class Scheme(object):
# ------------------------------------------------------------------------------#
def __init__(self, gb):
self.gb = gb
# -- flow -- #
self.discr_flow = Flow(gb)
shape = self.discr_flow.shape()
self.flux_pressure = np.zeros(shape)
# -- temperature -- #
self.discr_temperature = Heat(gb)
shape = self.discr_temperature.shape()
self.temperature = np.zeros(shape)
self.temperature_old = np.zeros(shape)
# -- solute and precipitate -- #
self.discr_solute_advection_diffusion = Transport(gb)
self.discr_solute_precipitate_reaction = Reaction(gb)
shape = self.discr_solute_advection_diffusion.shape()
self.solute = np.zeros(shape)
self.precipitate = np.zeros(shape)
self.solute_old = np.zeros(shape)
self.precipitate_old = np.zeros(shape)
# -- porosity -- #
self.discr_porosity = Porosity(gb)
shape = self.discr_porosity.shape()
self.porosity = np.zeros(shape)
self.porosity_old = np.zeros(shape)
self.porosity_star = np.zeros(shape)
# -- aperture -- #
self.discr_aperture = Aperture(gb)
shape = self.discr_aperture.shape()
self.aperture = np.zeros(shape)
self.aperture_old = np.zeros(shape)
self.aperture_star = np.zeros(shape)
# -- composite variables -- #
self.porosity_aperture_times_solute = np.zeros(shape)
self.porosity_aperture_times_precipitate = np.zeros(shape)
# ------------------------------------------------------------------------------#
def compute_flow(self):
A, b = self.discr_flow.matrix_rhs()
return sps.linalg.spsolve(A, b)
# ------------------------------------------------------------------------------#
def compute_temperature(self, porosity_star, aperture_star):
# compute the matrices
A, M, b = self.discr_temperature.matrix_rhs()
# compute the effective thermal capacity, keeping in mind that the fracture
# contains only water
rc_w = self.discr_temperature.data["rc_w"]
rc_s = self.discr_temperature.data["rc_s"]
c_star = rc_w * (porosity_star + aperture_star) + rc_s * (1 - porosity_star)
c_old = rc_w * (self.porosity_old + self.aperture_old) + rc_s * (1 - self.porosity_old)
# the mass term which considers the contribution from the effective thermal capacity
M_star = M * sps.diags(c_star, 0)
M_old = M * sps.diags(c_old, 0)
# compute the new temperature
return sps.linalg.spsolve(M_star + A, M_old * self.temperature_old + b)
# ------------------------------------------------------------------------------#
def compute_solute_precipitate_advection_diffusion(self, porosity_star, aperture_star):
# compute the matrices
A, M, b = self.discr_solute_advection_diffusion.matrix_rhs()
# the mass term which considers both the porosity and aperture contribution
M_star = M * sps.diags(porosity_star + aperture_star, 0)
M_old = M * sps.diags(self.porosity_old + self.aperture_old, 0)
# compute the new solute
return sps.linalg.spsolve(M_star + A, M_old * self.solute_old + b)
# ------------------------------------------------------------------------------#
def compute_solute_precipitate_rection(self, solute_half, precipitate_half):
# the dof associated to the porous media and fractures, are the first
dof = self.gb.num_cells()
# temporary solution vectors
solute = np.zeros(self.discr_solute_advection_diffusion.shape())
precipitate = np.zeros(self.discr_solute_advection_diffusion.shape())
# compute the new solute and precipitate
solute[:dof], precipitate[:dof] = self.discr_solute_precipitate_reaction.step(
solute_half[:dof],
precipitate_half[:dof],
self.temperature[:dof])
return solute, precipitate
# ------------------------------------------------------------------------------#
def set_old_variables(self):
self.temperature_old = self.temperature.copy()
self.solute_old = self.solute.copy()
self.precipitate_old = self.precipitate.copy()
self.porosity_old = self.porosity.copy()
self.aperture_old = self.aperture.copy()
