A fully differentiable geothermal doublet: History matching and control optimization

Geothermal   StartToFinish   Advanced   HistoryMatching   Optimization   Differentiability  

We are going to set up a conceptual geothermal doublet model in 2D and perform gradient based history matching. This example serves two main purposes:

1. It demonstrates the conceptual workflow for setting up a geothermal model from scratch with a fairly straightforward mesh setup.

2. It shows how to set up a gradient based history matching workflow with the generic optimization interface that allows for optimizing any input parameter used in the setup of a model.

Load packages and define units

using Jutul, JutulDarcy, HYPRE, GLMakie
meter, kilogram, bar, year, liter, second, darcy, day = si_units(:meter, :kilogram, :bar, :year, :liter, :second, :darcy, :day)

(1.0, 1.0, 100000.0, 3.1556952e7, 0.001, 1.0, 9.86923266716013e-13, 86400.0)

Set up the reservoir mesh

The model is a typical geothermal case where there is a layer of high permeability in the middle, confined between two low-permeable layers. For a geothermal model, the low permeable layers are important, as they store significant amounts of heat that can be conducted to the high permeable layer during production.

We set up the mesh so that the high permeable layer where most of the advective transport occurs has a higher lateral resolution than the low permeable layers. The model is also essentally 2D as there is only one cell thickness in the y direction - a choice that is made to make the example fast to run, especially during the later optimization stages where many simulations must be run to achieve convergence.

nx = 50
ntop = 5
nmiddle = 10
nbottom = 5
nz = ntop + nmiddle + nbottom

20

Set up layer thicknesses and vertical cell thicknesses

top_layer_thickness = 300.0*meter
middle_layer_thickness = 200.0*meter
bottom_layer_thickness = 300.0*meter
dz = Float64[]
for i in 1:ntop
    push!(dz, top_layer_thickness/ntop)
end
for i in 1:nmiddle
    push!(dz, middle_layer_thickness/nmiddle)
end
for i in 1:ntop
    push!(dz, bottom_layer_thickness/nbottom)
end

cmesh = CartesianMesh((nx, 1, nz), (2000.0, 50.0, dz))
rmesh = UnstructuredMesh(cmesh, z_is_depth = true)

UnstructuredMesh with 1000 cells, 1930 faces and 2140 boundary faces

Define regions based on our selected depths

We tag each cell with a region number based on its depth. The top layer is region 1, the middle layer is region 2, and the bottom layer is region 3.

geo = tpfv_geometry(rmesh)
depths = geo.cell_centroids[3, :]
regions = Int[]
for (i, d_i) in enumerate(depths)
    if d_i <= top_layer_thickness
        r = 1
    elseif d_i <= top_layer_thickness + middle_layer_thickness
        r = 2
    else
        r = 3
    end
    push!(regions, r)
end

Plot the mesh and regions

fig, ax, plt = plot_cell_data(rmesh, regions,
    alpha = 0.5,
    outer = true,
    transparency = true,
    colormap = Categorical(:heat)
)
ax.elevation[] = 0.0
ax.azimuth[] = π/2
plot_mesh_edges!(ax, rmesh)
fig

Define functions for setting up the simulation

We will define a function that takes in a Dict with different values and sets up the simulation. The key idea is that we can then optimize the values in the Dict to perform optimization. As we can define any such Dict to set up the model, this interface is very flexible and can be used for both control optimization and history matching with respect to almost any parameter of the model. The disadvantage is that the setup function will be called many times, which can be a substantial cost compared to the more structured optimization interface that only allows for optimization of the numerical parameters (e.g. for the CGNet example).

Define the time schedule

We set up a time schedule for the simulation. The total simulation time is 30 years, and we report the results every 120 days. We also define ten different intervals in this 30 year period, which are the period where we will allow the rates and temperatures to vary during the last part of the optimization tutorial.

total_time = 30.0*year
report_step_length = 120.0*day
dt = fill(report_step_length, Int(ceil(total_time/report_step_length)))
num_intervals = 10
interval_interval = total_time/num_intervals
interval_for_step = map(t -> min(Int(ceil(t/interval_interval)), num_intervals), cumsum(dt))

92-element Vector{Int64}:
  1
  1
  1
  1
  1
  1
  1
  1
  1
  2
  ⋮
 10
 10
 10
 10
 10
 10
 10
 10
 10

Define the wells

We set up two wells, one injector and one producer. The injector is located at the left side of the model, and the producer is located at the right side. We use multisegment wells.

base_rate = 15*liter/second
base_temp = 15.0

domain = reservoir_domain(rmesh)
inj_well = setup_vertical_well(domain, 5, 1,
    heel = ntop+1,
    toe = ntop+nmiddle,
    name = :Injector,
    simple_well = false
)
prod_well = setup_vertical_well(domain, nx - 5, 1,
    heel = ntop+1,
    toe = ntop+nmiddle,
    name = :Producer,
    simple_well = false
)

model_base = setup_reservoir_model(
    domain, :geothermal,
    wells = [inj_well, prod_well],
);

Set up a helper to define the forces for a given rate and temperature

function setup_doublet_forces(model, inj_temp, inj_rate)
    T_Kelvin = convert_to_si(inj_temp, :Celsius)
    rate_target = TotalRateTarget(inj_rate)
    ctrl_inj  = InjectorControl(rate_target, [1.0],
        density = 1000.0, temperature = T_Kelvin)

    bhp_target = BottomHolePressureTarget(50*bar)
    ctrl_prod = ProducerControl(bhp_target)

    control = Dict(:Injector => ctrl_inj, :Producer => ctrl_prod)
    return setup_reservoir_forces(model, control = control)
end

setup_doublet_forces (generic function with 1 method)

Define the main setup function

This function sets up the model based on the parameters provided in the Dict. It takes in two arguments: The required parameters in a Dict and an optional step_info argument that can be used to set up the model for a specific time step. The function returns a JutulCase object that can be used to simulate the reservoir. Here, we ignore the step_info argument and set up the entire schedule every time. Jutul will then automatically use the correct force based on the time step in the simulation.

function setup_doublet_case(prm, step_info = missing)
    model = deepcopy(model_base)
    rdomain = reservoir_domain(model)
    rdomain[:permeability] = prm["layer_perm"][regions]
    rdomain[:porosity] = prm["layer_porosities"][regions]
    rdomain[:rock_heat_capacity] = prm["layer_heat_capacity"][regions]

    T0 = convert_to_si(70, :Celsius)
    thermal_gradient = 20.0/1000.0*meter
    eql = EquilibriumRegion(model, 50*bar, 0.0, temperature_vs_depth = z -> T0 + z*thermal_gradient)
    state0 = setup_reservoir_state(model, eql)

    forces_per_interval = map((T, rate) -> setup_doublet_forces(model, T, rate),
        prm["injection_temperature_C"], prm["injection_rate"])

    forces = forces_per_interval[interval_for_step]

    return JutulCase(model, dt, forces, state0 = state0)
end

setup_doublet_case (generic function with 2 methods)

Perform a history match

We first set up a truth case that we will use to generate the data for the history match. We define high perm and porosity in the middle layer, and low perm and porosity in the top and bottom layers before simulating the model.

prm_truth = Dict(
    "injection_rate" => fill(base_rate, num_intervals),
    "injection_temperature_C" => fill(base_temp, num_intervals),
    "layer_porosities" => [0.1, 0.3, 0.1],
    "layer_perm" => [0.01, 0.8, 0.02].*darcy,
    "layer_heat_capacity" => [500.0, 600.0, 450.0], # Watt / m K
)
case_truth = setup_doublet_case(prm_truth)
ws, states = simulate_reservoir(case_truth)

ReservoirSimResult with 92 entries:

  wells (2 present):
    :Producer
    :Injector
    Results per well:
       :lrat => Vector{Float64} of size (92,)
       :wrat => Vector{Float64} of size (92,)
       :temperature => Vector{Float64} of size (92,)
       :control => Vector{Symbol} of size (92,)
       :Aqueous_mass_rate => Vector{Float64} of size (92,)
       :bhp => Vector{Float64} of size (92,)
       :wcut => Vector{Float64} of size (92,)
       :mass_rate => Vector{Float64} of size (92,)
       :rate => Vector{Float64} of size (92,)
       :mrat => Vector{Float64} of size (92,)

  states (Vector with 92 entries, reservoir variables for each state)
    :Pressure => Vector{Float64} of size (1000,)
    :TotalMasses => Matrix{Float64} of size (1, 1000)
    :TotalThermalEnergy => Vector{Float64} of size (1000,)
    :FluidEnthalpy => Matrix{Float64} of size (1, 1000)
    :Temperature => Vector{Float64} of size (1000,)
    :PhaseMassDensities => Matrix{Float64} of size (1, 1000)
    :RockInternalEnergy => Vector{Float64} of size (1000,)
    :FluidInternalEnergy => Matrix{Float64} of size (1, 1000)

  time (report time for each state)
     Vector{Float64} of length 92

  result (extended states, reports)
     SimResult with 92 entries

  extra
     Dict{Any, Any} with keys :simulator, :config

  Completed at Feb. 23 2026 15:30 after 4 seconds, 393 milliseconds, 459.2 microseconds.

