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handbook: finalize fluid frameworks chapter
(at least for Dumux 2.1)
This commit is contained in:
Andreas Lauser
Andreas Lauser
parent
d3f2bdb3e6
commit
5efb7f0256
@ -43,17 +43,20 @@
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\usepackage{rotating}
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\usepackage{subfig}
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\ifpdf
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\usepackage{auto-pst-pdf}
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\fi
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\usepackage{pstricks}
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\usepackage[normalem]{ulem}
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\usepackage{tabularx}
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\usepackage{graphics}
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\usepackage{pstricks}
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\newcommand{\snakeline}{%
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% {\uwave{\makebox[\linewidth]{\mbox{}}}}
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\uwave{\mbox{}}
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}
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\usepackage{layout}
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%\usepackage{ngerman}
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\usepackage[english]{babel}
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@ -37,23 +37,24 @@ The \Dumux fluid framework currently features the following concepts
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parameters depending on the quantities which changed since the last
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update.
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\item[Constraint solver:] Constraint solvers are auxiliary tools to
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make sure that a fluid state adheres to some thermodynamic
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make sure that a fluid state is consistent with some thermodynamic
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constraints. All constraint solvers specify a well defined set of
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input variables make sure that the resulting fluid state is
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input variables and make sure that the resulting fluid state is
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consistent with a given set of thermodynamic equations. See section
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\ref{sec:constraint_solvers} for a detailed description of the
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constraint solvers which are currently available in \Dumux.
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\item[Equation of state:] Equations of state (EOS) are auxiliary
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classes which provide relations between a fluid phase's temperature,
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pressure and density. Since these classes are only used internally
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in fluid systems, their programming intereface is currently ad-hoc.
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pressure, composition and density. Since these classes are only used
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internally in fluid systems, their programming interface is
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currently ad-hoc.
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\item[Component:] Components are fluid systems which provide the
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thermodynamic relations for the liquid and gas phase of a single
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chemical species or a fixed mixture of species. Their main purpose
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is to provide a convenient way to access these quantities from
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full-fledged fluid systems. Components are not supposed to be used
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by models directly.
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\item[Binary coefficient:] Binary coefficients express the relations
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\item[Binary coefficient:] Binary coefficients describe the relations
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of a mixture of two components. Typical binary coefficients are
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\textsc{Henry} coefficients or binary molecular diffusion
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coefficients. So far, the programming interface for accessing binary
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@ -63,91 +64,94 @@ The \Dumux fluid framework currently features the following concepts
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\section{Fluid States}
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Fluid state objects express the complete thermodynamic state of a
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system at a given spatial and temporal position. {\bf All} fluid
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states {\bf must} export the following constants:
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system at a given spatial and temporal position.
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\subsection{Exported Constants}
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{\bf All} fluid states {\bf must} export the following constants:
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\begin{description}
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\item[numPhases:] The number of fluid phases considered.
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\item[numComponents:] The number of considered chemical
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species or pseudo-species.
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\end{description}
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\subsection{Accessible Thermodynamic Quantities}
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Also, {\bf all} fluid states {\bf must} provide the following methods:
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\begin{description}
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\item[temperature():] The absolute temperature $T_\alpha$ of
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a fluid phase $\alpha$.
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\item[pressure():] The absolute pressure $p_\alpha$ of a
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fluid phase $\alpha$.
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\item[saturation():] The saturation $S_\alpha$ of a fluid
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phase $\alpha$. The saturation is defined as the pore space occupied by the
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fluid divided by the total pore space:
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\item[saturation():] The saturation $S_\alpha$ of a fluid phase
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$\alpha$. The saturation is defined as the pore space occupied by
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the fluid divided by the total pore space:
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\[
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\saturation_\alpha := \frac{\porosity \mathcal{V}_\alpha}{\porosity \mathcal{V}}
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\]
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\item[moleFraction():] Returns the molar fraction
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$x^\kappa_\alpha$ of a component $\kappa$ in a fluid phase
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$\alpha$. The molar fraction $x^\kappa_\alpha$ is defined as the number
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of molecules of a component in a mixture divided by the total number
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of molecules in the fluid.
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\item[moleFraction():] Returns the mass fraction
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$X^\kappa_\alpha$ of a component $\kappa$ in a fluid phase
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$\alpha$. The mass fraction $X^\kappa_\alpha$ is defined as the
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weight of a component in a mixture divided by the total mass of the
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fluid. It is related with the component's mole fraction by means of
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the relation
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\item[moleFraction():] Returns the molar fraction $x^\kappa_\alpha$ of
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the component $\kappa$ in fluid phase $\alpha$. The molar fraction
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$x^\kappa_\alpha$ is defined as the ratio of the number of molecules
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of component $\kappa$ and the total number of molecules of the phase
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$\alpha$.
