def gss(t, s):
'''THN_GSS - First guess for the parameters of the Theis model with a no-flow boundary
Syntax: p = hp.thn.gss(t,s)
p(1) = a = slope of Jacob straight line
p(2) = t0 = intercept of the Jacob straight line
p(3) = ti = time of intersection between the 2 straight lines
t = time
s = drawdown
Description:
First guess for the parameters of theis solution with a no-flow
boundary
See also: thn_dmo, thn_rpt, thn_dim
'''
#Automatic identification of the "control" points
td, d = hp.ldiffs(t, s, npoints=10) #First log derivative
tdd, dd = hp.ldiffs(td, d, npoints=10) #Second log derivative
#Calculation of the parameters of the model
tmp = np.amax(dd)
tmp = np.float(tmp)
i = np.argmax(dd)
ti = tdd[i - 1]
#Slope of Jacob's straight line
a = d[-1] * 2.30 / 2
#Origin of jacob straight line
t0 = math.pow(10, (a * math.log10(t[-1] * t[-1] / ti) - s[-1]) / a)
p = []
p.append(a)
p.append(t0)
p.append(ti)
return p
def gss(t, s):
'''PCW_GSS - First guess for the parameters of the Papadopulos Cooper solution
Syntax: p = hp.pcw.gss(t,s)
p(1) = a = slope of Jacob straight line for late time
p(2) = t0 = intercept of the Jacob straight line for late time
p(3) = Cd = Dimensionless coefficient (1/2alpha)
t = time
s = drawdown
Description:
First guess for the parameters of Papadopulos Cooper solution
See also: pcw_dim, pcw_dmo, pcw_rpt'''
td, d = hp.ldiffs(t, s, npoints=10)
if d[-1] > 0:
a = math.log(10) * d[-1]
t0 = t[-1] * math.exp(-s[-1] / d[-1])
else:
p = hp.ths.gss(t, s)
a = p[0]
t0 = p[1]
if t0 <= 0:
t0 = 1e-5
condition = (np.greater(t, 0) & np.greater(s, 0))
sp = np.extract(condition, s)
tp = np.extract(condition, t)
if not tp.all():
print(
'HYTOOL: Error in pcw_gss - the vector t and s do not contain positive data'
)
p = float('NaN')
return
else:
cd = 0.8905356 * d[-1] / sp[0] * tp[0] / t0
p = []
p.append(a)
p.append(t0)
p.append(cd)
return p
def gss(t,s):
'''WAR_GSS - First guess for the parameters of the Warren and Root solution
Syntax: p = war_gss(t,s)
p(1) = a = slope of Jacob Straight Line
p(2) = t0 = intercept with the horizontal axis for
the early time asymptote
p(3) = t1 = intercept with the horizontal axis for
the late time asymptote
p(4) = tm = time of the minimum of the derivative
t = time
s = drawdown
Description:
First guess for the parameters of the Warren and Root solution
See also: war_dmo, war_dim, war_rpt'''
td,d = hp.ldiffs(t,s,npoints=40)
dd = np.mean(d[len(d)-4:len(d)])
a = math.log(10)*dd
t0 = t[0]/math.exp(s[-1]/dd)
t1 = t[-1]/math.exp(s[-1]/dd)
i = np.argmin(d)
tm = td[i-2]
tm = np.float(tm)
p = []
p.append(a)
p.append(t0)
p.append(t1)
p.append(tm)
return p
def rpt(p,
t,
s,
d,
name,
ttle='Interference test',
Author='My name',
Rapport='My Rapport',
filetype='img'):
'''THN_RPT - Produces the final figure and results for the Theis model with a no flow boundary
Syntax: hp.thn.rpt( p, t, s, d, ttle )
p = parameters of the model
t = measured time
s = measured drawdown
d(1) = Q = Pumping rate
d(2) = r = Distance between the observation and the pumping well
ttle = Title of the figure (Optional)
Description:
Produces the final figure and results for Theis model (1935) with
a no flow boundary.
