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Description:

petboxdca 1.1.1

Empirical analysis of production data requires implementation of several decline curve models spread over years and multiple SPE publications. Additionally, comprehensive analysis requires graphical analysis among multiple diagnostics plots and their respective plotting functions. While each model’s q(t) (rate) function may be simple, the N(t) (cumulative volume) may not be. For example, the hyperbolic model has three different forms (hyperbolic, harmonic, exponential), and this is complicated by potentially multiple segments, each of which must be continuous in the rate derivatives. Or, as in the case of the Power-Law Exponential model, the N(t) function must be numerically evaluated.
This library defines a single interface to each of the implemented decline curve models. Each model has validation checks for parameter values and provides simple-to-use methods for evaluating arrays of time to obtain the desired function output.
Additionally, we also define an interface to attach a GOR/CGR yield function to any primary phase model. We can then obtain the outputs for the secondary phase as easily as the primary phase.
Analytic functions are implemented wherever possible. When not possible, numerical evaluations are performed using scipy.integrate.fixed_quad. Given that most of the functions of interest that must be numerically evaluated are monotonic, this generally works well.

Primary Phase
Transient Hyperbolic,
Modified Hyperbolic,
Power-Law Exponential,
Stretched Exponential,
Duong

Secondary Phase
Power-Law Yield

Water Phase
Power-Law Yield

The following functions are exposed for use

Base Functions
rate(t),
cum(t),
D(t),
beta(t),
b(t),

Interval Volumes
interval_vol(t),
monthly_vol(t),
monthly_vol_equiv(t),

Transient Hyperbolic
transient_rate(t),
transient_cum(t),
transient_D(t),
transient_beta(t),
transient_b(t)

Primary Phase
add_secondary(model),
add_water(model)

Secondary Phase
gor(t),
cgr(t)

Water Phase
wor(t),
wgr(t)

Utility
bourdet(y, x, …),
get_time(…),
get_time_monthly_vol(…)

Getting Started
Install the library with pip:
pip install petbox-dca
A default time array of evenly-logspaced values over 5 log cycles is provided as a convenience.
>>> from petbox import dca
>>> t = dca.get_time()
>>> mh = dca.MH(qi=1000.0, Di=0.8, bi=1.8, Dterm=0.08)
>>> mh.rate(t)
array([986.738, 982.789, 977.692, ..., 0.000])
We can also attach secondary phase and water phase models, and evaluate the rate just as easily.
>>> mh.add_secondary(dca.PLYield(c=1200.0, m0=0.0, m=0.6, t0=180.0, min=None, max=20_000.0))
>>> mh.secondary.rate(t)
array([1184.086, 1179.346, 1173.231, ..., 0.000])

>>> mh.add_water(dca.PLYield(c=2.0, m0=0.0, m=0.1, t0=90.0, min=None, max=10.0))
>>> mh.water.rate(t)
array([1.950, 1.935, 1.917, ..., 0.000])
Once instantiated, the same functions and process for attaching a secondary phase work for any model.
>>> thm = dca.THM(qi=1000.0, Di=0.8, bi=2.0, bf=0.8, telf=30.0, bterm=0.03, tterm=10.0)
>>> thm.rate(t)
array([968.681, 959.741, 948.451, ..., 0.000])

>>> thm.add_secondary(dca.PLYield(c=1200.0, m0=0.0, m=0.6, t0=180.0, min=None, max=20_000.0))
>>> thm.secondary.rate(t)
array([1162.417, 1151.690, 1138.141, ..., 0.000])

>>> ple = dca.PLE(qi=1000.0, Di=0.1, Dinf=0.00001, n=0.5)
>>> ple.rate(t)
array([904.828, 892.092, 877.768, ..., 0.000])

>>> ple.add_secondary(dca.PLYield(c=1200.0, m0=0.0, m=0.6, t0=180.0, min=None, max=20_000.0))
>>> ple.secondary.rate(t)
array([1085.794, 1070.510, 1053.322, ..., 0.000])
Applying the above, we can easily evaluate each model against a data set.
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(121)
>>> ax2 = fig.add_subplot(122)

>>> ax1.plot(t_data, rate_data, 'o')
>>> ax2.plot(t_data, cum_data, 'o')

>>> ax1.plot(t, thm.rate(t))
>>> ax2.plot(t, thm.cum(t) * cum_data[-1] / thm.cum(t_data[-1])) # normalization

>>> ax1.plot(t, ple.rate(t))
>>> ax2.plot(t, ple.cum(t) * cum_data[-1] / ple.cum(t_data[-1])) # normalization

>>> ...

>>> plt.show()

See the API documentation for a complete listing, detailed use examples, and model comparison.

Development
petbox-dca is maintained by David S. Fulford (@dsfulf). Please post an issue or pull request in this repo for any problems or suggestions!

Version History

1.1.0

Bug Fix

Fix bug in sign in MultisegmentHyperbolic.secant_from_nominal

Other changes

Add mpmath to handle precision requires of THM transient functions (only required to use the functions)
Adjust default degree of THM transient function quadrature integration from 50 to 10 (scipy default is 5)
Update package versions for docs and builds
Address various floating point errors, suppress numpy warnings for those which are mostly unavoidable
Add test/doc_exapmles.py and update figures (not sure what happened to the old file)
Adjust range of values in tests to avoid numerical errors in numpy and scipy functions… these were near-epsilon impractical values anyway

1.0.8

New functions

Added WaterPhase.wgr method

Other changes

Adjust yield model rate function to return consistent units if primary phase is oil or gas
Update to numpy v1.20 typing

1.0.7

Allow disabling of parameter checks by passing an interable of booleans, each indicating a check
to each model parameter.

Explicitly handle floating point overflow errors rather than relying on numpy.

1.0.6

New functions

Added WaterPhase class
Added WaterPhase.wor method
Added PrimaryPhase.add_water method

Other changes

A yield model may inherit both SecondaryPhase and WaterPhase, with the respective methods removed upon attachment to a PrimaryPhase.

1.0.5

New functions

Bourdet algorithm

Other changes

Update docstrings
Add bourdet data derivatives to detailed use examples

1.0.4

Fix typos in docs

1.0.3

Add documentation
Genericize numerical integration
Various refactoring

0.0.1 - 1.0.2

Internal releases