URTeC: 2879159

Physics-Driven Optimization of Drained Rock Volume for Multistage Fracturing: Field Example from the Wolfcamp Formation, Midland Basin Sergei G. Parsegov*, Kiran Nandlal, David S. Schechter, Ruud Weijermars Copyright 2018, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/urtec-2018-2879159

This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 23-25 July 2018.

The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper

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Abstract

This paper presents a new workflow comprised of using hydraulic fracture modeling outputs (effective length,

height, and conductivity) for the next step – a discrete fracture flow model which visualizes the drainage pattern in

3D based on history matched production data.

The first part of the paper is designated to fracture forward modeling and prediction of the proppant placement

geometry and conductivity of hydraulic fractures in a multistage horizontal well. The influence of wellbore

deviations and other local initial conditions are all taken into account and explain localized fracture initiation,

fracture asymmetry, and propagation, as well as proppant placement efficiency. The primary model focus is on the

creation of fracture conductivity maps, one for each transverse fracture.

The second part of this study shows the process of import and conversion of 2D fracture conductivity maps for

further use in fluid flow allocation to the individual fractures. The 3D Drained Rock Volume (DRV) is rendered

based on 2D streamline and time-of-flight maps for drainage, velocity and pressure depletion with 5 ft vertical

resolution layers representing the reservoir. Instead of using a grid-based numerical simulation, we apply a meshless

flow model based on Complex Analysis Methods (CAM) to solve linear differential equations. The fluid velocity

field is computed for narrowly discretized time steps, which allows high-resolution visualization of hydrocarbon

flow near and into each of the discrete fractures.

Honoring critical physical interaction of fracture fluid, rock mechanics, proppant transport, the fracture propagation

model coupled with the flow model for discrete fractures, provides a powerful tool to pinpoint the drained rock

volume. Our systematic study highlights trade-offs between fracture design inputs and the total drained rock volume.

Field data from the Wolfcamp Formation, Midland Basin in West Texas, provides a real-world case to demonstrate

our workflow. Recommendations are made for adjusting frac design and improving the recovery factor of

hydrocarbons in place.

1. Introduction

Whether in high or low-price environments, operators in unconventional oil and gas fields continually strive for

reductions of well cost. However, with more fluid and proppant pumped per wellbore feet and with longer laterals

drilled, fracture treatment improves well productivity but leaves little room for further cost reduction. What is

needed is the realization of the best producing well for a given fracture treatment expenditure.

Physics-driven flow models in hydraulically fractured rock volumes make significant progress in completion design

possible. Such models attempt to solve a coupled problem of rock mechanics, fluid flow, and proppant transport

during fracturing and fluid flow to the wellbore. The key problem here is to integrate all information available about

rock properties (Izadi et al. 2017; Kresse et al. 2013, 2011; Niu et al. 2017; Parsegov and Schechter 2017; Weng

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2015; Weng et al. 2011), and reconstructed reservoir depletion (Weijermars et al. 2017b, 2017a, Yu et al. 2018,

2017a, 2017b, 2016). A common objective of the models is the maximization of the recovery of original

hydrocarbon from the acreage by minimizing unstimulated and undrained regions, which prompts for the tightest

possible well spacing while avoiding adverse effects due to well interference.

Prior work (Ajani and Kelkar 2012; Kurtoglu and Salman 2015) shows that the intensity of well interference

increases when the well spacing decreases. In particular, fracture hits may negatively affect well performance and

play an essential role in optimizing well spacing to maximize overall recovery (Malpani et al. 2015; Yaich et al.

2014). Tighter well spacing in multi-well pads may intensify well-to-well interference causing fracture hits (King

and Valencia 2016; Lawal et al. 2013; Yu et al. 2017a, 2017b). Such fracture hits may involve connecting hydraulic

and natural fractures.

In our present study, we use the conductivity attribute obtained from a history-matched hydraulic fracturing model

to build a reservoir drainage model that uses streamline tracing and time-of-flight contours and identifies the

locations of the drained rock volume. We demonstrate our workflow by the retrospective analysis of a field case

from the Wolfcamp Formation, Midland Basin, Texas. However, the methodology developed in our study can be

equally applied to the field development planning stage using pilot hole logs and offset well data for the fracture

propagation model and type curves for flux allocation to the drained rock volume (DRV) in the reservoir simulation.

The DRV can be estimated by coupling a calibrated hydraulically fracturing model with a fluid flow model near the

fractures based on history matching of production data.

With fracture treatment leaving significant portions of the near-wellbore region unstimulated (Parsegov et al., 2018)

and the production flux not draining dead zones between the fractures and between interfering wells (Weijermars et

al. 2017b, 2017a; Weijermars and Nascentes Alves 2018) there is room for improvement of completion designs. We

build forward on previous insights by proposing a practical workflow and by making recommendations for physics-

driven optimization of the rock volume drained by wells with multistage hydraulic fracturing in unconventional

reservoirs.

