def F_b2_k_1(p, m, S, yd, ywd, yed, xd, xwd, xed, zd, zwd, zed, Ld, xbound,
ybound, subtract_inf):
if subtract_inf:
sbtr_inf = 0
else:
sbtr_inf = 1
k = m
n = p
if xbound == "n":
part__1 = cos(k * pi * xd / xed) * cos(k * pi * xwd / xed)
elif xbound == "c":
part__1 = sin(k * pi * xd / xed) * sin(k * pi * xwd / xed)
else:
part__1 = 0
if ybound == "n":
sign = 1
elif ybound == "c":
sign = -1
else:
sign = 1
e_n_k = sqrt(S + (n * pi * Ld)**2 + k**2 * pi**2 / xed**2)
F_b2_k_1 = sin(pi * k / xed) * part__1 / e_n_k / k * (
(sign * exp(-e_n_k * (yd + ywd)) + sign * exp(-e_n_k *
(2 * yed - yd - ywd)) +
exp(-e_n_k * (2 * yed - abs(yd - ywd)))) *
(1 + sumexp(e_n_k, yed)) + exp(-e_n_k * abs(yd - ywd)) *
(sbtr_inf + sumexp(e_n_k, yed)))
return F_b2_k_1
def pd_b1(S, yd, ywd, yed, xed, xbound, ybound, subtract_inf=True):
if xbound == "c":
pd_b1 = 0
return pd_b1
if ybound == "n":
# no flow boundary parallel to fracture
signum = 1
elif ybound == "c":
# constant pressure parallel to fracture
signum = -1
else:
signum = 1
if subtract_inf:
sbtr_inf = 0
else:
sbtr_inf = 1
if S < small / yed**2:
# this is long time approximation - large t_DA - boundary dominated flow
# It seems that in in SPE-18616-PA formula (51) is an error
# That is their expression works only yd > yw
# pd_b1 = 1 / (u ^ 2 * yed * xed) + yed / xed * (1 / 3 - yd / yed + (yd ^ 2 + ywd ^ 2) / (2 * yed ^ 2))
# should be:
# no flow y boundary: 1 / (u ^ 2 * yed * xed) + yed / xed * (1 / 3 - 1 / 2 * (abs(yd - ywd) + (yd + ywd))/ yed + (yd ^ 2 + ywd ^ 2) / (2 * yed ^ 2))
# constant pressure: yed / xed * (1 / 2 ((yd + ywd) - abs(yd - ywd))/ yed - (yd ywd) / (yed ^ 2))
#
if ybound == "n":
Pd = yed / xed * (1 / 3 - 1 / 2 * (abs(yd - ywd) +
(yd + ywd)) / yed +
(yd**2 + ywd**2) / (2 * yed**2))
if S > 0:
# if S is positive we add 2 * PI * tdA material balance pressure decline
# Negative S indicates that long time approximation (real space) should be applied
Pd = Pd + 1 / (S * yed * xed)
else:
# this is constant pressure south and north (yd = 0 and yd=yed)
Pd = yed / xed * (1 / 2 * ((yd + ywd) - abs(yd - ywd)) / yed -
(yd * ywd) / yed**2)
else:
# small time - not using boundary dominated formulas
u = sqrt(S)
summ = sumexp(u, yed)
yd1 = yed - abs(yd - ywd)
yd2 = yed - (yd + ywd)
Pd = 1 / 2 / u / xed * (exp(-u * abs(yd - ywd)) * (sbtr_inf + summ) +
(signum * exp(-u * (yd + ywd)) + signum *
exp(-u * (yed + yd2)) + exp(-u *
(yed + yd1))) *
(1 + summ))
pd_b1 = Pd
return pd_b1
def F_b1_k(k, S, xed, yd, ywd, yed, zd, zwd, zed, Ld, xbound, ybound,
subtract_inf):
if subtract_inf:
sbtr_inf = 0
else:
