(modules/porous_flow/examples/ates/ates.i)
# Simulation designed to assess the recovery efficiency of a single-well ATES system
# Using KT stabilisation
# Boundary conditions: fixed porepressure and temperature at top, bottom and far end of model.
#####################################
flux_limiter = minmod # minmod, vanleer, mc, superbee, none
# depth of top of aquifer (m)
depth = 400
inject_fluid_mass = 1E8 # kg
produce_fluid_mass = ${inject_fluid_mass} # kg
inject_temp = 90 # degC
inject_time = 91 # days
store_time = 91 # days
produce_time = 91 # days
rest_time = 91 # days
num_cycles = 5 # Currently needs to be <= 10
cycle_length = '${fparse inject_time + store_time + produce_time + rest_time}'
end_simulation = '${fparse cycle_length * num_cycles}'
# Note: I have setup 10 cycles but you can set num_cycles less than 10.
start_injection1 = 0
start_injection2 = ${cycle_length}
start_injection3 = '${fparse cycle_length * 2}'
start_injection4 = '${fparse cycle_length * 3}'
start_injection5 = '${fparse cycle_length * 4}'
start_injection6 = '${fparse cycle_length * 5}'
start_injection7 = '${fparse cycle_length * 6}'
start_injection8 = '${fparse cycle_length * 7}'
start_injection9 = '${fparse cycle_length * 8}'
start_injection10 = '${fparse cycle_length * 9}'
end_injection1 = '${fparse start_injection1 + inject_time}'
end_injection2 = '${fparse start_injection2 + inject_time}'
end_injection3 = '${fparse start_injection3 + inject_time}'
end_injection4 = '${fparse start_injection4 + inject_time}'
end_injection5 = '${fparse start_injection5 + inject_time}'
end_injection6 = '${fparse start_injection6 + inject_time}'
end_injection7 = '${fparse start_injection7 + inject_time}'
end_injection8 = '${fparse start_injection8 + inject_time}'
end_injection9 = '${fparse start_injection9 + inject_time}'
end_injection10 = '${fparse start_injection10 + inject_time}'
start_production1 = '${fparse end_injection1 + store_time}'
start_production2 = '${fparse end_injection2 + store_time}'
start_production3 = '${fparse end_injection3 + store_time}'
start_production4 = '${fparse end_injection4 + store_time}'
start_production5 = '${fparse end_injection5 + store_time}'
start_production6 = '${fparse end_injection6 + store_time}'
start_production7 = '${fparse end_injection7 + store_time}'
start_production8 = '${fparse end_injection8 + store_time}'
start_production9 = '${fparse end_injection9 + store_time}'
start_production10 = '${fparse end_injection10 + store_time}'
end_production1 = '${fparse start_production1 + produce_time}'
end_production2 = '${fparse start_production2 + produce_time}'
end_production3 = '${fparse start_production3 + produce_time}'
end_production4 = '${fparse start_production4 + produce_time}'
end_production5 = '${fparse start_production5 + produce_time}'
end_production6 = '${fparse start_production6 + produce_time}'
end_production7 = '${fparse start_production7 + produce_time}'
end_production8 = '${fparse start_production8 + produce_time}'
end_production9 = '${fparse start_production9 + produce_time}'
end_production10 = '${fparse start_production10 + produce_time}'
synctimes = '${start_injection1} ${end_injection1} ${start_production1} ${end_production1}
${start_injection2} ${end_injection2} ${start_production2} ${end_production2}