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\item[moleFraction():] Returns the mass fraction $X^\kappa_\alpha$ of
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component $\kappa$ in fluid phase $\alpha$. The mass fraction
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$X^\kappa_\alpha$ is defined as the weight of all molecules of a
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component divided by the total mass of the fluid phase. It is
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related with the component's mole fraction by means of the relation
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\[
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X^\kappa_\alpha = x^\kappa_\alpha \frac{M^\kappa}{\overline M_\alpha}\;,
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\]
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where $M^\kappa$ is the molar mass of component $\kappa$ and
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$\overline M_\alpha$ is the mean molar mass of a molecule of phase
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$\alpha$.
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\item[averageMolarMass():] Returns $\overline M_\alpha$, the
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mean molar mass of a molecule of phase $\alpha$. For a mixture of $N
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> 0$ components, $\overline M_\alpha$ is defined as
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\item[averageMolarMass():] Returns $\overline M_\alpha$, the mean
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molar mass of a molecule of phase $\alpha$. For a mixture of $N > 0$
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components, $\overline M_\alpha$ is defined as
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\[
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\overline M_\alpha = \sum_{\kappa=1}^{N} x^\kappa_\alpha M^\kappa
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\]
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\item[density():] Returns the density $\rho_\alpha$ of a
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fluid phase $\alpha$.
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\item[molarDensity():] Returns the molar density
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$\rho_{mol,\alpha}$ of a fluid phase $\alpha$. The molar density can
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be defined using the mass density $\rho_\alpha$ and the mean molar mass $\overline M_\alpha$ by
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\item[density():] Returns the density $\rho_\alpha$ of the fluid phase
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$\alpha$.
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\item[molarDensity():] Returns the molar density $\rho_{mol,\alpha}$
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of a fluid phase $\alpha$. The molar density is defined by the mass
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density $\rho_\alpha$ and the mean molar mass $\overline M_\alpha$:
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\[
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\rho_{mol,\alpha} = \frac{\rho_\alpha}{\overline M_\alpha} \;.
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\]
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\item[molarVolume():] Returns the molar volume
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$V_{mol,\alpha}$ of a fluid phase $\alpha$. This quantity is just
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the inverse of the molar density.
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\item[molarity():] Returns the molar concentration
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$c^\kappa_\alpha$ of component $\kappa$ in fluid
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phase $\alpha$.
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\item[fugacity():] Returns the fugacity $f^\kappa_\alpha$ of
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component $\kappa$ in fluid phase $\alpha$. The fugacity is defined
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as
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\item[molarVolume():] Returns the molar volume $v_{mol,\alpha}$ of a
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fluid phase $\alpha$. This quantity is the inverse of the molar
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density.
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\item[molarity():] Returns the molar concentration $c^\kappa_\alpha$
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of component $\kappa$ in fluid phase $\alpha$.
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\item[fugacity():] Returns the fugacity $f^\kappa_\alpha$ of component
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$\kappa$ in fluid phase $\alpha$. The fugacity is defined as
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\[
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f_\alpha^\kappa := \Phi^\kappa_\alpha x^\kappa_\alpha p_\alpha \;,
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\]
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where $\Phi^\kappa_\alpha$ is the {\em fugacity
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coefficient}~\cite{reid1987}. The physical meaning of
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fugacity becomes clear from the equation
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coefficient}~\cite{reid1987}. The physical meaning of fugacity
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becomes clear from the equation
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\[
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f_\alpha^\kappa = p_\alpha \exp\left\{\frac{\zeta^\kappa_\alpha}{R T_\alpha} \right\} \;,
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\]
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where $\zeta^\kappa_\alpha$ represents the $\kappa$'s chemical
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potential in phase $\alpha$, $R$ stands for the
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ideal gas constant, and $T_\alpha$ for the absolute
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temperature phase $\alpha$. Assuming thermal equilibrium, there is a
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one-to-one mapping between a component's chemical potential
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potential in phase $\alpha$, $R$ stands for the ideal gas constant,
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and $T_\alpha$ for the absolute temperature of phase
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$\alpha$. Assuming thermal equilibrium, there is a one-to-one
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mapping between a component's chemical potential
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$\zeta^\kappa_\alpha$ and its fugacity $f^\kappa_\alpha$. In this
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case chemical equilibrium can thus be expressed by
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\[
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f^\kappa = f^\kappa_\alpha = f^\kappa_\beta \forall \alpha, \beta
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f^\kappa := f^\kappa_\alpha = f^\kappa_\beta\quad\forall \alpha, \beta
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\]
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\item[fugacityCoefficient():] Returns the fugacity coefficient $\Phi^\kappa_\alpha$ of
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component $\kappa$ in fluid phase $\alpha$.