2. The Setting of the Completion Zone

The present study expands our earlier work on wells in the Wolfcamp Formation, Midland Basin. Previous studies

included an analysis of fracture treatment efficiency (Parsegov et al. 2018) and the high-resolution visualization of

the drained rock volume using flow simulation based on Complex Analysis Methods (Weijermars et al. 2017b,

2017a). The basic insight from our previous work is as follows. Fracture propagation modeling was used to estimate

the final orientations and dimensions of the hydraulic fractures initiated from the perforations in each stage based on

history matching of known pumping schedules, proppant load and using geomechanical data of a nearby pilot well.

Extensive stress shadowing between the closely spaced fractures lead to individual fractures propagating upward

and downward, alternating between stages, leaving significant portions of near-wellbore rock volume unstimulated

(Parsegov et al. 2018). Separately, a high-resolution study of drainage around individual fractures of a horizontal

multi-stage fractured well (only 3.5 miles due south from the stacked wells currently studied) identified the

occurrence of stagnation (dead zones) between adjacent fractures, where the drainage is inefficiently slow. The

recovery factor of the Wolfcamp well in the previous study was estimated to be only 4% of original oil in place,

after five years of production, and no more than 6% after 40 years (Weijermars et al. 2017b).

2.1 Wolfcamp Formation

Our study focuses on a Wolfcamp section with stacked laterals located on University Lands in the Midland Basin,

Texas. The wells were completed with a stacked well field development plan. Fig. 1a shows a gunbarrel view,

looking due north, of the four Wolfcamp production wells (44H, 45H, 46H, and 49H) with adjacent microseismic

monitoring well (47H). The landing zones are labeled by their stratigraphic production unit (WC-B2, WC-B3, WC-

C1, and WC-D) as inferred from log data. Vertical offset between the horizontal wells is 350 ft (between wells 44H

and 45H) and 375 ft (between wells 45H and 46H). The spacing of the production wells in horizontal direction

varies from 200 to 600 ft. Our in-depth analysis uses detailed frac files and production data from Well 46H (Fig.

1a). We will place our results for Well 46H in the broader context of well interference and field development

optimization.

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Fig. 2 - Traditional petroleum provinces in the Midland Basin. The

wells of our study area located in Upton County near the

overlapping Spraberry Trend and Wolfcamp Oil Shale (modified

from http://www.shaleexperts.com/plays/permian-basin/Overview).

Fig. 1 – a) Gunbarrel view (looking north) of four Wolfcamp production wells (44H, 45H, 46H, and 49H) with adjacent

microseismic monitoring well (47H), for which data are presented in Section 6.2; b) Stratigraphic units and drilling targets in the

Midland Basin. Modified from (Scott et al. 2015).

Analyzing well completions in the Wolfcamp formation is a timely topic because the deeper formations in the

Midland Basin have seen a renewed interest from the oil and gas industry. Four formations, mappable and

continuous across the Midland Basin with hydrocarbon target drilling zones, are Clear Fork, Spraberry, Dean and

Wolfcamp (Fig. 1b). A hearing by the Railroad Commission of Texas adopted as type log the Haupt-1 well (3 miles

south of Midland, TX) with a correlation interval of 3,740 ft between TVD 6,865-10,605 ft (Dubois and Miles-

Valdez 2013; RRC 2014).

Before the advent of horizontal drilling with

fracture treatment in 2011, the Wolfcamp was

only marginally productive. Only vertical wells

were used, and although the first well in the

Midland Wolfcamp was drilled in 1923. Santa

Rita-1 produced until shutdown in 1990. No major

drilling activity was seen in the Midland basin

until the 1940s (Blomquist 2016). From the 1940s

till about 2010, the Spraberry was the primary

target with extensive water injection starting in the

1960s to maintain pressure in the under-pressured

Spraberry Trend Area comprised mainly of the

Upper Spraberry. Infill drilling in the 1980s and

reduction of vertical well spacing to 40-acres in

1997 and 20-acre units in 2008 have led to

sustained production from the Spraberry Trend

Area. Drilling activity steeply accelerated in 2011

with 57 new wells in the Wolfcamp Formation

after no wells were completed between 2001-2006

and only six wells in 2007-2010 (Blomquist

2016). Before 2010 development of the Spraberry

Field was developed with vertical wells, although

TVD, ft a) b)

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a few horizontal wells in the upper sands were tested.

As of 2016, over 3,000 new horizontals have been completed in the Wolfcamp Formation, Midland Basin, all with

fracture treatment for enhanced recovery. The average initial production of the wells is 680 BOPD, with

24 wells - greater than 2,000 BOPD (Blomquist 2016). With the shift of production from the Spraberry to the deeper

Wolfcamp Formation, in 2013 it was estimated that 50 billion barrels of recoverable oil remained in the Spraberry

Trend Field (Dubois and Miles-Valdez 2013). The estimation was based on 140-acre spacing for stacked lateral

horizontal wells over the 4 million acres areal extent of the field.

To improve drilling access to the various vertically severed mineral leases, the Railroad Commission of Texas

ordered new field rules for the Spraberry (Trend Area) Field in Final Order No. 7c& 0283443 by deconsolidation

into four surviving fields: Clear Fork, Spraberry, Dean and Wolfcamp fields (RRC 2014). The above fields are

based on correlation intervals as shown on the logs of the Houpt lease, Well no. 1 (API 42-329-31029) in Midland

County.

