivity. The cross-linking reaction selectivity is a measure of the preference of cumyloxy to proceed either with a hydrogen abstraction reaction, which produces cumyl alcohol, or with a β -scission reaction, which produces acetophenone and CH 4 . The simulation results show that, during cable production, a significant amount of CH 4 is generated in the XLPE layer, which diffuses out of the cable and into the conductor part of the cable. Therefore, the diffusion pattern becomes a non-uniform radial distribution of CH 4 at the cable take-up point, which corresponds well with existing experimental data. Using the model, we perform a series of parametric studies to determine the effect of the cable production conditions, such as the curing temperature, line speed, and cooling water flow rate, on CH 4 generation and transport during cable production. The results show that the curing temperature has the largest impact on the amount of CH 4 generated and its distribution within the cable. We found that under similar curing and cooling conditions, varying the line speed induces a notable effect on the CH 4 transport within the cable, while the cooling water flow rate had no significant impact.
  • Molecular insight on competitive adsorption and diffusion characteristics of shale gas in water-bearing channels

    Gong, Liang; Shi, Ji Hong; Ding, Bin; Huang, Zhao Qin; Sun, Shuyu; Yao, Jun (Fuel, Elsevier BV, 2020-06-20) [Article]
    The shale gas adsorption and flow characteristics play essential roles in improving shale gas recovery. Motivated by the desire to clarify these characteristics carefully and precisely, a series of shale models with different water contents from 0.6 to 2.4 wt% were established. Presumably, these characteristics were sought to pin down answers by using the grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) methods respectively. Importantly, the analysis of the pore structure of these models is firstly taken into account considering its microstructure to meet the demand for the explanation of the adsorption characteristics of methane. The results showed that the enterable volumes decrease significantly with the increase of water content due to the diffusion and aggregation of water molecules in the middle of enterable pores. Intuitively, it could lead to a marked linear decrease in the adsorption amount of methane from 1.2 mmol/g to 0.6 mmol/g. A curiosity of this study is that the diffusion coefficients of methane increase as the increase of temperature and ensuring the low pressure outside the channel could boost the flux of methane intriguingly. Suffice to say, the optimum development shale gas conditions in this work are at the temperature of 358 K and in the presence of water content of 2.4 wt%. Hence, there is an expectation that this study would provide a guidance for the exploitation of shale gas in the presence of water.
  • An Expanded Mixed Finite Element Method for Space Fractional Darcy Flow in Porous Media.

    Chen, Huangxin; Sun, Shuyu (Computational Science – ICCS 2020, Springer International Publishing, 2020-06-15) [Book Chapter]
    In this paper an expanded mixed formulation is introduced to solve the two dimensional space fractional Darcy flow in porous media. By introducing an auxiliary vector, we derive a new mixed formulation and the well-possedness of the formulation can be established. Then the locally mass-conservative expanded mixed finite element method is applied for the solution. Numerical results are shown to verify the efficiency of the proposed algorithm.
  • Numerical Investigation of Solute Transport in Fractured Porous Media Using the Discrete Fracture Model.

    El-Amin, Mohamed F.; Kou, Jisheng; Sun, Shuyu (Computational Science – ICCS 2020, Springer International Publishing, 2020-06-15) [Conference Paper]
    In this paper, we investigate flow with solute transport in fractured porous media. The system of the governing equations consists of the continuity equation, Darcy’s law, and concentration equation. A discrete-fracture model (DFM) has been developed to describe the problem under consideration. The multiscale time-splitting method was used to handle different sizes of time-step for different physics, such as pressure and concentration. Some numerical examples are presented to show the efficiency of the multi-scale time-splitting approach.
  • A self-adaptive deep learning algorithm for accelerating multi-component flash calculation

    Zhang, Tao; Li, Yu; Li, Yiteng; Sun, Shuyu; Gao, Xin (Computer Methods in Applied Mechanics and Engineering, Elsevier BV, 2020-06-11) [Article]
    In this paper, the first self-adaptive deep learning algorithm is proposed in details to accelerate flash calculations, which can quantitatively predict the total number of phases in the mixture and related thermodynamic properties at equilibrium for realistic reservoir fluids with a large number of components under various environmental conditions. A thermodynamically consistent scheme for phase equilibrium calculation is adopted and implemented at specified moles, volume and temperature, and the flash results are used as the ground truth for training and testing the deep neural network. The critical properties of each component are considered as the input features of the neural network and the final output is the total number of phases at equilibrium and the molar compositions in each phase. Two network structures are well designed, one of which transforms the input of various numbers of components in the training and the objective fluid mixture into a unified space before entering the productive neural network. “Ghost components” are defined and introduced to process the data padding work in order to modify the dimension of input flash calculation data to meet the training and testing requirements of the target fluid mixture. Hyperparameters on both two neural networks are carefully tuned in order to ensure the physical correlations underneath the input parameters are preserved properly through the learning process. This combined structure can make our deep learning algorithm to be self-adaptive to the change of input components and dimensions. Furthermore, two Softmax functions are used in the last layer to enforce the constraint that the summation of mole fractions in each phase is equal to 1. An example is presented that the flash calculation results of a 8-component Eagle Ford oil is used as input to estimate the phase equilibrium state of a 14-component Eagle Ford oil. The results are satisfactory with very small estimation errors. The capability of the proposed deep learning algorithm is also verified that simultaneously completes phase stability test and phase splitting calculation. Remarks are concluded at the end to provide some guidance for further research in this direction, especially the potential application of newly developed neural network models.
  • Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect

    El-Amin, Mohamed F.; Kou, Jisheng; Sun, Shuyu (Oil and Gas Science and Technology, EDP Sciences, 2020-06-05) [Article]
    In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

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