sbtr_inf = 1
n = k
part__1 = cos(n * pi * zd / zed) * cos(n * pi * zwd / zed)
if ybound == "n":
sign = 1
elif ybound == "c":
sign = -1
else:
sign = 1
e_n = sqrt(S + (n * pi * Ld)**2)
F_b1_k = part__1 / e_n * (
(sign * exp(-e_n * (yd + ywd)) + sign * exp(-e_n *
(2 * yed - yd - ywd)) +
exp(-e_n * (2 * yed - abs(yd - ywd)))) *
(1 + sumexp(e_n, yed)) + exp(-e_n * abs(yd - ywd)) *
(sbtr_inf + sumexp(e_n, yed)))
return F_b1_k
def pd_b2_k(k, S, xd, xwd, xed, yd, ywd, yed, xbound, ybound, compl_type,
subtract_inf):
if xbound == 'n':
part__1 = 2 / xed * cos(k * pi * xd / xed) * cos(k * pi * xwd / xed)
elif xbound == "c":
part__1 = 2 / xed * sin(k * pi * xd / xed) * sin(k * pi * xwd / xed)
else:
part__1 = 0
if compl_type == "frac":
#'coefficient like 2/2 are remained to remember where they come from
part__1 = 2 / 2 * xed / pi / k * sin(k * pi / xed) * part__1
elif compl_type == "vert":
part__1 = part__1
else:
pd_b2_k = 0
return pd_b2_k
if ybound == "n":
signum = 1
elif ybound == "c":
signum = -1
else:
signum = 1
if subtract_inf:
sbtr_inf = 0
else:
sbtr_inf = 1
ek = sqrt(S + k**2 * pi**2 / xed**2)
smexp = sumexp(ek, yed)
part__2 = exp(
(-1) * ek * abs(yd - ywd)) * (sbtr_inf + smexp) + (signum * exp(
(-1) * ek * (yd + ywd)) + exp(
(-1) * ek * (2 * yed - abs(yd - ywd))) + signum * exp(
(-1) * ek * (2 * yed - (yd + ywd)))) * (1 + smexp)
part__2 = 1 / (2 * ek) * part__2
pd_b2_k = part__1 * part__2
return pd_b2_k
def pd_b1(S, yd, ywd, yed, xed, xbound, ybound, subtract_inf=True):
if xbound == "c":
pd_b1 = 0
return pd_b1
if ybound == "n":
#'no flow boundary parallel to fracture
signum = 1
elif ybound == "c":
#'constant pressure parallel to fracture
signum = -1
else:
signum = 1
if subtract_inf:
sbtr_inf = 0
else:
sbtr_inf = 1
if S < small / yed**2:
if ybound == "n":
Pd = yed / xed * (1 / 3 - 1 / 2 * (abs(yd - ywd) +
(yd + ywd)) / yed +
(yd**2 + ywd**2) / (2 * yed**2))
if S > 0:
#'if S is positive we add 2 * PI * tdA material balance pressure decline
#'Negative S indicates that long time approximation (real space) should be applied
Pd = Pd + 1 / (S * yed * xed)
else:
#'this is constant pressure south and north (yd = 0 and yd=yed)
Pd = yed / xed * (1 / 2 * ((yd + ywd) - abs(yd - ywd)) / yed -
(yd * ywd) / yed**2)
else:
#'small time - not using boundary dominated formulas
u = sqrt(S)
summ = sumexp(u, yed)
yd1 = yed - abs(yd - ywd)
yd2 = yed - (yd + ywd)
Pd = 1 / 2 / u / xed * (exp(-u * abs(yd - ywd)) * (sbtr_inf + summ) +
(signum * exp(-u * (yd + ywd)) + signum *
exp(-u * (yed + yd2)) + exp(-u *
(yed + yd1))) *
(1 + summ))
pd_b1 = Pd
return pd_b1