A more complex compositional model

Compositional  

This example sets up a more complex compositional simulation with five different components. Other than that, the example is similar to the others that include wells and is therefore not commented in great detail.

using MultiComponentFlash

n2_ch4 = MolecularProperty(0.0161594, 4.58e6, 189.515, 9.9701e-05, 0.00854)
co2 = MolecularProperty(0.04401, 7.3866e6, 304.200, 9.2634e-05, 0.228)
c2_5 = MolecularProperty(0.0455725, 4.0955e6, 387.607, 2.1708e-04, 0.16733)
c6_13 = MolecularProperty(0.117740, 3.345e6, 597.497, 3.8116e-04, 0.38609)
c14_24 = MolecularProperty(0.248827, 1.768e6, 698.515, 7.2141e-04, 0.80784)

bic = [0.11883 0.00070981 0.00077754 0.01 0.011;
       0.00070981 0.15 0.15 0.15 0.15;
       0.00077754 0.15 0 0 0;
       0.01 0.15 0 0 0;
       0.011 0.15 0 0 0]

mixture = MultiComponentMixture([n2_ch4, co2, c2_5, c6_13, c14_24], A_ij = bic, names = ["N2-CH4", "CO2", "C2-5", "C6-13", "C14-24"])
eos = GenericCubicEOS(mixture, PengRobinson())

using Jutul, JutulDarcy, GLMakie
Darcy, bar, kg, meter, Kelvin, day = si_units(:darcy, :bar, :kilogram, :meter, :Kelvin, :day)
nx = ny = 20
nz = 2

dims = (nx, ny, nz)
g = reservoir_mesh(dims, (1000.0, 1000.0, 1.0))
nc = number_of_cells(g)
K = repeat([0.05*Darcy], 1, nc)
res = reservoir_domain(g, porosity = 0.25, permeability = K, temperature = 387.45*Kelvin)

DataDomain wrapping UnstructuredMesh with 800 cells, 1920 faces and 960 boundary faces with 20 data fields added:
  800 Cells
    :permeability => 1×800 Matrix{Float64}
    :porosity => 800 Vector{Float64}
    :rock_thermal_conductivity => 800 Vector{Float64}
    :fluid_thermal_conductivity => 800 Vector{Float64}
    :rock_heat_capacity => 800 Vector{Float64}
    :component_heat_capacity => 800 Vector{Float64}
    :rock_density => 800 Vector{Float64}
    :temperature => 800 Vector{Float64}
    :cell_centroids => 3×800 Matrix{Float64}
    :volumes => 800 Vector{Float64}
  1920 Faces
    :neighbors => 2×1920 Matrix{Int64}
    :areas => 1920 Vector{Float64}
    :normals => 3×1920 Matrix{Float64}
    :face_centroids => 3×1920 Matrix{Float64}
  3840 HalfFaces
    :half_face_cells => 3840 Vector{Int64}
    :half_face_faces => 3840 Vector{Int64}
  960 BoundaryFaces
    :boundary_areas => 960 Vector{Float64}
    :boundary_centroids => 3×960 Matrix{Float64}
    :boundary_normals => 3×960 Matrix{Float64}
    :boundary_neighbors => 960 Vector{Int64}

Set up a vertical well in the first corner, perforated in all layers

prod = setup_vertical_well(g, K, nx, ny, name = :Producer)

DataDomain wrapping SimpleWell [Producer] (1 nodes, 0 segments, 2 perforations) with 20 data fields added:
  2 Perforations
    :Kh => 2 Vector{Float64}
    :skin => 2 Vector{Float64}
    :perforation_radius => 2 Vector{Float64}
    :well_index => 2 Vector{Float64}
    :perforation_centroids => 3×2 Matrix{Float64}
    :drainage_radius => 2 Vector{Float64}
    :perforation_direction => 2 Vector{Symbol}
    :cell_dims => 2 Vector{Tuple{Float64, Float64, Float64}}
    :thermal_well_index => 2 Vector{Float64}
    :net_to_gross => 2 Vector{Float64}
    :permeability => 1×2 Matrix{Float64}
  1 Cells
    :cell_length => 1 Vector{Float64}
    :radius => 1 Vector{Float64}
    :radius_inner => 1 Vector{Float64}
    :cell_centroids => 3×1 Matrix{Float64}
    :volume_multiplier => 1 Vector{Float64}
    :casing_thickness => 1 Vector{Float64}
    :grouting_thickness => 1 Vector{Float64}
    :casing_thermal_conductivity => 1 Vector{Float64}
    :grouting_thermal_conductivity => 1 Vector{Float64}

