def energy_calculations(D, L, nu): #Here we change lenght and height! xm, xp, ym, yp, xbar, ybar, D, L = discretize_geometry(D, L) N = xp.shape[0] inn = np.linspace(0, N, N, endpoint=True) dx = xp - xm dy = yp - ym ds = np.sqrt(dx**2 + dy**2) n1 = -(yp-ym)/ds n2 = (xp-xm)/ds phi0 = np.exp(nu*(ybar - complex(0,1)*xbar)) ss = np.zeros((N, N), dtype=complex) for i in range(N): for j in range(N): xa = xbar[j] - xbar[i] yb = ybar[j] + ybar[i] zz = nu*(yb - complex(0, 1)*xa) f1 = -2*np.exp(zz)*mpm.e1(zz) + np.log(zz) zz = nu*(yb - complex(0, 1)*xa) # (91) f1 = -2*np.exp(zz)*(mpm.e1(zz) + np.log(zz) - np.log(-zz)) #(88) from lec-notes f2 = 2*np.pi*np.exp(zz) #(90) g2 = f1.real + complex(0, 1)*f2.real #() arg0 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] - ybar[i]))/\ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] - ybar[i])))).imag if j - i == 0: arg0 = -np.pi arg1 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] + ybar[i]))/ \ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] + ybar[i])))).imag help1 = (n1[j]*(f1.imag + complex(0, 1)*f2.imag) + n2[j]* \ (f1.real + complex(0, 1)*f2.real))*nu*ds[j] ss[i, j] = arg0 + arg1 + help1 rhsD = -2*np.pi*phi0 phiD = np.linalg.solve(ss, rhsD) XX2 = phiD*n2*ds sXX2 = sum(XX2) X2 = -complex(0, 1)*sXX2 return phiD, inn, X2
def pressao(anp, q, B, mi, k, h, rw, ct, phi, r, t, S):
if t == 0:
return 0
if anp:
ctd = k * 0.0003484 / (phi * mi * ct * rw * rw)
cpd = k * h / (q * B * mi * 19.03)
else:
ctd = k * 0.0002637 / (phi * mi * ct * rw * rw)
cpd = k * h / (q * B * mi * 141.2)
x = (r * r / (rw * rw)) / (4 * ctd * t)
Pd = float(e1(x)) / 2
if r == rw:
DeltaPressao = Pd / cpd + S / cpd
else:
DeltaPressao = Pd / cpd
return DeltaPressao
def test_immediately_after_underflow():
x = np.nextafter(-MINEXP, np.inf)
assert sc.e1(x) == float(mpmath.e1(x))
def lhs_rhs(D, L): nu = 0.9 #Here we change lenght and height! xm, xp, ym, yp, xbar, ybar, D, L = discretize_geometry(D, L) N = xp.shape[0] inn = np.linspace(0, N, N, endpoint=True) dx = xp - xm dy = yp - ym ds = np.sqrt(dx**2 + dy**2) n1 = -(yp-ym)/ds n2 = (xp-xm)/ds xg1 = -0.5*dx/np.sqrt(3) + xbar xg2 = 0.5*dx/np.sqrt(3) + xbar yg1 = -0.5*dy/np.sqrt(3) + ybar yg2 = 0.5*dy/np.sqrt(3) + ybar phi0 = np.exp(nu*(ybar - complex(0,1)*xbar)) phi0n = nu*(n2 - complex(0, 1)*n1)*phi0 gg = np.zeros((N, N), dtype=complex) ss = np.zeros((N, N), dtype=complex) #for i in range(N+1): for i in range(N): for j in range(N): xa1 = xg1[j] - xbar[i] xa2 = xg2[j] - xbar[i] ya1 = yg1[j] - ybar[i] ya2 = yg2[j] - ybar[i] ra1 = np.sqrt(xa1**2 + ya1**2) ra2 = np.sqrt(xa2**2 + ya2**2) g0 = 0.5*(np.log(ra1) + np.log(ra2)) #midpoint rule xa = xbar[j] - xbar[i] yb = ybar[j] + ybar[i] rb = np.sqrt(xa**2 + yb**2) g1 = -np.log(rb) zz = nu*(yb - complex(0, 1)*xa) # (91) f1 = -2*np.exp(zz)*(mpm.e1(zz) + np.log(zz) - np.log(-zz)) #(88) from lec-notes f2 = 2*np.pi*np.exp(zz) #(90) g2 = f1.real + complex(0, 1)*f2.real #() gg[i, j] = (g0 + g1 + g2)*ds[j] arg0 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] - ybar[i]))/\ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] - ybar[i])))).imag if j - i == 0: arg0 = np.pi arg1 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] + ybar[i]))/ \ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] + ybar[i])))).imag help1 = (n1[j]*(f1.imag + complex(0, 1)*f2.imag) + n2[j]* \ (f1.real + complex(0, 1)*f2.real))*nu*ds[j] ss[i][j] = (arg0 + arg1 + help1) #print(ss) rhs = np.matmul(gg, phi0n) lhs = np.matmul(ss, phi0) return lhs, rhs, inn, D, L