# ------------------------------------------------------------------------------#
def set_data(self, param):
# set the initial condition
assembler = self.discr_solute_advection_diffusion.assembler
dof = np.cumsum(np.append(0, np.asarray(assembler.full_dof)))
for (g, _), bi in assembler.block_dof.items():
#g = pair[0]
if isinstance(g, pp.Grid):
dof_loc = slice(dof[bi], dof[bi+1])
data = param["temperature"]["initial"]
self.temperature[dof_loc] = data(g, param, param["tol"])
data = param["solute_advection_diffusion"]["initial_solute"]
self.solute[dof_loc] = data(g, param, param["tol"])
data = param["solute_advection_diffusion"]["initial_precipitate"]
self.precipitate[dof_loc] = data(g, param, param["tol"])
data = param["porosity"]["initial"]
self.porosity[dof_loc] = data(g, param, param["tol"])
data = param["aperture"]["initial"]
self.aperture[dof_loc] = data(g, param, param["tol"])
# set the old variables
self.set_old_variables()
# save the initial porosity and aperture
self.discr_porosity.extract(self.porosity, "porosity_initial")
self.discr_aperture.extract(self.aperture, "aperture_initial")
# extract the initialized variables, useful for setting the data
self.extract()
# set now the data for each scheme
self.discr_flow.set_data(param["flow"], param["time"])
self.discr_temperature.set_data(param["temperature"], param["time"])
self.discr_solute_advection_diffusion.set_data(param["solute_advection_diffusion"], param["time"])
self.discr_solute_precipitate_reaction.set_data(param["solute_precipitate_reaction"], param["time"])
self.discr_porosity.set_data(param["porosity"])
self.discr_aperture.set_data(param["aperture"])
# ------------------------------------------------------------------------------#
def extract(self):
self.discr_flow.extract(self.flux_pressure)
self.discr_temperature.extract(self.temperature, "temperature")
self.discr_solute_advection_diffusion.extract(self.solute, "solute")
self.discr_solute_advection_diffusion.extract(self.precipitate, "precipitate")
self.discr_porosity.extract(self.porosity, "porosity")
self.discr_porosity.extract(self.porosity_old, "porosity_old")
self.discr_aperture.extract(self.aperture, "aperture")
self.discr_aperture.extract(self.aperture_old, "aperture_old")
self.discr_solute_advection_diffusion.extract(self.porosity_aperture_times_solute,
"porosity_aperture_times_solute")
self.discr_solute_advection_diffusion.extract(self.porosity_aperture_times_precipitate,
"porosity_aperture_times_precipitate")
# ------------------------------------------------------------------------------#
def vars_to_save(self):
name = ["solute", "precipitate", "porosity", "aperture", "temperature"]
name += ["porosity_aperture_times_solute", "porosity_aperture_times_precipitate"]
return name + [self.discr_flow.pressure, self.discr_flow.P0_flux]
# ------------------------------------------------------------------------------#
def one_step_splitting_scheme(self):
# the dof associated to the porous media and fractures, are the first
dof = slice(0, self.gb.num_cells())
# POINT 1) extrapolate the precipitate to get a better estimate of porosity
precipitate_star = 2*self.precipitate - self.precipitate_old
# POINT 2) compute the porosity and aperture star
porosity_star = self.discr_porosity.step(self.porosity_old, precipitate_star, self.precipitate_old)
self.discr_porosity.extract(porosity_star, "porosity_star")
aperture_star = self.discr_aperture.step(self.aperture_old, precipitate_star, self.precipitate_old)
self.discr_aperture.extract(aperture_star, "aperture_star")
# -- DO THE FLOW PART -- #
# POINT 3) update the data from the previous time step
self.discr_flow.update_data()
# POINT 4) solve the flow part
self.flux_pressure = self.compute_flow()
self.discr_flow.extract(self.flux_pressure)