For the stacked wells in our study (Fig. 1), the gunbarrel spacing measured perpendicular to the orientation of the

horizontal drain hole shall be no more than 300 ft with stacked laterals (SL) included in the well lease name,

according to the new field rules (but the wells were just completed before the new rule). Standard drilling and

proration units were established at 80 acres (RRC 2014). The fields are not subject to any maximum of the diagonal

well spacing (in gunbarrel view), which remains unregulated in the fields.

2.2 Initial State of the Target Zone

Wellbore spacing, the effectiveness of the fracture treatment and subsequent productivity of the engineered wells, all

are affected not only by the engineering decisions but also by the pre-development state of the reservoir. The

relevant initial state parameters include hydrocarbon maturity of the target zone, the native stress field and

geomechanical properties, original hydrocarbons in place and recovery constraints due to the reservoir properties

such as fluid mobility. Therefore, a brief review of the geological setting, geomechanical parameters, and reservoir

properties is merited, before discussing our model approach and results in the main body of our paper (Section 3 and

onward).

Geology. The Midland Basin began to form in the Early Pennsylvanian with an uplift of the Central Basin which

separated the Tobosa Basin into two sub-basins. Lower Permian units in the Midland Basin were deposited in a

deep-water environment. The basin was surrounded by shallow-water carbonate platforms. Estimates of maximum

water depth in the Midland Basin range from 1,000 ft during deposition of Wolfcamp-C and D units (Hobson et al.

1985) to 2,000 ft during deposition of the Wolfcamp-A unit and Spraberry Formation in early Leonardian time

(Montgomery 1996). Tectonism was the most active during the Early Pennsylvanian but persisted into the Early

Permian - Wolfcampian (Ross 1986). That is why we assume low tectonic stress and strain in the middle Wolfcamp

Formation. This tectonic compression also created the Ozona Arch and the Val Verde Basin.

Second order sea level changes laid down deep-water mudstone facies interbedded with carbonate debris flows from

the Central Basin Platform (Fig. 2). The interlayered mudstones and carbonate facies created a very heterogeneous

mechanical structure, both vertically and spatially. This heterogeneity is one of the reasons, why hydraulic fracturing

design is challenging, especially without sufficient open hole logs and seismic data coverage.

The most recent core analysis and facies model studies (Baumgardner et al. 2014; Hamlin and Baumgardner 2012)

conclude that Wolfcamp “shale” is, in fact, an interlayered system of carbonate and silica-rich mudstones with

micrometer scale laminations and with a clay content of less than 20%. To improve log correlations between wells,

in the absence of dense well control and enough core material, lithofacies models with 2 ft vertical resolution was

proposed by (Casey 2018). Unfortunately, the lateral resolution of 300 ft x 300 ft of the model is still an order of

magnitude larger than the characteristic length of the system – the distance between clusters of an individual stage.

Reservoir Geomechanics. Our forward modeling workflow for hydraulic fractures of well 46H is similar to that

described in (Parsegov et al. 2018). We analyze publicly available logs for the target well 46H as well as for an

offset well 31H (wellbores are 500 ft apart) and use regional correlations to construct realistic synthetic logs for the

static Poisson’s ratio (PR) and Young’s Modulus (YMS).

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With known PR, Biot’s coefficient (𝛼), and pore pressure (𝑃𝑝), the minimum horizontal stress (or closure pressure -

𝑃𝑐) can be estimated using Eaton’s formula (Svatek 2017, p. 565):

𝑃𝑐 =𝑃𝑅

1−𝑃𝑅(𝑆𝑉 − 𝛼𝑃𝑝) + 𝛼𝑃𝑝 + 𝜀 ∙ 𝑌𝑀𝑆 + 𝑆𝑡 (1)

or in more simple terms (after Mullen et al. 2007):

𝑃𝑐 =𝑃𝑅

1−𝑃𝑅(𝑆𝑉 − 𝛼𝑃𝑝) + 𝛼𝑃𝑝 + 𝑆𝑡 (2)

DFIT or falloff test data may improve our understanding of the closure stress profile. For the sake of brevity, we

refer to Parsegov et al. (2018) and provide in Fig. 3 only the final results of 1D geomechanical modeling - which

identifies the main geomechanical parameters, reservoir properties, and composition at each depth in the reservoir.

Individual parameters and workflows are discussed in more detail below.

Fig. 3 - Mineral composition and reservoir parameters used in our model. All synthetic logs are calculated with workflows

proposed in (Parsegov et al. 2018) and (Svatek 2017).

Stress State and Horizontal Stress Anisotropy.

In the area of interest (North-East part of Upton county) horizontal wells are usually drilled along the lease

boundaries (in North or South direction). Fortunately, the drilling direction is also conducive to the creation of

transverse fractures. Multiple observations suggest that the maximum horizontal stress in the area is predominantly

aligned to East-West compression (Fig. 4). The actual magnitude of the maximum horizontal stress is relevant for

stress shadow modeling and the prediction of secondary fissures opening and related Pressure Dependent Leakoff

(PDL). Once the treatment pressure exceeds some value related to SHmax, and depending on the orientation of natural

fractures (Smith and Montgomery 2015, p. 131), some of the fractures will be mechanically opened, which will

drastically increase local leakoff and may lead to proppant bridging causing near-wellbore screen-out (Svatek 2017,

p. 273).

