def source_temperature(self, g) -> np.ndarray:
"""
Sources are handled by ScalarSource discretizations.
The implicit scheme yields multiplication of the rhs by dt, but
this is not incorporated in ScalarSource, hence we do it here.
"""
injection, production = self.source_flow_rates()
# Injection well
t_in = -70
weight = (self.density(g, dT=t_in * self.temperature_scale) *
self.fluid.specific_heat_capacity(self.background_temp_C) *
self.time_step / self.T_0_Kelvin)
rhs = t_in * weight * injection * g.tags["well_cells"].clip(min=0)
# Production well during phase III
weight = (self.density(g) *
self.fluid.specific_heat_capacity(self.background_temp_C) *
self.time_step / self.T_0_Kelvin)
dp, p1, p0 = self._variable_increment(g, "p", self.scalar_scale)
lhs = (weight * production.clip(max=0) *
g.tags["well_cells"].clip(max=0) / g.cell_volumes)
# Set this directly into d to avoid additional return
d = self.gb.node_props(g)
pp.initialize_data(g, d, self.production_well_key,
{"mass_weight": lhs})
return rhs
def _set_scalar_parameters(self) -> None:
super()._set_scalar_parameters()
tensor_scale = self.scalar_scale / self.length_scale**2
kappa = self.params.get("kappa", 1.) * tensor_scale
mass_weight = self.params.get("s0", 1.) * self.scalar_scale
for g, d in self.gb:
bc = self._bc_type_scalar(g)
bc_values = self._bc_values_scalar(g)
source_values = self._source_scalar(g)
specific_volume = self._specific_volume(g)
diffusivity = pp.SecondOrderTensor(kappa * specific_volume *
np.ones(g.num_cells))
alpha = self.params.get("alpha", 1.) * self._biot_alpha(g)
pp.initialize_data(
g,
d,
self.scalar_parameter_key,
{
"bc": bc,
"bc_values": bc_values,
"mass_weight": mass_weight * specific_volume,
"biot_alpha": alpha,
"source": source_values,
"second_order_tensor": diffusivity,
"time_step": self.time_step,
"vector_source": np.zeros(g.num_cells * self.gb.dim_max()),
"ambient_dimension": self.gb.dim_max(),
},
)
def _assign_data(self, u_bot, u_top):
"""
u_bot and u_top are the u_h in the neighbouring cells on the two sides of the fracture.
Ordering is hard-coded according to the grids defined in _make_grid
"""
u_h = np.zeros(self.nd * self.g_h.num_cells)
if self.nd == 3:
u_h[0:6] = u_bot.ravel(order="f")
u_h[12:18] = u_top.ravel(order="f")
else:
u_h[2:6] = u_bot.ravel(order="f")
u_h[10:14] = u_top.ravel(order="f")
# Project to interface
e = (self.g_h, self.g_l)
d_j = self.gb.edge_props(e)
mg = d_j["mortar_grid"]
trace = np.abs(pp.fvutils.vector_divergence(self.g_h)).T
u_j = mg.primary_to_mortar_avg(nd=self.nd) * trace * u_h
pp.set_iterate(d_j, {self.model.mortar_displacement_variable: u_j})
# Parameters used by the propagation class
for g, d in self.gb:
if g.dim == self.nd:
param = {"shear_modulus": self.mu, "poisson_ratio": self.poisson}
else:
param = {"SIFs_critical": np.ones((self.nd, g.num_faces))}
pp.initialize_data(g, d, self.model.mechanics_parameter_key, param)
def set_data(self, data, data_time):
self.data = data
self.data_time = data_time
for g, d in self.gb:
param = {}
unity = np.ones(g.num_cells)
zeros = np.zeros(g.num_cells)
empty = np.empty(0)
alpha = self.data.get("alpha", 2)
d["deviation_from_plane_tol"] = 1e-4
d["is_tangential"] = True
d["tol"] = data["tol"]
# assign permeability
if g.dim < self.gb.dim_max():
aperture = d[pp.STATE]["aperture"]
aperture_initial = d[pp.STATE]["aperture_initial"]
k = np.power(aperture / aperture_initial,
alpha + 1) * self.data["k_t"]
perm = pp.SecondOrderTensor(kxx=k, kyy=1, kzz=1)
else:
porosity = d[pp.STATE]["porosity"]
porosity_initial = d[pp.STATE]["porosity_initial"]
k = np.power(porosity / porosity_initial,
alpha) * self.data["k"]
perm = pp.SecondOrderTensor(kxx=k, kyy=k, kzz=1)
# no source term is assumed by the user
param["second_order_tensor"] = perm
param["source"] = zeros
# Boundaries
b_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if b_faces.size:
labels, param["bc_values"] = data["bc"](g, data, data["tol"])
param["bc"] = pp.BoundaryCondition(g, b_faces, labels)
else:
param["bc_values"] = np.zeros(g.num_faces)
param["bc"] = pp.BoundaryCondition(g, empty, empty)
pp.initialize_data(g, d, self.model, param)
for e, d in self.gb.edges():
mg = d["mortar_grid"]
g_l = self.gb.nodes_of_edge(e)[0]
check_P = mg.slave_to_mortar_avg()
aperture = self.gb.node_props(g_l, pp.STATE)["aperture"]
aperture_initial = self.gb.node_props(g_l,
pp.STATE)["aperture_initial"]
k = 2 * check_P * (np.power(aperture / aperture_initial, alpha - 1)
* self.data["k_n"])
pp.initialize_data(mg, d, self.model, {"normal_diffusivity": k})