# -- DO THE HEAT PART -- #
# POINT 5) set the flux and update the data from the previous time step
self.discr_temperature.set_flux(self.discr_flow.flux, self.discr_flow.mortar)
self.discr_temperature.update_data()
# POINT 5) solve the temperature part
self.temperature = self.compute_temperature(porosity_star, aperture_star)
# -- DO THE TRANSPORT PART -- #
# set the flux and update the data from the previous time step
self.discr_solute_advection_diffusion.set_flux(self.discr_flow.flux, self.discr_flow.mortar)
self.discr_solute_advection_diffusion.update_data()
# POINT 6) solve the advection and diffusion part to get the intermediate solute solution
solute_half = self.compute_solute_precipitate_advection_diffusion(porosity_star, aperture_star)
# POINT 7) Since in the advection-diffusion step we have accounted for porosity changes using
# phi_star, the new solute concentration accounts for the change in pore volume, thus, the
# precipitate needs to be updated accordingly
factor = np.zeros(self.porosity_old.size)
factor[dof] = (self.porosity_old[dof] + self.aperture_old[dof]) / (porosity_star[dof] + aperture_star[dof])
precipitate_half = self.precipitate_old * factor
# POINT 8) solve the reaction part
solute_star_star, precipitate_star_star = self.compute_solute_precipitate_rection(solute_half, precipitate_half)
# -- DO THE POROSITY PART -- #
# POINT 9) solve the porosity and aperture part with the true concentration of precipitate
self.porosity = self.discr_porosity.step(self.porosity, precipitate_star_star, self.precipitate_old)
self.aperture = self.discr_aperture.step(self.aperture, precipitate_star_star, self.precipitate_old)
# POINT 10) finally, we correct the concentrations to account for the difference between the extrapolated
# and "true" new porosity to ensure mass conservation
factor = np.zeros(self.porosity_old.size)
factor[dof] = (porosity_star[dof] + aperture_star[dof]) / (self.porosity[dof] + self.aperture[dof])
self.solute = solute_star_star * factor
self.precipitate = precipitate_star_star * factor
# set the old variables
self.set_old_variables()
# compute composite variables
factor = self.porosity + self.aperture
self.porosity_aperture_times_solute = factor * self.solute
self.porosity_aperture_times_precipitate = factor * self.precipitate
# extract all the variables, useful for exporting
self.extract()
class Scheme(object):
# ------------------------------------------------------------------------------#
def __init__(self, gb):
self.gb = gb
# -- flow -- #
self.discr_flow = Flow(gb)
shape = self.discr_flow.shape()
self.flux_pressure = np.zeros(shape)
# -- temperature -- #
self.discr_temperature = Heat(gb)
# -- solute and precipitate -- #
self.discr_solute_advection_diffusion = Transport(gb)
self.discr_solute_precipitate_reaction = Reaction(gb)
# -- porosity -- #
self.discr_porosity = Porosity(gb)
# -- fracture aperture -- #
self.discr_fracture_aperture = FractureAperture(
gb, "fracture_aperture")
# -- layer porosity and aperture -- #
self.discr_layer_porosity = Porosity(gb, "layer_porosity")
self.discr_layer_aperture = LayerAperture(gb, "layer_aperture")
# the actual time of the simulation
self.time = 0
# ------------------------------------------------------------------------------#
def compute_precipitate_temperature_star(self):
for g, d in self.gb:
d[pp.STATE]["precipitate_star"] = 2 * d[
pp.STATE]["precipitate"] - d[pp.STATE]["precipitate_old"]
d[pp.STATE]["temperature_star"] = 2 * d[
pp.STATE]["temperature"] - d[pp.STATE]["temperature_old"]
# ------------------------------------------------------------------------------#
def compute_porosity_aperture_star(self):
dim_max = self.gb.dim_max()
# only the rock matrix has the variable porosity
for g in self.gb.grids_of_dimension(dim_max):
d = self.gb.node_props(g)
d[pp.STATE]["porosity_star"] = self.discr_porosity.step(