However, estimating the maximum horizontal stress and the associated stress anisotropy is challenging. We define

total stress horizontal anisotropy (ANI) in the same way as Svatek (2017, p.43):

𝐴𝑁𝐼 = 𝑆𝐻𝑚𝑎𝑥−𝑆ℎ𝑚𝑖𝑛

𝑆ℎ𝑚𝑖𝑛 (3)

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Multiple studies (Agharazi 2016; Patterson 2017; Wilson et al. 2016) propose that the Wolfcamp Formation in the

Midland Basin is in normal faulting stress regime. Total stress anisotropy (ANI) ranges from 3% (Wilson et al.

2016) to 18% (Patterson 2017, for Wolfcamp-B).

Lately, however, Snee and Zoback (2018) published a regional stress regime study suggesting a mixed mode of

Normal Faulting – Strike-Slip (green background color in the area of interest outlined on Fig. 4). The scaling

parameter 𝐴𝜑, first defined by Simpson (1997), is in the range 0.75-0.9. Assuming Sv = 1.1 psi/ft and Shmin = 0.8

psi/ft, with n = 0, 𝐴𝜑 simplifies to:

𝐴𝜑 = 𝑛 + 0.5 + (−1)𝑛(𝜑 − 0.5) = 𝜑 (4)

We can now estimate the stress anisotropy from:

𝜑 =𝑆2−𝑆3

𝑆1−𝑆3=

𝑆𝐻𝑚𝑎𝑥−𝑆ℎ𝑚𝑖𝑛

𝑆𝑣−𝑆ℎ𝑚𝑖𝑛=

𝑆𝐻𝑚𝑎𝑥−𝑆ℎ𝑚𝑖𝑛

𝑆ℎ𝑚𝑖𝑛

𝑆ℎ𝑚𝑖𝑛

𝑆𝑣−𝑆ℎ𝑚𝑖𝑛= 𝐴𝑁𝐼

𝑆ℎ𝑚𝑖𝑛

𝑆𝑣−𝑆ℎ𝑚𝑖𝑛 (5)

and hence:

𝐴𝑁𝐼 =𝑆𝑣−𝑆ℎ𝑚𝑖𝑛

𝑆ℎ𝑚𝑖𝑛 𝜑 =

1.1−0.8

0.8𝜑 = 0.375 ∙ 𝜑 (6)

For 𝐴𝜑 = 𝜑 ranging from 0.75-0.9, the stress anisotropy (ANI) would be in the range of 28-34%, which would

imply ΔS = (SHmax - Shmin) = 2,100-2,600 psi horizontal stress difference for Well 46H at TVD = 9,400 ft. At such

high stress anisotropy, one should expect a confined cloud of microseismic events and the development of long

planar fractures, which is not supported by microseismic data (see Section 6.2).

In our fracture propagation model, we use the SHmax direction and horizontal stress anisotropy estimated by Agharazi

(2016) from microseismic focal mechanism solutions: the azimuth of the maximum horizontal stress is N 1030

E,

and the stress anisotropy is 8% (equivalent to ΔS ~ 600 psi for TVD=9,400 ft).

Fig. 4 - Stress state in the area of interest. Black solid lines show the direction of the maximum horizontal stress, color-coded

map – stress regime in terms of Aφ. Modified from (Snee and Zoback 2018). Snee and Zoback (2018) proposed that the stress regime is depth-independent and thus assumed a 2D stress map

(Fig. 4). At the same time, the stress state is known to vary vertically with lithology (Xu and Zoback 2015): “The

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

of vertical variations in stress and stress response can be inferred from a horizontal core as described by Lorenz et al.

(2002). One set of regional, Mode I (tensile) fractures are observed in the 1U sand of the Upper Spraberry and are

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strongly oriented along a strike of ~ N45oE. At a greater depth of 150 ft (1U of Upper Spraberry at ~ 7000 ft TVD

and 5U sand ~ 7150 ft TVD) in the 5U silt, two distinct fracture sets were logged from the horizontal core. An

intersection of the two sets striking NNE-ENE in the 5U was cored. Fractography resulted in subtle indications of

shear along the faces of the natural fractures in the 5U indicating Mode II, conjugate shear fractures.

Lorenz et al. (2002) postulated that the higher clay content in the 5U resulted in slightly more ductile behavior as

opposed to the brittle, low clay content of the 1U. Natural fractures were observed in the fluorescent siltstones of the

1U and 5U and natural fractures were observed in the non-fluorescent shale above the net pay zones. However, in

two complete core barrels with 60 total feet of core, no natural fractures were observed below the 5U pay. In

summary, the results observed from 106 natural fractures from 300 feet of the horizontal core that meandered in and

out of pay demonstrated significant variability in natural fractures over a gross interval of ~150 ft. Subtle changes in

mechanical properties in the highly layered system that comprises the Upper Spraberry result in relatively intense

fracturing with three separate fracture sets. The observed permeability anisotropy (Schechter, 2002) during fluid

flow across hundreds of square miles is quite pronounced and is further evidence of the general stress anisotropy

across the vast Upper Spraberry and throughout the entire Permian Basin.