${start_injection3} ${end_injection3} ${start_production3} ${end_production3}
${start_injection4} ${end_injection4} ${start_production4} ${end_production4}
${start_injection5} ${end_injection5} ${start_production5} ${end_production5}
${start_injection6} ${end_injection6} ${start_production6} ${end_production6}
${start_injection7} ${end_injection7} ${start_production7} ${end_production7}
${start_injection8} ${end_injection8} ${start_production8} ${end_production8}
${start_injection9} ${end_injection9} ${start_production9} ${end_production9}
${start_injection10} ${end_injection10} ${start_production10} ${end_production10}'
#####################################
# Geometry in RZ coordinates
# borehole radius (m)
bh_r = 0.1
# model radius (m)
max_r = 1000
# aquifer thickness (m)
aq_thickness = 20
# cap thickness (m)
cap_thickness = 40
# injection region top and bottom (m). Note, the mesh is created with the aquifer in y = (-0.5 * aq_thickness, 0.5 * aq_thickness), irrespective of depth (depth only sets the insitu porepressure and temperature)
screen_top = '${fparse 0.5 * aq_thickness}'
screen_bottom = '${fparse -0.5 * aq_thickness}'
# number of elements in radial direction
num_r = 25
# number of elements across half height of aquifer
num_y_aq = 10
# number of elements across height of cap
num_y_cap = 8
# mesh bias in radial direction
bias_r = 1.22
# mesh bias in vertical direction in aquifer top
bias_y_aq_top = 0.9
# mesh bias in vertical direction in cap top
bias_y_cap_top = 1.3
# mesh bias in vertical direction in aquifer bottom
bias_y_aq_bottom = '${fparse 1.0 / bias_y_aq_top}'
# mesh bias in vertical direction in cap bottom
bias_y_cap_bottom = '${fparse 1.0 / bias_y_cap_top}'
depth_centre = '${fparse depth + aq_thickness/2}'
#####################################
# temperature at ground surface (degC)
temp0 = 20
# Vertical geothermal gradient (K/m). A positive number means temperature increases downwards.
geothermal_gradient = 20E-3
#####################################
# Gravity
gravity = -9.81
#####################################
half_aq_thickness = '${fparse aq_thickness * 0.5}'
half_height = '${fparse half_aq_thickness + cap_thickness}'
approx_screen_length = '${fparse screen_top - screen_bottom}'
# Thermal radius (note this is not strictly correct, it should use the bulk specific heat
# capacity as defined below, but it doesn't matter here because this is purely for
# defining the region of refined mesh)
th_r = '${fparse sqrt(inject_fluid_mass / 1000 * 4.12e6 / (approx_screen_length * 3.1416 * aq_specific_heat_cap * aq_density))}'
# radius of fine mesh
fine_r = '${fparse th_r * 2}'
bias_r_fine = 1
num_r_fine = '${fparse int(fine_r/1)}'
######################################
# aquifer properties
aq_porosity = 0.25
aq_hor_perm = 1E-11 # m^2
aq_ver_perm = 2E-12 # m^2
aq_density = 2650 # kg/m^3
aq_specific_heat_cap = 800 # J/Kg/K
aq_hor_thermal_cond = 3 # W/m/K
aq_ver_thermal_cond = 3 # W/m/K
aq_disp_parallel = 0 # m
aq_disp_perp = 0 # m
# Bulk volumetric heat capacity of aquifer:
aq_vol_cp = '${fparse aq_specific_heat_cap * aq_density * (1 - aq_porosity) + 4180 * 1000 * aq_porosity}'
# Thermal radius (correct version using bulk cp):
R_th = '${fparse sqrt(inject_fluid_mass * 4180 / (approx_screen_length * 3.1416 * aq_vol_cp))}'
