Utilities

This section describes various utilities that do not fit in other sections.

CO2 and brine correlations

These functions are not exported, but can be found inside the CO2Properties submodule. The functions described here are a Julia port of the MRST module described in [6] They can be accessed by explicit import:

julia

import JutulDarcy.CO2Properties: name_of_function

JutulDarcy.CO2Properties.compute_co2_brine_props Function

julia

props = compute_co2_brine_props(p_pascal, T_K, salt_mole_fractions = Float64[], salt_names = String[];
    check=true,
    iterate=false,
    maxits=15,
    ionized=false
)
props = compute_co2_brine_props(200e5, 273.15 + 30.0)

Get pure phase properties (density, viscosity) and equilibrium constants for brine and water. This functions and the functions used in this function are heavily based on comparable code in the the co2lab-mit MRST module developed by Lluis Salo.

The salt mole fractions are of the total brine (i.e. including H2O in the calculation) and can any subset of the following names provided:

("NaCl", "KCl", "CaSO4", "CaCl2", "MgSO4", "MgCl2")

JutulDarcy.CO2Properties.pvt_brine_RoweChou1970 Function

julia

[rho_brine, c_brine] = pvt_brine_RoweChou1970(T, P, S)

Calculate brine density and/or compressibility using Rowe and Chou"s (1970) correlation.

Parameter range for correlation:

P <= 35 MPa 293.15 <= T <= 423.15 K

Arguments:

T: Scalar with temperature value in Kelvin
P: Scalar with pressure value in bar
S: Salt mass fraction

Outputs

rho_brine: Scalar with density value in kg/m3
c_brine: Scalar with compressibility value in 1/kPa

JutulDarcy.CO2Properties.activity_co2_DS2003 Function

julia

gamma_co2 = activity_co2_DS2003(T, P, m_io)

Calculate a CO2 pseudo activity coefficient based on a virial expansion of excess Gibbs energy.

Arguments

T: Scalar with temperature value in Kelvin
P: Scalar with pressure value in bar
m_io: Vector where each entry corresponds to the molality of a particular ion in the initial brine solution. The order is as follows: [ Na(+), K(+), Ca(2+), Mg(2+), Cl(-), SO4(2-)]

Outputs

V_m: Scalar with molar volume in [cm^3/mol]
rhox: Scalar with density in [mol/m^3]
rho: Scalar with density in [kg/m^3]

JutulDarcy.CO2Properties.viscosity_brine_co2_mixture_IC2012 Function

julia

mu_b_co2 = viscosity_brine_co2_mixture_IC2012(T, P, m_nacl, w_co2)

Calculate the dynamic viscosity of a solution of H2O + NaCl (brine) with dissolved CO2.

Parameter range for correlation:

For pure water + CO2, the model is based on experimental data by Kumagai et al. (1998), which is for p up to 400 bar and T up to 50 C, and Bando et al. (2004), which is valid in 30-60C and 10-20MPa. The model of Mao & Duan (2009) for brine viscosity reaches 623K, 1000 bar and high ionic strength. However, the model used to determine the viscosity when co2 dissolves in the brine (Islam & Carlson, 2012) is based on experimental data by Bando et al. (2004) and Fleury and Deschamps (2008), who provided experimental data up to P = 200 bar, T extrapolated to 100 C, and maximum salinity of 2.7M.

Arguments

T: Scalar with temperature value in Kelvin
P: Scalar with pressure value in bar
m_nacl: Salt molality (NaCl) in mol/kg solvent
w_co2: Mass fraction of CO2 in the aqueous solution (i.e. brine)

Outputs

mu_b_co2: Scalar with dynamic viscosity in Pa*s

JutulDarcy.CO2Properties.pvt_brine_BatzleWang1992 Function

julia

rho_b = pvt_brine_BatzleWang1992(T, P, w_nacl)

Calculate the brine (H2O + NaCl) density based on Batzle & Wang (1992). These authors used the data of Rowe and Chou (1970), Zarembo & Fedorov (1975) and Potter & Brown (1977) to expand the P, T validity range.

Parameter range for correlation:

P valid from 5 to 100 MPa, T from 20 to 350 C (Adams & Bachu, 2002)

Arguments

T: Temperature value in Kelvin
P: Pressure value in bar
w_nacl: Salt (NaCl) mass fraction

Outputs

rho_b: Scalar with brine density in kg/m3

JutulDarcy.CO2Properties.viscosity_co2_Fenghour1998 Function

julia

mu = viscosity_co2_Fenghour1998(T, rho)

Calculate CO2 viscosity from Vesovic et al., J Phys Chem Ref Data (1990) and Fenghour et al., J Phys Chem Ref Data (1998), as described in Hassanzadeh et al., IJGGC (2008).