def set_data(self, data, data_time):
self.data = data
self.data_time = data_time
for g, d in self.gb:
param_diff = {}
param_adv = {}
param_mass = {}
param_source = {}
unity = np.ones(g.num_cells)
zeros = np.zeros(g.num_cells)
empty = np.empty(0)
d["Aavatsmark_transmissibilities"] = True
d["tol"] = data["tol"]
# assign permeability
if g.dim < self.gb.dim_max():
diff = data["d_t"] * d[pp.STATE]["aperture"]
else:
diff = data["d"] * d[pp.STATE]["porosity"]
param_diff["second_order_tensor"] = pp.SecondOrderTensor(diff)
param_mass["mass_weight"] = data["mass_weight"] / data_time["step"]
param_source["source"] = zeros
# Boundaries
b_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if b_faces.size:
labels_diff, labels_adv, bc_val = data["bc"](g, data, data["tol"])
param_diff["bc"] = pp.BoundaryCondition(g, b_faces, labels_diff)
param_adv["bc"] = pp.BoundaryCondition(g, b_faces, labels_adv)
else:
bc_val = np.zeros(g.num_faces)
param_diff["bc"] = pp.BoundaryCondition(g, empty, empty)
param_adv["bc"] = pp.BoundaryCondition(g, empty, empty)
param_diff["bc_values"] = bc_val
param_adv["bc_values"] = bc_val
models = [self.diff_name, self.adv_name, self.mass_name, self.source_name]
params = [param_diff, param_adv, param_mass, param_source]
for model, param in zip(models, params):
pp.initialize_data(g, d, model, param)
for e, d in self.gb.edges():
mg = d["mortar_grid"]
g_l = self.gb.nodes_of_edge(e)[0]
check_P = mg.slave_to_mortar_avg()
aperture = self.gb.node_props(g_l, pp.STATE)["aperture"]
diff = 2 * check_P * (self.data["d_n"] / aperture)
models = [self.diff_name, self.adv_name]
params = [{"normal_diffusivity": diff}, {}]
for model, param in zip(models, params):
pp.initialize_data(mg, d, model, param)
def _source_temperature(self, g) -> np.ndarray:
"""
Sources are handled by ScalarSource discretizations.
The implicit scheme yields multiplication of the rhs by dt, but
this is not incorporated in ScalarSource, hence we do it here.
The sink (production well) is discretized using the MassMatrix
discretization to ensure the extracted energy matches the current
production well temperature.
"""
injection, production = self._source_flow_rates()
# Injection well
dT = -30
T_in = self.T_0_Kelvin + dT
weight = (self._fluid_density(g, dT=dT * self.temperature_scale) *
self.fluid.specific_heat_capacity(self.background_temp_C) *
self.time_step / self.T_0_Kelvin)
rhs = T_in * weight * injection * g.tags["well_cells"].clip(min=0)
# Production well, discretized by MassMatrix on the lhs
weight = (self._fluid_density(g) *
self.fluid.specific_heat_capacity(self.background_temp_C) *
self.time_step / self.T_0_Kelvin)
lhs = (weight * production.clip(max=0) *
g.tags["well_cells"].clip(max=0) / g.cell_volumes)
# HACK: Set this directly into d to avoid additional return
d = self.gb.node_props(g)
pp.initialize_data(g, d, self.production_well_key,
{"mass_weight": lhs})
return rhs
def set_data(self, data):
self.data = data
for g, d in self.gb:
param = {}
d["deviation_from_plane_tol"] = 1e-8
d["is_tangential"] = True
# assign permeability
k = data["k"](g, d, self)
# no source term is assumed by the user
param["second_order_tensor"] = pp.SecondOrderTensor(kxx=k,
kyy=1,
kzz=1)
param["source"] = data["source"](g, d, self)
param["vector_source"] = data["vector_source"](g, d, self)
# Boundaries
b_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if b_faces.size:
labels, param["bc_values"] = data["bc"](g, data, data["tol"],
self)
param["bc"] = pp.BoundaryCondition(g, b_faces, labels)
else:
param["bc_values"] = np.zeros(g.num_faces)
param["bc"] = pp.BoundaryCondition(g, np.empty(0), np.empty(0))
pp.initialize_data(g, d, self.model, param)
def _set_mechanics_parameters(self) -> None:
super()._set_mechanics_parameters()
gb = self.gb
for g, d in gb:
# Rock parameters
lam = self.params.get("lame_lambda", 1.) * np.ones(
g.num_cells) / self.scalar_scale
mu = self.params.get("lame_mu", 1.) * np.ones(
g.num_cells) / self.scalar_scale
C = pp.FourthOrderTensor(mu, lam)
# Define boundary condition
bc = self._bc_type_mechanics(g)
# BC and source values
bc_val = self._bc_values_mechanics(g)
source_val = self._source_mechanics(g)
pp.initialize_data(
g,
d,
self.mechanics_parameter_key,
{
"bc": bc,
"bc_values": bc_val,
"source": source_val,
"fourth_order_tensor": C,
"time_step": self.time_step,
"biot_alpha": self._biot_alpha(g),
"p_reference": np.zeros(g.num_cells),
},
)
def set_permeability_from_aperture(self):
"""
Cubic law in fractures, rock permeability in the matrix.