Define a mismatch objective function

The mismatch objective function is defined as the sum of squares difference between the simulated values and the reference values observed in the wells. Note that we only make use of the well data:

• The temperature at the producer well

• The mass rate at the producer well (since it is controlled on BHP)

• The BHP at the injector well (since it is controlled on rate)

We use the get_1d_interpolator function to create interpolators for the reference values, since we cannot assume that the simulator will use exactly the same time-steps as the reference values.

prod_rate = ws.wells[:Producer][:wrat]
prod_temp = ws.wells[:Producer][:temperature]
inj_bhp = ws.wells[:Injector][:bhp]

prod_temp_by_time = get_1d_interpolator(ws.time, prod_temp)
prod_rate_by_time = get_1d_interpolator(ws.time, prod_rate)
inj_pressure_by_time = get_1d_interpolator(ws.time, inj_bhp)

import JutulDarcy: compute_well_qoi
function mismatch_objective(m, s, dt, step_info, forces)
    current_time = step_info[:time]
    # Current values
    T_at_prod = compute_well_qoi(m, s, forces, :Producer, :temperature)
    rate = compute_well_qoi(m, s, forces, :Producer, :wrat)
    bhp = compute_well_qoi(m, s, forces, :Injector, :bhp)
    # Reference values
    T_at_prod_ref = prod_temp_by_time(current_time)
    rate_ref = prod_rate_by_time(current_time)
    bhp_ref = inj_pressure_by_time(current_time)
    # Define mismatch by scaling each term
    T_mismatch = (T_at_prod_ref - T_at_prod)
    rate_mismatch = (rate_ref - rate)*1000
    bhp_mismatch = (bhp - bhp_ref)/bar
    return dt * sqrt(T_mismatch^2 + rate_mismatch^2 + bhp_mismatch^2) / total_time
end

mismatch_objective (generic function with 1 method)

Pick an initial guess

We set up an initial guess for the parameters that we will optimize. We assume the injection rate and temperature to be known and we set the porosities and permeabilities to uniform values. The heat capacity is given a bit of layering, but still with completely wrong values.

prm_guess = Dict(
    "injection_rate" => fill(base_rate, num_intervals),
    "injection_temperature_C" => fill(base_temp, num_intervals),
    "layer_porosities" => [0.2, 0.2, 0.2],
    "layer_perm" => [0.2, 0.2, 0.2].*darcy,
    "layer_heat_capacity" => [400.0, 400.0, 400.0]
)
case_guess = setup_doublet_case(prm_guess)
ws_guess, states_guess = simulate_reservoir(case_guess)

ReservoirSimResult with 92 entries:

  wells (2 present):
    :Producer
    :Injector
    Results per well:
       :lrat => Vector{Float64} of size (92,)
       :wrat => Vector{Float64} of size (92,)
       :temperature => Vector{Float64} of size (92,)
       :control => Vector{Symbol} of size (92,)
       :Aqueous_mass_rate => Vector{Float64} of size (92,)
       :bhp => Vector{Float64} of size (92,)
       :wcut => Vector{Float64} of size (92,)
       :mass_rate => Vector{Float64} of size (92,)
       :rate => Vector{Float64} of size (92,)
       :mrat => Vector{Float64} of size (92,)

  states (Vector with 92 entries, reservoir variables for each state)
    :Pressure => Vector{Float64} of size (1000,)
    :TotalMasses => Matrix{Float64} of size (1, 1000)
    :TotalThermalEnergy => Vector{Float64} of size (1000,)
    :FluidEnthalpy => Matrix{Float64} of size (1, 1000)
    :Temperature => Vector{Float64} of size (1000,)
    :PhaseMassDensities => Matrix{Float64} of size (1, 1000)
    :RockInternalEnergy => Vector{Float64} of size (1000,)
    :FluidInternalEnergy => Matrix{Float64} of size (1, 1000)

  time (report time for each state)
     Vector{Float64} of length 92

  result (extended states, reports)
     SimResult with 92 entries

  extra
     Dict{Any, Any} with keys :simulator, :config

  Completed at Feb. 23 2026 15:30 after 828 milliseconds, 85 microseconds, 692 nanoseconds.

Set up the optimization

We define a dictionary optimization problem that will optimize the parameters in the prm_guess dictionary. We start by setting up the object itself, which takes in the initial guess Dict and the corresponding setup function.

opt = JutulDarcy.setup_reservoir_dict_optimization(prm_guess, setup_doublet_case)

DictParameters with 5 parameters (0 active), and 0 multipliers:
No active optimization parameters.
Inactive optimization parameters
┌─────────────────────────┬──────────────────┬───────┬─────┬─────┐
│                    Name │ Initial value    │ Count │ Min │ Max │
├─────────────────────────┼──────────────────┼───────┼─────┼─────┤
│     layer_heat_capacity │ 400.0 ± 0.0      │     3 │   - │   - │
│          injection_rate │ 0.015 ± 3.47e-18 │    10 │   - │   - │
│ injection_temperature_C │ 15.0 ± 0.0       │    10 │   - │   - │
│              layer_perm │ 1.97e-13 ± 0.0   │     3 │   - │   - │
│        layer_porosities │ 0.2 ± 2.78e-17   │     3 │   - │   - │
└─────────────────────────┴──────────────────┴───────┴─────┴─────┘
No multipliers set.

Define active parameters and their limits

Note that while the parameters get listed, they are all marked as inactive. We need to explicitly make them free/active and specify a range for each parameter before we can optimize them. We use wide absolute limits for each entry.

free_optimization_parameter!(opt, "layer_perm", abs_max = 1.5*darcy, abs_min = 0.01*darcy)
free_optimization_parameter!(opt, "layer_heat_capacity", abs_max = 1000.0, abs_min = 400.0)
free_optimization_parameter!(opt, "layer_porosities", abs_max = 0.35, abs_min = 0.05)

DictParameters with 5 parameters (3 active), and 0 multipliers:
Active optimization parameters
┌─────────────────────┬────────────────┬───────┬──────────┬──────────┐
│                Name │ Initial value  │ Count │      Min │      Max │
├─────────────────────┼────────────────┼───────┼──────────┼──────────┤
│          layer_perm │ 1.97e-13 ± 0.0 │     3 │ 9.87e-15 │ 1.48e-12 │
│ layer_heat_capacity │ 400.0 ± 0.0    │     3 │    400.0 │   1000.0 │
│    layer_porosities │ 0.2 ± 2.78e-17 │     3 │     0.05 │     0.35 │
└─────────────────────┴────────────────┴───────┴──────────┴──────────┘
Inactive optimization parameters
┌─────────────────────────┬──────────────────┬───────┬─────┬─────┐
│                    Name │ Initial value    │ Count │ Min │ Max │
├─────────────────────────┼──────────────────┼───────┼─────┼─────┤
│          injection_rate │ 0.015 ± 3.47e-18 │    10 │   - │   - │
│ injection_temperature_C │ 15.0 ± 0.0       │    10 │   - │   - │
└─────────────────────────┴──────────────────┴───────┴─────┴─────┘
No multipliers set.