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\item[enthalpy():] Returns specific enthalpy $h_\alpha$ of a
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fluid phase $\alpha$.
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\item[internalEnergy():] Returns specific internal energy $u_\alpha$ of a
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fluid phase $\alpha$. The specific internal energy is defined by the relation
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\item[fugacityCoefficient():] Returns the fugacity coefficient
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$\Phi^\kappa_\alpha$ of component $\kappa$ in fluid phase $\alpha$.
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\item[enthalpy():] Returns specific enthalpy $h_\alpha$ of a fluid
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phase $\alpha$.
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\item[internalEnergy():] Returns specific internal energy $u_\alpha$
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of a fluid phase $\alpha$. The specific internal energy is defined
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by the relation
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\[
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u_\alpha = h_\alpha - \frac{p_\alpha}{\rho_\alpha}
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\]
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@ -155,36 +159,35 @@ Also, {\bf all} fluid states {\bf must} provide the following methods:
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$\mu_\alpha$ of fluid phase $\alpha$.
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\end{description}
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Currently, the following fluid states are available in \Dumux:
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\subsection{Available Fluid States}
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Currently, the following fluid states are provided by \Dumux:
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\begin{description}
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\item[NonEquilibriumFluidState:] This is the most general
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fluid state supplied. It does not assume thermodynamic equilibrium
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and this stores all phase compositions (using mole fractions) and
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fugacity coefficients, as well as all phase temperatures, pressures,
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saturations and enthalpies.
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\item[CompositionalFluidState:] The
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\texttt{Non\-Equilibrium\-Fluid\-State} with the difference
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\texttt{Compositional\-Fluid\-State} is similar to the difference that
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is assumes thermodynamic equilibrium. In the context of multi-phase
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flow in porous media, this means that only a single temperature
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needs to be stored.
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\item[ImmisicibleFluidState:] This fluid state assumes that
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the fluid phases are immiscible, which implies that the phase
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compositions and the fugacity coefficients do not need to be stored
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explicitly.
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\item[PressureOverlayFluidState:] This is a so-called {\em
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overlay} fluid state. It allows to set the pressure of all fluid
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phases but forwards everything else to an other fluid state.
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\item[SaturationOverlayFluidState:] This fluid state is like
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the \texttt{PressureOverlayFluidState}, except that the phase
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\item[NonEquilibriumFluidState:] This is the most general fluid state
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supplied. It does not assume thermodynamic equilibrium and thus
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stores all phase compositions (using mole fractions), fugacity
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coefficients, phase temperatures, phase pressures, saturations and
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specific enthalpies.
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\item[CompositionalFluidState:] This fluid state is very similar to
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the \texttt{Non\-Equilibrium\-Fluid\-State} with the difference that
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the \texttt{Compositional\-Fluid\-State} assumes thermodynamic
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equilibrium. In the context of multi-phase flow in porous media,
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this means that only a single temperature needs to be stored.
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\item[ImmisicibleFluidState:] This fluid state assumes that the fluid
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phases are immiscible, which implies that the phase compositions and
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the fugacity coefficients do not need to be stored explicitly.
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\item[PressureOverlayFluidState:] This is a so-called {\em overlay}
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fluid state. It allows to set the pressure of all fluid phases but
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forwards everything else to another fluid state.
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\item[SaturationOverlayFluidState:] This fluid state is like the
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\texttt{PressureOverlayFluidState}, except that the phase
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saturations are settable instead of the phase pressures.
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\item[TempeatureOverlayFluidState:] This fluid state is like
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the \texttt{PressureOverlayFluidState}, except that the temperature
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is settable instead of the phase pressures. Note that this overlay
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\item[TempeatureOverlayFluidState:] This fluid state is like the
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\texttt{PressureOverlayFluidState}, except that the temperature is
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settable instead of the phase pressures. Note that this overlay
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state assumes thermal equilibrium regardless of underlying fluid
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state.
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\item[CompositionOverlayFluidState:] This fluid state is like
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the \texttt{PressureOverlayFluidState}, except that the phase
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\item[CompositionOverlayFluidState:] This fluid state is like the
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\texttt{PressureOverlayFluidState}, except that the phase
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composition is settable (in terms of mole fractions) instead of the
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phase pressures.
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\end{description}
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@ -197,41 +200,38 @@ quantities of a fluid state.
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\subsection{Parameter Caches}
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All fluid systems must export a type for their \texttt{ParameterCache}
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objects which caches parameters which are expensive to compute and are
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required in multiple thermodynamic relations. For fluid systems which
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do not require to cache parameters, \Dumux provides a
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\texttt{NullParameterCache} class.