aq_lambda_eff_hor = '${fparse aq_hor_thermal_cond + 0.3 * aq_disp_parallel * R_th * aq_vol_cp / (inject_time * 60 * 60 * 24)}'
aq_lambda_eff_ver = '${fparse aq_ver_thermal_cond + 0.3 * aq_disp_perp * R_th * aq_vol_cp / (inject_time * 60 * 60 * 24)}'
aq_hor_dry_thermal_cond = '${fparse aq_lambda_eff_hor * 60 * 60 * 24}' # J/day/m/K
aq_ver_dry_thermal_cond = '${fparse aq_lambda_eff_ver * 60 * 60 * 24}' # J/day/m/K
aq_hor_wet_thermal_cond = '${fparse aq_lambda_eff_hor * 60 * 60 * 24}' # J/day/m/K
aq_ver_wet_thermal_cond = '${fparse aq_lambda_eff_ver * 60 * 60 * 24}' # J/day/m/K
# cap-rock properties
cap_porosity = 0.25
cap_hor_perm = 1E-16 # m^2
cap_ver_perm = 1E-17 # m^2
cap_density = 2650 # kg/m^3
cap_specific_heat_cap = 800 # J/kg/K
cap_hor_thermal_cond = 3 # W/m/K
cap_ver_thermal_cond = 3 # W/m/K
cap_hor_dry_thermal_cond = '${fparse cap_hor_thermal_cond * 60 * 60 * 24}' # J/day/m/K
cap_ver_dry_thermal_cond = '${fparse cap_ver_thermal_cond * 60 * 60 * 24}' # J/day/m/K
cap_hor_wet_thermal_cond = '${fparse cap_hor_thermal_cond * 60 * 60 * 24}' # J/day/m/K
cap_ver_wet_thermal_cond = '${fparse cap_ver_thermal_cond * 60 * 60 * 24}' # J/day/m/K
######################################
[Mesh]
coord_type = RZ
[aq_top_fine]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r_fine}
xmin = ${bh_r}
xmax = ${fine_r}
bias_x = ${bias_r_fine}
bias_y = ${bias_y_aq_top}
ny = ${num_y_aq}
ymin = 0
ymax = ${half_aq_thickness}
[]
[cap_top_fine]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r_fine}
xmin = ${bh_r}
xmax = ${fine_r}
bias_x = ${bias_r_fine}
bias_y = ${bias_y_cap_top}
ny = ${num_y_cap}
ymax = ${half_height}
ymin = ${half_aq_thickness}
[]
[aq_and_cap_top_fine]
type = StitchMeshGenerator
inputs = 'aq_top_fine cap_top_fine'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'top bottom'
[]
[aq_bottom_fine]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r_fine}
xmin = ${bh_r}
xmax = ${fine_r}
bias_x = ${bias_r_fine}
bias_y = ${bias_y_aq_bottom}
ny = ${num_y_aq}
ymax = 0
ymin = -${half_aq_thickness}
[]
[cap_bottom_fine]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r_fine}
xmin = ${bh_r}
xmax = ${fine_r}
bias_x = ${bias_r_fine}
bias_y = ${bias_y_cap_bottom}
ny = ${num_y_cap}
ymin = -${half_height}
ymax = -${half_aq_thickness}
[]
[aq_and_cap_bottom_fine]
type = StitchMeshGenerator
inputs = 'aq_bottom_fine cap_bottom_fine'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'bottom top'
merge_boundaries_with_same_name = false
[]
[aq_and_cap_fine]
type = StitchMeshGenerator
inputs = 'aq_and_cap_bottom_fine aq_and_cap_top_fine'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'top bottom'
[]
[aq_top]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r}
xmin = ${fine_r}
xmax = ${max_r}
bias_x = ${bias_r}
bias_y = ${bias_y_aq_top}
ny = ${num_y_aq}
ymin = 0
ymax = ${half_aq_thickness}
[]
[cap_top]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r}
xmin = ${fine_r}
xmax = ${max_r}
bias_x = ${bias_r}
bias_y = ${bias_y_cap_top}
ny = ${num_y_cap}
ymax = ${half_height}
ymin = ${half_aq_thickness}
[]
[aq_and_cap_top]
type = StitchMeshGenerator
inputs = 'aq_top cap_top'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'top bottom'
[]
[aq_bottom]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r}
