def test_permTensor_dim2_perm3(self):
self.rock2.perm = np.array([[5, 3, 1], [5, 3, 1], [5, 3, 7], [5, 3,
7]])
K_prst = permTensor(self.rock2, 2)
K_mrst = np.array([[5, 3, 3, 1], [5, 3, 3, 1], [5, 3, 3, 7],
[5, 3, 3, 7]])
assert np.array_equal(K_prst, K_mrst)
def test_permTensor_dim3_perm1(self):
self.rock3.perm = np.array([[5], [5], [5], [5]])
K_prst = permTensor(self.rock3, 3)
K_mrst = np.array([[5, 0, 0, 0, 5, 0, 0, 0, 5],
[5, 0, 0, 0, 5, 0, 0, 0, 5],
[5, 0, 0, 0, 5, 0, 0, 0, 5],
[5, 0, 0, 0, 5, 0, 0, 0, 5]])
assert np.array_equal(K_prst, K_mrst)
def test_permTensor_dim3_perm3(self):
self.rock3.perm = np.array([[5, 3, 1], [5, 3, 1], [5, 3, 7], [5, 3,
7]])
K_prst = permTensor(self.rock3, 3)
K_mrst = np.array([[5, 0, 0, 0, 3, 0, 0, 0, 1],
[5, 0, 0, 0, 3, 0, 0, 0, 1],
[5, 0, 0, 0, 3, 0, 0, 0, 7],
[5, 0, 0, 0, 3, 0, 0, 0, 7]])
assert np.array_equal(K_prst, K_mrst)
def test_permTensor_dim3_perm6(self):
self.rock3.perm = np.array([[5, 3, 1, 6, 6, 6], [5, 3, 1, 6, 6, 6],
[5, 3, 7, 6, 6, 6], [5, 3, 7, 6, 6, 6]])
K_prst = permTensor(self.rock3, 3)
K_mrst = np.array([[5, 3, 1, 3, 6, 6, 1, 6, 6],
[5, 3, 1, 3, 6, 6, 1, 6, 6],
[5, 3, 7, 3, 6, 6, 7, 6, 6],
[5, 3, 7, 3, 6, 6, 7, 6, 6]])
assert np.array_equal(K_prst, K_mrst)
def computeTrans(G, rock, K_system="xyz", cellCenters=None, cellFaceCenters=None,
verbose=False):
"""
Compute transmissibilities for a grid.
Synopsis:
T = computeTrans(G, rock)
T = computeTrans(G, rock, **kwargs)
Arguments:
G (Grid):
prst.gridprocessing.Grid instance.
rock (Rock):
prst.params.rock.Rock instance with `perm` attribute. The
permeability is assumed to be in units of metres squared (m^2).
Use constant `darcy` from prst.utils.units to convert to m^2, e.g.,
from prst.utils.units import *
perm = convert(perm, from_=milli*darcy, to=meter**2)
if the permeability is provided in units of millidarcies.
The field rock.perm may have ONE column for a scalar permeability in each cell,
TWO/THREE columns for a diagonal permeability in each cell (in 2/D
D) and THREE/SIX columns for a symmetric full tensor permeability.
In the latter case, each cell gets the permability tensor.
K_i = [ k1 k2 ] in two space dimensions
[ k2 k3 ]
K_i = [ k1 k2 k3 ] in three space dimensions
[ k2 k4 k5 ]
[ k3 k5 k6 ]
K_system (Optional[str]):
The system permeability. Valid values are "xyz" and "loc_xyz".
cellCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellCenters rather
than default G.cells.centroids. Must have shape (n,2) for 2D and
(n,3) for 3D.
cellFaceCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellFaceCenters rather
than default `G.faces.centroids[G.cells.faces[:,0], :]`.
Returns:
T: Half-transmissibilities for each local face of each grid cell in the
grid. The number of half-transmissibilities equals the number of rows
in `G.cells.faces`. 2D column array.
Comments:
PLEASE NOTE: Face normals are assumed to have length equal to the
corresponding face areas. This property is guaranteed by function
`computeGeometry`.
See also:
computeGeometry, computeMimeticIP (MRST), darcy, permTensor, Rock
"""
if K_system not in ["xyz", "loc_xyz"]:
raise TypeError(
"Specified permeability coordinate system must be a 'xyz' or 'loc_xyz'")
if verbose:
print("Computing one-sided transmissibilites.")
# Vectors from cell centroids to face centroids
assert G.cells.facePos.ndim == 2, "facePos has wrong dimensions"
cellNo = rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos, axis=0))
if cellCenters is None:
C = G.cells.centroids
else:
C = cellCenters
if cellFaceCenters is None:
C = G.faces.centroids[G.cells.faces[:,0],:] - C[cellNo,:]
else:
C = cellFaceCenters - C[cellNo,:]
# Normal vectors
sgn = 2*(cellNo == G.faces.neighbors[G.cells.faces[:,0], 0]) - 1
N = sgn[:,np.newaxis] * G.faces.normals[G.cells.faces[:,0],:]
if K_system == "xyz":
K, i, j = permTensor(rock, G.gridDim, rowcols=True)
assert K.shape[0] == G.cells.num, \
"Permeability must be defined in active cells only.\n"+\
"Got {} tensors, expected {} (== num cells)".format(K.shape[0], G.cells.num)
# Compute T = C'*K*N / C'*C. Loop based to limit memory use.
T = np.zeros(cellNo.size)
for k in range(i.size):
tmp = C[:,i[k]] * K[cellNo,k] * N[:,j[k]]
# Handle both 1d and 2d array.
if tmp.ndim == 1:
T += tmp
else:
T += np.sum(tmp, axis=1)
T = T / np.sum(C*C, axis=1)
elif K_system == "loc_xyz":
if rock.perm.shape[1] == 1:
rock.perm = np.tile(rock.perm, (1, G.gridDim))
if rock.perm.shape[1] != G.cartDims.size:
raise ValueError(
"Permeability coordinate system `loc_xyz` is only "+\
"valid for diagonal tensor.")