Using natural fracture systems as stress indicators for the present-day requires supporting evidence that tectonic

stresses responsible for fracture formation in the geologic past are still prevalent today. In fact, mini-fracs

corroborate the low-stress contrast that exists between thin, adjacent Spraberry beds of shale, dolomitic silt and

fluorescent sandstone/siltstone (total clay < 15%). Thus, fractures may propagate downward to the Wolfcamp-A

unit, and localized communication between the Spraberry/Dean and the Wolfcamp via natural and hydraulic

fractures is feasible. The Wolfcamp Formation in the Spraberry Trend Area (several hundred thousand acres, Fig.

2), is significantly less fractured and the in-situ stress likely is less anisotropic. Consequently, the background color

of Fig. 4 should be warmer for the Spraberry Trend Area (associated with higher anisotropy) and cooler for the

underlying Wolfcamp Formation. That is why Aφ should not only vary with depth but also with lithology. This depth

dependency may be an explanation of the higher anisotropy predicted by Snee and Zoback (2018, Table A4).

Another explanation may be in a limited number of observations (18 data points) for the whole Permian Basin

region.

Pore Pressure.

The lower Wolfcamp Formation in the Upton and Reagan Counties has an estimated effective pore pressure

gradient, based on multiple DFIT tests, of 0.61-0.66 psi/ft (Loughry et al. 2015). There are two methods to model

the pore pressure in the reservoir as a function of TVD inside the target interval:

a) Assuming a constant apparent pore pressure gradient (0.622 psi/ft in our case) multiplied by TVD.

b) Adopting a hydrostatic normal hydrostatic gradient 0.44 psi/ft and a pressure offset, as proposed by Svatek

(2017, p. 266).

While the second method with constant offset is more applicable for conventional reservoirs (including tight sands)

especially in case of depletion, the first method is more reliable for source rocks with extremely low permeability

and limited vertical hydraulic communication. That is why we use a constant apparent pressure gradient, for our

depth and location, of 0.622 psi/ft (Fig. 3) following Loughry et al. (2015).

Rock Permeability and Permeability-Porosity Correlation. GRI Methodology.

Hydraulic fracturing fluid leakoff depends, among other factors, on rock permeability. Reliable estimation of matrix

permeability is a challenging task for low permeability formations. Since standard steady-state flow rate methods for

permeability estimates are unfeasible, crushed core samples (20/35 mesh) in helium pressure decay tests (GRI

methodology as described by Guidry et al., 1996) provide a more practical method (with a reported cost of $100-

$500 per sample). Fig. 5 exhibits an example of a cross plot with correlations of total gas porosity and GRI

permeability for several rock samples from offset wells and for different formations based on the GRI methodology

using crushed rock samples.

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Fig. 5 - GRI (crushed rock) permeability versus total gas porosity for offset wells. Samples (20/35 mesh size) were extracted in

Dean Stark and dried at 230 °F.

For a typical porosity (7%) the matrix permeability is expected to range from 20 to 200 nD, with a median value of

100 nD. However, some nuance is needed concerning the GRI methodology using crushed rock sample for low

permeability estimations. In the test samples, all microfractures larger than 20/35 mesh grains are destroyed. These

microfractures dominate flow, so the effective permeability in the reservoir based on gas production may exceed the

measured value of matrix permeability by three orders of magnitude (Guidry et al. 1996; Luffel et al. 1993).

Additionally, no confining pressure is applied during the tests, which distorts the measured matrix permeability.

That is why Luffel et al. (1993) stated that the most critical information to evaluate formation producibility is the

bulk permeability as opposed to the matrix permeability. Jones (1997) proposed a pulse decay method to measure

the bulk permeability in the range of 0.01 μD to 0.1 mD at the confined condition for short (1’’ in length) and wide

(1.5’’ in diameter) core plugs to measure matrix and microfractures permeabilities in a single measurement.

A common practice to estimate the bulk permeability is to analyze pressure response during Diagnostic Fracture

Injection Tests (DFIT) as proposed by Barree et al. (2015). However, without reliable DFIT analysis available to us,

we use the GRI-based matrix permeability estimates, consistent with previous industry studies (Mohan et al. 2013;

Niu et al. 2017; Parsegov et al. 2018). Using this approach, we achieved a good match with the average treating

pressure by varying other leakoff parameters. However, we are aware of the need to calibrate reservoir permeability

further when reliable results of DFIT interpretation become available for complex fracturing settings (McClure

2014). Effective reservoir permeability during production is further discussed in Section 5.2.

3. Fracture Propagation Model

A suite of fracture propagation and proppant transport simulation platforms is available for estimating the

conductivity of hydraulic fractures as a result of the fracture stimulation treatment plan. Although earliest attempts

to compare hydraulic fracturing simulators may be traced back to Warpinski et al. (1994), as of today, there is no

consensus regarding the relative merits of the various fracture propagation modeling platforms. The American Rock

Mechanics Association (ARMA) has recently initiated seven benchmark tests for 20 participating models (Han

2017) with the intent to showcase recognized physics of hydraulic fracturing.

