1. INTRODUCTION

The successful exploitation of unconventional resources depends on the ability to develop strategic engineering designs using economic considerations as the primary drivers. In shale oil plays, like the Bakken for instance, suitable wellpad geometries and well trajectories are first determined and then repeated many times in an efficient pattern in order to reduce drilling costs. Similarly, hydraulic fracture treatments are commonly performed in repeatable patterns across many wells. This methodology is attractive from an economic standpoint, but given that heterogeneity exists in all reservoirs and that operational difficulties can arise, the approach may not always result in the optimal recovery for a given well. Evidence from field data has indicated that productivity of individual wells, and even individual completion stages, can be highly variable [1, 2]. It is useful to develop tests that can be applied in the field in order to assess the recovery efficiency of wells and individual completion stages within each well. This information can be helpful from a reservoir management perspective, for example, in order to estimate ultimate recovery or to determine appropriate spacing for infill drilling in a given asset.

In this paper, we investigate a field test proposed originally by Dohmen et al. [1] called microseismic

depletion delineation (MDD). The MDD technique is an approach that can be used to identify the extent of the depleted region near a horizontal well that has been produced for an extended period of time. MDD relies on the fact that as depletion occurs and pressure in the reservoir drops, poroelastic effects cause the in-situ stresses thoughout the reservoir to change. Naturally occurring fractures will be exposed to an altered state of stress not only due to changes in fluid pressure, but also due to the poroelastic effects. Therefore, by injecting fluid at carefully determined pressures into a well that has been produced previously and monitoring for microseismic activity, the new state of stress can be leveraged to identify zones in the reservoir that have experienced depletion.

Dohmen et al. [1] proposed the overall strategy that can be used in the field to perform the MDD test, and Dohmen et al. [2] presented results from a pilot field study at a Bakken well that demonstrated the utility of the technique. Here, we perform numerical simulations using a fully-coupled fluid flow and geomechanics reservoir simulator to validate the approach from a more theoretical perspective. The remainder of the paper is organized as follows. In Section 2, we describe the overall MDD simulation framework. In Section 3, we interpret the results of the simulation. In Section 4, we discuss the practical applications of using numerical

ARMA 15-763 Simulation of a Microseismic Depletion Delineation Test Norbeck, J.H. and Horne, R.N. 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: In unconventional hydrocarbon resources, the estimation of the expected ultimate recovery for individual wells and the appropriate spacing for infill drilling near existing wells both have strong economic implications. A field test called microseismic depletion delineation has previously been proposed as a method to probe the reservoir directly to determine the extent of the depleted region near horizontal wells that have been produced for a significant period of time. In this work, we performed a numerical simulation of a microseismic depletion delineation field test in order to further understand the physical mechanisms that underpin the method. The modeling framework developed herein can be used to help design field tests and interpret field observations. We observed that application of a model that coupled fluid flow, fracture mechanics, poroelasticity, and geologic structure was able to produce the physical behavior necessary to interpret observations from microseismic depletion delineation field tests.

simulation to design MDD tests and interpret field data as well as provide several concluding remarks.

2. SIMULATION OF A MICROSEISMIC DELINEATION FIELD TEST In this paper, we considered a horizontal well that existed in a naturally fractured reservoir. We first simulated a multi-stage hydraulic fracture stimulation of the well. Following the stimulation treatment, we simulated one year of production from the well in order to cause pressure drawdown throughout the reservoir. Finally, after the production phase, we simulated a short two day period of injection into the well. The reservoir and operational parameters were based loosely on the field data from a well in the Middle Bakken reported by Dohmen et al. [2]. In the simulations, the stress regime was strike-slip. Details of each phase of the simulation are provided below, and a list of the important parameters used in the simulation is given in Table 1. The well, completion stage, and natural fracture geometries are illustrated in Fig. 1.