"""
viscosity = self.fluid.dynamic_viscosity() / self.scalar_scale
gb = self.gb
key = self.scalar_parameter_key
for g, d in gb:
if g.dim < self.Nd:
# Use cubic law in fractures
apertures = self.compute_aperture(g)
apertures_unscaled = apertures * self.length_scale
k = np.power(apertures_unscaled, 2) / 12
kxx = k / viscosity / self.length_scale**2
else:
# Use the rock permeability in the matrix
kxx = (self.rock.PERMEABILITY / viscosity *
np.ones(g.num_cells) / self.length_scale**2)
K = pp.SecondOrderTensor(kxx)
d[pp.PARAMETERS][key]["second_order_tensor"] = K
# Normal permeability inherited from fracture
for e, d in gb.edges():
mg = d["mortar_grid"]
g_s, g_m = gb.nodes_of_edge(e)
data_s = gb.node_props(g_s)
a = self.compute_aperture(g_s)
# We assume isotropic permeability in the fracture
k_s = data_s[pp.PARAMETERS][
self.scalar_parameter_key]["second_order_tensor"].values[0, 0]
kn = 2 * mg.slave_to_mortar_int() * np.divide(k_s, a)
pp.initialize_data(mg, d, self.scalar_parameter_key,
{"normal_diffusivity": kn})
def add_transport_data(self):
"""
Add the transport data to the grid bucket
"""
keyword = self.transport_keyword
self.gb.add_node_props(["param", "is_tangential"])
for g, d in self.gb:
param = {}
d["is_tangential"] = True
unity = np.ones(g.num_cells)
zeros = np.zeros(g.num_cells)
empty = np.empty(0)
# Specific volume.
specific_volume = np.power(
self.param["aperture"], self.gb.dim_max() - g.dim
)
param["specific_volume"] = specific_volume
# Tangential diffusivity
if g.dim == self.gb.dim_max():
kxx = self.param["Dm"] * unity
else:
kxx = self.param["Df"] * specific_volume * unity
perm = pp.SecondOrderTensor(kxx)
param["second_order_tensor"] = perm
# Source term
param["source"] = zeros
# Mass weight
param["mass_weight"] = specific_volume * self.param["porosity"] * unity
# Boundaries
bound_faces = g.get_boundary_faces()
bc_val = np.zeros(g.num_faces)
if bound_faces.size == 0:
param["bc"] = pp.BoundaryCondition(g, empty, empty)
else:
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces] = 0
param["bc"] = pp.BoundaryCondition(g, bound_faces, "dir")
param["bc_values"] = bc_val
pp.initialize_data(g, d, keyword, param)
# Normal diffusivity
for e, d in self.gb.edges():
# Get higher dimensional grid
g_h = self.gb.nodes_of_edge(e)[1]
param_h = self.gb.node_props(g_h, pp.PARAMETERS)
mg = d["mortar_grid"]
specific_volume_h = (
np.ones(mg.num_cells) * param_h[keyword]["specific_volume"]
)
dn = self.param["Dn"] * specific_volume_h / (self.param["aperture"] / 2)
param = {"normal_diffusivity": dn}
pp.initialize_data(e, d, keyword, param)
def _setup_simulation_tracer(gb, data, direction):
min_coord = gb.bounding_box()[0][direction]
max_coord = gb.bounding_box()[1][direction]
parameter_keyword = "transport"
for g, d in gb:
param = d[pp.PARAMETERS]
transport_parameter_dictionary = {}
param.update_dictionaries(parameter_keyword,
transport_parameter_dictionary)
param.set_from_other(parameter_keyword, "flow", ["aperture"])
d[pp.DISCRETIZATION_MATRICES][parameter_keyword] = {}
unity = np.ones(g.num_cells)
if g.dim == gb.dim_max():
porosity = 0.2 * unity
else:
porosity = 0.8 * unity
specified_parameters = {"mass_weight": porosity}
bound_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if bound_faces.size > 0:
hit_out = np.where(
np.abs(g.face_centers[direction, bound_faces] -
max_coord) < 1e-8)[0]
hit_in = np.where(
np.abs(g.face_centers[direction, bound_faces] -
min_coord) < 1e-8)[0]
bound_type = np.array(["neu"] * bound_faces.size)
bound_type[hit_out] = "dir"
bound_type[hit_in] = "dir"
bound = pp.BoundaryCondition(g, bound_faces.ravel("F"), bound_type)
bc_val = np.zeros(g.num_faces)
bc_val[bound_faces[hit_out]] = 0
bc_val[bound_faces[hit_in]] = 1
specified_parameters.update({"bc": bound, "bc_values": bc_val})
d["inlet_faces"] = bound_faces[hit_in]
else:
bc = pp.BoundaryCondition(g)
specified_parameters.update({
"bc": bc,
"bc_values": np.zeros(g.num_faces)
})
pp.initialize_data(g, d, parameter_keyword, specified_parameters)
for e, d in gb.edges():
d[pp.PARAMETERS].update_dictionaries(parameter_keyword, {})
d[pp.DISCRETIZATION_MATRICES][parameter_keyword] = {}
return gb
def set_permeability(self):
"""
Cubic law in fractures, rock permeability in the matrix.
If "blocking_perm" is present in self.params, this value is used for
Fracture 2.
