1. INTRODUCTION

The Permian Basin represents one of the nation’s oldest and most widely recognized hydrocarbon bearing regions. Unlike other plays such as the Bakken and Eagle Ford, the Permian shows much greater geologic complexity, consisting of several unique sub-basins (Fig. 1), each with its own unique characteristics [1].

Fig. 1. Geological map of Permian Basin [2].

The specific area studied in this research is in Midland Basin, which is east of the Central Basin Platform, west of the Eastern Shelf, and north of the Val Verde Basin. The formations discussed in this paper are the Spraberry, Dean, and Wolfcamp series, which are at the bottom of the Permian system. The three formations are mainly shale facies, but with high mechanical complexity. Fig. 2 shows the wells we studied, which are drilled in the Spraberry/Dean/Wolfcamp formations. Most data, including sonic log data, Formation Microresistivity Image (FMI) data, and core test data, come from the monitor well M. Besides, we analyze the Diagnostic Fracture Injection Test (DFIT) in four horizontal wells, A, B, C, and D.

Fig. 2. Side view and map view of the study wells.

ARMA 15-189 Analysis of stress variations with depth in the Permian Basin Spraberry/Dean/Wolfcamp Shale Xu, Shaochuan and Zoback, M.D. Stanford University, Stanford, California, USA

Copyright 2015 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 49th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 28 June- 1 July 2015. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: This research examines stress variations with depth in the Permian Basin Spraberry/Dean/Wolfcamp Shale to understand why many microseismic events occur at upper formations when we hydraulically fracture the lower formations. An interesting phenomenon of drilling-induced tensile fractures is observed in the image log. That is, there are drilling-induced tensile fractures in the Spraberry and Dean formations, but there are no drilling-induced tensile fractures in the Wolfcamp formation. This brings out a question: how variable is the stress state with depth? We estimate the pore pressure and the three principal stresses with depth to answer this question. The pore pressures and minimum principal stresses are analyzed from the Diagnostic Fracture Injection Test, which are consistent with literatures. Maximum horizontal stress in the Spraberry formation is constrained by observation of drilling-induced tensile fractures, while maximum horizontal stress in the Wolfcamp formation is constrained through the estimation of Uniaxial Compressive Strength. We find the stresses in the Wolfcamp formation are more isotropic than those in the Spraberry formation. More importantly, the decreasing of the pore pressure gradient and the frac gradient when going from the lower formation to the upper formation leads to many out-of-zone microseismic events.

The way of investigating stress variations with depth in the study area is to determine pore pressure (Pp), overburden stress (SV), minimum principal stress, and maximum horizontal stress (SHmax) through several techniques. The pore pressures are analyzed from the DFIT, which are consistent with the pore pressures documented in the literature; the overburden stress is calculated from the density log; the minimum principal stress in the Wolfcamp formation is picked up from the DFIT, while the minimum principal stress in the Spraberry formation is obtained from literatures; the maximum horizontal stress in the Spraberry formation is constrained by using knowledge of drilling-induced tensile fractures, but the maximum horizontal stress in the Wolfcamp formation is more difficult to obtain, because there are no drilling-induced tensile fractures or breakouts. Therefore, we constrain it through the estimation of Co (Uniaxial Compressive Strength). Finally, we get stress state with depth by plotting Pp, Sv, Shmin, and SHmax with depth together. During this process, we also obtain the mechanical properties of rocks in the Spraberry/Dean/Wolfcamp formations, which are important to understand the stress variation with depth.

2. DETERMINING PORE PRESSURE AND MINIMUM PRINCIPAL STRESS FROM DFIT In a Diagnostic Fracture Injection Test, a small volume of low viscosity fluid (KCL water) is injected until fracture initiation. Then, the wellhead is shut-in allowing the pressure to fall off naturally over a long time. The pore pressure could be calculated from the radial flow part of the pressure-time curve, while the minimum principal stress could be picked from the pressure-time curve after instantaneously shut-in the wellhead.