d[pp.STATE]["porosity_old"], d[pp.STATE]["precipitate_star"],
d[pp.STATE]["precipitate_old"])
# only the fracture and the layer have the variable aperture
for g in self.gb.grids_of_dimension(dim_max - 1):
d = self.gb.node_props(g)
if "fracture" in g.name:
d[pp.STATE][
"fracture_aperture_star"] = self.discr_fracture_aperture.step(
d[pp.STATE]["fracture_aperture_old"],
d[pp.STATE]["precipitate_star"],
d[pp.STATE]["precipitate_old"])
if "layer" in g.name:
d[pp.STATE]["layer_aperture_star"] = d[
pp.STATE]["layer_aperture_old"]
d[pp.STATE][
"layer_porosity_star"] = self.discr_layer_porosity.step(
d[pp.STATE]["layer_porosity_old"],
d[pp.STATE]["precipitate_star"],
d[pp.STATE]["precipitate_old"])
# ------------------------------------------------------------------------------#
def compute_flow(self):
A, b = self.discr_flow.matrix_rhs()
x = sps.linalg.spsolve(A, b)
if not np.all(np.isfinite(x)):
raise ValueError
self.discr_flow.extract(x)
# ------------------------------------------------------------------------------#
def compute_temperature(self):
A, b = self.discr_temperature.matrix_rhs()
x = sps.linalg.spsolve(A, b)
if not np.all(np.isfinite(x)):
raise ValueError
self.discr_temperature.extract(x, "temperature")
# ------------------------------------------------------------------------------#
def compute_solute_precipitate_advection_diffusion(self):
A, b = self.discr_solute_advection_diffusion.matrix_rhs()
x = sps.linalg.spsolve(A, b)
if not np.all(np.isfinite(x)):
raise ValueError
self.discr_solute_advection_diffusion.extract(x, "solute_half")
# ------------------------------------------------------------------------------#
def correct_precipitate_with_star(self):
for g, d in self.gb:
vol_star = d[pp.STATE]["porosity_star"] + d[pp.STATE]["fracture_aperture_star"] +\
d[pp.STATE]["layer_porosity_star"]
vol_old = d[pp.STATE]["porosity_old"] + d[pp.STATE]["fracture_aperture_old"] + \
d[pp.STATE]["layer_porosity_old"]
d[pp.STATE]["precipitate_half"] = d[
pp.STATE]["precipitate_old"] * (vol_old / vol_star)
# ------------------------------------------------------------------------------#
def compute_solute_precipitate_rection(self):
for g, d in self.gb:
d[pp.STATE]["solute_star_star"], d[pp.STATE]["precipitate_star_star"] = \
self.discr_solute_precipitate_reaction.step(d[pp.STATE]["solute_half"],
d[pp.STATE]["precipitate_half"],
d[pp.STATE]["temperature"])
# ------------------------------------------------------------------------------#
def compute_porosity_aperture(self):
dim_max = self.gb.dim_max()
# only the rock matrix has the variable porosity
for g in self.gb.grids_of_dimension(dim_max):
d = self.gb.node_props(g)
d[pp.STATE]["porosity"] = self.discr_porosity.step(
d[pp.STATE]["porosity"], d[pp.STATE]["precipitate_star_star"],
d[pp.STATE]["precipitate_old"])
# only the fracture and the layer have the variable aperture
for g in self.gb.grids_of_dimension(dim_max - 1):
d = self.gb.node_props(g)
if "fracture" in g.name:
d[pp.STATE][
"fracture_aperture"] = self.discr_fracture_aperture.step(
d[pp.STATE]["fracture_aperture"],
d[pp.STATE]["precipitate_star_star"],
d[pp.STATE]["precipitate_old"])
if "layer" in g.name:
flux_fracture = np.zeros(g.num_cells)
solute_fracture = np.zeros(g.num_cells)
porosity = np.zeros(g.num_cells)
for e, d_e in self.gb.edges_of_node(g):
g_m = d_e["mortar_grid"]
g_l, g_h = self.gb.nodes_of_edge(e)
if g_h.dim < self.gb.dim_max():
# save the flux from the fracture
flux_fracture = -g_m.master_to_mortar_avg().T * d_e[
pp.STATE][self.discr_flow.mortar] / g.cell_volumes
d_fracture = self.gb.node_props(g_l if "fracture" in
g_l.name else g_h)
solute_fracture = g_m.slave_to_mortar_avg(
) * d_fracture[pp.STATE]["solute"]
else:
cell_cell = g_m.mortar_to_master_int(
).T * g_h.cell_faces