def calculate_phi(D, L, nu): #Here we change lenght and height! xm, xp, ym, yp, xbar, ybar, D, L = discretize_geometry(D, L) N = xp.shape[0] inn = np.linspace(0, N, N, endpoint=True) dx = xp - xm dy = yp - ym ds = np.sqrt(dx**2 + dy**2) n1 = -(yp-ym)/ds n2 = (xp-xm)/ds xg1 = -0.5*dx/np.sqrt(3) + xbar xg2 = 0.5*dx/np.sqrt(3) + xbar yg1 = -0.5*dy/np.sqrt(3) + ybar yg2 = 0.5*dy/np.sqrt(3) + ybar phi0 = np.exp(nu*(ybar - complex(0,1)*xbar)) phi0n = nu*(n2 - complex(0, 1)*n1)*phi0 gg = np.zeros((N, N), dtype=complex) ss = np.zeros((N, N), dtype=complex) #for i in range(N+1): for i in range(N): for j in range(N): xa1 = xg1[j] - xbar[i] xa2 = xg2[j] - xbar[i] ya1 = yg1[j] - ybar[i] ya2 = yg2[j] - ybar[i] ra1 = np.sqrt(xa1**2 + ya1**2) ra2 = np.sqrt(xa2**2 + ya2**2) g0 = 0.5*(np.log(ra1) + np.log(ra2)) #midpoint rule xa = xbar[j] - xbar[i] yb = ybar[j] + ybar[i] rb = np.sqrt(xa**2 + yb**2) g1 = -np.log(rb) zz = nu*(yb - complex(0, 1)*xa) # (91) f1 = -2*np.exp(zz)*(mpm.e1(zz) + np.log(zz) - np.log(-zz)) #(88) from lec-notes f2 = 2*np.pi*np.exp(zz) #(90) g2 = f1.real + complex(0, 1)*f2.real #() gg[i, j] = (g0 + g1 + g2)*ds[j] arg0 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] - ybar[i]))/\ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] - ybar[i])))).imag if j - i == 0: arg0 = -np.pi arg1 = (np.log((xm[j] - xbar[i] + complex(0, 1)*(ym[j] + ybar[i]))/ \ (xp[j] - xbar[i] + complex(0, 1)*(yp[j] + ybar[i])))).imag help1 = (n1[j]*(f1.imag + complex(0, 1)*f2.imag) + n2[j]* \ (f1.real + complex(0, 1)*f2.real))*nu*ds[j] ss[i][j] = (arg0 + arg1 + help1) rhs = np.matmul(gg, n2) phi2 = np.linalg.solve(ss, rhs) ff22 = phi2*n2*ds sum_ff22 = sum(ff22) AM2 = complex(0, 1)*(phi2*(nu*n2 - nu*complex(0, 1)*n1) - n2)*phi0*ds AP2 = complex(0, 1)*(phi2*(nu*n2 + nu*complex(0, 1)*n1) - n2)*np.conj(phi0)*ds sum_AM2 = sum(AM2) sum_AP2 = sum(AP2) dampingb22 = 0.5*(sum_AM2*np.conj(sum_AM2) + sum_AP2*np.conj(sum_AP2)) v1H = sum(-complex(0, 1)*(phi0*n2 - phi2*phi0n)*ds) return phi2, inn, sum_ff22, sum_AM2, sum_AP2, v1H, dampingb22
def theis_solution(permeability_val=None,
density_val=None,
viscosity_val=None,
filename=None,
use_mobility=None,
flux_function=None,
b=None,
well_area=None,
Kw=None,
phi=None,
t_end=None,
z_plot_loc=None,
fixed_axis=None,
pp_loc=None,
P0=None,
symmetry=True):
import numpy as np
import matplotlib.pyplot as plt
import mpmath
import os
if filename == None:
filename = 'simple_theis_k1_csv_pressure_0009.csv'
if permeability_val == None:
permeability_val = 1.0 # m2
if density_val == None:
density_val = 1.0
#kg/m3
if viscosity_val == None:
viscosity_val = 1.0
#Pa-s
if flux_function == None:
flux_function = -0.233426704015
if b == None:
b = 1.0
# aquifer thickness (m)
if Kw == None:
Kw = 1.0 # compressibility of water (Pa^-1)
if phi == None:
phi = 0.1 # porosity
if t_end == None:
t_end = 100.0
#seconds
if use_mobility == None:
use_mobility = False
if z_plot_loc == None:
z_plot_loc = -199.77360637445
if fixed_axis == None:
fixed_axis = 2 # integer telling which axis should be fixed (x = 0, y = 1, z = 2)
if pp_loc == None:
pp_loc = -1 #integer to tell where the pore pressure is found in csv file
if P0 == None:
P0 = 0.
