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Reports: UNI852300-UNI8: A Field-Based Geomechanical Study of the Formation, Deformation, and Internal Structure of Reservoir-Scale Sandstone Dikes, Sheep Mountain Anticline, WY

W. Ashley Griffith, PhD, University of Texas Arlington

This grant has supported a mix of field work, travel to national conferences, tuition, and stipend for an M.S. student, Jennifer Beyer, and, during the first year of the project, undergraduate student Monet Alvarado.  During the second year of the project, results were presented at the 2014 GSA Annual Meeting in Vancouver, B.C. Additional results have been presented at the 2014 AAPG Student Expo in Houston and the ACES student research symposium at UT-Arlington in the spring of 2014 and 2015.  Jennifer Beyer is now enrolled as a PhD student working with Dr. Michele Cooke at the University of Massachusetts.  A manuscript, Downward propagating sandstone injectites at Sheep Mountain Anticline, WY: A case study of natural hydraulic fracture containment, summarizing the results of the work supported by this grant, and forming the basis of Jennifer’s MS thesis, will be submitted to Geosphere within the next few weeks. An excerpt of the current draft of the manuscript is included on the following pages.  In this excerpt, we are examining vertical profiles of injectites that propagated downward, and using these to understand the fluid overpressures associated with their formation. Sheep Mountain Anticline (SMA) offers unique exposures of sandstone injectites that have been subsequently deformed (Figure 1, Figure 2). We characterized injectites at SMA located around the nose and west flank of the fold.. These injectites were sourced by the Peay Sandstone of the Frontier Formation and propagated downward into the Mowry Shale Formation in orientations consistent with the two major joint sets found throughout the field area. Sand injection was driven by overpressurized pore fluids in the Peay Sandstone.             In order to gain insight into the controls on downward injectite propagation, we modeled the injectites at SMA as single-segment vertical blade-like cracks (Figure 3a) because all injectites are roughly tabular bodies, longer laterally than they are tall (Table 1).  Using vector position data obtained while mapping the injectites, the apertures for each injectite were plotted as a function of elevation (Figure 3c). We considered three simple contributions to crack loading (Figure 3b), for which analytical solutions are available: a uniform normal stress, a linear normal stress gradient resulting in a symmetrical stress distribution, and a linear normal stress gradient resulting in an asymmetric stress distribution (Delaney and Pollard, 1981; Lachenbruch, 1961; and Pollard and Muller, 1976). For a vertical 2D dike with half length, a, position along the dike, z, and aperture, vo,we define dimensionless variables Z = z/a and D(Z)=vo/a. In this coordinate system, the origin is fixed at the center of the injectite, and the positive y-direction is up (Figure 3b). The opening distribution along the crack can be written as: , (1) where  (2)  (3) , (4) and ,  (5) Here So, Ss, and Sa are the uniform, linear symmetric, and linear asymmetric overpressure distributions respectively (Figure 3b). The total pressure distribution is a sum of the three loading conditions, such that: . (6) Because we lack tight constraints on in situ compliance, represented by (1-ν)/a, exact magnitudes of the calculated overpressure gradients are less important than the general trends in the gradients. We determined the relative contribution of each loading condition (Table 1) to the total overpressure distribution within the injectites using a multiple-linear regression model. The predicted dilation calculated as a function of the three loading conditions (Figure 3d) better predicts the opening distribution than when calculated from only uniform loading (Figure 3c), indicating the vertical pressure distributions were non-uniform. Pressure profiles were calculated for seven of the eighteen injectites (Table 1). 

Injectite

Average Injectite Strike (deg)

Height (m)

Length (m)

Max Aperture (m)

C1

C2

C3

3

N35E

58.3

234.7

1.66

-0.0022

0.1008

0.0605

8

N05W

142.9

217.3

2.7

0.0135

0.0016

0.0025

9

N53E

82.2

175.7

2.71

-0.0016

0.0212

0.02

10

N60E

7.7

31.1

0.44

-0.0171

0.0702

0.0136

13

N21W

43.1

60.0

1.66

-0.0071

0.1029

0.0538

15

N50E

10.3

30.4

0.87

0.0237

0.0888

0.0067

17

N71E

30.0

220.2

2.54

-0.0269

0.0586

0.0189

Table 1 In most cases, the constant C1 is negative while the constants C2 and C3 are positive. Because C1  and C2 are symmetric terms, and C3 is positive, this implies that the driving stress (fluid overpressure) is largest near the top of the injectite; however because C2 is non-zero, this gradient is not constant.  Given the heterogeneity of the upper Mowry formation, the assumption of uniform material compliance is probably unreasonable. Therefore, although part of this trend is likely due to the actual fluid overpressures in the dike, some may be due to variations in effective elastic properties, cohesion, or inelastic deformation along the fault (e.g., Burgmann et al., 1994; Willemse and Pollard, 1998; Martel, 1999). In addition, the pressure maxima occurring near the tips imply large stress intensities there.  If the injectites exploited pre-existing joints, we would expect near-zero stress intensities near the injectite tips, consistent with an opening distribution that asymptotically approaches zero near the crack tips, similar to the bell-curve displacement distribution that results from cohesive endzone models. What we observe instead are blunt ends to the opening distributions (Figure 3 C, D), consistent with stress intensity factors larger than those predicted by the simple uniform loading case. In the field injectite segments can be found exploiting joints and bedding discontinuities, but otherwise cross-cutting bedding layers.  Therefore we conclude that the injectites either forcefully connected previously discontinuous joints confined to individual mechanical layers, or they formed at the same time as the joints, contrary to previous interpretations.

 

Figure 1 – Injectites crop out in the Lower Cretaceous Upper Mowry Formation.

 

Figure 2 – Three examples of injectite outcrops.

Figure 3 – (A) Blade-like crack idealization. (B) Cross-section of a crack subjected to uniform normal stress, symmetrical linear stress gradient, and asymmetrical linear stress gradient (Modified from Delaney and Pollard, 1981). (C) Predicted crack dilation for Injectite #3 under uniform loading. (D) Predicted crack dilation for Injectite #3 as a function of all three loading conditions.