See also: thn_dmo, thn_dim, thn_gss'''
#rename the parameters for a more intuitive check of the formulas
a = p[0]
t0 = p[1]
ti = p[2]
q = d[0]
r = d[1]
#Compute the transmissivity, storativity and radius of influence
T = 0.1832339 * q / a
S = 2.458394 * T * t0 / r**2
Ri = math.sqrt(2.2458394 * T * ti / S)
#Calls an internalscript that computes drawdown, derivative and residuals
#script rpt.cmp
tc, sc, mr, sr, rms = hp.script.cmp(p, t, s, 'thn')
#script rpt_plt
#calculate the derivative of the data
td, sd = hp.ldiffs(t, s, npoints=30)
#keep only positive derivatives
td, sd = hp.hyclean(td, sd)
#compute the derivative of the model
tdc, sdc = hp.ldiff(tc, sc)
#keep only positive derivatives
tdc, sdc = hp.hyclean(tdc, sdc)
#plots the data and model in bi-logarithmic scale
if filetype == 'pdf':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.3,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity S : {:3.1e} '.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Distance to image well Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.5,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.55,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept ti : {:0.2g} m'.format(ti),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='r', marker='+', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='b', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Theis (1935) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('thn_rapport.pdf', bbox_inches='tight')
if filetype == 'img':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.3,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity S : {:3.1e} '.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Distance to image well Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.5,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.55,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept ti : {:0.2g} m'.format(ti),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='r', marker='+', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='b', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Theis (1935) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('thn_rapport.png', bbox_inches='tight')
def rpt(p,
t,
s,
d,
name,
ttle='Interference test',
Author='My name',
Rapport='My Rapport',
filetype='img'):
'''THS_RPT - Reports graphically the results of a pumping test interpreted with the Theis (1935) model.
Syntax: ths_rpt( p, t, s, d, name, ttle, Author, Rapport, filetype )
p = parameters of the model
p(1) = a = slope of the straight line
p(2) = t0 = intercept with the horizontal axis for s = 0
t = measured time % s = measured drawdown
d(1) = q = Pumping rate
d(2) = r = distance from the pumping well
ttle = Title of the figure
Description:
Produces the final figure and results for Theis model (1935).
See also: ths_dmo, ths_dim, ths_gss'''
#rename the parameters for a more intuitive check of the formulas
a = p[0]
t0 = p[1]
q = d[0]
r = d[1]
#Compute the transmissivity, storativity and radius of influence
T = 0.1832339 * q / a
S = 2.458394 * T * t0 / r**2
Ri = 2 * math.sqrt(T * t[len(t) - 1] / S)
#Calls an internalscript that computes drawdown, derivative and residuals
#script rpt.cmp
#keep only the positive time
t, s = hp.hyclean(t, s)
#define regular points to plot the calculated drawdown
tc = np.logspace(np.log10(t[0]),
np.log10(t[len(t) - 1]),
num=len(t),
endpoint=True,
base=10.0,
dtype=np.float64)
#compute the drawdown with the model
if name == 'ths':
sc = hp.ths.dim(p, tc)
if name == 'Del':
sc = hp.Del.dim(p, tc)
#keep only the positive drawdown
tc, sc = hp.hyclean(tc, sc)
#Compute the residuals and their statistics
residuals = s - hp.ths.dim(p, t)
mr = np.mean(residuals)
sr = 2 * np.nanstd(residuals)
rms = math.sqrt(np.mean(residuals**2))
#script rpt_plt
#calculate the derivative of the data
td, sd = hp.ldiffs(t, s, npoints=30)
#keep only positive derivatives
td, sd = hp.hyclean(td, sd)
#compute the derivative of the model
tdc, sdc = hp.ldiff(tc, sc)
#keep only positive derivatives
tdc, sdc = hp.hyclean(tdc, sdc)
#plots the data and model in bi-logarithmic scale
if filetype == 'pdf':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.3,
'Transmissivity T : {:3.2e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity S : {:3.2e} '.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Radius of Investigation Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.5,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.55,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='r', marker='+', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='b', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Theis (1935) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('ths_rapport.pdf', bbox_inches='tight')