xmin = ${fine_r}
xmax = ${max_r}
bias_x = ${bias_r}
bias_y = ${bias_y_aq_bottom}
ny = ${num_y_aq}
ymax = 0
ymin = -${half_aq_thickness}
[]
[cap_bottom]
type = GeneratedMeshGenerator
dim = 2
nx = ${num_r}
xmin = ${fine_r}
xmax = ${max_r}
bias_x = ${bias_r}
bias_y = ${bias_y_cap_bottom}
ny = ${num_y_cap}
ymin = -${half_height}
ymax = -${half_aq_thickness}
[]
[aq_and_cap_bottom]
type = StitchMeshGenerator
inputs = 'aq_bottom cap_bottom'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'bottom top'
[]
[aq_and_cap]
type = StitchMeshGenerator
inputs = 'aq_and_cap_bottom aq_and_cap_top'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'top bottom'
[]
[aq_and_cap_all]
type = StitchMeshGenerator
inputs = 'aq_and_cap_fine aq_and_cap'
clear_stitched_boundary_ids = true
stitch_boundaries_pairs = 'right left'
[]
[aquifer]
type = ParsedSubdomainMeshGenerator
input = aq_and_cap_all
combinatorial_geometry = 'y >= -${half_aq_thickness} & y <= ${half_aq_thickness}'
block_id = 1
[]
[top_cap]
type = ParsedSubdomainMeshGenerator
input = aquifer
combinatorial_geometry = 'y >= ${half_aq_thickness}'
block_id = 2
[]
[bottom_cap]
type = ParsedSubdomainMeshGenerator
input = top_cap
combinatorial_geometry = 'y <= -${half_aq_thickness}'
block_id = 3
[]
[injection_area]
type = ParsedGenerateSideset
combinatorial_geometry = 'x<=${bh_r}*1.000001 & y >= ${screen_bottom} & y <= ${screen_top}'
included_subdomains = 1
new_sideset_name = 'injection_area'
input = 'bottom_cap'
[]
[rename]
type = RenameBlockGenerator
old_block = '1 2 3'
new_block = 'aquifer caps caps'
input = 'injection_area'
[]
[]
[GlobalParams]
PorousFlowDictator = dictator
gravity = '0 ${gravity} 0'
[]
[Variables]
[porepressure]
[]
[temperature]
scaling = 1E-5
[]
[]
[PorousFlowFullySaturated]
coupling_type = ThermoHydro
porepressure = porepressure
temperature = temperature
fp = tabulated_water
stabilization = KT
flux_limiter_type = ${flux_limiter}
use_displaced_mesh = false
temperature_unit = Celsius
pressure_unit = Pa
time_unit = days
[]
[ICs]
[porepressure]
type = FunctionIC
variable = porepressure
function = insitu_pressure
[]
[temperature]
type = FunctionIC
variable = temperature
function = insitu_temperature
[]
[]
[BCs]
[outer_boundary_porepressure]
type = FunctionDirichletBC
preset = true
variable = porepressure
function = insitu_pressure
boundary = 'bottom right top'
[]
[outer_boundary_temperature]
type = FunctionDirichletBC
preset = true
variable = temperature
function = insitu_temperature
boundary = 'bottom right top'
[]
[inject_heat]
type = FunctionDirichletBC
variable = temperature
function = ${inject_temp}
boundary = 'injection_area'
[]
[inject_fluid]
type = PorousFlowSink
variable = porepressure
boundary = injection_area
flux_function = injection_rate_value
[]
[produce_heat]
type = PorousFlowSink
variable = temperature
boundary = injection_area
flux_function = production_rate_value
fluid_phase = 0
use_enthalpy = true
save_in = heat_flux_out
[]
[produce_fluid]
type = PorousFlowSink
variable = porepressure
boundary = injection_area
flux_function = production_rate_value
[]
[]
[Controls]
[inject_on]
type = ConditionalFunctionEnableControl
enable_objects = 'BCs::inject_heat BCs::inject_fluid'
conditional_function = inject
implicit = false