The simulation was performed with a fluid flow, geomechanics, and fracture propagation simulator called CFRAC [4]. Fluid flow was assumed to be single-phase water and isothermal. Mass transfer between the fracture and matrix rock was calculated using an embedded fracture discretization strategy [5]. The simulation domain was two-dimensional, so all of the hydraulic fractures and natural fractures had the same height. Poroelastic effects were considered, but the coupling was only in one direction so that changes in the in-situ stress only affected deformation of the fractures and did not affect the porosity of the matrix rock. Mechanical interaction between fractures as they deformed was accounted for, and was assumed to occur quasistatically. Permeability of natural and hydraulic fractures was a function of the local state of stress. Proppant transport was not modeled during the hydraulic fracture simulation. For details of the flow, geomechanics, and poroelasticity calculations performed by CFRAC, the reader is referred to McClure and Horne [4] and Norbeck and Horne [5].

2.1. Hydraulic Stimulation Treatment Phase The lateral section of the well was 500 m long. The well was completed by performing hydraulic fracturing in five separate stages (each 100 m long), starting at the toe of the well and proceeding towards the heel. During each completion stage, fluid was injected at a constant mass rate of 50 kg/s for a period of 30 minutes.

Table 1. Model parameters for MDD simulation.

Fig. 1. The horizontal well was 500 m long, shown here as a black line. The green squares mark the separation between each of the five completion stages. The natural fractures are shown as blue lines.

The maximum horizontal stress was in the y-direction. The hydraulic fractures were assumed to propagate in the direction of the maximum principal stress. A large number of potentially forming hydraulic fractures that intersected the well and the natural fractures were randomly specified at the beginning of the simulation, and a subset of them eventually formed during the simulation.

In order to mimic a scenario where several of the stages were ineffective, hydraulic fractures were not allowed to initiate in the first two stages. For example, this scenario might occur if a fault caused large volumes of the fracturing fluid to be lost to the formation, preventing the energy going into pumping the fluid from creating fracture growth [2]. The stimulated fracture network at the end of the hydraulic fracture treatment is illustrated in Fig. 2. Note that the stimulated region is confined to the final three completion stages. This was expected to influence the evolution of the depleted region during the production phase.

Fig. 2. The stimulated fracture network at the end of the stimulation treatment. The fractures in red are new tensile fractures or natural fractures that experienced pressure perturbation during hydraulic fracturing.

2.2. Production Phase Following the stimulation phase, the well was bled off at a pressure of 40 MPa for a period of one week. The well was then set on production for a period of one year. The initial reservoir pressure was 47 MPa, and the full drawdown of 30 MPa was realized by producing the well at constant bottomhole pressures of 37 MPa, 27 MPa, and 17 MPa for four-month periods. The permeability of the matrix rock was 1×10-18 m2 (1 microdarcy).

2.3. Reinjection Phase: The MDD Test During the production phase, it is reasonable to assume that depletion is confined to volumes of rock close to the network of fractures connected to the well because of the extremely low intrinsic permeability of the reservoir rock. The premise of the MDD technique is that depletion-induced poroelastic stress changes throughout the reservoir will alter the state of stress acting on natural fractures. Because the poroelastic effect tends to reduce the in-situ normal stresses acting on the fracture surfaces, the fractures will be prone to experience shear failure at relatively low injection pressures if fluid is reinjected after the well has been on production for an extended period of time. Monitoring for microseismic activity while reinjecting at carefully determined pressures will provide the locations of natural fractures that exist within the depleted region.