# the cells are already ordered according to the layer ordering of the cells given by the mortar
# map
interface_cells = cell_cell.indices
d_h = self.gb.node_props(g_h)
porosity = d_h[pp.STATE]["porosity"][interface_cells]
temperature = d_h[
pp.STATE]["temperature"][interface_cells]
lmbda = self.discr_solute_precipitate_reaction.data[
"lambda"](temperature)
d[pp.STATE]["layer_aperture"] = self.discr_layer_aperture.step(
flux_fracture, porosity, lmbda, self.time, solute_fracture)
d[pp.STATE]["layer_porosity"] = self.discr_layer_porosity.step(
d[pp.STATE]["layer_porosity"],
d[pp.STATE]["precipitate_star_star"],
d[pp.STATE]["precipitate_old"])
# ------------------------------------------------------------------------------#
def correct_precipitate_solute(self):
for g, d in self.gb:
vol_star = d[pp.STATE]["porosity_star"] + d[pp.STATE]["fracture_aperture_star"] +\
d[pp.STATE]["layer_porosity_star"]
vol = d[pp.STATE]["porosity"] + d[pp.STATE]["fracture_aperture"] + \
d[pp.STATE]["layer_porosity"]
d[pp.STATE]["solute"] = d[pp.STATE]["solute_star_star"] * (
vol_star / vol)
d[pp.STATE]["precipitate"] = d[
pp.STATE]["precipitate_star_star"] * (vol_star / vol)
# ------------------------------------------------------------------------------#
def set_old_variables(self):
for g, d in self.gb:
d[pp.STATE]["temperature_old"] = d[pp.STATE]["temperature"].copy()
d[pp.STATE]["solute_old"] = d[pp.STATE]["solute"].copy()
d[pp.STATE]["precipitate_old"] = d[pp.STATE]["precipitate"].copy()
d[pp.STATE]["porosity_old"] = d[pp.STATE]["porosity"].copy()
d[pp.STATE]["fracture_aperture_old"] = d[
pp.STATE]["fracture_aperture"].copy()
d[pp.STATE]["layer_aperture_old"] = d[
pp.STATE]["layer_aperture"].copy()
d[pp.STATE]["layer_porosity_old"] = d[
pp.STATE]["layer_porosity"].copy()
# ------------------------------------------------------------------------------#
def set_data(self, param):
for g, d in self.gb:
data = param["temperature"]["initial"]
d[pp.STATE]["temperature"] = data(g, param, param["tol"])
d[pp.STATE]["temperature_star"] = d[pp.STATE]["temperature"].copy()
data = param["solute_advection_diffusion"]["initial_solute"]
d[pp.STATE]["solute"] = data(g, param, param["tol"])
data = param["solute_advection_diffusion"]["initial_precipitate"]
d[pp.STATE]["precipitate"] = data(g, param, param["tol"])
d[pp.STATE]["precipitate_star"] = d[pp.STATE]["precipitate"].copy()
data = param["porosity"]["initial"]
d[pp.STATE]["porosity_initial"] = data(g, param, param["tol"])
d[pp.STATE]["porosity_star"] = d[
pp.STATE]["porosity_initial"].copy()
d[pp.STATE]["porosity"] = d[pp.STATE]["porosity_initial"].copy()
data = param["fracture_aperture"]["initial"]
d[pp.STATE]["fracture_aperture_initial"] = data(
g, param, param["tol"])
d[pp.STATE]["fracture_aperture_star"] = d[
pp.STATE]["fracture_aperture_initial"].copy()
d[pp.STATE]["fracture_aperture"] = d[
pp.STATE]["fracture_aperture_initial"].copy()
data = param["layer_aperture"]["initial"]
d[pp.STATE]["layer_aperture_initial"] = data(
g, param, param["tol"])
d[pp.STATE]["layer_aperture_star"] = d[
pp.STATE]["layer_aperture_initial"].copy()
d[pp.STATE]["layer_aperture"] = d[
pp.STATE]["layer_aperture_initial"].copy()
data = param["layer_porosity"]["initial"]
d[pp.STATE]["layer_porosity_initial"] = data(
g, param, param["tol"])
d[pp.STATE]["layer_porosity_star"] = d[
pp.STATE]["layer_porosity_initial"].copy()
d[pp.STATE]["layer_porosity"] = d[
pp.STATE]["layer_porosity_initial"].copy()
vol = d[pp.STATE]["porosity"] + d[pp.STATE]["fracture_aperture"] +\
d[pp.STATE]["layer_aperture"] * d[pp.STATE]["layer_porosity"]
d[pp.STATE]["porosity_aperture_times_solute"] = vol * d[
pp.STATE]["solute"]
d[pp.STATE]["porosity_aperture_times_precipitate"] = vol * d[
pp.STATE]["precipitate"]
d[pp.STATE]["pressure"] = np.zeros(g.num_cells)