Call the optimizer

Now that we have freed a few parameters, we can call the optimizer with the objective function. The defaults for the optimizer are fairly reasonable, so we do not tweak the convergence criteria or the maximum number of iterations. Note that by default the optimizer uses LBFGS, but it is also possible to pass other optimizers as a function callable. The default for the optimizer is to minimize the objective function, which is the case for a history match. By passing for example lbfgs_num = 1, max_it = 50 it is possible to obtain a better match, but this is not necessary for the purpose of this example.

prm_opt = JutulDarcy.optimize_reservoir(opt, mismatch_objective, max_it = 50, gradient_scaling = false, optimizer = :lbfgsb_qp);

setup_reservoir_state: Received primary variable Saturations, but this is not known to reservoir model.
Optimization: Starting calibration of 9 parameters.
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Setting up adjoint storage.
Optimization: Finished setup in 61.547319057 seconds.
Optimization: Adjoint solve took 34.403553174 seconds.

Optimization: Objective #1: 1.81499e+01, gradient 2-norm: 8.40785e+12
It:  0 | v: 1.815e+01 | ls-its:  0 | pg: 8.03e+12 | ρ:       NaN | qp-its:  0 +  0 | n-active:   0
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.007099802 seconds.

Optimization: Objective #2: 5.85646e+01 (f/f0=3.227e+00), gradient 2-norm: 5.74716e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.829908347 seconds.

Optimization: Objective #3: 1.42655e+01 (f/f0=7.860e-01), gradient 2-norm: 3.55326e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.963686241 seconds.

Optimization: Objective #4: 5.85646e+01 (f/f0=3.227e+00), gradient 2-norm: 5.74716e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.904947928 seconds.

Optimization: Objective #5: 1.56059e+01 (f/f0=8.598e-01), gradient 2-norm: 2.68161e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.820980434 seconds.

Optimization: Objective #6: 1.36118e+01 (f/f0=7.500e-01), gradient 2-norm: 5.83781e+13
Hessian not updated during iteration 1.
It:  1 | v: 1.361e+01 | ls-its:  5 | pg: 5.18e+13 | ρ:  1.35e+00 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.849156688 seconds.

Optimization: Objective #7: 1.84651e+01 (f/f0=1.017e+00), gradient 2-norm: 2.51501e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.837194557 seconds.

Optimization: Objective #8: 2.01529e+01 (f/f0=1.110e+00), gradient 2-norm: 3.14677e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.947132856 seconds.

Optimization: Objective #9: 1.56340e+01 (f/f0=8.614e-01), gradient 2-norm: 5.51693e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.827792008 seconds.

Optimization: Objective #10: 1.34540e+01 (f/f0=7.413e-01), gradient 2-norm: 4.57268e+13
Hessian not updated during iteration 2.
It:  2 | v: 1.345e+01 | ls-its:  4 | pg: 4.06e+13 | ρ:  1.40e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.990009155 seconds.

Optimization: Objective #11: 6.27248e+01 (f/f0=3.456e+00), gradient 2-norm: 6.13877e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.896537605 seconds.

Optimization: Objective #12: 1.26267e+01 (f/f0=6.957e-01), gradient 2-norm: 3.21132e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.833603382 seconds.

Optimization: Objective #13: 1.13807e+01 (f/f0=6.270e-01), gradient 2-norm: 1.14628e+14
Hessian not updated during iteration 3.
It:  3 | v: 1.138e+01 | ls-its:  3 | pg: 1.08e+14 | ρ:  7.99e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.890675415 seconds.

Optimization: Objective #14: 1.76893e+01 (f/f0=9.746e-01), gradient 2-norm: 2.34045e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.846400961 seconds.

Optimization: Objective #15: 1.86313e+01 (f/f0=1.027e+00), gradient 2-norm: 4.05026e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.965919827 seconds.

Optimization: Objective #16: 1.38003e+01 (f/f0=7.604e-01), gradient 2-norm: 6.70483e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.867297666 seconds.

Optimization: Objective #17: 1.07225e+01 (f/f0=5.908e-01), gradient 2-norm: 7.08001e+13
Hessian not updated during iteration 4.
It:  4 | v: 1.072e+01 | ls-its:  4 | pg: 6.38e+13 | ρ:  1.88e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.976903604 seconds.

Optimization: Objective #18: 6.33520e+01 (f/f0=3.490e+00), gradient 2-norm: 6.17367e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.856060825 seconds.

Optimization: Objective #19: 1.08161e+01 (f/f0=5.959e-01), gradient 2-norm: 3.33163e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.933284342 seconds.

Optimization: Objective #20: 8.76220e+00 (f/f0=4.828e-01), gradient 2-norm: 9.97974e+13
Hessian not updated during iteration 5.
It:  5 | v: 8.762e+00 | ls-its:  3 | pg: 8.30e+13 | ρ:  7.36e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.918058121 seconds.

Optimization: Objective #21: 1.67969e+01 (f/f0=9.255e-01), gradient 2-norm: 1.92142e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.861492292 seconds.

Optimization: Objective #22: 1.70529e+01 (f/f0=9.396e-01), gradient 2-norm: 4.78261e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.924038395 seconds.

Optimization: Objective #23: 1.15286e+01 (f/f0=6.352e-01), gradient 2-norm: 8.12133e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.846141788 seconds.

Optimization: Objective #24: 8.41309e+00 (f/f0=4.635e-01), gradient 2-norm: 8.49765e+13
Hessian not updated during iteration 6.
It:  6 | v: 8.413e+00 | ls-its:  4 | pg: 7.98e+13 | ρ:  1.75e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.251432339 seconds.

Optimization: Objective #25: 6.40248e+01 (f/f0=3.528e+00), gradient 2-norm: 6.20940e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.845095311 seconds.

Optimization: Objective #26: 1.05522e+01 (f/f0=5.814e-01), gradient 2-norm: 3.86686e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 3.2046977 seconds.

Optimization: Objective #27: 7.18648e+00 (f/f0=3.960e-01), gradient 2-norm: 9.47106e+13
Hessian not updated during iteration 7.
It:  7 | v: 7.186e+00 | ls-its:  3 | pg: 6.97e+13 | ρ:  6.66e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.912573459 seconds.

Optimization: Objective #28: 1.63057e+01 (f/f0=8.984e-01), gradient 2-norm: 1.44108e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.929843367 seconds.

Optimization: Objective #29: 1.58417e+01 (f/f0=8.728e-01), gradient 2-norm: 5.18004e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.920123807 seconds.

Optimization: Objective #30: 1.00076e+01 (f/f0=5.514e-01), gradient 2-norm: 8.97529e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.993015793 seconds.

Optimization: Objective #31: 6.97730e+00 (f/f0=3.844e-01), gradient 2-norm: 9.21663e+13
Hessian not updated during iteration 8.
It:  8 | v: 6.977e+00 | ls-its:  4 | pg: 8.81e+13 | ρ:  1.57e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.922118803 seconds.

Optimization: Objective #32: 6.44678e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23182e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.931157234 seconds.

Optimization: Objective #33: 1.05931e+01 (f/f0=5.836e-01), gradient 2-norm: 4.19768e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.879038824 seconds.

Optimization: Objective #34: 6.17543e+00 (f/f0=3.402e-01), gradient 2-norm: 8.78918e+13
Hessian not updated during iteration 9.
It:  9 | v: 6.175e+00 | ls-its:  3 | pg: 7.01e+13 | ρ:  6.49e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.896992806 seconds.

Optimization: Objective #35: 1.62273e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31302e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.845092436 seconds.

Optimization: Objective #36: 1.50089e+01 (f/f0=8.269e-01), gradient 2-norm: 5.37728e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.980901591 seconds.

Optimization: Objective #37: 8.65614e+00 (f/f0=4.769e-01), gradient 2-norm: 9.69542e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.840755916 seconds.

Optimization: Objective #38: 6.05543e+00 (f/f0=3.336e-01), gradient 2-norm: 9.31091e+13
Hessian not updated during iteration 10.
It: 10 | v: 6.055e+00 | ls-its:  4 | pg: 9.06e+13 | ρ:  1.63e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.995740129 seconds.

Optimization: Objective #39: 6.44696e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23201e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.889665107 seconds.

Optimization: Objective #40: 1.08660e+01 (f/f0=5.987e-01), gradient 2-norm: 4.44329e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.949107175 seconds.

Optimization: Objective #41: 5.60421e+00 (f/f0=3.088e-01), gradient 2-norm: 8.26109e+13
Hessian not updated during iteration 11.
It: 11 | v: 5.604e+00 | ls-its:  3 | pg: 7.55e+13 | ρ:  6.45e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.928695409 seconds.