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objects. Parameter caches can be used to cache parameter that are
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expensive to compute and are required in multiple thermodynamic
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relations. For fluid systems which do need to cache parameters,
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\Dumux provides a \texttt{NullParameterCache} class.
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The parameters stored by parameter cache objects are specific to the
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fluid system and no assumptions on what they provide can be made
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outside of their fluid system. Parameter cache objects provide a
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The actual quantities stored by parameter cache objects are specific
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to the fluid system and no assumptions on what they provide should be
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made outside of their fluid system. Parameter cache objects provide a
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well-defined set of methods to make them coherent with a given fluid
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state, though. Parameter cache objects must at least provide the
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following update methods
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state, though. These update are:
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\begin{description}
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\item[updateAll(fluidState, except):] Update all cached quantities in
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\item[updateAll(fluidState, except):] Update all cached quantities for
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all phases. The \texttt{except} argument contains a bit field of the
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quantities which have not changed since the last call to a
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quantities which have not been modified since the last call to a
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\texttt{update()} method.
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\item[updateAllPresures(fluidState):]
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Update all cached quantities which depend on pressure for
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all phases.
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\item[updateAllTemperatures(fluidState):]
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Update all cached quantities which depend on temperature for
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all phases.
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\item[updatePhase(fluidState, phaseIdx, except):] Update all cached
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quantities for a given phase. The quantities specified by the
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\texttt{except} bit field have not been modified since the last
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call to an \texttt{update()} method.
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\item[updateTemperature(fluidState, phaseIdx):] Update all cached
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quantities which depend on the temperature of a given phase.
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\item[updatePressure(fluidState, phaseIdx):] Update all cached
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quantities which depend on the pressure of a given phase.
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\item[updateComposition(fluidState, phaseIdx):] Update all cached
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quantities which depend on the composition of a given phase.
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\item[updateSingleMoleFraction(fluidState, phaseIdx, compIdx):]
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Update all cached quantities which depend on the value of a mole
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fraction of a given components of a given phase.
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\item[updateAllPresures(fluidState):] Update all cached quantities
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which depend on the pressure of any fluid phase.
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\item[updateAllTemperatures(fluidState):] Update all cached quantities
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which depend on temperature of any fluid phase.
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\item[updatePhase(fluidState, phaseIdx, except):] Update all cached
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quantities for a given phase. The quantities specified by the
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\texttt{except} bit field have not been modified since the last call
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to an \texttt{update()} method.
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\item[updateTemperature(fluidState, phaseIdx):] Update all cached
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quantities which depend on the temperature of a given phase.
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\item[updatePressure(fluidState, phaseIdx):] Update all cached
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quantities which depend on the pressure of a given phase.
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\item[updateComposition(fluidState, phaseIdx):] Update all cached
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quantities which depend on the composition of a given phase.
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\item[updateSingleMoleFraction(fluidState, phaseIdx, compIdx):] Update
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all cached quantities which depend on the value of the mole fraction
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of a component in a phase.
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\end{description}
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Note, that the parameter cache interface only guarantees that if a
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more specialized \texttt{update()} method is called, it is not slower
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@ -242,9 +242,9 @@ general \texttt{update()} method once than multiple calls to
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specialized \texttt{update()} methods.
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To make usage of parameter caches easier for the case where all cached
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quantities ought to be re-calculated if the respective phase was
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changed, it is possible to just define the \texttt{updatePhase()}
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method and derive a parameter cache from
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quantities ought to be re-calculated if a quantity of a phase was
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changed, it is possible to only define the \texttt{updatePhase()}
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method and derive the parameter cache from
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\texttt{Dumux::ParameterCacheBase}.
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\subsection{Exported Constants and Capabilities}
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@ -254,49 +254,54 @@ fluid systems need to export the following constants and auxiliary
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methods:
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\begin{description}
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\item[numPhases:] The number of considered fluid phases.
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\item[numComponents:] The number of considered chemical (pseudo-) species.
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\item[init():] Initialize the fluid system. This is usually
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used tabulated to tabulate some quantities
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\item[phaseName():] Given the index of a fluid phase, return a
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human-readable string as its name.
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\item[componentName():] Given the index of a component,
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return a human-readable string as its name.
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\item[isLiquid():] Return whether the phase is a liquid, given the index of a phase.
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\item[isIdealMixture():] Return whether the phase is an ideal
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mixture, given the index of a phase. In the context of the \Dumux
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fluid framework a phase $\alpha$ is an ideal mixture if, and only if
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all its fugacity coefficients $\Phi^\kappa_\alpha$ do not depend on
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the phase composition. (Although they might very well depend on
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\item[numComponents:] The number of considered chemical (pseudo-)
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species.