d[pp.STATE]["P0_darcy_flux"] = np.zeros((3, g.num_cells))
for e, d in self.gb.edges():
d[pp.STATE][self.discr_flow.mortar] = np.zeros(
d["mortar_grid"].num_cells)
# set the old variables
self.set_old_variables()
# extract the initialized variables, useful for setting the data
###self.extract()
# set now the data for each scheme
self.discr_flow.set_data(param["flow"], param["time"])
self.discr_temperature.set_data(param["temperature"], param["time"])
self.discr_solute_advection_diffusion.set_data(
param["solute_advection_diffusion"], param["time"])
self.discr_solute_precipitate_reaction.set_data(
param["solute_precipitate_reaction"], param["time"])
self.discr_porosity.set_data(param["porosity"])
self.discr_fracture_aperture.set_data(param["fracture_aperture"])
self.discr_layer_aperture.set_data(param["layer_aperture"],
param["time"])
self.discr_layer_porosity.set_data(param["layer_porosity"])
# ------------------------------------------------------------------------------#
def compute_composite_variables(self):
for g, d in self.gb:
vol = d[pp.STATE]["porosity"] + d[pp.STATE]["fracture_aperture"] +\
d[pp.STATE]["layer_aperture"] * d[pp.STATE]["layer_porosity"]
d[pp.STATE]["porosity_aperture_times_solute"] = vol * d[
pp.STATE]["solute"]
d[pp.STATE]["porosity_aperture_times_precipitate"] = vol * d[
pp.STATE]["precipitate"]
# ------------------------------------------------------------------------------#
def vars_to_save(self):
name = [
"solute", "precipitate", "porosity", "fracture_aperture",
"layer_aperture", "layer_porosity", "temperature"
]
name += [
"porosity_aperture_times_solute",
"porosity_aperture_times_precipitate", "fracture", "layer"
]
return name + [self.discr_flow.pressure, self.discr_flow.P0_flux]
# ------------------------------------------------------------------------------#
def one_step_splitting_scheme(self, time):
# save the time of the current step
self.time = time
# POINT 1) extrapolate the precipitate to get a better estimate of porosity
self.compute_precipitate_temperature_star()
# POINT 2) compute the porosity and aperture star for both the fracture and layer
self.compute_porosity_aperture_star()
# -- DO THE FLOW PART -- #
# POINT 3) update the data from the previous time step
self.discr_flow.update_data()
# POINT 4) solve the flow part
self.compute_flow()
# -- DO THE HEAT PART -- #
# set the flux and update the data from the previous time step
self.discr_temperature.set_flux(self.discr_flow.flux,
self.discr_flow.mortar)
self.discr_temperature.update_data()
# POINT 5) solve the temperature part
self.compute_temperature()
# -- DO THE TRANSPORT PART -- #
# set the flux and update the data from the previous time step
self.discr_solute_advection_diffusion.set_flux(self.discr_flow.flux,
self.discr_flow.mortar)
self.discr_solute_advection_diffusion.update_data()
# POINT 6) solve the advection and diffusion part to get the intermediate solute solution
self.compute_solute_precipitate_advection_diffusion()
# POINT 7) Since in the advection-diffusion step we have accounted for porosity changes using
# phi_star and aperture_star, the new solute concentration accounts for the change in pore volume, thus, the
# precipitate needs to be updated accordingly
self.correct_precipitate_with_star()
# POINT 8) solve the reaction part
self.compute_solute_precipitate_rection()
# -- DO THE POROSITY PART -- #
# POINT 9) solve the porosity and aperture (fracture and layer) part with the true concentration of precipitate
self.compute_porosity_aperture()
# POINT 10) finally, we correct the concentrations to account for the difference between the extrapolated
# and "true" new porosity to ensure mass conservation
self.correct_precipitate_solute()
# set the old variables
self.set_old_variables()
# compute composite variables
self.compute_composite_variables()