Optimization: Objective #42: 1.62273e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31272e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.904820201 seconds.

Optimization: Objective #43: 1.43325e+01 (f/f0=7.897e-01), gradient 2-norm: 5.62771e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.930623759 seconds.

Optimization: Objective #44: 7.16109e+00 (f/f0=3.946e-01), gradient 2-norm: 1.03940e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.833887712 seconds.

Optimization: Objective #45: 5.52793e+00 (f/f0=3.046e-01), gradient 2-norm: 8.97159e+13
Hessian not updated during iteration 12.
It: 12 | v: 5.528e+00 | ls-its:  4 | pg: 8.90e+13 | ρ:  2.74e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.977808115 seconds.

Optimization: Objective #46: 6.44703e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23208e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.902066298 seconds.

Optimization: Objective #47: 1.12814e+01 (f/f0=6.216e-01), gradient 2-norm: 4.69052e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.961537671 seconds.

Optimization: Objective #48: 5.32345e+00 (f/f0=2.933e-01), gradient 2-norm: 8.16699e+13
Hessian not updated during iteration 13.
It: 13 | v: 5.323e+00 | ls-its:  3 | pg: 7.73e+13 | ρ:  6.40e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.883574804 seconds.

Optimization: Objective #49: 1.62273e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31258e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.804746448 seconds.

Optimization: Objective #50: 1.38945e+01 (f/f0=7.655e-01), gradient 2-norm: 5.79281e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.93170689 seconds.

Optimization: Objective #51: 6.42360e+00 (f/f0=3.539e-01), gradient 2-norm: 1.05416e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.852665391 seconds.

Optimization: Objective #52: 5.26907e+00 (f/f0=2.903e-01), gradient 2-norm: 8.76928e+13
Hessian not updated during iteration 14.
It: 14 | v: 5.269e+00 | ls-its:  4 | pg: 8.74e+13 | ρ:  3.32e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.00524635 seconds.

Optimization: Objective #53: 6.44707e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23213e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.905520699 seconds.

Optimization: Objective #54: 1.14159e+01 (f/f0=6.290e-01), gradient 2-norm: 4.77424e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.980426717 seconds.

Optimization: Objective #55: 5.13834e+00 (f/f0=2.831e-01), gradient 2-norm: 8.07871e+13
Hessian not updated during iteration 15.
It: 15 | v: 5.138e+00 | ls-its:  3 | pg: 7.77e+13 | ρ:  6.47e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.904220435 seconds.

Optimization: Objective #56: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31250e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.921555275 seconds.

Optimization: Objective #57: 1.35549e+01 (f/f0=7.468e-01), gradient 2-norm: 5.91906e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.939273479 seconds.

Optimization: Objective #58: 5.96626e+00 (f/f0=3.287e-01), gradient 2-norm: 1.05188e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.876288605 seconds.

Optimization: Objective #59: 5.09648e+00 (f/f0=2.808e-01), gradient 2-norm: 8.64863e+13
Hessian not updated during iteration 16.
It: 16 | v: 5.096e+00 | ls-its:  4 | pg: 8.63e+13 | ρ:  3.68e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.02702941 seconds.

Optimization: Objective #60: 6.44711e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23216e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.963439348 seconds.

Optimization: Objective #61: 1.14831e+01 (f/f0=6.327e-01), gradient 2-norm: 4.81709e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.9824697 seconds.

Optimization: Objective #62: 5.00206e+00 (f/f0=2.756e-01), gradient 2-norm: 8.00322e+13
Hessian not updated during iteration 17.
It: 17 | v: 5.002e+00 | ls-its:  3 | pg: 7.76e+13 | ρ:  6.48e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.865564365 seconds.

Optimization: Objective #63: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31244e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.880775463 seconds.

Optimization: Objective #64: 1.32664e+01 (f/f0=7.309e-01), gradient 2-norm: 6.02746e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.946260155 seconds.

Optimization: Objective #65: 5.64382e+00 (f/f0=3.110e-01), gradient 2-norm: 1.04153e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.919524534 seconds.

Optimization: Objective #66: 4.96850e+00 (f/f0=2.737e-01), gradient 2-norm: 8.52709e+13
Hessian not updated during iteration 18.
It: 18 | v: 4.968e+00 | ls-its:  4 | pg: 8.52e+13 | ρ:  3.93e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.975531711 seconds.

Optimization: Objective #67: 6.44714e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23219e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.948740914 seconds.

Optimization: Objective #68: 1.15256e+01 (f/f0=6.350e-01), gradient 2-norm: 4.84408e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.939634484 seconds.

Optimization: Objective #69: 4.89578e+00 (f/f0=2.697e-01), gradient 2-norm: 7.93446e+13
Hessian not updated during iteration 19.
It: 19 | v: 4.896e+00 | ls-its:  3 | pg: 7.74e+13 | ρ:  6.52e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.030908741 seconds.

Optimization: Objective #70: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31239e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.921781221 seconds.

Optimization: Objective #71: 1.30132e+01 (f/f0=7.170e-01), gradient 2-norm: 6.12277e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.947110698 seconds.

Optimization: Objective #72: 5.40522e+00 (f/f0=2.978e-01), gradient 2-norm: 1.02758e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.857166739 seconds.

Optimization: Objective #73: 4.86813e+00 (f/f0=2.682e-01), gradient 2-norm: 8.42347e+13
Hessian not updated during iteration 20.
It: 20 | v: 4.868e+00 | ls-its:  4 | pg: 8.42e+13 | ρ:  4.10e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.987345487 seconds.

Optimization: Objective #74: 6.44717e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23221e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.894324662 seconds.

Optimization: Objective #75: 1.15544e+01 (f/f0=6.366e-01), gradient 2-norm: 4.86224e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.955047862 seconds.

Optimization: Objective #76: 4.80966e+00 (f/f0=2.650e-01), gradient 2-norm: 7.86708e+13
Hessian not updated during iteration 21.
It: 21 | v: 4.810e+00 | ls-its:  3 | pg: 7.70e+13 | ρ:  6.55e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.920088251 seconds.

Optimization: Objective #77: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31235e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.044566715 seconds.

Optimization: Objective #78: 1.27847e+01 (f/f0=7.044e-01), gradient 2-norm: 6.20814e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.894896469 seconds.

Optimization: Objective #79: 5.22083e+00 (f/f0=2.877e-01), gradient 2-norm: 1.01258e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.002295733 seconds.

Optimization: Objective #80: 4.78637e+00 (f/f0=2.637e-01), gradient 2-norm: 8.32492e+13
Hessian not updated during iteration 22.
It: 22 | v: 4.786e+00 | ls-its:  4 | pg: 8.32e+13 | ρ:  4.24e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.937336906 seconds.

Optimization: Objective #81: 6.44719e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23224e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.938133441 seconds.

Optimization: Objective #82: 1.15758e+01 (f/f0=6.378e-01), gradient 2-norm: 4.87560e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.982448076 seconds.

Optimization: Objective #83: 4.73802e+00 (f/f0=2.610e-01), gradient 2-norm: 7.80118e+13
Hessian not updated during iteration 23.
It: 23 | v: 4.738e+00 | ls-its:  3 | pg: 7.66e+13 | ρ:  6.58e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.909196633 seconds.

Optimization: Objective #84: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31231e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.036737328 seconds.

Optimization: Objective #85: 1.25751e+01 (f/f0=6.928e-01), gradient 2-norm: 6.28747e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.884624982 seconds.

Optimization: Objective #86: 5.07420e+00 (f/f0=2.796e-01), gradient 2-norm: 9.96629e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.046621847 seconds.

Optimization: Objective #87: 4.71810e+00 (f/f0=2.600e-01), gradient 2-norm: 8.23425e+13
Hessian not updated during iteration 24.
It: 24 | v: 4.718e+00 | ls-its:  4 | pg: 8.23e+13 | ρ:  4.34e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.934903168 seconds.

Optimization: Objective #88: 6.44721e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23226e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.966462949 seconds.

Optimization: Objective #89: 1.15922e+01 (f/f0=6.387e-01), gradient 2-norm: 4.88565e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.940114668 seconds.