Arguments:

T: Scalar of temperature value in Kelvin
rho: Scalar of density value in kg/m^3

Outputs

mu: Dynamic viscosity in Pa*s

JutulDarcy.CO2Properties.pvt_co2_RedlichKwong1949 Function

julia

[V_m, rhox, rho] = pvt_co2_RedlichKwong1949(T, P)
[V_m, rhox, rho] = pvt_co2_RedlichKwong1949(T, P, a_m, b_m)

Calculate CO2 molar volume and density using Redlich and Kwong (1949) EoS (= RK EoS).

Parameter range for correlation:

Tested by Spycher et al. (2003) with constant intermolecular attraction parameters to yield accurate results in the T range ~10 to ~100C and P range up to 600 bar, for (1) CO2 compressibility factor, (2) CO2 fugacity coefficient and (3) mutual solubilities of H2O and CO2 in the gas and aqueous phase (respectively).

Arguments

T: Scalar with temperature value in Kelvin
P: Scalar with pressure value in bar

Optional arguments:

a_m: Intermolecular attraction constant (of the mixture) in bar_cm^6_K^0.5/mol^2
b_m: Intermolecular repulsion constant (of the mixture) in cm^3/mol

Outputs

V_m: Scalar with molar volume in [cm^3/mol]
rhox: Scalar with density in [mol/m^3]
rho: Scalar with density in [kg/m^3]

JutulDarcy.CO2Properties.viscosity_gas_mixture_Davidson1993 Function

julia

viscMixture = viscosity_gas_mixture_Davidson1993(x, M, mu)

Calculate the viscosity of a gas mixture following Davidson (1993). In principle, valid for any range within which the individual components' viscosities are valid.

Arguments:

x: Mole fraction of each component
M: Molar mass of each component
mu: Viscosity of each component in user chosen units

Each input should be a Float64 Vector of length n where n is the total number of components

Outputs

viscMixture: Scalar viscosity of the mixture in same units as mu

Relative permeability functions

JutulDarcy.brooks_corey_relperm Function

julia

brooks_corey_relperm(s; n = 2.0, residual = 0.0, kr_max = 1.0, residual_total = residual)

Evaluate Brooks-Corey relative permeability function at saturation s for exponent n and a given residual and maximum relative permeability value. If considering a two-phase system, the total residual value over both phases should also be passed if the other phase has a non-zero residual value.

CO2 inventory

JutulDarcy.co2_inventory Function

julia

inventory = co2_inventory(model, ws, states, t; cells = missing, co2_name = "CO2")
inventory = co2_inventory(model, result::ReservoirSimResult; cells = missing)

Compute CO2 inventory for each step for a given model, well results ws and reporting times t. If provided, the keyword argument cells will compute inventory inside the region defined by the cells, and let any additional CO2 be categorized as "outside region".

The inventory will be a Vector of Dicts where each entry contains a breakdown of the status of the CO2 at that time, including residual and dissolution trapping.

JutulDarcy.plot_co2_inventory Function

julia

fig = JutulDarcy.plot_co2_inventory(t, inventory, plot_type = :stack)

Plots the CO2 inventory over time or steps, with options for stacked or line plots. inventory is the output from co2_inventory while t can either be omitted, be a list of reporting time in seconds or a index list of steps where the solution is given.

Arguments

t: A vector representing time or steps. If t is of type Float64, it is assumed to represent time in seconds and will be converted to years.
inventory: A vector of dictionaries, where each dictionary contains CO2 mass data for different categories (e.g., :dissolved, :mobile, :residual, etc.).
plot_type: (Optional) A symbol specifying the type of plot. Can be :stack for stacked plots or :lines for line plots. Default is :stack.

Notes

This function is only available if Makie is loaded (through for example GLMakie or CairoMakie)

API utilities

JutulDarcy.reservoir_model Function

julia

reservoir_model(model)

Get the reservoir model from a MultiModel or return the model itself if it is not a MultiModel.

Missing docstring.

Missing docstring for JutulDarcy.reservoir_storage. Check Documenter's build log for details.

JutulDarcy.well_symbols Function

julia

well_symbols(model::MultiModel)

Get the keys of a MultiModel models that correspond to well models.

Adjoints and gradients

JutulDarcy.reservoir_sensitivities Function

julia

result, sens = reservoir_sensitivities(case::JutulCase, objective::Function; sim_arg = NamedTuple(), kwarg...)

Simulate a case and calculate parameter sensitivities with respect to an objective function on the form:

obj(model, state, dt_n, n, forces_for_step_n)

The objective is summed up for all steps.

julia

reservoir_sensitivities(case::JutulCase, rsr::ReservoirSimResult, objective::Function; kwarg...)

Calculate parameter sensitivities with respect to an objective function on the form for a case and a simulation result from that case. The objective function is on the form:

obj(model, state, dt_n, n, forces_for_step_n)

The objective is summed up for all steps.

julia

reservoir_sensitivities(case, rsr, objective; kwarg...)

JutulDarcy.well_mismatch Function

julia

well_mismatch(qoi, wells, model_f, states_f, model_c, state_c, dt, step_no, forces; <keyword arguments>)

Compute well mismatch for a set of qoi's (well targets) and a set of well symbols.