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\item[init():] Initialize the fluid system. This is usually used to
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tabulate some quantities
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\item[phaseName():] Given the index of a fluid phase, return its name
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as human-readable string.
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\item[componentName():] Given the index of a component, return its
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name as human-readable string.
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\item[isLiquid():] Return whether the phase is a liquid, given the
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index of a phase.
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\item[isIdealMixture():] Return whether the phase is an ideal mixture,
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given the phase index. In the context of the \Dumux fluid
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framework a phase $\alpha$ is an ideal mixture if, and only if, all
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its fugacity coefficients $\Phi^\kappa_\alpha$ do not depend on the
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phase composition. (Although they might very well depend on
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temperature and pressure.)
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\item[isIdealGas():] Return whether a phase $\alpha$ is an ideal
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gas, i.e. it adheres to the relation
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\item[isIdealGas():] Return whether a phase $\alpha$ is an ideal gas,
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i.e. it adheres to the relation
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\[
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p_\alpha V_{mol,\alpha} = R T_\alpha \;,
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p_\alpha v_{mol,\alpha} = R T_\alpha \;,
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\]
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with $R$ being the ideal gas constant.
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\item[isCompressible():] Return whether a phase $\alpha$ is
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compressible, i.e. its density depends on pressure $p_\alpha$.
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\item[molarMass():] Given a component index, return the molar
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mass of the corresponding component.
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\item[molarMass():] Given a component index, return the molar mass of
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the corresponding component.
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\end{description}
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\subsection{Thermodynamic Relations}
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Fluid systems have been explicitly designed to provide as few
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thermodynamic relations as necessary. A full-fledged fluid system thus
|
||||
thermodynamic relations as possible. A full-fledged fluid system thus
|
||||
only needs to provide the following thermodynamic relations:
|
||||
\begin{description}
|
||||
\item[density():] Given a fluid state, an up-to-date parameter
|
||||
cache and a phase index, return the mass density $\rho_\alpha$ of the phase.
|
||||
\item[fugacityCoefficient:] Given a fluid state, an up-to-date
|
||||
\item[density():] Given a fluid state, an up-to-date parameter cache
|
||||
and a phase index, return the mass density $\rho_\alpha$ of the
|
||||
phase.
|
||||
\item[fugacityCoefficient():] Given a fluid state, an up-to-date
|
||||
parameter cache as well as a phase and a component index, return the
|
||||
fugacity coefficient $\Phi^\kappa_\alpha$ of a the component for the phase.
|
||||
\item[viscosity():] Given a fluid state, an up-to-date parameter
|
||||
cache and a phase index, return the dynamic viscosity $\mu_\alpha$ of the phase.
|
||||
\item[diffusionCoefficient():] Given a fluid state, an
|
||||
up-to-date parameter cache and a phase index, return the dynamic
|
||||
viscosity of the phase, calculate the molecular diffusion
|
||||
coefficient for a component in a fluid phase
|
||||
fugacity coefficient $\Phi^\kappa_\alpha$ of a the component for the
|
||||
phase.
|
||||
\item[viscosity():] Given a fluid state, an up-to-date parameter cache
|
||||
and a phase index, return the dynamic viscosity $\mu_\alpha$ of the
|
||||
phase.
|
||||
\item[diffusionCoefficient():] Given a fluid state, an up-to-date
|
||||
parameter cache, a phase and a component index, return the calculate
|
||||
the molecular diffusion coefficient for the component in the fluid
|
||||
phase.
|
||||
|
||||
Molecular diffusion of a component $\kappa$ in phase $\alpha$ is
|
||||
caused by a gradient of the chemical potential and follows the law
|
||||
@ -304,36 +309,36 @@ only needs to provide the following thermodynamic relations:
|
||||
J^\kappa_\alpha = - D^\kappa_\alpha\ \mathbf{grad} \zeta^\kappa_\alpha\;,
|
||||
\]
|
||||
where $\zeta^\kappa_\alpha$ is the component's chemical potential,
|
||||
$D^\kappa_\alpha$ is the diffusion coefficient and $J^\kappa_\alpha$ is the
|
||||
diffusive flux. $\zeta^\kappa_\alpha$ is connected to the
|
||||
$D^\kappa_\alpha$ is the diffusion coefficient and $J^\kappa_\alpha$
|
||||
is the diffusive flux. $\zeta^\kappa_\alpha$ is connected to the
|
||||
component's fugacity $f^\kappa_\alpha$ by the relation
|
||||
\[
|
||||
\zeta^\kappa_\alpha =
|
||||
R T_\alpha \mathrm{ln} \frac{f^\kappa_\alpha}{p_\alpha} \;.