Optimization: Objective #90: 4.67720e+00 (f/f0=2.577e-01), gradient 2-norm: 7.73701e+13
Hessian not updated during iteration 25.
It: 25 | v: 4.677e+00 | ls-its:  3 | pg: 7.61e+13 | ρ:  6.60e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.826057709 seconds.

Optimization: Objective #91: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31228e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.904343122 seconds.

Optimization: Objective #92: 1.23797e+01 (f/f0=6.821e-01), gradient 2-norm: 6.36370e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.869517976 seconds.

Optimization: Objective #93: 4.95467e+00 (f/f0=2.730e-01), gradient 2-norm: 9.80300e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.964999394 seconds.

Optimization: Objective #94: 4.65990e+00 (f/f0=2.567e-01), gradient 2-norm: 8.14944e+13
Hessian not updated during iteration 26.
It: 26 | v: 4.660e+00 | ls-its:  4 | pg: 8.15e+13 | ρ:  4.43e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.87869148 seconds.

Optimization: Objective #95: 6.44723e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23228e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.966822349 seconds.

Optimization: Objective #96: 1.16057e+01 (f/f0=6.394e-01), gradient 2-norm: 4.89367e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.8742956 seconds.

Optimization: Objective #97: 4.62477e+00 (f/f0=2.548e-01), gradient 2-norm: 7.67684e+13
Hessian not updated during iteration 27.
It: 27 | v: 4.625e+00 | ls-its:  3 | pg: 7.57e+13 | ρ:  6.62e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.901444385 seconds.

Optimization: Objective #98: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31225e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.891524633 seconds.

Optimization: Objective #99: 1.21973e+01 (f/f0=6.720e-01), gradient 2-norm: 6.43374e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.81192499 seconds.

Optimization: Objective #100: 4.85621e+00 (f/f0=2.676e-01), gradient 2-norm: 9.64619e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.959709094 seconds.

Optimization: Objective #101: 4.60960e+00 (f/f0=2.540e-01), gradient 2-norm: 8.06822e+13
Hessian not updated during iteration 28.
It: 28 | v: 4.610e+00 | ls-its:  4 | pg: 8.07e+13 | ρ:  4.50e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.86377923 seconds.

Optimization: Objective #102: 6.44725e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23230e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.952162711 seconds.

Optimization: Objective #103: 1.16167e+01 (f/f0=6.400e-01), gradient 2-norm: 4.90009e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.833751364 seconds.

Optimization: Objective #104: 4.57900e+00 (f/f0=2.523e-01), gradient 2-norm: 7.61850e+13
Hessian not updated during iteration 29.
It: 29 | v: 4.579e+00 | ls-its:  3 | pg: 7.52e+13 | ρ:  6.63e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.232052987 seconds.

Optimization: Objective #105: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31223e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.857463105 seconds.

Optimization: Objective #106: 1.20246e+01 (f/f0=6.625e-01), gradient 2-norm: 6.50042e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.841511865 seconds.

Optimization: Objective #107: 4.77335e+00 (f/f0=2.630e-01), gradient 2-norm: 9.49106e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.893990724 seconds.

Optimization: Objective #108: 4.56558e+00 (f/f0=2.515e-01), gradient 2-norm: 7.99270e+13
Hessian not updated during iteration 30.
It: 30 | v: 4.566e+00 | ls-its:  4 | pg: 7.99e+13 | ρ:  4.55e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.912523566 seconds.

Optimization: Objective #109: 6.44726e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23232e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.971670967 seconds.

Optimization: Objective #110: 1.16262e+01 (f/f0=6.406e-01), gradient 2-norm: 4.90535e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.089994446 seconds.

Optimization: Objective #111: 4.53863e+00 (f/f0=2.501e-01), gradient 2-norm: 7.56011e+13
Hessian not updated during iteration 31.
It: 31 | v: 4.539e+00 | ls-its:  3 | pg: 7.47e+13 | ρ:  6.65e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.866218198 seconds.

Optimization: Objective #112: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31221e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.904086749 seconds.

Optimization: Objective #113: 1.18623e+01 (f/f0=6.536e-01), gradient 2-norm: 6.56092e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.945408874 seconds.

Optimization: Objective #114: 4.70344e+00 (f/f0=2.591e-01), gradient 2-norm: 9.34183e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.859225041 seconds.

Optimization: Objective #115: 4.52666e+00 (f/f0=2.494e-01), gradient 2-norm: 7.91913e+13
Hessian not updated during iteration 32.
It: 32 | v: 4.527e+00 | ls-its:  4 | pg: 7.92e+13 | ρ:  4.60e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.987219218 seconds.

Optimization: Objective #116: 6.44728e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23233e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.844451134 seconds.

Optimization: Objective #117: 1.16343e+01 (f/f0=6.410e-01), gradient 2-norm: 4.90970e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.985712449 seconds.

Optimization: Objective #118: 4.50271e+00 (f/f0=2.481e-01), gradient 2-norm: 7.50541e+13
Hessian not updated during iteration 33.
It: 33 | v: 4.503e+00 | ls-its:  3 | pg: 7.43e+13 | ρ:  6.66e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.900765436 seconds.

Optimization: Objective #119: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31219e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.826915232 seconds.

Optimization: Objective #120: 1.17059e+01 (f/f0=6.450e-01), gradient 2-norm: 6.62419e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.876162406 seconds.

Optimization: Objective #121: 4.64288e+00 (f/f0=2.558e-01), gradient 2-norm: 9.20085e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.848837593 seconds.

Optimization: Objective #122: 4.49196e+00 (f/f0=2.475e-01), gradient 2-norm: 7.84896e+13
Hessian not updated during iteration 34.
It: 34 | v: 4.492e+00 | ls-its:  4 | pg: 7.85e+13 | ρ:  4.64e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.958402303 seconds.

Optimization: Objective #123: 6.44729e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23235e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.895341252 seconds.

Optimization: Objective #124: 1.16417e+01 (f/f0=6.414e-01), gradient 2-norm: 4.91353e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.930190893 seconds.

Optimization: Objective #125: 4.47053e+00 (f/f0=2.463e-01), gradient 2-norm: 7.45046e+13
Hessian not updated during iteration 35.
It: 35 | v: 4.471e+00 | ls-its:  3 | pg: 7.38e+13 | ρ:  6.66e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.849885584 seconds.

Optimization: Objective #126: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31218e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.875115085 seconds.

Optimization: Objective #127: 1.15592e+01 (f/f0=6.369e-01), gradient 2-norm: 6.68297e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.930791362 seconds.

Optimization: Objective #128: 4.59095e+00 (f/f0=2.529e-01), gradient 2-norm: 9.06549e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.855787468 seconds.

Optimization: Objective #129: 4.46081e+00 (f/f0=2.458e-01), gradient 2-norm: 7.78244e+13
Hessian not updated during iteration 36.
It: 36 | v: 4.461e+00 | ls-its:  4 | pg: 7.78e+13 | ρ:  4.67e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.984534024 seconds.

Optimization: Objective #130: 6.44730e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23236e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.897691882 seconds.

Optimization: Objective #131: 1.16480e+01 (f/f0=6.418e-01), gradient 2-norm: 4.91672e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.944187116 seconds.

Optimization: Objective #132: 4.44147e+00 (f/f0=2.447e-01), gradient 2-norm: 7.40047e+13
Hessian not updated during iteration 37.
It: 37 | v: 4.441e+00 | ls-its:  3 | pg: 7.34e+13 | ρ:  6.68e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.896825339 seconds.

Optimization: Objective #133: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31216e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.918249423 seconds.

Optimization: Objective #134: 1.14149e+01 (f/f0=6.289e-01), gradient 2-norm: 6.73833e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.994551801 seconds.

Optimization: Objective #135: 4.54490e+00 (f/f0=2.504e-01), gradient 2-norm: 8.93425e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.909579226 seconds.

Optimization: Objective #136: 4.43265e+00 (f/f0=2.442e-01), gradient 2-norm: 7.72119e+13
Hessian not updated during iteration 38.
It: 38 | v: 4.433e+00 | ls-its:  4 | pg: 7.72e+13 | ρ:  4.70e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.033257142 seconds.

Optimization: Objective #137: 6.44732e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23238e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.930789345 seconds.

