Compressible single phase fluid model

Overview

This model represents a compressible single-phase fluid with constant compressibility and pressure-dependent viscosity. For thermal simulations, fluid density and viscosity are temperature-dependent, governed by a constant thermal expansion coefficient and a constant temperature-viscosity coefficient, respectively. These assumptions are valid for slightly compressible fluids, such as water, and some types of oil with negligible amounts of dissolved gas.

Specifically, fluid density is computed as

$\rho(p) = \rho_0 e^{c_\rho(p - p_0)}$

for isothermal cases and,

$\rho(p,T) = \rho_0 e^{c_\rho(p - p_0)} e^{-\beta_\rho (T - T_0)}$

for thermal cases.

where $c_\rho$ is compressibility, $p_0$ is reference pressure, $\rho_0$ is the density at the reference pressure, $\beta_\rho$ is the fluid thermal expansion coefficient, $T_0$ is reference temperature.

Similarly,

$\mu(p) = \mu_0 e^{c_\mu(p - p_0)}$

for isothermal cases and,

$\mu(p,T) = \mu_0 e^{c_\mu(p - p_0)} e^{-\beta_\mu (T - T_0)}$

for thermal cases.

where $c_\mu$ is viscosibility (viscosity compressibility), $\mu_0$ is reference viscosity, $\beta_\rho$ is the fluid viscosity thermal coefficient.

Parameters

For the isothermal case, the model is represented by <CompressibleSinglePhaseFluid> node in the input.

The following attributes are supported:

XML Element: CompressibleSinglePhaseFluid

Name	Type	Default	Description
compressibility	real64	0	Fluid compressibility [Pa^-1]
defaultDensity	real64	required	Default value for density.
defaultViscosity	real64	required	Default value for viscosity.
densityModelType	geos_constitutive_ExponentApproximationType	exponential	Type of density model. Valid options: * exponential * linear * quadratic
name	groupName	required	A name is required for any non-unique nodes
referenceDensity	real64	1000	Reference fluid density
referencePressure	real64	0	Reference pressure [Pa]
referenceViscosity	real64	0.001	Reference fluid viscosity
viscosibility	real64	0	Fluid viscosity exponential coefficient
viscosityModelType	geos_constitutive_ExponentApproximationType	linear	Type of viscosity model. Valid options: * exponential * linear * quadratic

Example

<Constitutive>
  <CompressibleSinglePhaseFluid name="water"
                                referencePressure="2.125e6"
                                referenceDensity="1000"
                                compressibility="1e-19"
                                referenceViscosity="0.001"
                                viscosibility="0.0"/>
</Constitutive>

For the thermal case, the model is represented by <ThermalCompressibleSinglePhaseFluid> node in the input.

The following attributes are supported:

XML Element: ThermalCompressibleSinglePhaseFluid

Name	Type	Default	Description
compressibility	real64	0	Fluid compressibility [Pa^-1]
defaultDensity	real64	required	Default value for density.
defaultViscosity	real64	required	Default value for viscosity.
densityModelType	geos_constitutive_ExponentApproximationType	exponential	Type of density model. Valid options: * exponential * linear * quadratic
internalEnergyModelType	geos_constitutive_ExponentApproximationType	linear	Type of internal energy model. Valid options: * exponential * linear * quadratic
name	groupName	required	A name is required for any non-unique nodes
referenceDensity	real64	1000	Reference fluid density
referenceInternalEnergy	real64	0.001	Reference fluid internal energy
referencePressure	real64	0	Reference pressure [Pa]
referenceTemperature	real64	0	Reference temperature
referenceViscosity	real64	0.001	Reference fluid viscosity
specificHeatCapacity	real64	0	Fluid heat capacity. Unit: J/kg/K
temperatureViscosityCoefficient	real64	0	Fluid viscosity thermal expansion coefficient at the reference temperature. Unit: 1/K
thermalExpansionCoeff	real64	0	Fluid thermal expansion coefficient. Unit: 1/K
viscosibility	real64	0	Fluid viscosity exponential coefficient
viscosityModelType	geos_constitutive_ExponentApproximationType	linear	Type of viscosity model. Valid options: * exponential * linear * quadratic

Example

<Constitutive>
  <ThermalCompressibleSinglePhaseFluid  name="fluid"
                                        defaultDensity="1000"
                                        defaultViscosity="0.001"
                                        referencePressure="0.0"
                                        referenceTemperature="0"
                                        compressibility="5e-10"
                                        thermalExpansionCoeff="3e-4"
                                        viscosibility="0.0"
                                        viscosityExpansivity="6.21e-4"
                                        specificHeatCapacity="1"
                                        referenceInternalEnergy="0.99" />
</Constitutive>