2.1. Pore Pressure Estimated from Radial Flow For the after-closure pressure-time curve, the radial flow can be described by the equation:

!!P −Pi =

1694.4Vµkh

1(tp +Δt)

(1)

in which Pi is the initial reservoir pressure, i.e., pore pressure; P is the recorded bottom hole pressure; tp is pump time prior to shut-in; Δt is the time since pumping stopped; V, µ, k, h are injected volume, viscosity, permeability, and net pay thickness, respectively [3]. If we plot the bottom hole pressure versus !!1/(tp +Δt) ,

we can fit a linear line to the curve, and the interception with y-axis is the pore pressure (Fig. 3). In wells B, C, and D, the linear line can be fitted very well. In well A, however, much data was lost, so the pore pressure is determined from bottom hole pressure versus G-function of time. The estimated pore pressures at four depths in the Wolfcamp formation are listed in Table 1. Generally,

it is higher than the hydrostatic pore pressure 0.44 psi/ft. The pore pressures in the Spraberry and Dean formations come from published papers [4]. Pad ISIP methodology is used in this paper to obtain calculated pore pressure in Spraberry/Dean/Wolfcamp formations [4]. The pore pressure gradient in the Spraberry formation is about 0.31 psi/ft. In conclusion from this paper, the pore pressure in the Spraberry formation is smaller than that in the Wolfcamp formation.

Fig. 3. Pore pressure obtained from the radial flow of 4 DFIT.

Table 1. Pore pressure gradients at four different depths

Well A B C D Depth (ft) 6429 6606 6705 6980

Pp (psi) 3100 3540 3300 3400 Pp gradient

(psi/ft) 0.482 0.536 0.492 0.487

2.2. Minimum Principal Stress Determined by ISIP

A good measure of minimum principal stress is obtained from the Instantaneous Shut-in Pressure (ISIP). By expanding DFIT data around the moment of shut-in, we get curves in Fig. 4. In wells A, B, and C, the ISIP, i.e., minimum principal stress, is picked after abruptly stopping flow into the well. In well D, there are four cycles of injection and shut-in, so 4 ISIPs can be picked, and the minimum principal stress is their average. From the minimum principal stress, we can calculate the frac gradient. The estimated frac gradients at four depths in the Wolfcamp formation are listed in Table 2. Generally, it is around 0.80 psi/ft. There is no DFIT in the Spraberry formation. The minimum principal stresses in the Spraberry formation, however, are documented in several literatures [5, 6], from which we know the frac gradient in the Spraberry formation is smaller than that in the Wolfcamp formation. This could be due to the depletion of the Spraberry formation from the poroelastic perspective, as the Spraberry formation has

been produced for many years. Also, we calculated the overburden stress SV at this moment, and we found that the minimum principal stress is smaller than SV, so the minimum principal stress is the horizontal Shmin.

Fig. 4. ISIP picked from 4 DFIT.

Table 2. Frac gradients at four different depths

Well A B C D Depth (ft) 6429 6606 6705 6980 ISIP (psi) 5500 5200 5500 5550

Frac gradient (psi/ft) 0.855 0.787 0.820 0.795

3. ESTIMATING UNIAXIAL COMPRESSIVE STRENGTH FROM GEOPHYSICAL LOG DATA After we obtain pore pressure gradients and frac gradients with depth in the Spraberry/Dean/Wolfcamp formations, we need to constrain the maximum horizontal stress to get the stress variations with depth. The Uniaxial Compressive Strength (Co) is a critical parameter to constrain maximum horizontal stress if there are no drilling-induced tensile fractures, which is the case in the Wolfcamp formation (Fig. 10). One well-studied way to estimate Co is to relate Co to Young’s modulus (E) and derive E from sonic logs [7].

3.1. Fitted relation between Co and E In shales, the relationship between Co and E can be fitted using a power law. Despite the considerable scatter, there is a marked increase in strength with E [7]. In our case, there is a group of Co and dynamic E in Wolfcamp Shale from the same county as our study area, which is measured in the lab (Fig. 5). The reason we chose the dynamic E is that Young’s modulus calculated from sonic logs is dynamic. Therefore, we can use the power law to fit a relation between Co and dynamic E. The fitting is generally reasonable except for one outlier (Fig. 5).

Fig. 5. The relation between Co and E fitted by power law.

3.2. Estimating Co from Well Logs The dynamic Young’s modulus is calculated from the equation below.

!!E = ρVs

2 3Vp2 −4Vs2

Vp2 −Vs

2 (2)

in which ρ is the density of the formation, obtained from the density log; Vp and Vs are the compressional wave velocity and shear wave velocity, obtained from the sonic log. A median filter is used to the density log and the sonic log to eliminate strong scattering. The calculation of Young’s modulus at the depth of Spraberry/Dean/Wolfcamp formations is from 25 GPa to 38GPa, while the typical value of E for shale is from 1GPa to 70GPa. Then, applying the fitted relation from 3.1 into the calculated dynamic Young’s modulus with depth, we obtain the Co with depth, shown by the red dots in Fig. 6.

