Flash Calculations Research Articles

Data-driven guided physics-informed segmented neural network for liquid–vapor flash calculation

Liquid–vapor phase equilibrium is ubiquitous in industrial and engineering field, which involves the flash calculation. The conventional flash calculation is solved with the numerical simulator, accompanying with large computational efforts. In this paper, we propose a data-driven guided physics-informed segmented neural network (DDG-PISNN) for the liquid–vapor pressure–temperature flash calculation. The training of DDG-PISNN is divided into two stages. First, a classifier for determining the stability of the system and a guiding network are built using data-driven methods. Subsequently, various control equations are employed to construct loss functions based on the results of classifier. In this way, DDG-PISNN fully leverages the advantages of data-driven approaches and physical equations. The accuracy and robustness of DDG-PISNN are calibrated by experiments under different conditions, and the performance is compared with that of DDG-PINN. In addition, a surrogate model for flash calculation is constructed based on DDG-PISNN. The accuracy of the surrogate model is also validated against a numerical case, and the computational efficiency is more than 800 times. Then, the surrogate model is embedded into the reservoir simulation technique to perform the flash calculation and form a surrogate-based compositional model. The surrogate-based model is employed to simulate the process of CO2 displacing crude oil. The results are in good agreement with the results of numerical solution.

Improved phase-state identification bypass approach of the hydrocarbons-CO2-H2O system for compositional reservoir simulation

CO2 injection is a highly effective technique to enhance oil recovery, achieved through continuous or alternative injection. However, the intricate interactions between different phases within porous media present significant challenges when predicting the performance of CO2 injection. To address this, it is crucial to employ compositional simulation, which accounts for the multiphase multicomponent transport. Nonetheless, conventional multiphase flash calculations can be computationally inefficient for large-scale reservoir simulations. Therefore, it is necessary to accelerate the Equation-of-State (EoS)-based compositional simulation, given the widespread use of CO2 enhanced oil recovery (CO2-EOR) in recent years. The phase-state identification bypass method has proven to be superior to other methods in terms of efficiency. However, this approach struggles with regions near phase boundaries, resulting in reduced computational efficiency in those areas.In this study, an enhanced phase-state identification bypass approach is developed to address this limitation. The first step involves discretising the pressure-temperature space using rectangular grids. Additionally, the tie-simplexes, which represent regions defined by the maximum number of phases formed by the fluid under consideration, are discretized in the phase-fraction space at the pressure and temperature of each discretization node. Subsequently, the discretization grid associated with the given point (the overall composition, pressure, and temperature) is located, and the phase states of the grid nodes are determined using the conventional multiphase flash method. If all nodes exhibit the same phase state, that phase state is assigned to the given point. However, if multiple phase states are obtained, a novel process is proposed to determine the phase state of the given point. To validate this improvement to the phase-state identification bypass method, phase diagram calculations and simulation cases are conducted, and the results demonstrate the robustness of the proposed method and its superior computational efficiency compared to the previous method.

A Line-Search-Based Algorithm for Multiphase Flash Calculations with CO2-Hydrocarbon System.

Multiphase flash calculations are pivotal in compositional simulation, necessitating a robust and efficient computational algorithm. In this work, we have developed a line-search-based algorithm framework for stability analysis and multiphase flash calculations. This algorithm is rooted in the modified Newton step and line-search method. The modified Newton step, derived from modified Cholesky factorization, ensures a descent direction, while the line search determines the degree of decrease. This combination facilitates convergence even in challenging regions for phase stability analysis and multiphase flash calculations, exhibiting superlinear convergence speed. Unlike traditional approaches that rely on successive substitution iteration and may resort to Newton iteration only if the Hessian matrix is positive definite, our algorithm incorporates modification via modified Cholesky factorization upon encountering a nonpositive definite Hessian matrix. We tested our algorithm with several classical fluids, demonstrating its efficiency and robustness. Furthermore, we assessed the algorithm's performance by computing the pressure-composition diagram for the CO2-hydrocarbon system, where all calculations achieved rapid convergence without failure. This newly developed algorithm for phase stability analysis and multiphase flash calculations represents a significant advancement for compositional or chemical process simulations.