"""
# Viscosity has units of Pa s, and is consequently divided by the scalar scale.
viscosity = self.fluid.dynamic_viscosity() / self.scalar_scale
gb = self.gb
key = self.scalar_parameter_key
from_iterate = True
blocking_perm = self.params.get("blocking_perm", None)
for g, d in gb:
if g.dim < self.Nd:
# Set fracture permeability
specific_volumes = self.specific_volumes(g, from_iterate)
if d["node_number"] == 1 or blocking_perm is None:
# Use cubic law in fractures. First compute the unscaled
# permeability
apertures = self.aperture(g, from_iterate=from_iterate)
apertures_unscaled = apertures * self.length_scale
k = np.power(apertures_unscaled, 2) / 12 / viscosity
else:
# Blocking and intersection
k = blocking_perm
d[pp.PARAMETERS][key]["perm_nu"] = k
# Multiply with the cross-sectional area
k = k * specific_volumes
# Divide by fluid viscosity and scale back
kxx = k / self.length_scale ** 2
else:
# Use the rock permeability in the matrix
kxx = (
self.rock.PERMEABILITY
/ viscosity
* np.ones(g.num_cells)
/ self.length_scale ** 2
)
K = pp.SecondOrderTensor(kxx)
d[pp.PARAMETERS][key]["second_order_tensor"] = K
# Normal permeability inherited from the neighboring fracture g_l
for e, d in gb.edges():
mg = d["mortar_grid"]
g_l, _ = gb.nodes_of_edge(e)
data_l = gb.node_props(g_l)
a = self.aperture(g_l, from_iterate)
V = self.specific_volumes(g_l, from_iterate)
# We assume isotropic permeability in the fracture, i.e. the normal
# permeability equals the tangential one
k_s = data_l[pp.PARAMETERS][key]["second_order_tensor"].values[0, 0]
# Division through half the aperture represents taking the (normal) gradient
kn = mg.slave_to_mortar_int() * np.divide(k_s, a * V / 2)
pp.initialize_data(mg, d, key, {"normal_diffusivity": kn})
def set_parameters_cell_basis(self, gb: pp.GridBucket, data: Dict):
"""
Assign parameters for the micro gb. Very simple for now, this must be improved.
Args:
gb (TYPE): the micro gb.
Returns:
None.
"""
# First initialize data
for g, d in gb:
d["Aavatsmark_transmissibilities"] = True
domain_boundary = np.logical_and(
g.tags["domain_boundary_faces"],
np.logical_not(g.tags["fracture_faces"]),
)
boundary_faces = np.where(domain_boundary)[0]
if domain_boundary.size > 0:
bc_type = boundary_faces.size * ["dir"]
else:
bc_type = np.empty(0)
bc = pp.BoundaryCondition(g, boundary_faces, bc_type)
if hasattr(g, "face_on_macro_bound"):
micro_ind = g.face_on_macro_bound
macro_ind = g.macro_face_ind
bc.is_neu[micro_ind] = data["bc_macro"]["bc"].is_neu[macro_ind]
bc.is_dir[micro_ind] = data["bc_macro"]["bc"].is_dir[macro_ind]
param = {"bc": bc}
perm = data["g_data"](g)["second_order_tensor"]
param["second_order_tensor"] = perm
param["specific_volume"] = data["g_data"](g)["specific_volume"]
# Use python inverter for mpfa for small problems, where it does not pay off
# to fire up numba. The set threshold value is somewhat randomly picked.
if g.num_cells < 100:
param["mpfa_inverter"] = "python"
pp.initialize_default_data(g, d, self.keyword, param)
for e, d in gb.edges():
mg = d["mortar_grid"]
g1, g2 = gb.nodes_of_edge(e)
param = {}
if not hasattr(g1, "is_auxiliary") or not g1.is_auxiliary:
check_P = mg.secondary_to_mortar_avg()
param.update(data["e_data"](mg, g1, g2, check_P))
pp.initialize_data(mg, d, self.keyword, param)
def _copy_biot_discretizations(self) -> None:
"""The Biot discretization is designed to discretize a single term of the
grad_p type. It should not be difficult to generalize this, but pending such
an update, the below code copies the discretization matrices from the flow
related keywords to those of the temperature.
"""
g: pp.Grid = self.gb.grids_of_dimension(self._Nd)[0]
d: Dict = self.gb.node_props(g)
beta = self._biot_beta(g)
alpha = self._biot_alpha(g)