|
||||
\]
|
||||
\item[binaryDiffusionCoefficient():] Given a fluid state, an
|
||||
up-to-date parameter cache, a phase index and two
|
||||
component indices return the binary diffusion coefficient for
|
||||
components for the binary mixture. This method is less general than
|
||||
\texttt{diffusionCoefficient} method, but usually only binary
|
||||
diffusion coefficients can be found in the literature.
|
||||
\item[enthalpy():] Given a fluid state, an up-to-date parameter
|
||||
cache and a phase index, this method represents the specific
|
||||
enthalpy $h_\alpha$ of the phase.
|
||||
\item[thermalConductivity:] Given a fluid state, an
|
||||
up-to-date parameter cache and a phase index, this method expresses
|
||||
the thermal conductivity $\lambda_\alpha$ of the fluid phase. The
|
||||
thermal conductivity is defined by means of the relation
|
||||
up-to-date parameter cache, a phase index and two component indices,
|
||||
return the binary diffusion coefficient for the binary mixture. This
|
||||
method is less general than \texttt{diffusionCoefficient} method,
|
||||
but relations can only be found for binary diffusion coefficients in
|
||||
the literature.
|
||||
\item[enthalpy():] Given a fluid state, an up-to-date parameter cache
|
||||
and a phase index, this method calulates the specific enthalpy
|
||||
$h_\alpha$ of the phase.
|
||||
\item[thermalConductivity:] Given a fluid state, an up-to-date
|
||||
parameter cache and a phase index, this method returns the thermal
|
||||
conductivity $\lambda_\alpha$ of the fluid phase. The thermal
|
||||
conductivity is defined by means of the relation
|
||||
\[
|
||||
\dot Q = \lambda_\alpha \mathbf{grad} T_\alpha \;,
|
||||
\dot Q = \lambda_\alpha \mathbf{grad}\;T_\alpha \;,
|
||||
\]
|
||||
where $\dot Q$ is the heat flux caused by a temperature gradient
|
||||
$\mathbf{grad} T_\alpha$.
|
||||
\item[heatCapacity():] Given a fluid state, an up-to-date
|
||||
parameter cache and a phase index, this method represents the
|
||||
isobaric heat capacity $c_{p,\alpha}$ of the fluid phase. The
|
||||
isobaric heat capacity is defined as the partial derivative of the
|
||||
specific enthalpy $h_\alpha$ to the fluid pressure:
|
||||
where $\dot Q$ is the heat flux caused by the temperature gradient
|
||||
$\mathbf{grad}\;T_\alpha$.
|
||||
\item[heatCapacity():] Given a fluid state, an up-to-date parameter
|
||||
cache and a phase index, this method computes the isobaric heat
|
||||
capacity $c_{p,\alpha}$ of the fluid phase. The isobaric heat
|
||||
capacity is defined as the partial derivative of the specific
|
||||
enthalpy $h_\alpha$ to the fluid pressure:
|
||||
\[
|
||||
c_{p,\alpha} = \frac{\partial h_\alpha}{\partial p_\alpha}
|
||||
\]
|
||||
@ -342,58 +347,59 @@ only needs to provide the following thermodynamic relations:
|
||||
|
||||
Fluid systems may chose not to implement some of these methods and
|
||||
throw a \texttt{Dune::NotImplemented} exception instead. Obviously,
|
||||
such fluid systems cannot be used in conjunction with models that
|
||||
depend on those methods.
|
||||
such fluid systems cannot be used for models that depend on those
|
||||
methods.
|
||||
|
||||
\subsection{Available Fluid Systems}
|
||||
Currently, the following fluid states are available in \Dumux:
|
||||
|
||||
Currently, the following fluid systems are available in \Dumux:
|
||||
\begin{description}
|
||||
\item[Dumux::FluidSystems::TwoPImmiscible:] A two-phase fluid
|
||||
system featuring which assumes immiscibility of the fluid
|
||||
phases. The fluid phases are thus specified by means of their
|
||||
constituting components. This fluid system is intended to be used
|
||||
with models that assume immiscibility.
|
||||
\item[Dumux::FluidSystems::H2ON2:] A two-phase fluid system
|
||||
featuring the gas and liquid phases and distilled water ($H_2O$) and
|
||||
pure molecular Nitrogen ($N_2$) as components.
|
||||
\item[Dumux::FluidSystems::TwoPImmiscible:] A two-phase fluid system
|
||||
which assumes immiscibility of the fluid phases. The fluid phases
|
||||
are thus completely specified by means of their constituting
|
||||
components. This fluid system is intended to be used with models
|
||||
that assume immiscibility.
|
||||
\item[Dumux::FluidSystems::H2ON2:] A two-phase fluid system featuring
|
||||
gas and liquid phases and distilled water ($H_2O$) and pure
|
||||
molecular Nitrogen ($N_2$) as components.