Fig. 6. Co from geophysical logs and lab measurements.

3.3. Determining Co from Tri-axial Compressive Test

In addition to estimating Co from geophysical logs, we have Tri-axial Compressive Tests of four cores in the Dean and Wolfcamp formations, which can be used to verify the accuracy of our estimation from geophysical logs. In the Tri-axial Compressive Test, Co is determined by the following equation:

!!S1 =Co +nS3 (3)

in which S1 is the strength at failure, S3 is the confining pressure, and n is a coefficient related to internal friction [8]. The results of Co from Fig. 7 are plotted in Fig. 6 by black squares, which are consistent with the Co estimated from geophysical logs.

Fig. 7. Results of tri-axial compressive tests at four depths.

From Fig. 7, the range of Co at the depths of Spraberry/Dean/Wolfcamp formations is from 2776 psi (19.1MPa) to 6829 psi (47.1MPa), while the typical value of Co for shale is from 5MPa to 100MPa. Therefore, the rocks in three formations are weak.

4. CONSTRAIN MAXIMUM HORIZONTAL STRESS USING OBSERVATION FROM FMI In order to know the variation of all three principal stresses with depth and to determine the faulting regime, we need to constrain the maximum horizontal stress. The technique we used is stress polygon (Fig. 9, Fig. 11), which illustrates the range of allowable values for horizontal principal stresses in the earth’s crust for normal, strike-slip and reverse faulting environments at any given depth and pore pressure, given that stress in the crust is limited by the frictional strength of faults [8]. Any possible stress state should be within the stress polygon. Also, the stress states of drilling-induced tensile fractures and breakouts can be plotted in the

polygon, represented by blue lines and red lines respectively. The analytical equations of blue lines and red lines are:

!!SHmax =3Shmin −2Pp − ΔP −To −σΔT (4)

!!SHmax =

(Co +2Pp +ΔP +σ ΔT )− Shmin(1+2cos2θb)1−2cos2θb

(5)

in which ΔP is the difference between the mud pressure and the pore pressure, To is the Tensile Strength, σΔT is the term of thermal effect, 2θb is π minus the breakout width. The numbers on the blue lines are Tensile Strength (To), while the numbers on the red lines are Uniaxial Compressive Strength (Co). Therefore, for a given To, if drilling-induced tensile fractures appear, the stress state must be above the blue line; for a given Co, if breakouts appear, the stress state must be above the red line.

In the Spraberry formation, continuous drilling-induced tensile fractures are observed (Fig. 8), so the stress state should be between the diagonal black boundary in the SS region and the zero blue line (Fig. 9). It is known from 2.2, the frac gradient in the Spraberry formation is smaller than that in the Wolfcamp formation. So we choose the gradient of Shmin to be 0.60 psi/ft, which is a little bit higher than the possible minimum Shmin gradient in the stress polygon of Fig. 9. Therefore, the constrained gradient of SHmax is from 1.023 psi/ft to 1.217 psi/ft, that is, SHmax is from 6138 psi to 7302 psi at 6000 feet. Notice that we could choose gradient of Shmin larger than 0.60 psi/ft but still smaller than the frac gradient in the Wolfcamp formation. Nevertheless, this will result in the constrained SHmax to be larger, which will not influence the final conclusion.

Fig. 8. Drilling-induced tensile fractures in the monitor well M at the depth of the Spraberry formation.

Fig. 9. Constrained SHmax in the Spraberry formation from the occurrence of drilling induced tensile fractures

In the Wolfcamp formation, there are no drilling-induced tensile fractures or breakouts (Fig. 10), so we need to use the Uniaxial Compressive Strength (Co) to constrain SHmax. The estimated Co at depth 6600 feet is from 3500 psi to 5500 psi, shown by the blue error bar in Fig. 6. It is known from 2.2, the frac gradient in the Wolfcamp formation is around 0.80 psi/ft. Then, after we plot the 0.80 psi/ft green Shmin line in Fig. 11, we can find its intersections with the red lines whose Co are 3500 psi and 5500 psi. Their corresponding SHmax are the upper and lower limits of constrained SHmax. Therefore, the constrained SHmax gradient is from 0.841 psi/ft to 1.069 psi/ft, that is, SHmax is from 5551 psi to 7055 psi at 6600 feet.