NNEoS : Neural network-based thermodynamically consistent equation of state for fast and accurate flash calculations

Equations of state (EOS) correlate thermodynamic properties and are essential for flash calculations. However, solving for an EOS can be time-consuming, and EOS do not precisely represent physical reality, causing the deviation of flash results from phase equilibrium data. In this work, we propose a neural network-based EOS (NNEoS) inherently satisfying thermodynamic consistency. NNEoS first predicts the residual Gibbs energy and then derives other thermodynamic properties through differentiation. NNEoS can be trained using an analytical EOS and then serve as a reliable, computationally efficient substitute. NNEoS can also be fine-tuned with experimental data to better match flash results to experimental data. We evaluate the performance of NNEoS against analytical EOS on three case studies, including binary and multicomponent mixtures with and without cross-association. The results show that NNEoS achieves significantly faster flash calculations via GPU-based parallel computing and offers superior predictive accuracy after fine-tuning compared to analytical EOS.

Extraction of turpentine essential oil from Pinus pinaster ait: Comparison of yield and composition between conventional- or microwave assisted-hydro-distillation and vacuum distillation

Turpentine essential oil was extracted from Pinus pinaster Ait. resin, collected from “les Cévennes” area (south-eastern France). Three extraction processes were investigated: conventional hydro-distillation (CHD), microwaves assisted hydro-distillation (MWHD) under a limited amount of water and a solvent-free process, i.e. vacuum distillation (VD). The selected experimental conditions agreed with the theoretical flash region and equilibrium yield predicted by flash calculations described well the results.CHD using a low water/resin ratio of 2 showed a high yield (∼25%w/w) and a turpentine essential oil (EO) primarily rich in α- and β-pinenes, but also in sesquiterpene compounds such as β-caryophyllene. Microwave heating did not improve the total extraction staying around 20%w/w but depending on power condition, both the monoterpene/sesquiterpene ratio and the proportion of oxygenated compounds can be increased. Pressure, rather than temperature, was observed to have a greater impact on the VD extraction yield. At a temperature above or equal to 90 °C and a pressure of 1 kPa, the yield became comparable to that obtained by CHD but with a high pinenes and low sesquiterpenes content.

Data-efficient surrogate modeling of thermodynamic equilibria using Sobolev training, data augmentation and adaptive sampling

Modern thermodynamic models, such as the PC-SAFT equation of state, are very accurate but also computationally intensive, which limits their applicability to process design optimization, for example. Surrogate models, which can be evaluated quickly, can be used to approximate the thermodynamic equilibria. However, this requires many data points from the flash calculation routine. In this paper, we investigate three approaches to reduce the number of samples and thus the effort needed to train the surrogate models. First, Sobolev training is used, where the surrogate model is trained not only on the output values, but also on derivative information. Second, data augmentation along the tie lines in LLE systems is proposed to generate samples without additional flash calculations. Third, adaptive sampling is revisited with a novel quality criterion. It is shown that the combination of these techniques can be used to significantly reduce the number of samples required.

A method for calculating two-phase equilibrium: Constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation

Traditional methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles, are the mainstream methods used to solve the volume-temperature flash calculation (called NVT-flash), even though they suffer from drawbacks such as sensitivity to initial value and complexity of derivative calculations. A constrained backtracking search algorithm (CBSA), proposed in 2024, was the first and only metaheuristic algorithm to successfully tackle the NVT-flash problem, which overcomes shortcomings of traditional methods. Considering the advantages of metaheuristic algorithms, a constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (CGPE-QI) is proposed in this paper to deal with the NVT-flash problem. CGPE-QI considers total Helmholtz free energy as the objective function, moles vector, and volume of a single phase as variables. Constraints to solve the NVT-flash problem are addressed by using a direct search method and an exterior point method. Numerical experiments on two-phase equilibrium of pure substance and mixtures are carried out employing CGPE-QI. Experimental results are the same as those obtained by traditional methods, which confirms that CGPE-QI can effectively tackle the NVT-flash problem and possesses energy decay property. In particular, the results demonstrate that CGPE-QI is more competitive than CBSA in terms of convergence speed, stability, and calculation cost. CGPE-QI proposed in this paper is the second metaheuristic algorithm to successfully solve the NVT-flash problem, illustrating that metaheuristic algorithms have great potential in solving phase equilibrium calculation problems.