As pressure drops throughout the reservoir, poroelastic effects cause the reservoir rock to attempt to deform. Hooke’s law indicates that changes in reservoir pressure induce volumetric deformations [3]:

σ ij = 2Gεij +Λεkkδij +αΔpδij, (1)

where σ ij is the stress tensor, εij is the strain tensor, G is the shear modulus, Λ is Lame’s coefficient, α is Biot’s coefficient, Δp is the change in reservoir pressure, and δij is the Kronecker delta function. A

common reservoir engineering assumption is that rock deformation is constrained in the horizontal directions. This is a valid assumption if the lateral extent of the reservoir is much greater than its thickness and if the pressure perturbation is relatively uniform. Under this assumption of uniaxial strain, the change in horizontal stress due to a uniform pressure perturbation is [3]:

Δσ H = Δσ h =α1− 2ν1−ν

#

$%

&

'(Δp, (2)

where σ H is the maximum horizontal stress, σ h is the minimum horizontal stress, α is Biot’s coefficient, ν is Poisson’s ratio, and p is the reservoir pressure. It is evident from Eq. (2) that reservoir depletion causes a reduction in the compressive stress throughout the reservoir. Although the assumption of uniaxial strain is not strictly valid in cases where depletion has not occurred evenly throughout the reservoir, it provides a useful starting point for our analysis of MDD.

For natural fractures in the reservoir that bear normal stress, σ n , and shear stress, τ , the critical pressure that will initiate slip, p* , can be determined if their frictional properties are known:

p* =σ n −τ − cf, (3)

where f is the static coefficient of friction of the fracture and c is the fracture cohesion. The value of σ n reflects the sum of the initial remote state of stress and any poroelastically-induced stress.

Values for the critical pressure can be calculated for the initial and depleted reservoir states. In our simulation, the predominant set of natural fractures was oriented at roughly 30 degrees from the direction of maximum principal stress (see Fig. 1). Based on a reservoir depletion of Δp = −30 MPa and the frictional and elastic properties listed in Table 1, the critical pressures at the initial and depleted states were calculated as p0

* = 51.1 MPa and p1

* = 36.5 MPa, respectively.

These calculations were made using the assumption of uniaxial strain, and the poroelastic calculations performed in the numerical simulations were not constrained by this limiting assumption. However, we used these preliminary calculations to determine appropriate injection pressures during the reinjection phase. Following the one-year production phase, water was injected first at a constant pressure of 25 MPa (below p1

* ) for a short period of time. No microseismic events were expected during this phase. Then, injection was continued at a pressure of 45 MPa (above p1

* but below p0

* ) for one month. Microseismic activity that

occurred at this pressure was very likely to correspond to slip on fractures that must have existed within the depleted region.

3. INTERPRETATION OF MDD RESULTS The production phase caused a significant amount of depletion to occur within the matrix rock. In Fig. 3, we overlay contours of reservoir pressure on the stimulated fracture network at the end of one year of production. It is clear that the region near the three completion stages that were stimulated with hydraulic fracturing experienced significantly more drawdown than in the first two stages that were not stimulated. We hoped to be able to identify this type of heterogeneous depletion with the MDD surveillance technique.

During the reinjection phase, shear slip of the fractures was monitored. If a fracture experienced additional slip beyond that which occurred during the initial hydraulic fracturing phase, then the new slip was interpreted as a microseismic event. In Fig. 3, the white dots indicate the locations that experienced additional slip during the reinjection phase. Note that the reinjection occurred initially at a constant pressure of 25 MPa. No additional slip occurred during this initial phase of reinjection. Upon increasing the injection pressure to 45 MPa, some fractures experience additional slip. Because the reinjection was carried out at a pressure below the initial reservoir pressure (well below the critical injection pressure required to cause slip at the initial stress state), then it is clear that the poroelastic stresses that developed due to depletion allowed the additional slip to occur.

The poroelastically-induced changes in the normal stress in the x- and y-directions at the end of one year of production are shown in Figs. 4 and 5, repsectively. The magnitudes of the induced stress are on the order the predictions calculated using Eq. (2). The geometry of the depleted zone had a strong effect on the spatial distribution of the poroelastic stresses.

