Nomenclature

Table 1: List of variables and parameters used in documentation

SymbolUnitsPhysical description
kg.kgMass of absorbed species per mass of rock grain material
symbolicChemical species in phase
m.Lspecific reactive surface area for mineral
mLongitudional dispersivity of phase
mTransverse dispersivity of phase
dimensionlessBiot coefficient
KVolumetric coefficient of thermal expansion of the fluid
KVolumetric coefficient of thermal expansion of the drained porous skeleton (ie, the porous rock without fluid, or which a fluid that is free to move in and out of the rock)
m.sExternal force density acting on the porous solid. This could be gravitational acceleration, or a load-density from a platten
dimensionlessIndex representing phase. For example, might parameterise liquid (), gas () and NAPL ()
J.kg.KSpecific heat capacity of rock grains
PaDrained compliance tensor of the porous solid (ie, inverse of )
moles per litreconcentration of species
J.kg.KFluid specific heat capacity at constant volume
J.kg.KFluid specific heat capacity at constant pressure
kg.kgMass fraction of component present in phase
m.sFluid dispersion tensor for species in phase
m.sLongitudional dispersion coefficient for species in phase
m.sTransverse dispersion coefficient for species in phase
m.sMolecular diffusion coefficient for component in phase
dimenionlessKronecker delta, unity if , else zero
J.mEnergy density of the rock-fluid system
J.kgInternal energy of fluid phase
dimensionlessStrain tensor of the porous solid ()
dimensionlessElastic strain tensor of the porous solid. The total strain
dimensionlessPlastic strain tensor of the porous solid. The total strain
dimensionlessexponent in rate expression
PaDrained elasticity tensor of the porous skeleton (ie, this enters the stress-strain relation when fluid is allowed to freely drain from the skeleton, or when the skeleton is dry)
dimensionlessPorosity of the solid
dimensionlessVolume fraction of mineral in solid
kg.s.mFluid flux. This is a sum of the advective (Darcy) flux, and a diffusive-and-dispersive flux
J.s.mHeat flux. This is a sum of heat conduction through the rock-fluid system, and convection with the fluid
m.sAcceleration due to gravity. It is a vector pointing downwards (eg )
dimensionlessActivity coefficient of species in phase
J.kgSpecific enthalpy of fluid phase
PaHenry coefficient for species which describes the solubility of the species in the aqueous phase
mol.L.sMineral reaction rate
kg.m.sChemical precipitation and dissolution rate
dimensionlessIndex representing species. For example, might parameterise water (), air (), and H (). It parameterises things that cannot be decomposed into other species, but can change phase. For instance, sometimes it might be appropriate to consider air as a single species, while at other times it might be appropriate to consider it to be a mixture of nitrogen and oxygen ( and , say)
mPermeability tensor of rock
dimensionlessRelative permeability of phase . This is a nonlinear function of the independent variables. Often it is just a function of the phase's saturation, but with Klinkenberg effects it will be a function of the gas pressure too. In the single-phase, fully-saturated case it is unity
PaBulk modulus of the drained porous skeleton. In the anisotropic situation
depends on reactionequilibrium constant for secondary species in phase
PaBulk modulus of the fluid
mol.m.sMineral rate constant
sRadioactive decay rate of a fluid species
J.s.m.KThermal conductivity of the rock-fluid system (J.s.m.K kg.m.s.K). It is a tensorial quantity to allow modelling of anisotropic situations, and is a function of the rock and fluid-phase's thermal conductivities
J.s.m.KThermal conductivity of the rock-fluid system when aqueous phase saturation is zero
J.s.m.KThermal conductivity of the rock-fluid system when aqueous phase saturation is unity
kg.mMass density
Pa.sDynamic viscosity measured in Pa.s or kg.m.s. This is a nonlinear function of the independent variables
dimensionlessFraction of plastic-deformation energy that becomes heat energy. Probably is correct
dimensionlessStoichiometric coefficient of basis species in equilibrium reaction for secondary species
mSpatial differential operator
dimensionlessmineral saturation ratio
PaFluid porepressure
PaMeasure of porepressure used in the effective stress. Often this is chosen to be
PaLangmuir pressure
moles per litreTotal concentration of basis species in phase
kg.m.sFluid source
mol.L.sSource of chemical species
J.m.sHeat source
kg.mFluid density
kg.mGrain density of the rock (so that is the density of the dry porous rock)
kg.mThe mass-density of the fluid-filled porous solid
kg.mLangmuir density
dimensionlessSaturation
dimensionlessSaturation of aqueous phase
PaTotal stress. An externally applied mechanical force will create a nonzero , and conversely, resolving into forces yields the forces on nodes in the finite-element mesh
PaEffective stress
sTime
KTemperature
dimensionlessThe phase tortuosity, which includes a porous-medium dependent factor and a coefficient
sLangmuir desorption time constant
dimensionlessExponent in rate expression
m.sDeformation vector of the porous solid
m.sDarcy velocity (volume flux)
m.sVelocity of the solid = , where is the solid mechanical displacement vector of the porous solid
L.molmolar volume