# For grad p term of u equation
weight_grad_t = beta / alpha
# Account for scaling
weight_grad_t *= self.temperature_scale / self.scalar_scale
# Stabilization is derived from the grad p discretization
weight_stabilization = beta / alpha
weight_stabilization *= self.temperature_scale / self.scalar_scale
# The stabilization terms appear in the T/p equations, whereof only the first
# is divided by T_0_Kelvin.
weight_stabilization *= 1 / self.T_0_Kelvin
# Matrix dictionaries for the different subproblems
matrices_s = d[pp.DISCRETIZATION_MATRICES][self.scalar_parameter_key]
matrices_ms = d[pp.DISCRETIZATION_MATRICES][self.mechanics_parameter_key]
matrices_t = d[pp.DISCRETIZATION_MATRICES][self.temperature_parameter_key]
matrices_mt = {}
matrices_t["div_u"] = matrices_s["div_u"].copy()
matrices_t["bound_div_u"] = matrices_s["bound_div_u"].copy()
matrices_mt["grad_p"] = weight_grad_t * matrices_ms["grad_p"]
matrices_t["biot_stabilization"] = (
weight_stabilization * matrices_s["biot_stabilization"]
)
matrices_mt["bound_displacement_pressure"] = (
weight_grad_t * matrices_ms["bound_displacement_pressure"]
)
# For div u term of t equation
weight_div_u = beta
key_m_from_t = self.mechanics_temperature_parameter_key
d[pp.DISCRETIZATION_MATRICES][key_m_from_t] = matrices_mt
pp.initialize_data(
g,
d,
key_m_from_t,
{"biot_alpha": weight_div_u},
)
bc_dict = {"bc_values": self._bc_values_mechanics(g)}
state = {key_m_from_t: bc_dict}
pp.set_state(d, state)
def _set_scalar_parameters(self) -> None:
tensor_scale = self.scalar_scale / self.length_scale ** 2
kappa = 1 * tensor_scale
mass_weight = 1 * self.scalar_scale
for g, d in self.gb:
bc = self._bc_type_scalar(g)
bc_values = self._bc_values_scalar(g)
source_values = self._source_scalar(g)
specific_volume = self._specific_volume(g)
diffusivity = pp.SecondOrderTensor(
kappa * specific_volume * np.ones(g.num_cells)
)
alpha = self._biot_alpha(g)
pp.initialize_data(
g,
d,
self.scalar_parameter_key,
{
"bc": bc,
"bc_values": bc_values,
"mass_weight": mass_weight * specific_volume,
"biot_alpha": alpha,
"source": source_values,
"second_order_tensor": diffusivity,
"time_step": self.time_step,
},
)
# Assign diffusivity in the normal direction of the fractures.
for e, data_edge in self.gb.edges():
g_l, g_h = self.gb.nodes_of_edge(e)
mg = data_edge["mortar_grid"]
a_l = self._aperture(g_l)
# Take trace of and then project specific volumes from g_h
v_h = (
mg.primary_to_mortar_avg()
* np.abs(g_h.cell_faces)
* self._specific_volume(g_h)
)
# Division by a/2 may be thought of as taking the gradient in the normal
# direction of the fracture.
normal_diffusivity = kappa * 2 / (mg.secondary_to_mortar_avg() * a_l)
# The interface flux is to match fluxes across faces of g_h,
# and therefore need to be weighted by the corresponding
# specific volumes
normal_diffusivity *= v_h
data_edge = pp.initialize_data(
e,
data_edge,
self.scalar_parameter_key,
{"normal_diffusivity": normal_diffusivity},
)
def assign_parameters(time):
nf = g.num_faces
nc = g.num_cells
fn = g.face_normals
fc = g.face_centers
cc = g.cell_centers
V = g.cell_volumes
# Permeability tensor
perm = pp.SecondOrderTensor(K * np.ones(nc))
# Boundary condtions
top = np.where(np.abs(fc[1] - 1) < 1e-5)[0]
bottom = np.where(np.abs(fc[1]) < 1e-5)[0]
left = np.where(np.abs(fc[0]) < 1e-5)[0]
right = np.where(np.abs(fc[0] - 1) < 1e-5)[0]
bc_faces = g.get_boundary_faces()
bc_type = np.array(bc_faces.size * ["neu"])
bc_type[np.in1d(bc_faces, left)] = "dir"
bc_type[np.in1d(bc_faces, right)] = "dir"
bc = pp.BoundaryCondition(g, faces=bc_faces, cond=bc_type)
bc_values = np.zeros(g.num_faces)
pf = p_ex(fc[0], fc[1], time * np.ones(nf)) # exact face pressures
adv_f = advec_ex(fc[0], fc[1], time * np.ones(nf)) # exact advective velocities
Adv_f = adv_f[0] * fn[0] + adv_f[1] * fn[1] # exact advective fluxes
bc_values[top] = np.abs(Adv_f[top])
bc_values[bottom] = np.abs(Adv_f[bottom])
bc_values[left] = pf[left]
bc_values[right] = pf[right]
source_term = f_ex(cc[0], cc[1], time * np.ones(nc)) * V
# Initialize data dictionary
specified_data = {
"second_order_tensor": perm,
"bc": bc,
"bc_values": bc_values,
"source": source_term,
"mass_weight": phi * np.ones(g.num_cells),
}
# Assing (or update) parameters
if time == 0:
pp.initialize_data(g, d, param_key, specified_data)
else:
d[pp.PARAMETERS][param_key]["bc_values"] = bc_values
d[pp.PARAMETERS][param_key]["source"] = source_term
def add_flow_data(self):
"""
Add the flow data to the grid bucket
"""
keyword = self.flow_keyword
# Iterate over nodes and assign data
for g, d in self.gb:
param = {}
# Shorthand notation
unity = np.ones(g.num_cells)
zeros = np.zeros(g.num_cells)