if filetype == 'img':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1,
0.85,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.8,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.75,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1,
0.65,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.6,
'Transmissivity T : {:3.2e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.55,
'Storativity S : {:3.2e} '.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.5,
'Radius of Investigation Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1,
0.4,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.35,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.3,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.25,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(1.05,
0.2,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='r', marker='+', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='b', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Theis (1935) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('ths_rapport.png', bbox_inches='tight')
def rpt(p,
t,
s,
d,
name,
ttle='Interference test',
Author='My name',
Rapport='My Rapport',
filetype='img'):
'''PCW_RPT - Produces the final figure and results for the Papadopulos Cooper model
Syntax: hp.pcw.rpt( p, t, s, d, ttle )
p(1) = a = slope of the late time straight line
p(2) = t0 = intersept of late time straight line
p(3) = Cd = Well bore storage coefficient
t = measured time % s = measured drawdown
d(1) = Q = Pumping rate
d(2) = rw = Radius of well screen
d(3) = rc = Radius of the casing
ttle = Title of the figure % % Description:
Produces the final figure and results for the Papadopulos-Cooper model
Reference: Papadopulos, I.S., and H.H.J. Cooper. 1967. Drawdown in a
well of large diameter. Water Resources Research 3, no. 1: 241-244.
See also: pcw_dmo, pcw_pre, pcw_dim, pcw_gss'''
#rename the parameters for a more intuitive check of the formulas
q = d[0]
rw = d[1]
rc = d[2]
a = p[0]
t0 = p[1]
cd = p[2]
#Compute the transmissivity
T = 0.1832339 * q / a
#Calls an internalscript that computes drawdown, derivative and residuals
#script rpt.cmp
tc, sc, mr, sr, rms = hp.script.cmp(p, t, s, 'pcw')
#script rpt_plt
#calculate the derivative of the data
td, sd = hp.ldiffs(t, s, npoints=30)
#keep only positive derivatives
td, sd = hp.hyclean(td, sd)
#compute the derivative of the model
tdc, sdc = hp.ldiff(tc, sc)
#keep only positive derivatives
tdc, sdc = hp.hyclean(tdc, sdc)
#plots the data and model in bi-logarithmic scale
if filetype == 'pdf':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Well radius : {:0.2g} m '.format(rw),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.20,
'Casing radius : {:0.2g} m '.format(rc),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.30,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.45,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.50,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.55,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'C_D exp(2s) : {:3.1e}'.format(cd),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.66,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Papadopulos-Cooper (1967) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('pcw_rapport.pdf', bbox_inches='tight')
if filetype == 'img':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Well radius : {:0.2g} m '.format(rw),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.20,
'Casing radius : {:0.2g} m '.format(rc),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.30,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.45,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.50,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.55,
'intercept t0 : {:0.2g} m'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'C_D exp(2s) : {:3.1e}'.format(cd),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.66,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Papadopulos-Cooper (1967) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('pcw_rapport.png', bbox_inches='tight')
def rpt(p,
t,
s,
d,
name,
ttle='Interference test',
Author='My name',
Rapport='My Rapport',
filetype='img'):
'''BLT_RPT - Reports the results of the interpretation with the Boulton model
Syntax: blt_rpt( p, t, s, d, ttle )
p = parameters of the model
p(1) = a = slope of the straight lines
p(2) = t0 = intercept with the horizontal axis the first line
p(3) = t1 = intercept with the horizontal axis the second line
p(4) = phi = empirical parameter that trigger the delay
d(1) = q = pumping rate
d(2) = r = distance between pumping well and piezometer
t = measured time
s = measured drawdown
ttle = Title of the figure
Description:
Produces the final figure and results for the Boulton model (1963).