Optimization: Objective #138: 1.16538e+01 (f/f0=6.421e-01), gradient 2-norm: 4.91959e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.843180619 seconds.

Optimization: Objective #139: 4.41511e+00 (f/f0=2.433e-01), gradient 2-norm: 7.35067e+13
Hessian not updated during iteration 39.
It: 39 | v: 4.415e+00 | ls-its:  3 | pg: 7.29e+13 | ρ:  6.68e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.874029146 seconds.

Optimization: Objective #140: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31214e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.858905205 seconds.

Optimization: Objective #141: 1.12792e+01 (f/f0=6.214e-01), gradient 2-norm: 6.79141e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.973667183 seconds.

Optimization: Objective #142: 4.50478e+00 (f/f0=2.482e-01), gradient 2-norm: 8.81339e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.889134716 seconds.

Optimization: Objective #143: 4.40706e+00 (f/f0=2.428e-01), gradient 2-norm: 7.66035e+13
Hessian not updated during iteration 40.
It: 40 | v: 4.407e+00 | ls-its:  4 | pg: 7.66e+13 | ρ:  4.72e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.240351675 seconds.

Optimization: Objective #144: 6.44733e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23239e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.92878068 seconds.

Optimization: Objective #145: 1.16592e+01 (f/f0=6.424e-01), gradient 2-norm: 4.92214e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.94327477 seconds.

Optimization: Objective #146: 4.39107e+00 (f/f0=2.419e-01), gradient 2-norm: 7.30034e+13
Hessian not updated during iteration 41.
It: 41 | v: 4.391e+00 | ls-its:  3 | pg: 7.25e+13 | ρ:  6.68e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.924597889 seconds.

Optimization: Objective #147: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31213e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.937353046 seconds.

Optimization: Objective #148: 1.11496e+01 (f/f0=6.143e-01), gradient 2-norm: 6.84080e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.974579447 seconds.

Optimization: Objective #149: 4.46927e+00 (f/f0=2.462e-01), gradient 2-norm: 8.69924e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.934717157 seconds.

Optimization: Objective #150: 4.38367e+00 (f/f0=2.415e-01), gradient 2-norm: 7.60032e+13
Hessian not updated during iteration 42.
It: 42 | v: 4.384e+00 | ls-its:  4 | pg: 7.60e+13 | ρ:  4.75e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.88319222 seconds.

Optimization: Objective #151: 6.44734e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23240e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.903754841 seconds.

Optimization: Objective #152: 1.16640e+01 (f/f0=6.426e-01), gradient 2-norm: 4.92437e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 1.033233657 seconds.

Optimization: Objective #153: 4.36903e+00 (f/f0=2.407e-01), gradient 2-norm: 7.25378e+13
Hessian not updated during iteration 43.
It: 43 | v: 4.369e+00 | ls-its:  3 | pg: 7.20e+13 | ρ:  6.69e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.842564394 seconds.

Optimization: Objective #154: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31211e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.917087527 seconds.

Optimization: Objective #155: 1.10228e+01 (f/f0=6.073e-01), gradient 2-norm: 6.89201e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.853660135 seconds.

Optimization: Objective #156: 4.43730e+00 (f/f0=2.445e-01), gradient 2-norm: 8.58692e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.915010947 seconds.

Optimization: Objective #157: 4.36223e+00 (f/f0=2.403e-01), gradient 2-norm: 7.54447e+13
Hessian not updated during iteration 44.
It: 44 | v: 4.362e+00 | ls-its:  4 | pg: 7.54e+13 | ρ:  4.76e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.868120291 seconds.

Optimization: Objective #158: 6.44735e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23241e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.964061082 seconds.

Optimization: Objective #159: 1.16684e+01 (f/f0=6.429e-01), gradient 2-norm: 4.92644e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.868997586 seconds.

Optimization: Objective #160: 4.34875e+00 (f/f0=2.396e-01), gradient 2-norm: 7.20904e+13
Hessian not updated during iteration 45.
It: 45 | v: 4.349e+00 | ls-its:  3 | pg: 7.16e+13 | ρ:  6.69e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.932801149 seconds.

Optimization: Objective #161: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31210e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.872479345 seconds.

Optimization: Objective #162: 1.09007e+01 (f/f0=6.006e-01), gradient 2-norm: 6.94315e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.84469488 seconds.

Optimization: Objective #163: 4.40864e+00 (f/f0=2.429e-01), gradient 2-norm: 8.48132e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.893451377 seconds.

Optimization: Objective #164: 4.34248e+00 (f/f0=2.393e-01), gradient 2-norm: 7.48987e+13
Hessian not updated during iteration 46.
It: 46 | v: 4.342e+00 | ls-its:  4 | pg: 7.49e+13 | ρ:  4.78e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.919453121 seconds.

Optimization: Objective #165: 6.44736e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23241e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.99460347 seconds.

Optimization: Objective #166: 1.16727e+01 (f/f0=6.431e-01), gradient 2-norm: 4.92831e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.826957113 seconds.

Optimization: Objective #167: 4.33005e+00 (f/f0=2.386e-01), gradient 2-norm: 7.16558e+13
Hessian not updated during iteration 47.
It: 47 | v: 4.330e+00 | ls-its:  3 | pg: 7.12e+13 | ρ:  6.70e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.911166163 seconds.

Optimization: Objective #168: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31209e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.915855712 seconds.

Optimization: Objective #169: 1.07818e+01 (f/f0=5.940e-01), gradient 2-norm: 6.99199e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.846609706 seconds.

Optimization: Objective #170: 4.38271e+00 (f/f0=2.415e-01), gradient 2-norm: 8.38040e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.944314119 seconds.

Optimization: Objective #171: 4.32423e+00 (f/f0=2.383e-01), gradient 2-norm: 7.44021e+13
Hessian not updated during iteration 48.
It: 48 | v: 4.324e+00 | ls-its:  4 | pg: 7.44e+13 | ρ:  4.81e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.89435638 seconds.

Optimization: Objective #172: 6.44737e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23243e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.977065754 seconds.

Optimization: Objective #173: 1.16766e+01 (f/f0=6.433e-01), gradient 2-norm: 4.93001e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.891328689 seconds.

Optimization: Objective #174: 4.31272e+00 (f/f0=2.376e-01), gradient 2-norm: 7.12238e+13
Hessian not updated during iteration 49.
It: 49 | v: 4.313e+00 | ls-its:  3 | pg: 7.08e+13 | ρ:  6.70e-01 | qp-its:  1 +  0 | n-active:   3
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.903284701 seconds.

Optimization: Objective #175: 1.62274e+01 (f/f0=8.941e-01), gradient 2-norm: 1.31208e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.882679703 seconds.

Optimization: Objective #176: 1.06686e+01 (f/f0=5.878e-01), gradient 2-norm: 7.03663e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.823272761 seconds.

Optimization: Objective #177: 4.35932e+00 (f/f0=2.402e-01), gradient 2-norm: 8.28852e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.960155103 seconds.

Optimization: Objective #178: 4.30732e+00 (f/f0=2.373e-01), gradient 2-norm: 7.38933e+13
Hessian not updated during iteration 50.
It: 50 | v: 4.307e+00 | ls-its:  4 | pg: 7.39e+13 | ρ:  4.81e-01 | qp-its:  1 +  0 | n-active:   3
Optimization: Finished in 452.992763366 seconds.

Print the optimization overview

If we display the optimization overview, we can see that there are now additional columns indicating the optimized values. Note that while the permeability and porosities are well matched, the heat capacity of the low permeable layers are not very accurate. There is likely not enough data in the production profiles to constrain the heat capacity of the low permeable layers, as there is limited heat siphoned from these layers in the truth case.

opt

DictParameters with 5 parameters (3 active), and 0 multipliers:
Active optimization parameters
┌─────────────────────┬────────────────┬───────┬──────────┬──────────┬──────────
│                Name │ Initial value  │ Count │      Min │      Max │ Optimiz ⋯
├─────────────────────┼────────────────┼───────┼──────────┼──────────┼──────────
│          layer_perm │ 1.97e-13 ± 0.0 │     3 │ 9.87e-15 │ 1.48e-12 │ 1.45e-1 ⋯
│ layer_heat_capacity │ 400.0 ± 0.0    │     3 │    400.0 │   1000.0 │ 400.0 ± ⋯
│    layer_porosities │ 0.2 ± 2.78e-17 │     3 │     0.05 │     0.35 │ 0.0621, ⋯
└─────────────────────┴────────────────┴───────┴──────────┴──────────┴──────────
                                                               2 columns omitted
Inactive optimization parameters
┌─────────────────────────┬──────────────────┬───────┬─────┬─────┐
│                    Name │ Initial value    │ Count │ Min │ Max │
├─────────────────────────┼──────────────────┼───────┼─────┼─────┤
│          injection_rate │ 0.015 ± 3.47e-18 │    10 │   - │   - │
│ injection_temperature_C │ 15.0 ± 0.0       │    10 │   - │   - │
└─────────────────────────┴──────────────────┴───────┴─────┴─────┘
No multipliers set.