# Specific volume.
specific_volume = np.power(
self.param["aperture"], self.gb.dim_max() - g.dim
)
param["specific_volume"] = specific_volume
# Tangential permeability
if g.dim == self.gb.dim_max():
kxx = self.param["km"]
else:
kxx = self.param["kf"] * specific_volume
perm = pp.SecondOrderTensor(kxx * unity)
param["second_order_tensor"] = perm
# Source term
param["source"] = zeros
# Boundaries
bound_faces = g.get_boundary_faces()
bc_val = np.zeros(g.num_faces)
param["bc"] = pp.BoundaryCondition(g, bound_faces, "dir")
param["bc_values"] = bc_val
pp.initialize_data(g, d, keyword, param)
# Loop over edges and set coupling parameters
for e, d in self.gb.edges():
# Get higher dimensional grid
g_h = self.gb.nodes_of_edge(e)[1]
param_h = self.gb.node_props(g_h, pp.PARAMETERS)
mg = d["mortar_grid"]
specific_volume_h = (
np.ones(mg.num_cells) * param_h[keyword]["specific_volume"]
)
kn = self.param["kn"] * specific_volume_h / (self.param["aperture"] / 2)
param = {"normal_diffusivity": kn}
pp.initialize_data(e, d, keyword, param)
def set_scalar_parameters(self):
gb = self.gb
self.Nd = gb.dim_max()
tensor_scale = self.scalar_scale / self.length_scale**2
kappa = 1 * tensor_scale
mass_weight = 1
alpha = self.biot_alpha()
for g, d in gb:
bc = self.bc_type_scalar(g)
bc_values = self.bc_values_scalar(g)
source_values = self.source_scalar(g)
a = self.compute_aperture(g)
specific_volume = np.power(a,
self.gb.dim_max() - g.dim) * np.ones(
g.num_cells)
diffusivity = pp.SecondOrderTensor(kappa * specific_volume *
np.ones(g.num_cells))
pp.initialize_data(
g,
d,
self.scalar_parameter_key,
{
"bc": bc,
"bc_values": bc_values,
"mass_weight": mass_weight * specific_volume,
"biot_alpha": alpha,
"source": source_values,
"second_order_tensor": diffusivity,
"time_step": self.time_step,
},
)
# Assign diffusivity in the normal direction of the fractures.
for e, data_edge in self.gb.edges():
g1, _ = self.gb.nodes_of_edge(e)
a = self.compute_aperture(g1)
mg = data_edge["mortar_grid"]
normal_diffusivity = 2 / kappa * mg.slave_to_mortar_int() * a
data_edge = pp.initialize_data(
e,
data_edge,
self.scalar_parameter_key,
{"normal_diffusivity": normal_diffusivity},
)
def _set_data_nodes(self):
""" Method to set the data for the nodes (grids) of the grid bucket
"""
for g, d in self.gb:
param = {}
param_mass = {}
unity = np.ones(g.num_cells)
zeros = np.zeros(g.num_cells)
empty = np.empty(0)
d["tol"] = self.data["tol"]
# Boundaries
b_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if b_faces.size:
labels, bc_val = self.bc_flag(self.gb, g, self.data,
self.data["tol"])
param["bc"] = pp.BoundaryCondition(g, b_faces, labels)
else:
bc_val = np.zeros(g.num_faces)
param["bc"] = pp.BoundaryCondition(g, empty, empty)
param["bc_values"] = bc_val
pp.initialize_data(g, d, self.discr_name, param)
d[pp.PARAMETERS][self.discr_name][self.flux] = d[pp.STATE][
self.flow.flux]
param_mass["mass_weight"] = 1. / self.time_step
pp.initialize_data(g, d, self.mass_name, param_mass)
# set the primary variable
d[pp.PRIMARY_VARIABLES] = {self.variable: {"cells": 1}}
# set the discretization
node_discr = self.discr(self.discr_name)
node_mass = self.mass(self.mass_name)
d[pp.DISCRETIZATION] = {
self.variable: {
self.discr_name: node_discr,
self.mass_name: node_mass
}
}
# set the discretization matrix
d[pp.DISCRETIZATION_MATRICES] = {
self.discr_name: {},
self.mass_name: {}
}
def set_mechanics_parameters(self) -> None:
"""
Set the parameters for the simulation.
"""
super().set_mechanics_parameters()
for g, d in self.gb:
if g.dim == self.Nd:
pp.initialize_data(
g,
d,
self.mechanics_temperature_parameter_key,
{
"biot_alpha": self.biot_beta(g),
"bc_values": self.bc_values_mechanics(g),
},
)
def set_params_disrcetize(g, ambient_dim, method, periodic=False):
g.compute_geometry()
keyword = "flow"
if periodic:
south = g.face_centers[1] < np.min(g.nodes[1]) + 1e-8
north = g.face_centers[1] > np.max(g.nodes[1]) - 1e-8
bc = pp.BoundaryCondition(g, north + south, "per")
south_idx = np.argwhere(south).ravel()
north_idx = np.argwhere(north).ravel()
bc.set_periodic_map(np.vstack((south_idx, north_idx)))
else:
bc = pp.BoundaryCondition(g)
k = pp.SecondOrderTensor(np.ones(g.num_cells))
params = {
"bc": bc,
"second_order_tensor": k,
"mpfa_inverter": "python",
"ambient_dimension": ambient_dim,
}
data = pp.initialize_data(g, {}, keyword, params)
if method == "mpfa":
discr = pp.Mpfa(keyword)
elif method == "tpfa":
discr = pp.Tpfa(keyword)
discr.discretize(g, data)
flux = data[pp.DISCRETIZATION_MATRICES][keyword][discr.flux_matrix_key]
vector_source = data[pp.DISCRETIZATION_MATRICES][keyword][
discr.vector_source_matrix_key]
div = pp.fvutils.scalar_divergence(g)
return flux, vector_source, div
def _set_scalar_parameters(self) -> None:
"""Set parameters for the pressure / mass conservation equation."""
