Thermodynamics-Informed Neural Network (TINN) for Phase Equilibrium Calculations Considering Capillary Pressure

Abstract

The thermodynamic properties of fluid mixtures play a crucial role in designing physically meaningful models and robust algorithms for simulating multi-component multi-phase flow in subsurface, which is needed for many subsurface applications. In this context, the equation-of-state-based flash calculation used to predict the equilibrium properties of each phase for a given fluid mixture going through phase splitting is a crucial component, and often a bottleneck, of multi-phase flow simulations. In this paper, a capillarity-wise Thermodynamics-Informed Neural Network is developed for the first time to propose a fast, accurate and robust approach calculating phase equilibrium properties for unconventional reservoirs. The trained model performs well in both phase stability tests and phase splitting calculations in a large range of reservoir conditions, which enables further multi-component multi-phase flow simulations with a strong thermodynamic basis.

Phase Equilibrium Studies in the Geothermal Energy Development: The Effect of Hydrogen Bond on the Multi-Component Fluid

“…The tangent plane distance (TPD) function 27 is an effective approach indicating the number of phases at equilibrium and has been widely applied in a number of numerical scenarios representing various engineering applications. 28 Considering the NVT flash scheme derived based on Helmholtz free energy in this paper, the following equation is used to calculate the TPD function with respect to the Helmholtz free energy surface 14) where d denotes the vector of component molar densities and D E the TPD with respect to the Helmholtz free energy density E. Generally speaking, the fluid mixture can remain stable in the single phase region if the TPD function under that condition is calculated to be zero, while phase transition may occur if TPD is negative. The TPD function of the sample mixture is calculated and shown in Figure 1, as well as the corresponding number of phases at equilibrium.…”

Intelligent Natural Gas and Hydrogen Pipeline Dispatching Using the Coupled Thermodynamics-Informed Neural Network and Compressor Boolean Neural Network

“…Phase transition is not preferred in practical pipeline dispatching, as it may cause unsafe heat production, hydrate blockage and surface corrosion [16,17]. The accelerated phase equilibrium calculations using the thermodynamics-informed neural network (TINN) have been investigated thoroughly in [18][19][20]. Thus, it is meaningful to incorporate the flash calculation network and the pipeline dispatching network in order to construct a coupled deep neural network and the related deep learning algorithm to evaluate the safety performance in the natural gas pipeline dispatching.…”

Thermodynamically‐consistent flash calculation in energy industry: From iterative schemes to a unified thermodynamics‐informed neural network

“…NPT flash schemes are well developed with a long history in petroleum engineering mainly because of the easy understanding and implementation, but solving a cubic equation is often a challenge when selecting the best root with physical meanings. Besides, the constant environmental condition of pressure had been effective for conventional reservoir development, but the rising enthusiasm for shale gas in recent years has brought new challenges to the different pressure in each phase caused by capillarity 10 . Furthermore, the current well‐developed and widely‐recognized models describing interfacial tension are explicit functions of volume, temperature, and moles so that it is more straightforward to compute the thermodynamic properties with respect to volume than pressure in order to benefit further simulation of multiphase fluid flow 11 .…”

“…Besides, the constant environmental condition of pressure had been effective for conventional reservoir development, but the rising enthusiasm for shale gas in recent years has brought new challenges to the different pressure in each phase caused by capillarity. 10 Furthermore, the current well-developed and widely-recognized models describing interfacial tension are explicit functions of volume, temperature, and moles so that it is more straightforward to compute the thermodynamic properties with respect to volume than pressure in order to benefit further simulation of multiphase fluid flow. 11 Thus, we will present a comprehensive multicomponent multiphase NVT-type flash calculation scheme.…”