A Multiphase and Multicomponent Model and Numerical Simulation Technology for CO2 Flooding and Storage

In recent years, CO2 flooding has become an important technical measure for oil and gas field enterprises to further improve oil and gas recovery and achieve the goal of “dual carbon”. It is also one of the concrete application forms of CCUS. Numerical simulation based on CO2-EOR plays an indispensable role in the study of the mechanism of CO2 flooding and buried percolation, allowing for technical indicators to be selected and EOR/EGR prediction to be improved for reservoir engineers. This paper discusses the numerical simulation techniques related to CO2 flooding and storage, including mathematical models and solving algorithms. A multiphase and multicomponent mathematical model is developed to describe the flow mechanism of hydrocarbon components–CO2–water underground and to simulate the phase diagram of the components. The two-phase P-T flash calculation with SSI (+DEM) and the Newton method is adopted to obtain the gas–liquid phase equilibrium parameters. The extreme value judgment of the TPD function is used to form the phase stability test and miscibility identification model. A tailor-made multistage preconditioner is built to solve the linear equation of the strong-coupled, multiphase, multicomponent reservoir simulation, which includes the variables of pressure, saturation, and composition. The multistage preconditioner improves the computational efficiency significantly. A numerical simulation of CO2 injection in a carbonate reservoir in the Middle East shows that it is effective for researching the recovery factor and storage quantity of CO2 flooding based on the above numerical simulation techniques.

A novel method to accelerate the three-phase flash calculation of the hydrocarbon-CO2 system

To achieve high computational efficiency and simulation accuracy in the equation-of-state-based compositional simulation, the fast multiphase flash calculation approach is required for the hydrocarbon-CO2 system, allowing for the simultaneous existence of vapour, CO2-lean, and CO2-rich phases. However, the conventional step-by-step method for multiphase flash calculation is associated with a high cost in identifying the three-phase equilibrium, thereby significantly impeding the computation efficiency of compositional simulation when the three-phase equilibrium appears in most grids.To address this challenge, a novel approach to multiphase flash calculation is proposed. In this study, all trial phases exhibiting negative tangent plane distance are employed to identify the three-phase equilibrium, eliminating the need for additional phase stability analysis and two-phase split calculations. Furthermore, this new method incurs minimal computational cost and requires only minor modifications to the existing stepwise procedure. Phase diagram calculations conducted on four cases demonstrate that the newly proposed method dramatically accelerates the identification of the three-phase equilibrium.

A hybrid numerical model for coupled hydro-mechanical analysis during CO2 injection into heterogeneous unconventional reservoirs

This paper presents a hybrid numerical model for simulating compressible multiphase multicomponent transport in deformable, heterogeneous unconventional reservoirs. A fully implicit theoretical framework for coupled hydromechanical behaviour is established, in which the flash calculation is avoided. To preserve the local mass conversation, an element based finite volume method is used to spatially discretize mass conversation equations. Linear momentum equilibrium equation is discretized with finite element method. Two numerical approaches are coupled through sharing the same shape functions. An implicit mid-interval backwards difference algorithm is used to handle the temporal derivative. Reliability and efficiency of the developed model have been examined by verification tests against available analytical or numerical solutions. The coupled hydromechanical processes in heterogeneous reservoirs were simulated. The results of numerical experiments show that oscillatory problem for saturation in heterogeneous media can be eliminated, demonstrating better performance of developed model for heterogeneous reservoir simulations. Reservoir performance is significantly shaped by its heterogeneity through controlling fluid flow and time for CO2–CH4 displacement. Simulation results show that the time required for completion of CO2–CH4 displacement increases by about 250 days when considering heterogeneity effect. In conclusion, this study offers a valuable tool for facilitating the development of CO2-enhanced unconventional gas recovery.