# Most values are handled as if this was a poro-elastic problem
super()._set_scalar_parameters()
for g, d in self.gb:
t2s_coupling = (
self._scalar_temperature_coupling_coefficient(g)
* self._specific_volume(g)
* self.temperature_scale
)
pp.initialize_data(
g,
d,
self.t2s_parameter_key,
{"mass_weight": t2s_coupling, "time_step": self.time_step},
)
def set_scalar_parameters(self):
for g, d in self.gb:
a = self.compute_aperture(g)
specific_volumes = self.specific_volumes(g)
# Define boundary conditions for flow
bc = self.bc_type_scalar(g)
# Set boundary condition values
bc_values = self.bc_values_scalar(g)
biot_coefficient = self.biot_alpha(g)
compressibility = self.fluid.COMPRESSIBILITY
mass_weight = compressibility * self.porosity(g)
if g.dim == self.Nd:
mass_weight += (biot_coefficient -
self.porosity(g)) / self.rock.BULK_MODULUS
mass_weight *= self.scalar_scale * specific_volumes
pp.initialize_data(
g,
d,
self.scalar_parameter_key,
{
"bc": bc,
"bc_values": bc_values,
"mass_weight": mass_weight,
"biot_alpha": biot_coefficient,
"time_step": self.time_step,
"source": self.aperture_update(g, d),
},
)
t2s_coupling = (self.scalar_temperature_coupling_coefficient(g) *
specific_volumes * self.temperature_scale)
pp.initialize_data(
g,
d,
self.t2s_parameter_key,
{
"mass_weight": t2s_coupling,
"time_step": self.time_step
},
)
self.set_permeability_from_aperture()
def _initial_condition(self) -> None:
"""
In addition to the values set by the parent class, we set initial value for the
temperature variable, and a previous iterate value for the scalar value. The
latter is used for computation of Darcy fluxes, needed for the advective term of
the energy equation. The Darcy flux parameter is also initialized.
"""
super()._initial_condition()
for g, d in self.gb:
# Initial value for the scalar variable.
cell_zeros = np.zeros(g.num_cells)
state = {self.temperature_variable: cell_zeros}
iterate = {self.scalar_variable: cell_zeros} # For initial flux
pp.set_state(d, state)
pp.set_iterate(d, iterate)
# Initial Darcy fluxes for advective flux.
pp.initialize_data(
g,
d,
self.temperature_parameter_key,
{
"darcy_flux": np.zeros(g.num_faces),
},
)
for e, d in self.gb.edges():
mg = d["mortar_grid"]
cell_zeros = np.zeros(mg.num_cells)
state = {
self.mortar_temperature_variable: cell_zeros,
self.mortar_temperature_advection_variable: cell_zeros,
}
iterate = {self.mortar_scalar_variable: cell_zeros}
pp.set_state(d, state)
pp.set_iterate(d, iterate)
# Initial Darcy fluxes for advective flux.
d = pp.initialize_data(
e,
d,
self.temperature_parameter_key,
{
"darcy_flux": np.zeros(mg.num_cells),
},
)
def _set_mechanics_parameters(self) -> None:
"""
Set the parameters for the simulation.
"""
super()._set_mechanics_parameters()
for g, d in self.gb:
if g.dim == self._Nd:
pp.initialize_data(
g,
d,
self.mechanics_temperature_parameter_key,
{
"biot_alpha": self._biot_beta(g),
"bc_values": self._bc_values_mechanics(g),
"p_reference": np.zeros(g.num_cells),
},
)
def test_assembly(self):
# Test the assemble_matrix_rhs method, with vector sources included.
# The rest of the setup is identical to that in
# self.test_2d_horizontal_ambient_dim_2()
# Random size of the domain
dx = np.random.rand(1)[0]
# 2x2 grid of the random size
g = pp.CartGrid([2, 2], [2 * dx, 2 * dx])
# Hhe vector source is a 2-vector per cell
ambient_dim = 2
g.compute_geometry()
bc = pp.BoundaryCondition(g)
k = pp.SecondOrderTensor(np.ones(g.num_cells))
# Make source strength another random number
grav_strength = np.random.rand(1)
# introduce a source term in x-direction
g_x = np.zeros(g.num_cells * ambient_dim)
g_x[::ambient_dim] = -1 * grav_strength
params = {
"bc": bc,
"bc_values": np.zeros(g.num_faces),
"second_order_tensor": k,
"mpfa_inverter": "python",
"ambient_dimension": ambient_dim,
"vector_source": g_x,
}
data = pp.initialize_data(g, {}, self.keyword, params)
discr = pp.Mpfa(self.keyword)
discr.discretize(g, data)
A, b = discr.assemble_matrix_rhs(g, data)
p_x = np.linalg.pinv(A.toarray()).dot(b)
# The solution should be higher in the first x-row of cells, with magnitude
# controlled by grid size and source stregth
self.assertTrue(np.allclose(p_x[0] - p_x[1], dx * grav_strength))
self.assertTrue(np.allclose(p_x[2] - p_x[3], dx * grav_strength))
# The solution should be equal for equal x-coordinate
self.assertTrue(np.allclose(p_x[0], p_x[2]))
self.assertTrue(np.allclose(p_x[1], p_x[3]))
data[pp.STATE] = {"pressure": p_x}
pp.fvutils.compute_darcy_flux(g, data=data)
def set_scalar_parameters(self) -> None:
""" Set parameters for the pressure / mass conservation equation.