See also: blt_dmo, blt_dim, blt_pre, blt_gss'''
#Rename the parameters for a more intuitive check of the formulas
a = p[0]
t0 = p[1]
t1 = p[2]
phi = p[3]
q = d[0]
r = d[1]
#Compute the transmissivity, storativity and radius of influence
T = 0.1832339 * q / a
S = 2.2458394 * T * t0 / r**2
omegad = 2.2458394 * T * t1 / r**2 - S
Ri = 2 * math.sqrt(T * t[-1] / omegad)
#Calls an internalscript that computes drawdown, derivative and residuals
#script rpt.cmp
tc, sc, mr, sr, rms = hp.script.cmp(p, t, s, 'blt')
#script rpt_plt
#calculate the derivative of the data
td, sd = hp.ldiffs(t, s, npoints=30)
#keep only positive derivatives
td, sd = hp.hyclean(td, sd)
#compute the derivative of the model
tdc, sdc = hp.ldiff(tc, sc)
#keep only positive derivatives
tdc, sdc = hp.hyclean(tdc, sdc)
#plots the data and model in bi-logarithmic scale
if filetype == 'pdf':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.30,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity S : {:3.1e}'.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Drainage Porosity : {:3.1e}'.format(omegad),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.45,
'Radius of Investigation Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.55,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept t0 : {:0.2g} s'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'intercept t1 : {:0.2g} s'.format(t1),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'phi : {:0.2g} m'.format(phi),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.80,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.85,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Boulton (1963) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('blt_rapport.pdf', bbox_inches='tight')
if filetype == 'img':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.30,
'Transmissivity T : {:3.1e} m²/s'.format(T),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity S : {:3.1e}'.format(S),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Drainage Porosity : {:3.1e}'.format(omegad),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.45,
'Radius of Investigation Ri : {:0.2g} m'.format(Ri),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.55,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept t0 : {:0.2g} s'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'intercept t1 : {:0.2g} s'.format(t1),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'phi : {:0.2g} m'.format(phi),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.80,
'mean residual : {:0.2g} m'.format(mr),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.85,
'2 standard deviation : {:0.2g} m'.format(sr),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Boulton (1963) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('blt_rapport.png', bbox_inches='tight')
def rpt(p,
t,
s,
d,
name,
ttle='Interference test',
Author='My name',
Rapport='My Rapport',
filetype='img'):
'''WAR_RPT - Produces the final figure and results for the Warren and Root model
Syntax: hp.war.rpt( p, t, s, d, ttle )
p(1) = a = slope of Jacob Straight Line
p(2) = t0 = intercept with the horizontal axis for the early time asymptote
p(3) = t1 = intercept with the horizontal axis for the late time asymptote
p(4) = tm = time of the minimum of the derivative
t = measured time
s = measured drawdown
d(1) = Q = Pumping rate
d(2) = r = Distance to the pumping well
ttle = Title of the figure
Description:
Produces the final figure and results for the Warren and Root model
See also: war_dmo, war_dim, war_gss'''
#Rename the parameters for a more intuitive check of the formulas
Q = d[0]
r = d[1]
a = p[0]
t0 = p[1]
t1 = p[2]
tm = p[3]
#Compute the transmissivity, storativity and radius of influence
Tf = 0.1832339 * Q / a
Sf = 2.245839 * Tf * t0 / r**2
Sm = 2.245839 * Tf * t1 / r**2 - Sf
sigma = (t1 - t0) / t0
lambada = 2.2458394 * t0 * math.log(t1 / t0) / tm
#Calls an internalscript that computes drawdown, derivative and residuals
#script rpt.cmp
tc, sc, mr, sr, rms = hp.script.cmp(p, t, s, 'war')
#script rpt_plt
#calculate the derivative of the data
td, sd = hp.ldiffs(t, s, npoints=30)
#keep only positive derivatives
td, sd = hp.hyclean(td, sd)
#compute the derivative of the model