Phase equilibria calculations of a hydrocarbon system consisting water and asphaltene using association equation of state: A generalized auto-tune procedure

A generalized algorithm is proposed for four-phase flash calculations in hydrocarbon-water systems in which asphaltene has tendency to be precipitated. The systems which are going to be studied in this paper can be either single phase, two-phase, three-phase or four-phase of gas, oil-rich, asphaltene-rich and aqueous phases. The properties of vapor and oil-rich (liquid) phases can be predicted using any EOS while Henry's law is performed for calculating the properties of water-rich (aqueous) phase. In addition, an association equation of state (AEOS) has been used to predict the amount of the precipitated asphaltenes at different conditions. Using the proposed algorithm, one can predict the number and types of phases and also the properties of each phase, as accurate as possible. As tuning of EOS models is tedious and time consuming, a generalized and auto-tune method based on sensitivity and optimization algorithms is also applied in this study so that the best model could be found easily, quickly and automatically. The proposed approach proved to be efficient, and very good agreement between the results of the presented method and experimental data was found for different test problems. This new procedure can be very useful in compositional reservoir simulation of certain enhanced oil recovery methods and in surface facility process simulation.

Unified flash calculations with isenthalpic and isochoric constraints

In the unified flash procedure, a persistent set of unknowns and equations are solved in equilibrium calculations, allowing for simultaneous phase stability and split calculations. For fluids in a subcritical thermodynamic state characterized by pressure and temperature, modeling both liquid and gas phases with inequality conditions for phase fractions has been shown to incorporate the tangent-plane criterion and results in a consistent formulation of compositions for both present and absent phases. However, applications such as high-enthalpy systems in subsurface flow require a state definition using other state variables than pressure and temperature, as well as the capability to represent supercritical phases. Furthermore, the robustness of the flash across a wide range of state values is required if equilibrium dynamics are to be included in a flow and transport problem.This work introduces constraints in terms of enthalpy and volume to allow pressure and temperature to vary in the unified setting. The constraints are shown to arise from equilibrium conditions for the relevant state functions to be minimized. To increase the range of applicability, a modified extension procedure for the compressibility factor was devised, as well as procedures for the flash initialization.The unified formulation is extendable to allow isenthalpic and isochoric flash calculations. The initialization was devised using methodologies from the negative flash and Rachford–Rice equations. Extensive numerical tests with multiple equilibrium definitions in terms of state variables were performed. Gas–liquid, binary and a multicomponent mixture using Peng–Robinson EoS showed consistency of results which are verified using third-party code.

Enhancing the accuracy of physics-informed neural network surrogates in flash calculations using sparse grid guidance*

Flash calculations pose a significant performance bottleneck in compositional-flow simulations. While sparse grids have helped mitigate this bottleneck by shifting it to the offline stage, the accuracy of the surrogate model based on physics-informed neural networks (PINN) is still inferior to that of the sparse grid surrogate in many cases. To address this issue, we propose the sparse-grid guided PINN training algorithm. This approach involves rearranging the collocation points using sparse grids at each epoch to capture changes in the residual space. By doing so, the PINN surrogate achieves the required accuracy using the fewest collocation points possible, thereby avoiding potential performance bottlenecks. Moreover, the training time complexity of the sparse-grid guided PINN training is significantly lower compared to the normal training while maintaining the same level of accuracy. Consequently, the sparse-grid guided PINN training method enhances the accuracy of the PINN surrogate with minimal computational overhead. During the experiments, a flash calculation of methane-propane mixture is conducted using a PINN surrogate, guided by the principles of sparse grids. The collective experimental observations underscore the clear advantages of employing sparse-grid guided PINN training, showcasing superior outcomes in terms of convergence, stability, and accuracy.