"""
# Most values are handled as if this was a poro-elastic problem
super().set_scalar_parameters()
for g, d in self.gb:
a = self.compute_aperture(g)
specific_volume = np.power(a,
self.gb.dim_max() - g.dim) * np.ones(
g.num_cells)
t2s_coupling = (self.scalar_temperature_coupling_coefficient(g) *
specific_volume * self.temperature_scale)
pp.initialize_data(
g,
d,
self.t2s_parameter_key,
{
"mass_weight": t2s_coupling,
"time_step": self.time_step
},
)
def set_mechanics_parameters(self):
gb = self.gb
for g, d in gb:
if g.dim == self.Nd:
# Rock parameters
rock = self.rock
lam = rock.LAMBDA * np.ones(g.num_cells) / self.scalar_scale
mu = rock.MU * np.ones(g.num_cells) / self.scalar_scale
C = pp.FourthOrderTensor(mu, lam)
bc = self.bc_type_mechanics(g)
bc_values = self.bc_values_mechanics(g)
sources = self.source_mechanics(g)
pp.initialize_data(
g,
d,
self.mechanics_parameter_key,
{
"bc": bc,
"bc_values": bc_values,
"source": sources,
"fourth_order_tensor": C,
"biot_alpha": self.biot_alpha()
},
)
d[pp.PARAMETERS].set_from_other(
self.mechanics_parameter_key,
self.scalar_parameter_key,
["aperture", "time_step"],
)
elif g.dim == self.Nd - 1:
friction = self._set_friction_coefficient(g)
pp.initialize_data(
g,
d,
self.mechanics_parameter_key,
{"friction_coefficient": friction},
)
pp.initialize_data(g, d, self.mechanics_parameter_key, {})
for e, d in gb.edges():
mg = d["mortar_grid"]
# Parameters for the surface diffusion. No clue about values
mu = self.rock.MU
lmbda = self.rock.LAMBDA
pp.initialize_data(mg, d, self.mechanics_parameter_key, {
"mu": mu,
"lambda": lmbda
})
def _set_data_nodes(self):
""" Method to set the data for the nodes (grids) of the grid bucket
"""
for g, d in self.gb:
param = {}
d["Aavatsmark_transmissibilities"] = True
d["tol"] = self.data["tol"]
# assign permeability
if g.dim == 2:
perm = pp.SecondOrderTensor(kxx=self.data["kxx"], kyy=self.data["kyy"], kxy=self.data["kxy"])
param["second_order_tensor"] = perm
elif g.dim == 1:
k = self.data["k"][g.frac_num]
perm = pp.SecondOrderTensor(kxx=k*np.ones(g.num_cells))
param["second_order_tensor"] = perm
# Boundaries
b_faces = g.tags["domain_boundary_faces"].nonzero()[0]
if b_faces.size:
labels, bc_val = self.bc_flag(self.gb, g, self.data, self.data["tol"])
param["bc"] = pp.BoundaryCondition(g, b_faces, labels)
else:
bc_val = np.zeros(g.num_faces)
param["bc"] = pp.BoundaryCondition(g, np.empty(0), np.empty(0))
param["bc_values"] = bc_val
pp.initialize_data(g, d, self.model, param)
# set the primary variable
d[pp.PRIMARY_VARIABLES] = {self.variable: {"cells": 1}}
# set the discretization
node_discr = self.discr(self.model)
d[pp.DISCRETIZATION] = {self.variable: {self.discr_name: node_discr}}
# set the discretization matrix
d[pp.DISCRETIZATION_MATRICES] = {self.model: {}}
def vector_source(self):
""" Set gravity as a vector source term in the fluid flow equations"""
if not self.params.gravity:
return
gb = self.gb
scalar_key = self.scalar_parameter_key
ls, ss = self.params.length_scale, self.params.scalar_scale
for g, d in gb:
# minus sign to convert from positive z downward (depth) to positive upward.
gravity = -pp.GRAVITY_ACCELERATION * self.density(g) * (ls / ss)
vector_source = np.zeros((self.Nd, g.num_cells))
vector_source[-1, :] = gravity
vector_params = {
"vector_source": vector_source.ravel("F"),
"ambient_dimension": self.Nd,
}
pp.initialize_data(g, d, scalar_key, vector_params)
for e, de in gb.edges():
mg: pp.MortarGrid = de["mortar_grid"]
g_l, _ = gb.nodes_of_edge(e)
a_l = self.aperture(g_l, scaled=True)
# Compute gravity on the slave grid
rho_g = -pp.GRAVITY_ACCELERATION * self.density(g_l) * (ls / ss)
# Multiply by (a/2) to "cancel out" the normal gradient of the diffusivity
# (see also self.set_permeability_from_aperture)
gravity_l = rho_g * (a_l / 2)
# Take the gravity from the slave grid and project to the interface
gravity_mg = mg.slave_to_mortar_avg() * gravity_l
vector_source = np.zeros((self.Nd, mg.num_cells))
vector_source[-1, :] = gravity_mg
gravity = vector_source.ravel("F")
pp.initialize_data(mg, de, scalar_key, {"vector_source": gravity})