execute_on = 'initial timestep_begin'
[]
[produce_on]
type = ConditionalFunctionEnableControl
enable_objects = 'BCs::produce_heat BCs::produce_fluid'
conditional_function = produce
implicit = false
execute_on = 'initial timestep_begin'
[]
[]
[Functions]
[insitu_pressure]
type = ParsedFunction
expression = '(y - ${depth_centre}) * 1000 * ${gravity} + 1E5' # approx insitu pressure in Pa
[]
[insitu_temperature]
type = ParsedFunction
expression = '${temp0} + (${depth_centre} - y) * ${geothermal_gradient}'
[]
[inject]
type = ParsedFunction
expression = 'if(t >= ${start_injection1} & t < ${end_injection1}, 1,
if(t >= ${start_injection2} & t < ${end_injection2}, 1,
if(t >= ${start_injection3} & t < ${end_injection3}, 1,
if(t >= ${start_injection4} & t < ${end_injection4}, 1,
if(t >= ${start_injection5} & t < ${end_injection5}, 1,
if(t >= ${start_injection6} & t < ${end_injection6}, 1,
if(t >= ${start_injection7} & t < ${end_injection7}, 1,
if(t >= ${start_injection8} & t < ${end_injection8}, 1,
if(t >= ${start_injection9} & t < ${end_injection9}, 1,
if(t >= ${start_injection10} & t < ${end_injection10}, 1, 0))))))))))'
[]
[produce]
type = ParsedFunction
expression = 'if(t >= ${start_production1} & t < ${end_production1}, 1,
if(t >= ${start_production2} & t < ${end_production2}, 1,
if(t >= ${start_production3} & t < ${end_production3}, 1,
if(t >= ${start_production4} & t < ${end_production4}, 1,
if(t >= ${start_production5} & t < ${end_production5}, 1,
if(t >= ${start_production6} & t < ${end_production6}, 1,
if(t >= ${start_production7} & t < ${end_production7}, 1,
if(t >= ${start_production8} & t < ${end_production8}, 1,
if(t >= ${start_production9} & t < ${end_production9}, 1,
if(t >= ${start_production10} & t < ${end_production10}, 1, 0))))))))))'
[]
[injection_rate_value]
type = ParsedFunction
symbol_names = true_screen_area
symbol_values = true_screen_area
expression = '-${inject_fluid_mass}/(true_screen_area * ${inject_time})'
[]
[production_rate_value]
type = ParsedFunction
symbol_names = true_screen_area
symbol_values = true_screen_area
expression = '${produce_fluid_mass}/(true_screen_area * ${produce_time})'
[]
[heat_out_in_timestep]
type = ParsedFunction
symbol_names = 'dt heat_out'
symbol_values = 'dt heat_out_fromBC'
expression = 'dt*heat_out'
[]
[produced_T_time_integrated]
type = ParsedFunction
symbol_names = 'dt produced_T'
symbol_values = 'dt produced_T'
expression = 'dt*produced_T / ${produce_time}'
[]
[]
[AuxVariables]
[density]
family = MONOMIAL
order = CONSTANT
[]
[porosity]
family = MONOMIAL
order = CONSTANT
[]
[heat_flux_out]
outputs = none
[]
[]
[AuxKernels]
[density]
type = PorousFlowPropertyAux
variable = density
property = density
[]
[porosity]
type = PorousFlowPropertyAux
variable = porosity
property = porosity
[]
[]
[FluidProperties]
[true_water]
type = Water97FluidProperties
[]
[tabulated_water]
type = TabulatedBicubicFluidProperties
input_fp = true_water
temperature_min = 275 # K
temperature_max = 600
interpolated_properties = 'density viscosity enthalpy internal_energy'
fluid_property_output_file = water97_tabulated_modified.csv
# Comment out the fp parameter and uncomment below to use the newly generated tabulation
# fluid_property_file = water97_tabulated_modified.csv
[]
[]
[Materials]