EVALUATION OF MACHINE LEARNING ASSISTED PHASE BEHAVIOR MODELLING OF CO2-OIL SYSTEMS

This study evaluates machine learning (ML) methodologies in the pursuit of advancing thermodynamic flash calculations that are vital for carbon dioxide storage applications and for the oil and gas industry in general. We generated a dataset for training machine learning algorithms using a traditional physics-based model. This developed hybrid model incorporated into the machine learning model underlying physical constraints. While preliminary results from training and numerical matching were promising, the hybrid model's real-world application revealed non-trivial shortcomings. Specifically, mismatch in the multiphase region was observed during compositional space testing. Such subtle but significant flaws in machine learning methods have profound implications for the accurate physics of carbon storage projects. This article, therefore, presents advantages and disadvantages of employing ML for thermodynamic calculations, emphasizing the intricate balance between computational efficiency and representative physics.

Deep learning–assisted phase equilibrium analysis for producing natural hydrogen

The development of natural hydrogen is an emerging topic in the current energy transition trend. The production process involves compositional multiphase flow via subsurface porous media. This makes studying the compositional phase equilibrium behavior essential for reliable reservoir simulation and prediction. Herein, we develop an iterative flash calculation scheme and a deep learning algorithm using a thermodynamics-informed neural network (TINN) to perform accurate, robust, and fast phase equilibrium calculations for realistic fluid mixtures of natural hydrogen. The application of TINN architecture can accelerate the calculations for nearly 20 times. The effect of capillarity on phase equilibrium states is demonstrated. Based on simulation results, suggestions for the natural hydrogen industry chain are provided to control the possible phase transitions under certain environmental conditions that may be observed in the natural hydrogen reservoirs, storage and transportation facilities. The extremely low critical temperature of hydrogen challenges the robustness of flash calculations but facilitates the separation of impurities by liquefying certain undesired species. Moreover, phase transitions under control can be an effective approach for carbon dioxide capture and sequestration with optimized operating conditions over the phase equilibrium analysis.

Advanced modeling of diffusion and convection in multiphase compositional simulation for tight porous media

Small pore sizes influence the mass transport in gas enhanced oil recovery (EOR) in tight formations through complex phenomena such as diffusion and sorption. However, conventional simulators use relatively simple models for diffusion and sorption that do not properly represent non-ideal fluid interactions at high pressures. This paper presents a novel implementation of coupled diffusion and convection for multicomponent transport via the sorbed and bulk regions in tight porous media. Case studies highlight the important implication of convection in diffusion-dominant compositional transport in tight porous media.The simulator uses multicomponent diffusion based on the dusty-gas model (DGM), which uses the fugacity gradient as the driving force. The adsorption model used is an approximate solution based on the Multicomponent Potential Theory of Adsorption (MPTA) using the sorbed and central regions. The capillary pressure is included both in the flow equations and the flash calculations by minimizing the Helmholtz free energy using the Peng-Robinson equation of state at a fixed temperature, pore volume, and overall composition.A case study presents CO2 injection into a 1-D tight porous medium with a ternary mixture of methane, n-butane, and n-decane as the initial oil. Before CO2 injection, n-decane is most attracted to the pore wall and contained at a high concentration in the sorbed region. During CO2 injection, CO2 displaces n-decane from the pore wall, causing the counter-current transport of CO2 and n-decane.Simulation results show that the mixing of reservoir oil with CO2 in small pores results in local pressure changes, which tend to drive both diffusion and convection. In all cases, convection enhances multicomponent transport by dissipating these pressure changes. When CO2 is strongly attracted to the pore walls, a large pressure change on mixing accelerates the CO2 diffusion into the reservoir through the sorbed region and also the counter-current transport of oil components through the central region.

