def stretched_exponential(w=8, l=10, save=False):
field = 'WELTON'
prod = get_production('UK')[field].dropna()
fit_parms = get_fit_parms('UK', '2013-02-01').ix[field]
tau, beta, y0 = fit_parms['tau'], fit_parms['beta'], fit_parms['y0']
x, y = prepare_xy(prod)
yfit = y0 * exp(-(x/abs(tau))**beta)
fit = Series(yfit, index=prod.index)
lower_cutoff = '1996-08-01'
fig = plt.figure(figsize=(w, l))
ax = fig.gca()
prod.plot(ax=ax, marker='x', ls='')
l1 = ax.get_lines()[0]
l2, = ax.plot(fit[lower_cutoff:].index, fit[lower_cutoff:], '-k')
ax.legend([l1, l2], [field.lower().capitalize() + ' (UK)',
r'$y = y0 + exp(-(\frac{t}{\tau})^\beta)$'])
ax.set_xlabel('Time')
ax.set_ylabel('Prodction [barrels/day]')
fig.tight_layout()
if save:
os.chdir('article')
fig.savefig('stretched_exponential.pdf')
os.chdir('..')
else:
plt.show()
def extend_production(oil_field, fit_parms, fit_style='stretched exponential'):
"""Extend the production of a given oil field into the future, given the
fit_parms and the fit_style.
"""
start = oil_field.index[-1] + MonthBegin()
if fit_style == 'stretched exponential':
tau, beta, yo = fit_parms
lifetime = abs(tau) * (-log(MIN_PROD/yo)) ** (1./beta)
try:
end = oil_field.dropna().index[0] + lifetime * Day()
except:
lifetime = 200 * 365 if lifetime > 200 * 365 else lifetime
end = oil_field.dropna().index[0] + lifetime * Day()
end = MonthBegin().rollback(end) + DateOffset(months=1)
future = date_range(start, end, freq='MS')
nfuture = len(future)
if nfuture == 0:
return oil_field
oil_field = concat((oil_field, Series(len(future) * [1], index=future,
name=oil_field.name)))
x, y = prepare_xy(oil_field)
if fit_style == 'stretched exponential':
y = yo * exp(sign(tau) * (x[-nfuture:] / abs(tau))**beta)
oil_field[-nfuture:] = y
return oil_field
def perturb_fit_parms(fields=GOOD_FITS, fit_style='stretched exponential',
xmin='custom', perturbation=0.1, step=0.01):
"""We perturb the parameters of the fit and look how flat the cost_function
is. We will see how much perturbation the parameters can take for a fixed
difference in the value of the cost function (ex: 10%). Or the reverse: fix
the parms and look how the cost function varies.
"""
(fit_parms, oil_fields) = get_fit_parms(fields=fields, fit_style=fit_style,
xmin=xmin)
def get_xmin(field, MAXES):
return MAXES[field] if field in MAXES.keys() else 'max'
res = {}
for field_name in fit_parms.keys():
tau, beta, yo = fit_parms[field_name]
changes = arange(1.-perturbation, 1+perturbation+step, step)
taus = changes * tau
betas = changes * beta
xs, ys, zs = [], [], []
for tau in taus:
for beta in betas:
xs.append(tau)
ys.append(beta)
_x, _y = oil_fields[field_name], None
x_, y_ = prepare_xy(_x, _y)
xmin = xmin2xmin(get_xmin(field_name, MAXES), x_, y_, _x, _y)
x, y = chop_xy(x_, y_, xmin, 'None')
zs.append(cost_function((tau, beta, yo), x, y))
res[field_name] = (xs, ys, zs)
return res
def _extend_production(_prod, fit_parm, fit_style='stretched exponential'):
"""Extend the production of a given oil field into the future, given the
fit_parms and the fit_style.
Args:
_prod -> Series.
The time series of production of a given field.
fit_parm -> tuple.
The fit parameters for the particular field. Ex: (tau, beta, y0)
fit_style -> str.
The string representing the fit style.
Return:
_extended_prod -> Series.
The time series of the extended production (past + future) of the
field.
"""
#_prod is a time series of production i.e. the production of an individual
#field
extension_start = _prod.index[-1] + MonthBegin()
extraction_start = _prod.dropna().index[0]
if fit_style == 'stretched exponential':
tau, beta, yo = fit_parm
#The number of days until the production reaches MIN_PROD since the
#beginning of the extraction.
lifetime = abs(tau) * (-log(MIN_PROD/yo)) ** (1./beta)
#Timestamp don't extend beyond 2262-04-11
max_lifetime = (MAX_DATE - extraction_start).days
lifetime = min(lifetime, max_lifetime)
elif fit_style == 'power-law':
print 'power-law not implemented yet for extend_production()'
1/0
extension_end = extraction_start + lifetime * Day()
#we round end down to the beginning of the month (so that we stay for sure
#with end < 2262-04-11
extension_end = MonthBegin().rollback(extension_end)
future = date_range(extension_start, extension_end, freq='MS')
nfuture = len(future)
#Are we already very close (or below) MIN_PROD?
if nfuture == 0:
return _prod
#subtlety: I need to initialize _extended_prod with something for the
#extended part (in this case 42). Else, the whole extended part will be
#dropped in prepare_xy.
_extended_prod = concat((_prod, Series(nfuture*[42], index=future,
name=_prod.name)))
x, y = prepare_xy(_extended_prod)
if fit_style == 'stretched exponential':
#overwriting the placeholder (nfuture*[42])
y = yo * exp(sign(tau) * (x[-nfuture:] / abs(tau))**beta)
_extended_prod[-nfuture:] = y
return _extended_prod
def extend_productions(fields=GOOD_FITS, fit_parms='None',
fit_style='stretched exponential', xmin='custom', freq='M'):
"""Extends the production of the different oil fields into the future, given
the fit style.
"""
if fit_parms == 'None':
fit_parms, oil_fields = get_fit_parms(fields=fields,
fit_style=fit_style, xmin=xmin)
else:
fit_parms, oil_fields = fit_parms
extensions = []
for field in fields:
oil_field = oil_fields[field]
oil_field = extend_production(oil_field, fit_parms[field],
'stretched exponential')
start = oil_field.index[-1] + MonthBegin()
tau, beta, yo = fit_parms[field]
lifetime = abs(tau) * (-log(MIN_PROD/yo)) ** (1./beta)
try:
end = oil_field.dropna().index[0] + lifetime * Day()
except:
end = Timestamp('01-01-2260')
end = MonthBegin().rollback(end) + DateOffset(months=1)
future = date_range(start, end, freq='MS')
nfuture = len(future)
if nfuture == 0:
extensions.append(oil_field)
continue
oil_field = concat((oil_field, Series(len(future) * [1], index=future,
name=oil_field.name)))
x, y = prepare_xy(oil_field)
#from erpy.ipshell import ipshell
#ipshell('')
if fit_style == 'stretched exponential':
y = yo * exp(sign(tau) * (x[-nfuture:] / abs(tau))**beta)
oil_field[-nfuture:] = y
extensions.append(oil_field)
return concat(extensions, axis=1)