Fig. 10. Documentation of drilling-induced tensile fractures from FMI in the monitor well M.

Fig. 11. Constrained SHmax in the Wolfcamp formation from the estimated Uniaxial Compressive Strength (Co).

5. STRESS VARIATIONS WITH DEPTH AND DISCUSSION Integrating all the data above, we get Fig. 12. The black line is SV, which is about 1.10 psi/ft. SV is also used in Fig. 9 and Fig. 11. The green dash line is the hydrostatic pressure, which is about 0.44 psi/ft. The green circles are the pore pressures documented in the literature [4], and the four solid green dots are the pore pressures estimated from DFIT in 2.1. We can see they are consistent with each other in the Wolfcamp formation. The red solid dots are the Shmin measured in the Wolfcamp formation in 2.2, and the red line represents the Shmin fitted from four solid red dots. The two blue error bars are estimated SHmax in the Spraberry formation and in the Wolfcamp formation respectively from section 4. Finally, it turns out that the faulting regime in the Spraberry formation is Strike-Slip/Normal, while the faulting regime in the Wolfcamp formation is Normal. That is, the stresses in the Wolfcamp formation are more isotropic than that in the Spraberry formation.

From Fig. 12, it is obvious that the pore pressure in the Spraberry formation is smaller than the hydrostatic pressure, but the pore pressure in the Wolfcamp formation is larger than the hydrostatic pressure. That is, the Spraberry formation is under-pressured, while the Wolfcamp formation is over-pressured. This is critically important when understanding Fig. 10. There are drilling-induced tensile fractures in the Spraberry and Dean formations, but there are no drilling-induced tensile fractures in the Wolfcamp formation. Combined with the pore pressures variation in Fig. 12, the reason

for this phenomenon turns out to be as follows. Whether there are drilling-induced tensile fractures or not is controlled by whether there is a gap between the zero blue line and the diagonal boundary of SS region in the stress polygon in Fig. 9 and Fig. 11. This gap is determined by the ΔP in Eq. (4), the difference between the mud pressure and the pore pressure, assuming there is no thermal effect. When ΔP is large, the blue lines go down, and the drilling-induced tensile fractures occur; when ΔP is small, the blue lines go up, and the drilling-induced tensile fractures cannot occur. When we drill the well, the mud pressure gradient is almost constant. However, the pore pressure gradient is very low in the Spraberry formation but very high in the Wolfcamp formation, so ΔP is very large in the Spraberry formation but very small in the Wolfcamp formation. This is why we observe drilling-induced tensile fractures in the Spraberry formation, but do not observe drilling-induced tensile fractures in the Wolfcamp formation.

Knowing stress variations with depth is also very important when we hydraulically fracture the reservoir. Fig. 13 shows the microseismic events monitored by well M when we hydraulically fracture well D. It is obvious that a lot of microseismic events occur at the upper formation when we hydraulically fracture the lower formation. The events could occur at 6400 feet when we hydraulically fracture the horizontal well at 7000 feet. The reason why this happens is that the pore pressure gradient and the frac gradient decrease substantially when going from the lower formation to the upper formation. This variation is crucial when we design how to hydraulically fracture a specific formation in the future.

Fig. 12. Stresses variation with depth in the Permian Basin Spraberry/Dean/Wolfcamp shale.

Fig. 13. Microseismic events occur at the upper formation when we hydraulically fracture the lower formation (the color bar shows magnitudes).

6. SUMMARY

• The stresses in the Wolfcamp formation are more isotropic than the stresses in the Spraberry formation.

• The faulting regime of the Midland Basin Spraberry/Dean/Wolfcamp Shale is between normal and strike-slip.

• The rocks in the Spraberry/Dean/Wolfcamp

formations are soft and weak. • The Wolfcamp formation is over-pressured while

the Spraberry formation is under-pressured. This causes the occurrence of drilling-induced tensile fractures in the Spraberry formation, and the absence of drilling-induced tensile fractures in the Wolfcamp formation.

• The pore pressure gradient and the frac gradient

decrease significantly when going from the lower formation to the upper formation. This is the predominant reason why many microseismic events occur at upper formations when we hydraulically fracture the lower formations.

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