assert rock.perm.shape[0] == G.cells.num,\
"Permeability must be defined in active cells only. "+\
"Got {} tensors, expected {} == (num cells)".format(rock.perm.shape[0], G.cells.num)
dim = np.ceil(G.cells.faces[:,1] / 2)
raise NotImplementedError("Function not finished for K_system='loc_xyz'")
# See MRST, solvers/computeTrans.m
else:
raise ValueError("Unknown permeability coordinate system {}.".format(K_system))
is_neg = T < 0
if np.any(is_neg):
if verbose:
prst.log.warn("Warning: {} negative transmissibilities. ".format(np.sum(is_neg))+
"Replaced by absolute values...")
T[is_neg] = -T[is_neg]
return np.atleast_2d(T).transpose()
def computeTrans(G,
rock,
K_system="xyz",
cellCenters=None,
cellFaceCenters=None,
verbose=False):
"""
Compute transmissibilities for a grid.
Synopsis:
T = computeTrans(G, rock)
T = computeTrans(G, rock, **kwargs)
Arguments:
G (Grid):
prst.gridprocessing.Grid instance.
rock (Rock):
prst.params.rock.Rock instance with `perm` attribute. The
permeability is assumed to be in units of metres squared (m^2).
Use constant `darcy` from prst.utils.units to convert to m^2, e.g.,
from prst.utils.units import *
perm = convert(perm, from_=milli*darcy, to=meter**2)
if the permeability is provided in units of millidarcies.
The field rock.perm may have ONE column for a scalar permeability in each cell,
TWO/THREE columns for a diagonal permeability in each cell (in 2/D
D) and THREE/SIX columns for a symmetric full tensor permeability.
In the latter case, each cell gets the permability tensor.
K_i = [ k1 k2 ] in two space dimensions
[ k2 k3 ]
K_i = [ k1 k2 k3 ] in three space dimensions
[ k2 k4 k5 ]
[ k3 k5 k6 ]
K_system (Optional[str]):
The system permeability. Valid values are "xyz" and "loc_xyz".
cellCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellCenters rather
than default G.cells.centroids. Must have shape (n,2) for 2D and
(n,3) for 3D.
cellFaceCenters (Optional[ndarray]):
Compute transmissibilities based on supplied cellFaceCenters rather
than default `G.faces.centroids[G.cells.faces[:,0], :]`.
Returns:
T: Half-transmissibilities for each local face of each grid cell in the
grid. The number of half-transmissibilities equals the number of rows
in `G.cells.faces`. 2D column array.
Comments:
PLEASE NOTE: Face normals are assumed to have length equal to the
corresponding face areas. This property is guaranteed by function
`computeGeometry`.
See also:
computeGeometry, computeMimeticIP (MRST), darcy, permTensor, Rock
"""
if K_system not in ["xyz", "loc_xyz"]:
raise TypeError(
"Specified permeability coordinate system must be a 'xyz' or 'loc_xyz'"
)
if verbose:
print("Computing one-sided transmissibilites.")
# Vectors from cell centroids to face centroids
assert G.cells.facePos.ndim == 2, "facePos has wrong dimensions"
cellNo = rldecode(np.arange(G.cells.num), np.diff(G.cells.facePos, axis=0))
if cellCenters is None:
C = G.cells.centroids
else:
C = cellCenters
if cellFaceCenters is None:
C = G.faces.centroids[G.cells.faces[:, 0], :] - C[cellNo, :]
else:
C = cellFaceCenters - C[cellNo, :]
# Normal vectors
sgn = 2 * (cellNo == G.faces.neighbors[G.cells.faces[:, 0], 0]) - 1
N = sgn[:, np.newaxis] * G.faces.normals[G.cells.faces[:, 0], :]
if K_system == "xyz":
K, i, j = permTensor(rock, G.gridDim, rowcols=True)
assert K.shape[0] == G.cells.num, \
"Permeability must be defined in active cells only.\n"+\
"Got {} tensors, expected {} (== num cells)".format(K.shape[0], G.cells.num)
# Compute T = C'*K*N / C'*C. Loop based to limit memory use.
T = np.zeros(cellNo.size)
for k in range(i.size):
tmp = C[:, i[k]] * K[cellNo, k] * N[:, j[k]]
# Handle both 1d and 2d array.
if tmp.ndim == 1:
T += tmp
else:
T += np.sum(tmp, axis=1)
T = T / np.sum(C * C, axis=1)
elif K_system == "loc_xyz":
if rock.perm.shape[1] == 1:
rock.perm = np.tile(rock.perm, (1, G.gridDim))
if rock.perm.shape[1] != G.cartDims.size:
raise ValueError(
"Permeability coordinate system `loc_xyz` is only "+\
"valid for diagonal tensor.")
assert rock.perm.shape[0] == G.cells.num,\
"Permeability must be defined in active cells only. "+\
"Got {} tensors, expected {} == (num cells)".format(rock.perm.shape[0], G.cells.num)
dim = np.ceil(G.cells.faces[:, 1] / 2)
raise NotImplementedError(
"Function not finished for K_system='loc_xyz'")
# See MRST, solvers/computeTrans.m
else:
raise ValueError(
"Unknown permeability coordinate system {}.".format(K_system))
is_neg = T < 0
if np.any(is_neg):
if verbose:
prst.log.warn("Warning: {} negative transmissibilities. ".format(
np.sum(is_neg)) + "Replaced by absolute values...")
T[is_neg] = -T[is_neg]
return np.atleast_2d(T).transpose()