Simulate the optimized case

case_opt = setup_doublet_case(prm_opt)
ws_opt, states_opt = simulate_reservoir(case_opt)

ReservoirSimResult with 92 entries:

  wells (2 present):
    :Producer
    :Injector
    Results per well:
       :lrat => Vector{Float64} of size (92,)
       :wrat => Vector{Float64} of size (92,)
       :temperature => Vector{Float64} of size (92,)
       :control => Vector{Symbol} of size (92,)
       :Aqueous_mass_rate => Vector{Float64} of size (92,)
       :bhp => Vector{Float64} of size (92,)
       :wcut => Vector{Float64} of size (92,)
       :mass_rate => Vector{Float64} of size (92,)
       :rate => Vector{Float64} of size (92,)
       :mrat => Vector{Float64} of size (92,)

  states (Vector with 92 entries, reservoir variables for each state)
    :Pressure => Vector{Float64} of size (1000,)
    :TotalMasses => Matrix{Float64} of size (1, 1000)
    :TotalThermalEnergy => Vector{Float64} of size (1000,)
    :FluidEnthalpy => Matrix{Float64} of size (1, 1000)
    :Temperature => Vector{Float64} of size (1000,)
    :PhaseMassDensities => Matrix{Float64} of size (1, 1000)
    :RockInternalEnergy => Vector{Float64} of size (1000,)
    :FluidInternalEnergy => Matrix{Float64} of size (1, 1000)

  time (report time for each state)
     Vector{Float64} of length 92

  result (extended states, reports)
     SimResult with 92 entries

  extra
     Dict{Any, Any} with keys :simulator, :config

  Completed at Feb. 23 2026 15:37 after 915 milliseconds, 128 microseconds, 882 nanoseconds.

Plot the well responses

We plot the well responses for the producer temperature, producer water rate, and injector bottom hole pressure. These values represent the data used in the objective function. We observe good match, which is consistent with the reduction in the objective function valeu during the optimization.

get_wtime(w) = convert_from_si.(w.time, :day)
get_prod_temp(w) = convert_from_si.(w[:Producer, :temperature], :Celsius)
get_prod_rate(w) = -w[:Producer, :wrat]/si_unit(:liter)
get_inj_bhp(w) = convert_from_si.(w[:Injector, :bhp], :bar)

fig = Figure(size = (1200, 800))
ax = Axis(fig[1, 1], title = "Producer temperature", ylabel = "Temperature (°C)", xlabel = "Time (days)")
scatter!(ax, get_wtime(ws), get_prod_temp(ws), label = "Truth")
lines!(ax, get_wtime(ws_guess), get_prod_temp(ws_guess), label = "Initial guess")
lines!(ax, get_wtime(ws_opt), get_prod_temp(ws_opt), label = "Optimized")
axislegend(position = :rc)
ax = Axis(fig[2, 1], title = "Producer water rate", ylabel = "Liter / s", xlabel = "Time (days)")
scatter!(ax, get_wtime(ws), get_prod_rate(ws), label = "Truth")
lines!(ax, get_wtime(ws_guess), get_prod_rate(ws_guess), label = "Initial guess")
lines!(ax, get_wtime(ws_opt), get_prod_rate(ws_opt), label = "Optimized")
axislegend(position = :rc)
ax = Axis(fig[3, 1], title = "Producer bottom hole pressure", ylabel = "Pressure (bar)", xlabel = "Time (days)")
scatter!(ax, get_wtime(ws), get_inj_bhp(ws), label = "Truth")
lines!(ax, get_wtime(ws_guess), get_inj_bhp(ws_guess), label = "Initial guess")
lines!(ax, get_wtime(ws_opt), get_inj_bhp(ws_opt), label = "Optimized")
axislegend(position = :rc)
fig

Plot the spatial results

We plot the spatial results for the truth case, the initial guess, and the optimized case. The temperature is plotted in Celsius and we use the same color scale for all steps. Note that in terms of the optimizer itself, this is hidden data: The objective function only matches the well responses. Getting a good match in the spatial distribution of temperature is a side-effect of the physics and parametrization of the model, as different physics or a different parameterization could lead to good match in terms of the objective function, even without good match for the spatial distribution.

step = 80
cmap = reverse(to_colormap(:heat))
fig = Figure(size = (1200, 400))
ax = Axis3(fig[1, 1], title = "Truth")
plot_cell_data!(ax, rmesh, states[step][:Temperature] .- 273.15, colorrange = (10.0, 100.0), colormap = cmap)
ax.elevation[] = 0.0
ax.azimuth[] = -π/2
hidedecorations!(ax)

ax = Axis3(fig[1, 2], title = "Initial guess")
plot_cell_data!(ax, rmesh, states_guess[step][:Temperature] .- 273.15, colorrange = (10.0, 100.0), colormap = cmap)
ax.elevation[] = 0.0
ax.azimuth[] = -π/2
hidedecorations!(ax)

ax = Axis3(fig[1, 3], title = "Optimized")
plt = plot_cell_data!(ax, rmesh, states_opt[step][:Temperature] .- 273.15, colorrange = (10.0, 100.0), colormap = cmap)
ax.elevation[] = 0.0
ax.azimuth[] = -π/2
hidedecorations!(ax)
Colorbar(fig[2, 1:3], plt, vertical = false)
fig

Set up control optimization

We can also use the same setup to perform control optimization, where we now can take advantage of the per-interval selection of rates and temperatures. Admittely, this problems is fairly simple, so the optimization is more conceptual than realistic: We define a new objective function that uses a fixed cost for the injected water (per degree times rate) and a similar value of produced heat. To make the optimization problem non-trivial, the cost of additional water (or higher temperature water) is significantly higher than the value of produced water with the same temperature.

temperature_injection_cost = 20.0
temperature_production_value = 8.0

function optimization_objective(m, s, dt, step_info, forces)
    T_at_prod = convert_from_si(compute_well_qoi(m, s, forces, :Producer, :temperature), :Celsius)
    T_at_inj = convert_from_si(forces[:Facility].control[:Injector].temperature, :Celsius)

    mass_rate_injector = compute_well_qoi(m, s, forces, :Injector, :mass_rate)
    mass_rate_producer = compute_well_qoi(m, s, forces, :Producer, :mass_rate)

    cost_inj = abs(mass_rate_injector) * T_at_inj * temperature_injection_cost
    value_prod = abs(mass_rate_producer) * T_at_prod * temperature_production_value
    return dt * (value_prod - cost_inj) / total_time
end

opt_ctrl = JutulDarcy.setup_reservoir_dict_optimization(prm_truth, setup_doublet_case)

DictParameters with 5 parameters (0 active), and 0 multipliers:
No active optimization parameters.
Inactive optimization parameters
┌─────────────────────────┬─────────────────────────────┬───────┬─────┬─────┐
│                    Name │ Initial value               │ Count │ Min │ Max │
├─────────────────────────┼─────────────────────────────┼───────┼─────┼─────┤
│     layer_heat_capacity │ 500.0, 600.0, 450.0         │     3 │   - │   - │
│          injection_rate │ 0.015 ± 3.47e-18            │    10 │   - │   - │
│ injection_temperature_C │ 15.0 ± 0.0                  │    10 │   - │   - │
│              layer_perm │ 9.87e-15, 7.9e-13, 1.97e-14 │     3 │   - │   - │
│        layer_porosities │ 0.1, 0.3, 0.1               │     3 │   - │   - │
└─────────────────────────┴─────────────────────────────┴───────┴─────┴─────┘
No multipliers set.