In our study, we use a commercially available 3D coupled rock mechanics, fluids flow, and proppant transport

simulator with shear decoupling to predict fracture geometry and the final conductivity distribution. The treatment

horizontal well 46H was drilled in the Midland Basin, Wolfcamp C1 unit (Fig. 1a). Since well logs for the pilot

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holes were not available, we used a vertical section of an offset horizontal well 31H (~500 ft away). We use the

same workflow as described in Parsegov et al. (2018). The modeling results include the spatial distribution of

proppant, effective fracture conductivity, and width. For each transverse and longitudinal planar fracture, the 3D

decoupled simulator provides final fracture attributes for each grid cell: net pressure, leakoff, proppant

concentration, effective conductivity (Fig. 6), and aperture width.

The model accounts for the progressive shift of the fracture stages from toe to heel and therefore can capture the

time evolution of the fracture attributes in video output format to visually identify pitfalls for proposed geometrical

design during fracturing simulation of each stage.

Fig. 6 - Graphical output of effective conductivity attribute for Stage 2, cluster 3. Each gridlock is 5 ft height and 10 ft long.

Active fracture conductivity distribution is negativity affected by overflush at the end of the operation.

A major strength of fracture propagation models is the ability to predict proppant placement density (Fig. 6). For our

target zone, two major fracture barriers occur at TVD 9,320 ft and 9,400 ft, which effectively terminate vertical

fracture growth. The fracture barriers are identified by two low gamma log values intervals (interpreted as a

carbonate-rich rock). The wellbore landing zone (black cross in Fig. 6) is at 9,380 ft with a high-stress concentration

during fracture treatment, which leads to near-wellbore pinch out of the fracture and low-density proppant

placement above and below the landing zone. The pinchout may be due to overflushing at the end of the frac job

with slick water, which may have damaged the near-wellbore conductivity by displacing proppant rich X-gel slurry.

In our case, the hybrid fluid fails to uniformly suspend proppant, which is an indicator of proppant settlement.

3.1 Model Results

The final fracture geometry of the transverse hydraulic fractures initiated from 29 stages (five clusters 60 ft apart

from each other) is presented in Fig. 7. We observed that the first two fractures (or for some stages, first three) are

suppressed and have smaller width and height, but higher concentrations of proppant, as compared to fractures more

distant from the previous stage clusters. Similar to conclusions of Dohmen et al. (2014), the fractures tend to deflect

from each other in the vertically opposite directions to avoid stress shadowing (see insert in blue boxes in Fig. 7).

There is a strong indication for the existence of axial fractures along the wellbore with conductivity comparable to

that of the transverse fractures (see insert for stages 17-19 in Fig. 7 for more detail).

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Fig. 7 - 3D model of proppant concentration color-coded in [lb/ft2] for multistage hydraulic fracturing (with stress shadowing

effect accounted for individual fractures suppression and significant proppant placement into axial fractures). The inset represents

an interpretation of (Dohmen et al. 2014) of microseismic events for Utica well A with 70 ft cluster spacing (cluster spacing for

well 46H – 60 ft).

Instances of escalation in the measured Instantaneous Shut-In Pressure (ISIP) from toe to heel have been recorded in

multiple field operations (Manchanda et al. 2012; McClure and Zoback 2013; Roussel 2017). Such an escalation is

confirmed by ISIP data for Stages 2-26 of Well 46H (Fig. 8, bold blue line). Proppant concentration and fracture

geometry are included for quick comparison.

Fig. 8 – ISIP [psi] escalation from the toe (Stage 2) to heel stages is backed by proppant placement visualization [lb/ft2] to

correlate fracture geometry (height) and related ISIP escalation. Stage 1 was abandoned due to engineering issues.

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ISIP escalation from the toe stage to the current stage may be used further to diagnose stress shadowing effects and

reduce the risk of screen-out in the next stages. That is why operators record the ISIP for each stage by downhole

pressure gauges or with optical fiber. The following observations may be made from Fig. 8:

There is a strong ISIP escalation signature (200 psi/stage), corresponding to the growth of taller fractures in

the toe of the well 46H (Stages 2-12).

Fractures originating from perforation clusters in one stage may grow vertically in opposite directions. Each

stage with such “flipping” fractures tends to stop ISIP escalation.

Stages 13-23 are vertically confined (propped fracture height ~40 ft is comparable to the fracture spacing –

60 ft) and show constant ISIP of 4,100 psi (no ISIP escalation). With observation of suppressed fractures

near the previous stage we conclude that calculated fracture geometry is sufficient to justify measured

constant ISIP.

Individual transverse fractures may grow vertically in opposite directions to reduce interference (Stages 2-

9). Such change of vertical direction growth may be responsible for keeping ISIP relatively constant

(induced stress plateau).

