The empirical relation developed by Juarez-Badillo is of the form
Knowing that we need to find a power-law form to fit the observations, we can analyze this equation under the limit where the time of the experiment, t, is much less than the characteristic compaction time, , defined as when the sample has undergone exactly half of the final strain limit. This seems appropriate as we are making an effort to do lab experiments at much less than the time that we imagine these processing happening in the field.
Equation 2 then becomes
We notice now that the strain at time 1
Not only does this equation fit well with the observed data, but considering only progressive quartiles of the data, constant and stable values for the regressed parameters and d are obtained. This provides further justification in the selection of this model as this was one of the significant problems with use of the other models.
Now, assuming that our adoption of the Juarez-Badillo creep mechanism is correct, we have a model that helps explain our data. This fit implies several things:
Figure 4 One year hold uniaxial creep test. Exponential function still fits meaning and implying that reservoir material must have a characteristic creep time on the order of decades.Dudley and Myers (1994)