Time Scaling as Savior

One of the initial interests mentioned earlier was the use of these experiments to determine the compressability of reservoirs. As we noted above that it seems unlikely we will be able measure $\epsilon_{final}$ and $\tau$, let us hope that we can at least accomplish this. The unconsolidated deep water reservoirs commonly found today can compress so significantly as to

• cause costly tubing collapse and demand pressure maintenance, and/or
• obviate water flood necessity for production efficiency.

These two seemingly contradictory results make it quite important to understand the validity of these tests in order to make correct decisions.

As was shown in Figure 3, that the final strain value of each test cycle was identical and independent of the hold time, we see that each test results in the same stress-strain behavior in Figure 5.

 

ss Figure 5 Time scaling nature of the normalized hold-cycles results in each sample attaining the same strain value at the end of the hold time. Plotting final strain values from all cycles tested shows overlay of stress-strain behavior.Also important in this testing methodology is the pre-stressing of samples to pseudo-depth pressures. This removes 'closure' errors from consideration of the results.Dudley and Myers (1994)

We are now free to calculate the compaction curves as a function of pressure. This result will tell us the expected uniaxial compaction of a reservoir during the drainage phase that increases the vertical effective stress (VES) as pore pressure draws down ($VES=\sigma_1 - P_{pore}$), under the caveat that the production time does not approach the characteristic time $\tau$. If we violate this assumption, we will over-predict the amount of compaction the reservoir will experience. This allows us to present plots of the regressed parameter $\epsilon_1$ versus pressure such as Figure 6.

 

e1 Figure 6 Parameter $\epsilon(1)$ from all tests. All 750 psi steps overlay.Dudley and Myers (1994)

Data from several pressure step magnitudes are presented. By dividing by the magnitude of the pressure step, we effectively calculate C_z from equation 1 and watch the curves collapse onto one another.

 

cz Figure 7 Remarkably, uniaxial compaction coefficient Cz as calculated by 5 different testing methodologies remain consistent.Dudley and Myers (1994)

Figure 7 shows the quite compact distribution of the C_z parameter for 5 different samples each calculated with different stress-step and hold-time combinations. Thus the time scaling nature of these tests results in the pressure scaling of the tests as well due to the compulsion that the different tests must satisfy identical stress-strain behavior (as shown in Figure 5).