[porosity_aq]
type = PorousFlowPorosityConst
porosity = ${aq_porosity}
block = aquifer
[]
[porosity_caps]
type = PorousFlowPorosityConst
porosity = ${cap_porosity}
block = caps
[]
[permeability_aquifer]
type = PorousFlowPermeabilityConst
block = aquifer
permeability = '${aq_hor_perm} 0 0 0 ${aq_ver_perm} 0 0 0 0'
[]
[permeability_caps]
type = PorousFlowPermeabilityConst
block = caps
permeability = '${cap_hor_perm} 0 0 0 ${cap_ver_perm} 0 0 0 0'
[]
[aq_internal_energy]
type = PorousFlowMatrixInternalEnergy
block = aquifer
density = ${aq_density}
specific_heat_capacity = ${aq_specific_heat_cap}
[]
[caps_internal_energy]
type = PorousFlowMatrixInternalEnergy
block = caps
density = ${cap_density}
specific_heat_capacity = ${cap_specific_heat_cap}
[]
[aq_thermal_conductivity]
type = PorousFlowThermalConductivityIdeal
block = aquifer
dry_thermal_conductivity = '${aq_hor_dry_thermal_cond} 0 0 0 ${aq_ver_dry_thermal_cond} 0 0 0 0'
wet_thermal_conductivity = '${aq_hor_wet_thermal_cond} 0 0 0 ${aq_ver_wet_thermal_cond} 0 0 0 0'
[]
[caps_thermal_conductivity]
type = PorousFlowThermalConductivityIdeal
block = caps
dry_thermal_conductivity = '${cap_hor_dry_thermal_cond} 0 0 0 ${cap_ver_dry_thermal_cond} 0 0 0 0'
wet_thermal_conductivity = '${cap_hor_wet_thermal_cond} 0 0 0 ${cap_ver_wet_thermal_cond} 0 0 0 0'
[]
[]
[Postprocessors]
[true_screen_area] # this accounts for meshes that do not match screen_top and screen_bottom exactly
type = AreaPostprocessor
boundary = injection_area
execute_on = 'initial'
outputs = 'none'
[]
[dt]
type = TimestepSize
[]
[heat_out_fromBC]
type = NodalSum
variable = heat_flux_out
boundary = injection_area
execute_on = 'initial timestep_end'
outputs = 'none'
[]
[heat_out_per_timestep]
type = FunctionValuePostprocessor
function = heat_out_in_timestep
execute_on = 'timestep_end'
outputs = 'none'
[]
[heat_out_cumulative]
type = CumulativeValuePostprocessor
postprocessor = heat_out_per_timestep
execute_on = 'timestep_end'
outputs = 'csv console'
[]
[produced_T]
type = SideAverageValue
boundary = injection_area
variable = temperature
execute_on = 'initial timestep_end'
outputs = 'csv console'
[]
[produced_T_time_integrated]
type = FunctionValuePostprocessor
function = produced_T_time_integrated
execute_on = 'timestep_end'
outputs = 'none'
[]
[produced_T_cumulative]
type = CumulativeValuePostprocessor
postprocessor = produced_T_time_integrated
execute_on = 'timestep_end'
outputs = 'csv console'
[]
[]
[Preconditioning]
[basic]
type = SMP
full = true
petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
petsc_options_value = ' asm lu NONZERO 2'
[]
[]
[Executioner]
type = Transient
solve_type = Newton
end_time = ${end_simulation}
timestep_tolerance = 1e-5
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e-3
growth_factor = 2
[]
dtmax = 1
dtmin = 1e-5
# rough calc for fluid, |R| ~ V*k*1E6 ~ V*1E-5
# rough calc for heat, |R| ~ V*(lam*1E-3 + h*1E-5) ~ V*(1E3 + 1E-2)
# so scale heat by 1E-7 and go for nl_abs_tol = 1E-4, which should give a max error of
# ~1Pa and ~0.1K in the first metre around the borehole
nl_abs_tol = 1E-4
nl_rel_tol = 1E-5
[]
[Outputs]
sync_times = ${synctimes}
[ex]
type = Exodus
time_step_interval = 20
[]
[csv]
type = CSV
execute_postprocessors_on = 'initial timestep_end'
[]
[]