The locations of the microseismic events that occurred during reinjection helped to define the extent of the depleted region, but they did not demarcate an extremely accurate geometry of the depleted zone. The majority of the microseismic events occurred within areas of the reservoir that observed a minimum of 15 MPa of pressure drawdown (roughly corresponding to the black contours in Fig. 3). Outside of this zone, perhaps the poroelastic effect did not have a strong enough impact on reducing the fractures’ shear strength. Alternatively, the pressure front during reinjection may not have reached those areas during the 30-day period because the flow rates necessary to achieve constant pressure production were very low.

Fig. 3. The contours of pressure show the extent of the depleted region near the well. The white dots show locations that experienced additional slip during reinjection at 45 MPa, and were interpreted as microseismic events. The events lie within the region that experienced the largest pressure drawdown. The colormap range is from 17 MPa to 47 MPa.

Fig. 4. The contours illustrate the poroelastic change in normal stress in the x-direction. The colormap range is from -14.5 MPa to 0.75 MPa.

Fig. 5. The contours illustrate the poroelastic change in normal stress in the y-direction. The colormap range is from -8.5 MPa to 2.2 MPa.

4. CONCLUDING REMARKS In this work, we performed a numerical simulation that replicated a field surveillance technique called microseismic depletion delineation. The MDD approach can be applied in the field to determine the extent of the depleted region near horizontal wells that have been on

production for an extended period of time. The field test leverages poroelastic effects that develop due to reservoir depletion. Monitoring for microseismic activity while reinjecting into a depleted well can allow for the depleted region to be identified.

We simulated a multi-stage hydraulic fracture stimulation of a horizontal well. We intentionally skipped the first two completion stages to mimic a common scenario that has been observed in the field where several stages are ineffective. We then simulated one year of production. In this phase, the reservoir drawdown was affected significantly by the geometry of the stimulated zone, and occurred very heterogeneously. Finally, we simulated reinjection at a constant pressure (below the initial reservoir pressure) for a period of one month. During the reinjection phase, fractures were monitored for additional slip.

We observed that some fractures did experience slip during reinjection at a constant pressure of 45 MPa. The poroelastic changes in stress that occurred due to depletion reduced the effective normal stress acting on the natural fractures. This allowed slip to occur at a relatively low injection pressure. These slip events were interpreted as microseismic events. Their locations occurred within the areas of the reservoir that experienced the most significant pressure drawdown. While the events helped to define the extent of the depleted region, they certainly did not define the depleted region’s geometry perfectly. The MDD modeling framework deserves further study.

In practice, MDD would serve as a direct measurement technique to determine the shape of the depleted zone near horizontal wells. This information would be helpful to determine appropriate spacing for infill drilling, estimate important reservoir flow properties, and to evaluate the expected ultimate recovery for a given well. Numerical modeling can be used to design MDD field tests or to interpret the information obtained from the field.

ACKNOWLEDGEMENTS The financial support of the industrial affiliates of the Stanford Center for Induced and Triggered Seismicity is gratefully acknowledged.

REFERENCES 1. Dohmen, T., J. Zhang, C. Li, J.P. Blangy, K.M, Simon,

D.N. Valleau, J.D. Ewles, S. Morton, and S. Checkles. 2013. A new surveillance method for delineation of depletion using microseismic and its application to development of unconventional reservoirs. Paper SPE 166274 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 30 September - 2 October.

2. Dohmen, T., J.P. Blangy, and J. Zhang. 2014. Microseismic depletion delineation. Interpretation. 2 (3): SG1-SG13.

3. Jaeger, J.C., N.G.W. Cook, and R. Zimmerman. 2007. Fundamentals of Rock Mechanics. Oxford: Blackwell Publishing Ltd., 4th ed.

4. McClure, M.W. and R.N. Horne. 2013. Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics. Springer. Doi: 10.1007/978-3-319-00383-2.

5. Norbeck, J.H. and R.N. Horne. 2015. Injection-triggered seismicity: an investigation of porothermoelastic effects using a rate-and-state friction model. In Proc., Fourtieth Workshop on Geothermal Reservoir Engineering, Stanford, California, USA, 26-28 January.