Well Test Analysis for a Well in Gas Storage Reservoirs With the Formation Containing High Salinity Water

Abstract The production capacity of the gas wells is seriously affected by salt deposition during the injection and production process for underground gas storage with high salt content, so it is necessary to predict the production performance through well test technology. However, the existing well test analysis methods cannot be reliably used to interpret the well test data affected by salt deposition phase change and high-speed non-Darcy flow during the injection and production process. Therefore, this paper first determines the relationship between salt deposition and temperature and pressure through flash calculation of phase equilibrium of saltwater and hydrocarbon system, then establishes a porosity and permeability model considering the effect of salt deposition, and further establishes a high-speed injection-production well test analysis model considering the effect of salt deposition in combination with Forchheimer’s percolation law. Finally, the model is solved by numerical method, and the dynamic changes of reservoir pressure and salt deposition are simulated and calculated. The results show that the higher the salinity of formation water is, the greater the risk of salt deposition in the reservoir is, and the permeability of the reservoir will significantly decrease after salt deposition occurs; the non-Darcy flow effect will aggravate the risk of salt deposition in the reservoir. The research results provide a theoretical method for the evaluation of reservoir parameters and production performance prediction of salt gas storage reservoirs.

Hybrid Multiphase Flash Calculation Algorithm Based on Simultaneous Solution of Equilibrium Ratios and Phase Fractions

A robust flash calculation algorithm can increase the possibility of correctly performing multiphase equilibrium calculations. This work develops a new hybrid multiphase flash calculation algorithm adopting both equilibrium ratios and phase fractions as iteration variables. Different from the standalone implementation of the Newton–Raphson method documented in the literature, the hybrid algorithm properly hybridizes Newton–Raphson and trust-region methods to achieve a higher computational efficiency and better robustness. We show the fast convergence behavior of the hybrid algorithm in some scenarios where the conventional Newton–Raphson method encounters convergence difficulties. Specifically, the hybrid algorithm is capable of reducing the number of iterations consumed in the flash calculations from several hundreds to only tens. We also demonstrate the good performance of the hybrid algorithm by constructing phase diagrams for several reservoir fluid mixtures.

Nanometer-Scale CO2-Shale Oil Minimum Miscibility Pressure Calculations Based on Modified PR-EOS

CO2 flooding is recognized as an efficient method for enhancing shale oil recovery, while CO2-oil MMP (minimum miscibility pressure) in the micro-nanoscale is a crucial parameter. This paper presents a method for calculating the MMPs of pure hydrocarbons (C4H10, C6H14, C8H18, and C10H22) and CO2 systems in nanopores (3 nm to 10 nm) with temperature ranging from 290.15 K to 373.15 K. Firstly, we modify the Peng-Robinson equation of state (PR-EOS) by considering the influence of confinement effect and capillary pressure in nanopores. Secondly, the flash calculation algorithm is employed to determine whether the oil and gas phases in nanopores have reached an equilibrium state according to the equality of the fugacity of the two phases. Thirdly, we calculate the interfacial tension (IFT) between the two phases using the Macleod-Sugden equation. When the extrapolated IFT is zero, we treat the corresponding pressure as the MMP of the CO2-oil system in nanopores. Simulation results indicate that the calculated MMP using this method has a relative error of about 0.62% compared to the MMP calculated using the multiple mixing cell (MMC) method, indicating high reliability for MMP prediction. Moreover, the measured MMP at the nanoscale is generally smaller than that in the bulk phase due to the influence of the confinement effect. The MMP is positively correlated with the reservoir temperature, the carbon atom number in alkanes, and the nanopore radius.

Removing the performance bottleneck of pressure–temperature flash calculations during both the online and offline stages by using physics-informed neural networks

Pressure–temperature (PT) flash calculations are a performance bottleneck of compositional-flow simulations. With the sparse grid surrogate, the computing burden of PT flash calculations is shifted from the online stage to the offline stage of the compositional-flow simulations, and a great acceleration is achieved. It is known that the data-driven neural network can also be a surrogate of PT flash calculations. However, flash calculations are carried out in the training stage, i.e., the offline stage, which means the computing burden of PT flash calculations still exists in the offline stage. With physics-informed neural networks, the two heavy-burden routines of PT flash calculations, the successive substitution technique and stability analysis, are not carried out in the offline stage, and therefore, the computing burden in the offline stage is removed. After training, the phase condition and the compositions are the output of the neural network. The numerical experiments demonstrate the correctness and the applicability of the work. To the best of our knowledge, this is the first work to remove the performance bottleneck of PT flash calculations during both the online and offline stages of compositional-flow simulations.