tdc, sdc = hp.ldiff(tc, sc)
#keep only positive derivatives
tdc, sdc = hp.hyclean(tdc, sdc)
#plots the data and model in bi-logarithmic scale
if filetype == 'pdf':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(Q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.30,
'Transmissivity Tf : {:3.1e} m²/s'.format(Tf),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity Sf : {:3.1e}'.format(Sf),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Storativity Sm : {:3.1e}'.format(Sm),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.45,
'Interporosity flow lambda : {:0.2e}'.format(lambada),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.55,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept t0 : {:0.2g} s'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'intercept t1 : {:0.2g} s'.format(t1),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'Minimum deruvatuve tm : {:0.2g} s'.format(tm),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Warren and Root (1965) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('war_rapport.pdf', bbox_inches='tight')
if filetype == 'img':
fig = plt.figure()
fig.set_size_inches(8, 6)
fig.text(0.125,
1,
Author,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
0.95,
Rapport,
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.05,
'Test Data : ',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.1,
'Discharge rate : {:3.2e} m³/s'.format(Q),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.15,
'Radial distance : {:0.2g} m '.format(r),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.25,
'Hydraulic parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.30,
'Transmissivity Tf : {:3.1e} m²/s'.format(Tf),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.35,
'Storativity Sf : {:3.1e}'.format(Sf),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.40,
'Storativity Sm : {:3.1e}'.format(Sm),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.45,
'Interporosity flow lambda : {:0.2e}'.format(lambada),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.125,
-0.55,
'Fitting parameters :',
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.60,
'slope a : {:0.2g} m '.format(a),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.65,
'intercept t0 : {:0.2g} s'.format(t0),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.70,
'intercept t1 : {:0.2g} s'.format(t1),
fontsize=14,
transform=plt.gcf().transFigure)
fig.text(0.135,
-0.75,
'Minimum deruvatuve tm : {:0.2g} s'.format(tm),
fontsize=14,
transform=plt.gcf().transFigure)
ax1 = fig.add_subplot(111)
ax1.set_xlabel('Time in seconds')
ax1.set_ylabel('Drawdown in meters')
ax1.set_title(ttle)
ax1.loglog(t, s, c='b', marker='o', linestyle='', label='drawdown')
ax1.loglog(td, sd, c='r', marker='x', linestyle='', label='Derivative')
ax1.loglog(tc, sc, c='g', label='Warren and Root (1965) Model')
ax1.loglog(tdc, sdc, c='y', label='Model derivative')
ax1.grid(True)
ax1.legend()
plt.show()
fig.savefig('war_rapport.png', bbox_inches='tight')
def gss(t, s):
'''THC_GSS - First guess for the parameters of the Theis model with a constant head boundary.
Syntax: p = hp.thc.gss(t,s)
p(1) = a = slope of Jacob straight line
p(2) = t0 = iintercept of the first segment of straight line
p(3) = ti = time of intersection between the 2 straight lines
t = time
s = drawdown
Description:
First guess for the parameters of theis solution with a constant head
boundary.
See also: thc_dim, thc_dmo, thc_rpt
'''
td, d = hp.ldiffs(t, s, npoints=10)
sl = np.amax(s)
sl = np.float(sl)
du = np.amax(d)
du = np.float(du)
i = np.argmax(d)
tu = td[i]
tu = np.float(tu)
condition = np.greater(t, tu)
l = np.where(condition == True)
w = l[0][0]
ta = t[w]
sa = s[w]
ts = td[-1]
ds = d[-1]
#Calculation of the parameters of the model
#Dimensionless distance
a = sl / du
rd = ird(a)
#Slope of Jacob's straight line
b = sl / 2 / math.log10(rd)
#Origin of jacob straight line
if rd < 50:
t0 = 2 * tu * math.log(rd) / (0.5625 * (math.pow(rd, 2) - 1))
else:
t0 = ta * math.pow(10, -sa / b)
#Origin of the second line
t1 = math.pow(rd, 2) * t0
#Time of intersection of the two lines
ti = math.pow(t1, 2) / t0
p = []
p.append(b)
p.append(t0)
p.append(ti)
return p
