Stress Models¶

Stress models describe the stress fields that we apply to rocks to calculate insitu conditions. The most common one required for Petroleum modelling is the vertical $S_v$ and effective $S_e$ stress.

All stress models have three basic methods:

• get_summary which returns details of the stress model
• vertical_stress which returns the vertical stress of the model based upon some input properties, e.g. depth.
• effective_stress which returns the effective pressure, which is usually the vertical stress minus the formation pressure.

Additional properties or keyword arguments to each method can be added as differentiators when models become more complex.

There are two basic types of stress models but users can define their own to fit the current API. The two basic types are functional models FStressModel and linear gradient models LGStressModel.

In [1]:

from digirock import FStressModel, LGStressModel
import numpy as np
import matplotlib.pyplot as plt

from digirock import FStressModel, LGStressModel import numpy as np import matplotlib.pyplot as plt

Let's start with a linear gradient model. A construction, it takes two arguments; the stress gradient in MPa/m grad and the reference pressure (MPa) ref_pres at the reference depth (mTVDSS) ref_depth. Usually ref_depth is the surface so we set this to 0 by default.

In [2]:

lg_stress = LGStressModel(0.01, 0.1, name="MyLGStressModel")

lg_stress = LGStressModel(0.01, 0.1, name="MyLGStressModel")

Like other digirock classes you can print a dictionary summary or a tree.

In [3]:

print(lg_stress.get_summary(), '\n')
lg_stress.tree

print(lg_stress.get_summary(), '\n') lg_stress.tree

{'class': <class 'digirock._stress.LGStressModel'>, 'name': 'MyLGStressModel', 'props_keys': ['depth', 'pres'], 'grad': 0.01, 'ref_pres': 0.1, 'ref_depth': 0} 

Out[3]:

MyLGStressModel
├── class : <class 'digirock._stress.LGStressModel'>
├── props_keys : ['depth', 'pres']
├── grad : 0.01
├── ref_pres : 0.1
└── ref_depth : 0

We can then calculate the vertical stress and effective stress at any depth for a given formation pressure.

In [4]:

depth = np.arange(1500, 3100, 100)
plt.plot(lg_stress.vertical_stress({"depth":depth}), depth, label="Sv")
plt.plot(lg_stress.effective_stress({"depth":depth, "pres":10.0}), depth, label="Se")
plt.xlabel("Stress (MPa)")
plt.ylabel("Depth (mTVDSS)")
plt.legend()
plt.gca().invert_yaxis()

depth = np.arange(1500, 3100, 100) plt.plot(lg_stress.vertical_stress({"depth":depth}), depth, label="Sv") plt.plot(lg_stress.effective_stress({"depth":depth, "pres":10.0}), depth, label="Se") plt.xlabel("Stress (MPa)") plt.ylabel("Depth (mTVDSS)") plt.legend() plt.gca().invert_yaxis()

We can also define custom functions that return more complex depth trends or even 3D fields for Stress.

In [5]:

from scipy.interpolate import PchipInterpolator

def custom_sv():
    # PchipInterpolator takes x and y and draws straight lines between them
    # we define the Interpolater outside the function so it isn't created each time we run func
    f = PchipInterpolator([0, 1500, 2200, 3000], [0, 10, 20, 25], extrapolate=True)
    def func(props, **kwargs):
        return f(props["depth"])
    # adjust the function name so the meaning is clear get_summary()
    func.__name__ = "PchipI"
    return func

f_stress = FStressModel(custom_sv())

from scipy.interpolate import PchipInterpolator def custom_sv(): # PchipInterpolator takes x and y and draws straight lines between them # we define the Interpolater outside the function so it isn't created each time we run func f = PchipInterpolator([0, 1500, 2200, 3000], [0, 10, 20, 25], extrapolate=True) def func(props, **kwargs): return f(props["depth"]) # adjust the function name so the meaning is clear get_summary() func.__name__ = "PchipI" return func f_stress = FStressModel(custom_sv())

In [6]:

depth = np.arange(1500, 3100, 100)
plt.plot(f_stress.vertical_stress({"depth":depth}), depth, label="Sv")
plt.plot(f_stress.effective_stress({"depth":depth, "pres":10.0}), depth, label="Se")
plt.xlabel("Stress (MPa)")
plt.ylabel("Depth (mTVDSS)")
plt.legend()
plt.gca().invert_yaxis()

depth = np.arange(1500, 3100, 100) plt.plot(f_stress.vertical_stress({"depth":depth}), depth, label="Sv") plt.plot(f_stress.effective_stress({"depth":depth, "pres":10.0}), depth, label="Se") plt.xlabel("Stress (MPa)") plt.ylabel("Depth (mTVDSS)") plt.legend() plt.gca().invert_yaxis()

In [7]:

print(f_stress.get_summary(), '\n')
f_stress.tree

print(f_stress.get_summary(), '\n') f_stress.tree

{'class': <class 'digirock._stress.FStressModel'>, 'name': 'FStressModel_140541007916576', 'props_keys': ['depth', 'pres'], 'func': 'PchipI', 'func_argspec': ArgSpec(args=['props'], varargs=None, keywords='kwargs', defaults=None)} 

Out[7]:

FStressModel_140541007916576
├── class : <class 'digirock._stress.FStressModel'>
├── props_keys : ['depth', 'pres']
├── func : PchipI
└── func_argspec : ArgSpec(args=['props'], varargs=None, keywords='kwargs', defaults=None)