if well_area == None:
dx = 1.07131
dy = 1.0
#meters
well_area = dx * dy
# well area (m2)
print('well_area ', well_area)
## Calculations
if use_mobility:
Qm = -flux_function * density_val * permeability_val / viscosity_val * well_area
else:
Qm = -flux_function * well_area
print('Mass flow rate in (i.e. fluxes_in expected)', Qm)
ignore_density = False #Always False if use_mobility = False. Maybe also if use_mobility = True??
if ignore_density:
Q = Qm
else:
Q = Qm / density_val
print('volumetric flow rate (checked against Theis)', Q)
## Calculate the analytical solution my way
import pudb
pudb.set_trace()
if symmetry:
prefactor = 4.0 * Q * viscosity_val / (
4.0 * np.pi * b * permeability_val
) # Pa, multiplier of exponential integral, 4.0 factor is because of 1/4 grid symmetry
else:
prefactor = Q * viscosity_val / (
4.0 * np.pi * b * permeability_val
) # Pa, multiplier of exponential integral, 4.0 factor is because of 1/4 grid symmetry
r_anal = np.linspace(1, 200, 101)
#radius in meters
dP_anal = np.zeros(len(r_anal))
u = (r_anal**
2.0) * phi * viscosity_val / (4.0 * permeability_val * t_end * Kw)
for i in xrange(0, len(u)):
dP_anal[i] = prefactor * mpmath.e1(u[i])
plt.plot(r_anal, dP_anal)
x = np.zeros(40)
pp = np.zeros(40)
import csv
with open(filename) as csv_file:
csv_reader = csv.reader(csv_file, delimiter=',')
line_count = 0
for row in csv_reader:
if line_count == 0:
junkvar = 1
line_count += 1
else:
if float(row[fixed_axis]) > z_plot_loc - .1 and float(
row[fixed_axis]) < z_plot_loc + .1 and float(
row[0]) > 0:
x[line_count - 1] = float(row[0])
pp[line_count - 1] = float(row[pp_loc]) - P0
line_count += 1
# x = np.append([x],[row[0]]);
# pp = np.append([pp],[row[-1]]);
plt.plot(x, pp, '.')
def theis_solution(permeability_val=None,
density_val=None,
viscosity_val=None,
filename=None,
use_mobility=None,
flux_function=None):
import numpy as np
import matplotlib.pyplot as plt
import mpmath
import os
if filename == None:
filename = 'simple_theis_k1_csv_pressure_0009.csv'
if permeability_val == None:
permeability_val = 1.0 # m2
if density_val == None:
density_val = 1.0
#kg/m3
if viscosity_val == None:
viscosity_val = 1.0
#Pa-s
dx = 1.071
dy = 1.0
#meters
if flux_function == None:
flux_function = -0.233426704015
b = 1.0
# thickness (m)
Kw = 1.0 # compressibility of water (Pa^-1)
phi = 0.1 # porosity
t_end = 100.0
#seconds
if use_mobility == None:
use_mobility = False
## Calculations
well_area = dx * dy
# well area (m2)
print('well_area ', well_area)
if use_mobility:
Qm = -flux_function * density_val * permeability_val / viscosity_val * well_area
else:
Qm = -flux_function * well_area
print('Mass flow rate in (i.e. fluxes_in expected)', Qm)
ignore_density = False #Always False if use_mobility = False. Maybe also if use_mobility = True??
if ignore_density:
Q = Qm
else:
Q = Qm / density_val
print('volumetric flow rate (checked against Theis)', Q)
## Calculate the analytical solution my way
prefactor = 4.0 * Q * viscosity_val / (
4.0 * np.pi * b * permeability_val
) # Pa, multiplier of exponential integral, 4.0 factor is because of 1/4 grid symmetry
r_anal = np.linspace(1, 200, 101)
#radius in meters
dP_anal = np.zeros(len(r_anal))
t_final = 1.e2
# seconds
u = (r_anal**
2.0) * phi * viscosity_val / (4.0 * permeability_val * t_final * Kw)
for i in xrange(0, len(u)):
dP_anal[i] = prefactor * mpmath.e1(u[i])
plt.plot(r_anal, dP_anal)
x = np.zeros(40)
pp = np.zeros(40)
import csv
with open(filename) as csv_file:
csv_reader = csv.reader(csv_file, delimiter=',')
line_count = 0
for row in csv_reader:
if line_count == 0:
junkvar = 1
line_count += 1
else:
if float(row[2]) > -199.77360637445 - .1 and float(
row[2]) < -199.77360637445 + .1:
x[line_count - 1] = float(row[0])
pp[line_count - 1] = float(row[-1])
line_count += 1
# x = np.append([x],[row[0]]);
# pp = np.append([pp],[row[-1]]);
plt.plot(x, pp, '.')