3.2 Fracturing Stimulation Without Stress Shadowing

To further validate the importance of the stress shadowing effect, we recalculate the fracture geometry for a pressure

matched model by switching off the stress shadowing effect (Fig. 9). In such a case, individual stages (2-9) grow

upward and downward independent of each other, and proppant placement is more uniform among multiple

geological layers (higher concentration is in warm colors). Fractures from Stages 10-27 are still growing primarily

downward, but first three clusters are no longer suppressed by stress from the previous stage. By comparison of the

model results in Fig. 7 and Fig. 9, we can conclude that with stress shadowing effects taken into account:

1. The first three fractures of each stage will be significantly suppressed. The fluid and proppant amount

injected by the corresponding clusters will be considerably smaller. Examples are Fractures 1-3 for

Stages 17-19 in Fig. 7.

2. Axial fractures will take more proppant and will be higher and more prolonged (Fig. 7). This observation

may be critical for pressure and fluid communication between stages.

Fig. 9 - Side view of proppant concentration color-coded in [lb/ft2] for the treated well in the direction of transverse fractures.

The simulation is run without stress shadowing effect. The distance between individual transverse fractures (cluster spacing) is

60ft.

TVD, ft

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3.3 Scenario Analysis of the Fracturing Model

After preparing a base case of our forward model, we ran multiple scenarios to explore how the uncertainty of ill-

defined parameters may affect resulted in fracture geometry and conductivity. Non-uniqueness of pressure matching

may occur, which an engineer may wrongly attribute to be optimal. Therefore, it is essential to use as many

secondary data sources as possible to regularize optimization of workflows for the history matching of fracture

propagation models.

Pressure interference between treatment and offset wells by so-called “fracture hits” is a significant concern in

hydraulic fracture operations (Safari et al. 2017; Yu et al. 2017a, 2016). A possible primary cause of this

phenomenon is water breakthrough to the offset well during the treatment (Lindsay et al. 2018). The fact that water

breakthrough is not associated with proppant breakthrough into the offset well suggests that proppant is transported

ineffectively. In the ideal design, slurry with proppant should reach the fracture tip region at the end of the

operation. Such a result requires a dynamic fracture width for the target half-length, sufficiently large to transport

proppant in banking mode (> 3 diameters of proppant grain). Thus, for typical 40/70 brown sand (D=212-420 µm)

fracture width should be larger than 1.3 mm (0.05’’) to prevent Tip Screen-Out (TSO), which is achievable with a

proposed high pump rate of 80 bpm.

The typical reason for using a sizeable slick water pad at the beginning of a fracture treatment operation is to assure

the absence of near-wellbore screen-out due to non-linear leakoff. However, in low permeable formations leakoff in

mostly controlled by the mechanical opening of the secondary fissures (and favorably oriented natural fractures) as

proposed by Svatek (2017) and capillarity imbibition at the contact surface (F. Zhang et al. 2018; Fan Zhang et al.

2018). Classical fracture design is based on Carter’s leakoff model and fracturing fluid efficiency measured in

laboratory tests (Warpinski 1985). Nolte (1986) proposed a workflow to design the proppant schedule based on

measured leakoff and calculated fluid efficiency using the PKN, KGD models, and penny shape radial fracture

model. From his calculations, pad size may be in the range of 20-60% of the total volume pumped. For Well 46H

the operator selected a pad size of 40%, and proppant was added in “stair step” mode (Fig. 10; Smith and

Montgomery, 2015, p. 197).

Fig. 10 - Fluid and proppant schedule for typical well 46. Pad size = 40% of the total volume with “stair-step” increase to the

maximum concentration of 3.0 ppa. Insert with “ramp” schedule is from the original study of Nolte (1986).

To test the hypothesis of the sizeable, ineffective pad, we reduced the pad size by half which did not result in screen-

out in any of the stages. More importantly, proppant placement regions remained almost identical to that for the full

pad size, but total fracture lengths were shorter and hence less likely to be the cause of fracture hits (Fig. 11). For

further analysis of parent-child well interaction, the industry needs a reliable tool to predict pressure depletion

around the wellbore after multistage fracturing and several years of production (Safari et al. 2017).

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Fig. 11 - Result of fracture simulation with half of the original pad size as for showed in Fig. 7 simulation. Both simulations

imply stress shadowing, the only difference – the size of the pad. Original design is taken from (Parsegov et al. 2018), the

variation has half of the original slick water pad. Virtually the same proppant distribution was achieved with smaller hydraulic

fracture length, and related fracture hit risk.

4. Drainage and Pressure Depletion Model

We seek to model drained areas and pressure depletion using the novel analytical solution proposed by

Weijermars et al. (2017a, 2017b). The workflow to complete our objective is as follows:

Creation of 3D fracture model with appropriate inputs.

Determination of total well production using Duong decline curve.

Discretization of 3D fracture and assigning of fracture conductivity per node.

Allocation of production per fracture based on flux allocation algorithm.

Modeling of velocity and pressure depletion per discretized reservoir layer drained by the fracture.

Modeling of drained area realized in each discretized layer.

Interpolation of drained area per layer to create a 3D envelope of the drained rock volume (DRV).

4.1 Production Matching

We assume radial flow toward the wellbore in the fracture plane and 2D flow perpendicular to the fracture plane in

the reservoir (Al-Kobaisi et al. 2006). Justifications for this 2D flow idealization comes from Weijermars et al.