|
||||
\item[Dumux::FluidSystems::H2OAir:] A two-phase fluid system
|
||||
featuring the gas and liquid phases and distilled water ($H_2O$) and
|
||||
featuring gas and liquid phases and distilled water ($H_2O$) and
|
||||
air (Pseudo component composed of $79\%\;N_2$, $20\%\;O_2$ and
|
||||
$1\%\;Ar$) as components.
|
||||
\item[Dumux::FluidSystems::H2OAirMesitylene:] A three-phase fluid
|
||||
system featuring the gas, NAPL and water phases and distilled water
|
||||
($H_2O$) and air and Mesitylene ($C_6H_3(CH_3)_3$) as components. This fluid
|
||||
system assumes all phases to be ideal mixtures.
|
||||
\item[Dumux::FluidSystems::H2OAirXylene:] A three-phase fluid
|
||||
system featuring the gas, NAPL and water phases and distilled water
|
||||
($H_2O$) and air and Xylene ($C_8H_{10}$) as components. This fluid
|
||||
system assumes all phases to be ideal mixtures.
|
||||
\item[Dumux::FluidSystems::Spe5:] A three-phase fluid system
|
||||
featuring the gas, oil and water as phases and the seven components
|
||||
distilled water ($H_2O$), Methane ($C_1$), Propane ($C_3$), Pentane
|
||||
($C_5$), Heptane ($C_7$), Decane ($C_{10}$), Pentadecane
|
||||
($C_{15}$) and Icosane ($C_{20}$). For the water phase the IAPWS-97
|
||||
formulation is used as equation of state, while for the gas and oil
|
||||
phases a \textsc{Peng}-\textsc{Robinson} equation of state with
|
||||
slightly modified parameters is used. This fluid system is highly
|
||||
non-linear, and the gas and oil phases can also not be considered as
|
||||
ideal mixtures\cite{SPE5}.
|
||||
system featuring gas, NAPL and water phases and distilled water, air
|
||||
and Mesitylene ($C_6H_3(CH_3)_3$) as components. This fluid system
|
||||
assumes all phases to be ideal mixtures.
|
||||
\item[Dumux::FluidSystems::H2OAirXylene:] A three-phase fluid system
|
||||
featuring gas, NAPL and water as phases and distilled water, air and
|
||||
Xylene ($C_8H_{10}$) as components. This fluid system assumes all
|
||||
phases to be ideal mixtures.
|
||||
\item[Dumux::FluidSystems::Spe5:] A three-phase fluid system featuring
|
||||
gas, oil and water as phases and the seven components distilled
|
||||
water, Methane ($C_1$), Propane ($C_3$), Pentane ($C_5$), Heptane
|
||||
($C_7$), Decane ($C_{10}$), Pentadecane ($C_{15}$) and Icosane
|
||||
($C_{20}$). For the water phase the IAPWS-97 formulation is used as
|
||||
equation of state, while for the gas and oil phases a
|
||||
\textsc{Peng}-\textsc{Robinson} equation of state with slightly
|
||||
modified parameters is used. This fluid system is highly non-linear,
|
||||
and the gas and oil phases also cannot be considered ideal
|
||||
mixtures\cite{SPE5}.
|
||||
\end{description}
|
||||
|
||||
\section{Constraint Solvers}
|
||||
\label{sec:constraint_solvers}
|
||||
|
||||
Constraint solvers connect the thermodynamic relations of expressed by
|
||||
Constraint solvers connect the thermodynamic relations expressed by
|
||||
fluid systems with the thermodynamic quantities stored by fluid
|
||||
states. Using them is not mandatory for models, but given the fact
|
||||
that some thermodynamic constraints can be quite complex to solve,
|
||||
sharing this code between models makes a lot of sense. Currently,
|
||||
\Dumux provides the following constraint solvers:
|
||||
sharing this code between models makes sense. Currently, \Dumux
|
||||
provides the following constraint solvers:
|
||||
\begin{description}
|
||||
\item[CompositionFromFugacities:] This constraint takes all
|
||||
\item[CompositionFromFugacities:] This constraint solver takes all
|
||||
component fugacities, the temperature and pressure of a phase as
|
||||
input and calculates the composition of the fluid. This means that
|
||||
the thermodynamic constraints used by this solver are
|
||||
input and calculates the composition of the fluid phase. This means
|
||||
that the thermodynamic constraints used by this solver are
|
||||
\[
|
||||
f^\kappa = \Phi^\kappa_\alpha(\{x^\beta_\alpha \}, T_\alpha, p_\alpha) p_\alpha x^\kappa_\alpha\;,
|
||||
\]
|
||||
@ -408,19 +414,19 @@ sharing this code between models makes a lot of sense. Currently,
|
||||
\end{eqnarray*}
|
||||
where $p_{c\beta\alpha}$ is the capillary pressure between the
|
||||
fluid phases $\beta$ and $\alpha$.
