. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

/pdf/description-of-input-and-examples-for-phreeqc-version-3-a-31uu97pbtq.pdf

Description of Input and Examples for PHREEQC Version 3?A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations

Petroleum Reservoir Simulation

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "auto-diff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

/pdf/automatic-differentiation-in-machine-learning-a-survey-4s77ht2sqh.pdf

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

A consistent correction for Redlich-Kwong-Soave volumes

The development of a new two-constant equation of state in which the attractive pressure term of the semiempirical van der Waals equation has been modified is outlined. Examples of the use of the equation for predicting the vapor pressure and volumetric behavior of singie-component systems, and the phase behavior and volumetric behavior of binary, ternary, and multicomponent systems are given. The proposed equation combines simplicity and accuracy. It performs as well as or better than the Soave-Redlich-Kwong equation in all cases tested and shows its greatest advantages in the prediction of liquid phase densities.

http://dns2.asia.edu.tw/~ysho/ysho-english/2000 engineering/pdf/ind eng che fun15, 59.pdf

A New Two-Constant Equation of State

The development of the Peng - Robinson equation and its application to phase equilibrium in a system containing methanol

A recently proposed two-constant equation of state is used to predict the phase behaviour of systems exhibiting a water-rich liquid phase, a hydrocarbon-rich liquid phase and a vapor phase. The algorithm proposed is efficient and thermodynamically rigorous and it converges significantly faster than earlier models. Representative calculations are shown for the methane-n butane water system, the n butane-1 butane-water system, and a synthetic six-component hydrocarbon mixture containing waer.



On emploie une equation d'etat a deux constantes, qui a ete proposee recemment, pour prevoir le comportement des phases de systemes impliquant une phase liquide riche en eau, une phase liquide riche en hydrocarbure et une phase vapeur. L'algorithme propose est efficace et rigoreux au point de vue thermodynamique; il converge bien plus vite que ne le font des modeles anterieurs. On presente des calculs representatifs pour les deux systemes methane-butane normal-eau et butane normal-butene 1-eau, ainsi que pour un melange d'hydrocarbures dont six composants sont synthetiques et qui contient de l'eau.

Two and three phase equilibrium calculations for systems containing water

Applications of the Peng-Robinson Equation of State

Calculation of Three-Phase Solid-Liquid-Vapor Equilibrium Using an Equation of State

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