Set optimization to use injection rate and temperature

Note that as these are represented as per-interval values, we could also have passed vectors of equal length as the number of intervals for more fine-grained control over the limits. We specify that the dependencies include the whole case instead of just state0 and parameters since the forces depend on the optimization parameters.

free_optimization_parameter!(opt_ctrl, "injection_temperature_C", abs_max = 80.0, abs_min = 10.0)
free_optimization_parameter!(opt_ctrl, "injection_rate", abs_min = 1.0*liter/second, abs_max = 30.0*liter/second)

DictParameters with 5 parameters (2 active), and 0 multipliers:
Active optimization parameters
┌─────────────────────────┬──────────────────┬───────┬───────┬──────┐
│                    Name │ Initial value    │ Count │   Min │  Max │
├─────────────────────────┼──────────────────┼───────┼───────┼──────┤
│ injection_temperature_C │ 15.0 ± 0.0       │    10 │  10.0 │ 80.0 │
│          injection_rate │ 0.015 ± 3.47e-18 │    10 │ 0.001 │ 0.03 │
└─────────────────────────┴──────────────────┴───────┴───────┴──────┘
Inactive optimization parameters
┌─────────────────────┬─────────────────────────────┬───────┬─────┬─────┐
│                Name │ Initial value               │ Count │ Min │ Max │
├─────────────────────┼─────────────────────────────┼───────┼─────┼─────┤
│ layer_heat_capacity │ 500.0, 600.0, 450.0         │     3 │   - │   - │
│          layer_perm │ 9.87e-15, 7.9e-13, 1.97e-14 │     3 │   - │   - │
│    layer_porosities │ 0.1, 0.3, 0.1               │     3 │   - │   - │
└─────────────────────┴─────────────────────────────┴───────┴─────┴─────┘
No multipliers set.

Call the optimizer

prm_opt_ctrl = JutulDarcy.optimize_reservoir(opt_ctrl, optimization_objective, maximize = true, deps = :case, optimizer = :lbfgsb_qp);
opt_ctrl

DictParameters with 5 parameters (2 active), and 0 multipliers:
Active optimization parameters
┌─────────────────────────┬──────────────────┬───────┬───────┬──────┬───────────
│                    Name │ Initial value    │ Count │   Min │  Max │ Optimize ⋯
├─────────────────────────┼──────────────────┼───────┼───────┼──────┼───────────
│ injection_temperature_C │ 15.0 ± 0.0       │    10 │  10.0 │ 80.0 │ 10.8 ± 1 ⋯
│          injection_rate │ 0.015 ± 3.47e-18 │    10 │ 0.001 │ 0.03 │ 0.0154 ± ⋯
└─────────────────────────┴──────────────────┴───────┴───────┴──────┴───────────
                                                               2 columns omitted
Inactive optimization parameters
┌─────────────────────┬─────────────────────────────┬───────┬─────┬─────┐
│                Name │ Initial value               │ Count │ Min │ Max │
├─────────────────────┼─────────────────────────────┼───────┼─────┼─────┤
│ layer_heat_capacity │ 500.0, 600.0, 450.0         │     3 │   - │   - │
│          layer_perm │ 9.87e-15, 7.9e-13, 1.97e-14 │     3 │   - │   - │
│    layer_porosities │ 0.1, 0.3, 0.1               │     3 │   - │   - │
└─────────────────────┴─────────────────────────────┴───────┴─────┴─────┘
No multipliers set.

Plot the optimized injection rates and temperatures

The optimized injection rates and temperatures are plotted for each interval. The base case is shown in blue, while the optimized case is shown in orange. Note that the optimized case has reduced the injection temperature to the lower limit for all steps, and instead increase the injection rate significantly. The injection rate has a decrease part-way during the simulation, which increases the residence time of the injected water, allowing additional heat to be siphoned from the low permeable layers.

fig = Figure(size = (1200, 400))
ax = Axis(fig[1, 1], title = "Optimized injection temperature", ylabel = "Injection temperature (°C)", xlabel = "Interval")
scatter!(ax, prm_truth["injection_temperature_C"], label = "Base case")
scatter!(ax, prm_opt_ctrl["injection_temperature_C"], label = "Optimized case")
axislegend(position = :rc)

ax = Axis(fig[1, 2], title = "Optimized injection rate", ylabel = "Liter/second", xlabel = "Interval")
scatter!(ax, prm_truth["injection_rate"]./(liter/second), label = "Base case")
scatter!(ax, prm_opt_ctrl["injection_rate"]./(liter/second), label = "Optimized case")
axislegend(position = :rc)
fig

Simulate the optimized case

case_opt_ctrl = setup_doublet_case(prm_opt_ctrl)
ws_opt_ctrl, states_opt_ctrl = simulate_reservoir(case_opt_ctrl)

ReservoirSimResult with 92 entries:

  wells (2 present):
    :Producer
    :Injector
    Results per well:
       :lrat => Vector{Float64} of size (92,)
       :wrat => Vector{Float64} of size (92,)
       :temperature => Vector{Float64} of size (92,)
       :control => Vector{Symbol} of size (92,)
       :Aqueous_mass_rate => Vector{Float64} of size (92,)
       :bhp => Vector{Float64} of size (92,)
       :wcut => Vector{Float64} of size (92,)
       :mass_rate => Vector{Float64} of size (92,)
       :rate => Vector{Float64} of size (92,)
       :mrat => Vector{Float64} of size (92,)

  states (Vector with 92 entries, reservoir variables for each state)
    :Pressure => Vector{Float64} of size (1000,)
    :TotalMasses => Matrix{Float64} of size (1, 1000)
    :TotalThermalEnergy => Vector{Float64} of size (1000,)
    :FluidEnthalpy => Matrix{Float64} of size (1, 1000)
    :Temperature => Vector{Float64} of size (1000,)
    :PhaseMassDensities => Matrix{Float64} of size (1, 1000)
    :RockInternalEnergy => Vector{Float64} of size (1000,)
    :FluidInternalEnergy => Matrix{Float64} of size (1, 1000)

  time (report time for each state)
     Vector{Float64} of length 92

  result (extended states, reports)
     SimResult with 92 entries

  extra
     Dict{Any, Any} with keys :simulator, :config

  Completed at Feb. 23 2026 15:39 after 942 milliseconds, 751 microseconds, 850 nanoseconds.

Plot the distribution of temperature with and without optimization

step = 80
cmap = reverse(to_colormap(:heat))
fig = Figure(size = (1000, 400))
ax = Axis3(fig[1, 1], title = "Base case")
plot_cell_data!(ax, rmesh, states[step][:Temperature] .- 273.15, colorrange = (10.0, 100.0), colormap = cmap)
ax.elevation[] = 0.0
ax.azimuth[] = -π/2
hidedecorations!(ax)

ax = Axis3(fig[1, 2], title = "Optimized")
plt = plot_cell_data!(ax, rmesh, states_opt_ctrl[step][:Temperature] .- 273.15, colorrange = (10.0, 100.0), colormap = cmap)
ax.elevation[] = 0.0
ax.azimuth[] = -π/2
hidedecorations!(ax)
Colorbar(fig[2, 1:2], plt, vertical = false)
fig

Plot the total thermal energy in the reservoir

The total thermal energy in the reservoir is computed as the sum of the thermal energy in each cell, which is the result of the rock heat capacity, porosity, fluid heat capacity and the temperature in each cell. The optimized strategy significantly decreases the remaining thermal energy in the reservoir, while still producing less cost than the base case according to our objective. The 2D nature of this problem makes it easy to recover a large amount energy, as the majority of the cells are swept by the cold front.

total_energy = map(s -> sum(s[:TotalThermalEnergy]), states)
total_energy_opt = map(s -> sum(s[:TotalThermalEnergy]), states_opt_ctrl)

fig = Figure(size = (1200, 400))
ax = Axis(fig[1, 1], title = "Total thermal energy", ylabel = "Total remaining energy (megajoules)", xlabel = "Time (days)")
t = ws.time ./ si_unit(:day)
lines!(ax, t, total_energy./1e6, label = "Base case")
lines!(ax, t, total_energy_opt./1e6, label = "Optimized case")
axislegend(position = :rc)
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, or as a Jupyter Notebook

This example took 588.310558886 seconds to complete.

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