|
||||
\item[NcpFlash:] This is a so-called flash solver. A flash
|
||||
solver takes the total mass of all components per volume unit as
|
||||
input and calculates all phase temperatures, pressures, saturations
|
||||
and pressures. This flash solver works for an arbitrary number of
|
||||
phases $M > 0$ and components $N \geq M - 1$. In this case,
|
||||
the unknowns are the following:
|
||||
\item[NcpFlash:] This is a so-called flash solver. A flash solver
|
||||
takes the total mass of all components per volume unit and the phase
|
||||
temperatures as input and calculates all phase pressures,
|
||||
saturations and compositions. This flash solver works for an
|
||||
arbitrary number of phases $M > 0$ and components $N \geq M - 1$. In
|
||||
this case, the unknown quantities are the following:
|
||||
\begin{itemize}
|
||||
\item $M$ pressures $p_\alpha$
|
||||
\item $M$ saturations $\saturation_\alpha$
|
||||
\item $M\cdot N$ mole fractions $x^\kappa_\alpha$
|
||||
\end{itemize}
|
||||
This sums up to $M\cdot(N + 2)$. The equations side of things, can
|
||||
offer the following:
|
||||
This sums up to $M\cdot(N + 2)$. The equations side of things
|
||||
provides:
|
||||
\begin{itemize}
|
||||
\item $(M - 1)\cdot N$ equations stemming from the fact that the
|
||||
fugacity of any component is the same in all phases, i.e.
|
||||
@ -428,35 +434,36 @@ sharing this code between models makes a lot of sense. Currently,
|
||||
f^\kappa_\alpha = f^\kappa_\beta
|
||||
\]
|
||||
holds for all phases $\alpha, \beta$ and all components $\kappa$.
|
||||
\item $1$ equation originating from the closure condition of the saturations:
|
||||
\item $1$ equation comes from the fact that the whole pore space is
|
||||
filled by some fluid, i.e.
|
||||
\[
|
||||
\sum_{\alpha=1}^M \saturation_\alpha = 1
|
||||
\]
|
||||
\item $M - 1$ constraints are defined by the capillary pressures:
|
||||
\item $M - 1$ constraints are given by the capillary pressures:
|
||||
\[
|
||||
p_\beta = p_\alpha + p_{c\beta\alpha} \;,
|
||||
\]
|
||||
for all phases $\alpha$, $\beta$
|
||||
\item $N$ constraints come the fact that the total mass of each
|
||||
\item $N$ constraints come the fact that the total mass of each
|
||||
component is given:
|
||||
\[
|
||||
c^\kappa_{tot} = sum_{\alpha=1}^M \rho_{mol,\alpha} x_\alpha^\kappa = const
|
||||
c^\kappa_{tot} = \sum_{\alpha=1}^M x_\alpha^\kappa\;\rho_{mol,\alpha} = const
|
||||
\]
|
||||
\item And finally $M$ model constraints. This solver uses NCP
|
||||
constraints as proposed in~\cite{LHHW2011}:
|
||||
\item And finally $M$ model assumptions are used. This solver uses
|
||||
the NCP constraints proposed in~\cite{LHHW2011}:
|
||||
\[
|
||||
0 = \mathrm{min}\{\saturation_\alpha, 1 - \sum_{\kappa=1}^N x_\alpha^\kappa\}
|
||||
\]
|
||||
\end{itemize}
|
||||
|
||||
The number of equation also sums up to $M\cdot(N + 2)$. And the system
|
||||
of equations is closed.
|
||||
\item[ImmiscibleFlash:] This is a flash solver assuming
|
||||
immiscibility of the phases. It is similar to the \texttt{NcpFlash}
|
||||
solver but a lot simpler.
|
||||
\item[MiscibleMultiphaseComposition:] This solver calculates
|
||||
the composition of all phases provided that each of them is
|
||||
present. Currently, this solver does not support non-ideal mixtures.
|
||||
The number of equations also sums up to $M\cdot(N + 2)$. Thus, the
|
||||
system of equations is closed.
|
||||
\item[ImmiscibleFlash:] This is a flash solver assuming immiscibility
|
||||
of the phases. It is similar to the \texttt{NcpFlash} solver but a
|
||||
lot simpler.
|
||||
\item[MiscibleMultiphaseComposition:] This solver calculates the
|
||||
composition of all phases provided that each of the phases is
|
||||
potentially present. Currently, this solver does not support
|
||||
non-ideal mixtures.
|
||||
\end{description}
|
||||
|
||||
%%% Local Variables:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user