Comparison of Short-Term and Long-Term Creep Experiments in Shales and Carbonates from Unconventional Gas Reservoirs

Abstract

We carried out a series of long-term creep experiments on clay- and carbonate-rich shale samples from unconventional gas reservoirs to investigate creep over both relatively short-term (4-h) and long-term (4-week) periods. Results from each set of experiments were compared to evaluate the ability to predict the long-term behavior of reservoir rocks using relatively short-term creep experiments. The triaxial deformation experiments were performed in a time-cycling pattern, which included a series of four stages of loading, creep, unloading and recovery experiments conducted over different time spans. The loading conditions (tens of MPa) reflect current reservoir conditions and were far below the strength of the samples. Experiments were conducted on both horizontal and vertical shale samples to address anisotropy introduced by the bedding. A power-law model was fitted to the creep data to predict the long-term behavior of shale samples. Regardless of the applied loading history, results of the experiments show that the shale samples follow a single trend representing their creep behavior through time. We show that the simple power-law model is capable of describing creep over multiple time periods. Additionally, the value of the creep compliance factor is consistent over different creep testing periods and it is possible to characterize the behavior of these samples from relatively short-term (1 day) creep experiments.

Appendices

Appendix 1: Seasoning Effect

To study the behavior of the first creep cycles reported in Figs. 2, 3 and 14, we conducted a series of cyclic experiments on six different samples from Haynesville and Eagle Ford formations. The majority of the samples had a high amount of carbonate content. The mineral compositions of these samples are compared to the four samples described in the text in Fig. 15.

Fig. 15

Ternary plot of the composition of the samples used in cyclic experiments. The mineralogy of these samples (shown with squares) is compared to those of the samples used in time-cycling tests (diamond symbols)

These experiments followed the seasoning process of the samples discussed in studies by Brace et al. (1966), Bernabe (1986) and Wawersik and Brace (1971), where the sample is first loaded to allow for the sample to come into a consistent position in the loading frame. The main goal of running these experiments was to compare the behavior of the first creep cycle to the rest of the cyclic stages in our protocol. This initial loading step allows slight variations in response, resulting from small heterogeneities in the sample associated with recovery, sample preparation, and loading to be removed. After the seasoning cycle, the sample behaves more like the material in situ.

Here, we examined the seasoning process tests following the loading pattern used for time-cycling experiments (Fig. 16), which consists of four cycles of loading, creep, unloading and recovery stages. The time span of the first three creep stages was equal to 3 h, while the final loading stage lasted for 1 day. Similar to the time-cycling creep tests, both the confining pressure and differential creep stresses were kept constant at 40 MPa. The differential stress value was reduced to 2 MPa at the unloading steps.

Fig. 16

Loading and unloading triaxial creep experiment on “EV 7-5” to study the seasoning effect. The differential stress for all creep stages is equal to 40 MPa (red curve). The deformation response is shown in blue

The power-law parameters calculated for these experiments are shown in Fig. 17. As we expected, the n values for the first creep step of all these experiments (marked with red circles) are outliers, while the results for the other three steps are more uniform. This confirms our conclusion in Sect. 4.3 that to get a better prediction of the time-dependent behavior of the rocks within short periods of time, samples should be tested in a two-cycle pattern. The first few-hour cycle is to make the sample closer to the in situ state conditions, and the second creep cycle to calculate the n and B values for the viscoplastic behavior predictions.

Fig. 17

n and B values calculated for six different samples from Haynesville and Eagle Ford formations. The red circles show the constant values for the first cycle of the experiments. These points are outliers

Appendix 2

Total strains of all the samples using the method described in Sect. 4.1 are shown in Fig. 18. As mentioned before, regardless of the loading history, samples follow one time-dependent deformation trend.

Fig. 18

Total creep strain after attaching all the inelastic responses. This total creep is irrespective of the cyclic loading history

Appendix 3

Ultrasonic velocity measurements were conducted during the creep experiments presented in this study. These values were calculated from the recorded travel time of ultrasonic waves generated by piezoelectric crystals attached to the inner surface of the core holders. The resolution of the recorded ultrasonic waves is 0.04 μs at room temperature.

P-wave and cross-polarized S-wave velocities were measured and used to calculate vertical and horizontal Poisson’s ratio and E values shown in Figs. 19 and 20 from the following equations:

$$\mu = \rho V_{\text{s}}^{2}$$

(5)

$$K = \rho \left( {V_{\text{p}}^{2} - \frac{4}{3}V_{\text{s}}^{2} } \right)$$

(6)

$$\upsilon = \frac{3K - 2\mu }{{2\left( {3K + \mu } \right)}}$$

(7)

$$E = \frac{{\rho V_{\text{s}}^{2} \left( {3V_{\text{p}}^{2} - 4V_{\text{s}}^{2} } \right)}}{{V_{\text{p}}^{2} - V_{\text{s}}^{2} }},$$

(8)

where E, K and μ are elastic, volumetric and shear moduli, respectively; V_s and V_p are S-wave and P-wave velocities; and ρ is bulk density.

Fig. 19

Dynamic Young’s modulus of the samples calculated from ultrasonic velocities. The two columns show E values calculated from two orthogonal S-waves

Fig. 20

Poisson’s ratio of the samples calculated from ultrasonic velocities. The two columns show the Poisson’s ratio calculated from two orthogonal S-waves

Both horizontal samples have higher dynamic E values and Poisson’s ratio, which is in agreement with what we discussed above. The higher amount of Poisson’s ratio shows that the horizontal samples are more expandable because of bedding planes parallel to the loading axis.

The small difference between the values calculated from horizontal and vertical S-waves depends on the position of the core holders with respect to the bedding planes. Since in these experiments we were not interested in S-wave anisotropy, we did not choose the orientation of piezoelectric crystals with respect to the orientation of bedding planes in the samples.