Set up an injector in the opposite corner, perforated in all layers

inj = setup_vertical_well(g, K, 1, 1, name = :Injector)

rhoLS = 1000.0*kg/meter^3
rhoVS = 100.0*kg/meter^3

rhoS = [rhoLS, rhoVS]
L, V = LiquidPhase(), VaporPhase()

(LiquidPhase(), VaporPhase())

Define system and realize on grid

sys = MultiPhaseCompositionalSystemLV(eos, (L, V))
model = setup_reservoir_model(res, sys, wells = [inj, prod], block_backend = true);
kr = BrooksCoreyRelativePermeabilities(sys, 2.0, 0.0, 1.0)
model = replace_variables!(model, RelativePermeabilities = kr)

push!(model[:Reservoir].output_variables, :Saturations)

state0 = setup_reservoir_state(model, Pressure = 225*bar, OverallMoleFractions = [0.463, 0.01640, 0.20520, 0.19108, 0.12432]);

dt = repeat([2.0]*day, 365)
rate_target = TotalRateTarget(0.0015)
I_ctrl = InjectorControl(rate_target, [0, 1, 0, 0, 0], density = rhoVS)
bhp_target = BottomHolePressureTarget(100*bar)
P_ctrl = ProducerControl(bhp_target)

controls = Dict()
controls[:Injector] = I_ctrl
controls[:Producer] = P_ctrl
forces = setup_reservoir_forces(model, control = controls)
ws, states = simulate_reservoir(state0, model, dt, forces = forces);

Jutul: Simulating 1 year, 52.11 weeks as 365 report steps
╭────────────────┬───────────┬───────────────┬──────────╮
│ Iteration type │  Avg/step │  Avg/ministep │    Total │
│                │ 365 steps │ 367 ministeps │ (wasted) │
├────────────────┼───────────┼───────────────┼──────────┤
│ Newton         │   2.07945 │       2.06812 │  759 (0) │
│ Linearization  │   3.08493 │       3.06812 │ 1126 (0) │
│ Linear solver  │   4.10137 │       4.07902 │ 1497 (0) │
│ Precond apply  │   8.20274 │       8.15804 │ 2994 (0) │
╰────────────────┴───────────┴───────────────┴──────────╯
╭───────────────┬─────────┬────────────┬─────────╮
│ Timing type   │    Each │   Relative │   Total │
│               │      ms │ Percentage │       s │
├───────────────┼─────────┼────────────┼─────────┤
│ Properties    │ 35.1871 │    55.25 % │ 26.7070 │
│ Equations     │  4.0382 │     9.41 % │  4.5470 │
│ Assembly      │  3.3049 │     7.70 % │  3.7213 │
│ Linear solve  │  1.7529 │     2.75 % │  1.3304 │
│ Linear setup  │  4.7165 │     7.41 % │  3.5798 │
│ Precond apply │  0.3530 │     2.19 % │  1.0570 │
│ Update        │  1.6602 │     2.61 % │  1.2601 │
│ Convergence   │  2.6571 │     6.19 % │  2.9919 │
│ Input/Output  │  0.4653 │     0.35 % │  0.1708 │
│ Other         │  3.9121 │     6.14 % │  2.9693 │
├───────────────┼─────────┼────────────┼─────────┤
│ Total         │ 63.6820 │   100.00 % │ 48.3346 │
╰───────────────┴─────────┴────────────┴─────────╯

Once the simulation is done, we can plot the states

CO2 mole fraction

sg = states[end][:OverallMoleFractions][2, :]
fig, ax, p = plot_cell_data(g, sg)
fig

Gas saturation

sg = states[end][:Saturations][2, :]
fig, ax, p = plot_cell_data(g, sg)
fig

Pressure

p = states[end][:Pressure]
fig, ax, p = plot_cell_data(g, p)
fig

Example on GitHub

If you would like to run this example yourself, it can be downloaded from the JutulDarcy.jl GitHub repository as a script

This example took 99.957638305 seconds to complete.

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