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blt.py
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blt.py
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# -*- coding: utf-8 -*-
"""
Created on Sun Dec 3 14:10:24 2017
@author: Loïc
"""
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 27 14:19:25 2017
@author: pianarol
"""
import hypy as hp
import scipy as sp
import numpy as np
import math
import matplotlib.pyplot as plt
###function lap ###
def lap(x,p):
'''BLT_LAP - Boulton (1963) Laplace dimensionless domain solution
Syntax: s = hp.blt.lap( x, p)
x[1] = sigma = S / S_y
x[2] = phi = ( alpha r^2 S ) / T
p = Laplace parameter
See also: blt_dls'''
s = sp.special.kv(0, math.sqrt(p+x[1]*p/(x[0]*(p+x[1]))))/p
return s
###function dls ###
def dls(x,t):
'''BLT_DLS - Dimensionless drawdown of the Boulton model for an unconfined aquifer.
Syntax: s = hp.blt.dls( x, t)
Dimensionless solution
x[1] = sigma = S / S_y
x[2] = phi = ( alpha r^2 S ) / T
t = dimensionless time
See also: blt_lap'''
s = []
for i in range(0, len(t)):
s.append(hp.stefhest('blt.lap',x,t[i]))
return s
###function dim ###
def dim(p,t):
'''BLT_DIM(p,t) Boulton (1963) model for unconfined aquifer
Syntax: s = hp.blt.dim(p,t)
p = vector of the parameters
p(1) = a : slope of the late time Jacob's straight line in m
p(2) = t0 : intercept with the horizontal axis for s = 0
p(3) = t1
p(4) = phi
t = dimensionless time
t = time in seconds
s = drawdown in meters
Description:
Computes drawdon in the aquifer for a constant rate pumping test.
The aquifer is unconfined and homogeneous.
See also: blt_rpt, blt_gss'''
td = 0.445268*t/p[1]
sds = dls([p[1]/(p[1]+p[2]),2*p[3]*p[1]],td)
sd = []
for i in range(0,len(sds)):
sd.append(0.868589*p[0]*sds[i])
return sd
###function drw ###
###Not sure if useful and coded right
#def drw():
# '''BLT_DRW - Draw the type curves of Boulton (1963)
#
# Syntax: hp.blt.drw()
#
# Description:
# Draw a series of type curves of Boulton (1963).
#
# See also: blt_dim, blt_dls'''
#
##First figure
#
# sigma = 0.01
# t = np.logspace(-2, 6)
#
# s1 = dls([sigma,10^1],t)
# s2 = dls([sigma,10^2],t)
# s3 = dls([sigma,10^3],t)
# s4 = dls([sigma,10^4],t)
#
#
#
# st1,sts = hp.ths.dls(t)
# st2 = 0.5*sp.special.expn(1,1+sigma)/(4*t*sigma)
#
# fig = plt.figure()
#
# ax1 = fig.add_subplot(111)
#
#
# ax1.set_xlabel(r'$t_{D}$')
# ax1.set_ylabel(r'$s_{D}$')
#
# ax1.loglog(t,st1, c='black')
# ax1.loglog(t,st2,c='orange')
# ax1.loglog(t,s1, c='blue')
#
# ax1.loglog(t,s2, c='red')
#
# ax1.loglog(t,s3, c='green')
#
# ax1.loglog(t,s4, c='violet')
#
#
#
#
# ax1.set_ylim(ymin=1e-3)
# ax1.set_xlim(xmin=1e-2)
#
# plt.show()
###function gss ###
def gss(t,s):
'''BLT_GSS - First guess for the parameters of the Boulton model
Syntax: p = hp.blt.gss(t,s)
p(1) = a = slope of Jacob straight line for late time
p(2) = t0 = intercept with the horizontal axis for s = 0 for the early
asymptote
p(3) = t1 = intercept with the horizontal axis for s = 0 for the late
asymptote
p(4) = phi
t = time
s = drawdown
Description:
First guess for the parameters of Boulton solution.
See also: blt_dmo, blt_rpt, blt_dim'''
p = [1,2,3,4]
p[1] = t[0]
n = round(len(t)/3)
t1 = t[n-1:len(t)]
s1 = s[n-1:len(s)]
pj = hp.jcb.gss(t1,s1)
p[3] = 1e-4
p[0] = pj[0]
p[2] = pj[1]
return p
###function rpt ###
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: hp.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')