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. 04 2026 10:18 after 4 seconds, 544 milliseconds, 898.3 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. 04 2026 10:18 after 801 milliseconds, 215 microseconds, 880 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 66.792044372 seconds.
Optimization: Adjoint solve took 37.801887366 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 0.997142606 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 0.834857285 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 0.851617935 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 0.965972172 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 0.817198738 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 0.940392053 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 0.815713621 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 0.914053919 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 0.840868392 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 0.841363954 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 0.866116982 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 0.841299013 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 0.910883639 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 0.830989548 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 0.901379205 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 0.844410108 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 0.877597052 seconds.

Optimization: Objective #18: 6.33532e+01 (f/f0=3.491e+00), gradient 2-norm: 6.17373e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.843196999 seconds.

Optimization: Objective #19: 1.08161e+01 (f/f0=5.959e-01), gradient 2-norm: 3.33160e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.842791149 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 0.927468665 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 0.799817198 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 0.9101973 seconds.

Optimization: Objective #23: 1.15286e+01 (f/f0=6.352e-01), gradient 2-norm: 8.12134e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.785667192 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 0.904787335 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 0.861652734 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 0.828891257 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 0.855526227 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 0.822258747 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 0.944961625 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 0.837719305 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 0.920457939 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 0.835175367 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 0.918443037 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 0.847127694 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 0.829465433 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 0.862586632 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 0.811157715 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 0.885372898 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 0.811668777 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 0.905338754 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 0.81160108 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 0.896950021 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 0.793490891 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 0.900423408 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 0.841490805 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 0.843637035 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 0.84562337 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 0.811419923 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 0.893820499 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 0.859247724 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 0.921662057 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 0.84673094 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 0.897633417 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 0.832561168 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 0.91551981 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 0.806072132 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 0.829217632 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 0.857173794 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 0.819534774 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 0.902124688 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 0.856463577 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 0.919600304 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 0.802579492 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 0.882353953 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 0.829906807 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 0.961973655 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 0.82381166 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 0.810101915 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 0.857281319 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 0.815020957 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 0.872452137 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 0.843009914 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 0.948541763 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 0.82941408 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 0.915746527 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 0.814375911 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 0.891944496 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 0.78850537 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 0.826192684 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 0.861679569 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 0.830299058 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 0.893705687 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 0.80876885 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 0.901104281 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 0.81177485 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 0.939137346 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 0.856901986 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 0.891131689 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 0.817068604 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 0.815696809 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 0.824603225 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 0.80543044 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 0.877846436 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 0.834357897 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 0.953650333 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 0.830432222 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 0.912873654 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 0.839051602 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 0.909450504 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 0.834452249 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 0.902439116 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 0.845543974 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 0.833545167 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 0.825304726 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 0.826597427 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 0.861720233 seconds.

Optimization: Objective #107: 4.77336e+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 0.841087786 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 0.945780031 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 0.819208941 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 0.915304004 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 0.828981878 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 0.926986206 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 0.85799445 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 0.934634223 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 0.848548294 seconds.

Optimization: Objective #116: 6.44740e+01 (f/f0=3.552e+00), gradient 2-norm: 6.23242e+15
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.84747733 seconds.

Optimization: Objective #117: 1.16343e+01 (f/f0=6.410e-01), gradient 2-norm: 4.90968e+14
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.828728421 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 0.817196643 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 0.832991215 seconds.

Optimization: Objective #120: 1.17059e+01 (f/f0=6.450e-01), gradient 2-norm: 6.62420e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.87469447 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 0.89336756 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 0.828124912 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 0.911315884 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 0.815679378 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 0.906802639 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 0.800449244 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 0.903036538 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 0.836887726 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 0.921526727 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 0.802778026 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 0.825294327 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 0.817376094 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 0.813492299 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 0.840561532 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 0.808881112 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 0.90704486 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 0.844609921 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 0.939781375 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 0.823276515 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 0.924952037 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 0.809954838 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 0.914173668 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 0.853893603 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 0.930052126 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 0.844642695 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 0.907649504 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 0.839441073 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 0.834259471 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 0.837642462 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 0.858215269 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 0.816047552 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 0.834318207 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 0.842074357 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 0.834621371 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 0.944551208 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 0.843340276 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 0.95933735 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 0.877152933 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 0.922866021 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 0.830834468 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 0.883548855 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 0.843800937 seconds.

Optimization: Objective #163: 4.40864e+00 (f/f0=2.429e-01), gradient 2-norm: 8.48133e+13
Jutul: Simulating 30 years, 11.82 weeks as 92 report steps
Optimization: Adjoint solve took 0.932742868 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 0.859258177 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 0.853121114 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 0.847125764 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 0.825241793 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 0.846484299 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 0.825778725 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 0.866927922 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 0.874305052 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 0.864575523 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 0.854049559 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 0.912285245 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 0.797318917 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 0.894345648 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 0.85614242 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 427.187208045 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. 04 2026 10:25 after 896 milliseconds, 386 microseconds, 359 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 │ 0.0157 ± ⋯
└─────────────────────────┴──────────────────┴───────┴───────┴──────┴───────────
                                                               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. 04 2026 10:27 after 876 milliseconds, 133 microseconds, 617 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 562.236599684 seconds to complete.

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