(2017b) by assuming matrix flow is confined between an upper and lower finite boundary which thus imposes a 2D

flow geometry in the matrix. Production data is history matched with the Duong’s Decline Curve Model (Duong

1989) to generate a type curve for the given well. For oil production the equations used are:

𝑞𝑤𝑒𝑙𝑙(𝑡) = 𝑞𝑖 · 𝑡(𝑎, 𝑚) + 𝑞∞ (7)

with time exponent:

𝑡(𝑎, 𝑚) = 𝑡−𝑚 𝑒𝑎

(1−𝑚) (𝑡1−𝑚−1)

(8)

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and cumulative oil production 𝑁𝑝(𝑡) is given after integration as:

𝑁𝑝(𝑡) =𝑞

𝑎 𝑡𝑚 (9)

Based on historical production data parameters a, m, q∞, and qi can be determined using the least squares fit method.

The parameters are used to forecast production for Well 46H (Fig. 12). For the well modelled the parameters

obtained from curve fitting the monthly production data were: qi = 7,713 STB/month, q∞ = 0 STB/month, a = 1.81

month-1

and m = 1.5. Our curve fitting shows a good correlation to actual produced cumulative production values.

With these parameters, we forecast production for the well for 40 years life.

Fig. 12 - Well 46H actual production and type curve forecasts used for the flow model.

4.2 Production Matching Stage-by-Stage

Weijermars et al. (2017a, 2017b) introduced analytical solutions for the visualization of flow interference between

hydraulic fracture clusters based on Complex Analysis Methods (CAM). The CAM code was used to devise an

analytical streamline simulator, which can be used to produce high-resolution plots of the areas drained around

hydraulically fractured wells for comparison with pressure depletion plots and velocity fields around the fractures.

From this work, new insights were developed such as the fact that areas of high flow are better illustrated by

velocity plots rather than the pressure plots that are currently used as a proxy for drained regions. Another

significant insight was the recognition of so-called dead zones due to flow interference between the fractures.

Previous CAM-based flow models assumed the hydraulic fractures were planar features with uniform height and

length as determined from micro-seismic events. The fracture surface area was used as the control on the amount of

production each fracture was contributing. The present study assigns properties to the 3D fractures making use of a

greater dataset than just the micro-seismic events. By importing the fracture conductivity from the 3D fracture

model with a high resolution of the propped fracture variability a more accurate representation of the fluid flow

around individual fractures becomes possible.

The CAM flow model initially used a simple flux allocation algorithm that allocated well production rates to the

individual fractures in the drainage model. The amount of flow allocated to each fracture from the total type curve

output was based on the surface area of each fracture, labeled {1, 2, 3,…, k}, and the fracture height and length were

inferred from micro-seismic data available for 13 stages. A scaling term was used to prorate the total production

output of the sample Well 314H to just 13 out of the 33 fractures (Weijermars et al., 2017b):

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𝑞𝑘(𝑡) = (1 + 𝑊𝑂𝑅) · 𝑞𝑤𝑒𝑙𝑙(𝑡)13

33

𝐻𝑘 . 𝑋𝑓,𝑘

∑ 𝐻𝑘 . 𝑋𝑓,𝑘𝑘 (10)

To account for the oil formation volume factor (FVF) and reservoir porosity, the following expression was used in

the complex potential solution, where mk(t) represents the strength of the interval source at a time (t):

𝑚𝑘(𝑡) = 𝐹𝑉𝐹· 𝑞𝑘(𝑡)

𝐻𝑘 · 𝑃𝑂𝑅𝑂 (11)

This original method utilized flow reversal to help define the drained regions around the fractures. Production data

was analyzed using the Duong’s Decline Curve method (Duong 1989) to forecast long-term production. The

production was allocated back to individual fractures based on the production allocation algorithm. The initial

algorithm prorated production based on idealized planar, fracture height and length based on, for example, the

micro-seismic interpretations. Though this is a reasonable assumption, recent work shows that actual productive

fracture half lengths and heights may not exactly correlate to these micro-seismic events.

That is why, in this study, we make use of the result of a planar-3D hydraulic fracturing modeling to allocate

production to the individual fractures.

4.3 Discretization of 3D Fracture and Fracture Paneling

The adapted flux algorithm makes use of fracture conductivity data from the 3D geomechanical fracture model. 3D

baseline fracture conductivity from the 3D geomechanical model takes into account corrections for proppant pack

degradation and imperfect fracture cleanup as proposed by Parsegov et al. (2018). The improved flow allocation

algorithm can better capture the physics of the producing hydraulic fracture network and thus gives a better

representation of drained regions and the location of stagnation zones. Such detailed flow models may help to

improve well and fracture treatment design to achieve higher EUR and improve recovery factors.

The fracture model uses a grid of 5 ft by 10 ft nodes to represent the created hydraulic fracture (Fig. 13). Due to this,

we can discretize the fracture height into 5 ft thick layers, and fluid flow in each layer was modeled based on the

conductivity (Ck) of the grid blocks in that layer (Fig. 14). The conductivity within one layer can at times vary by

several orders of magnitude, which is captured by panels within each layer averaging the conductivities of grid

blocks that are relatively within the same order of magnitude. Each of these panels is used for flux allocation in the

CAM code to model fluid flow into the individual layers. For Stage 2 the paneling procedure represents the five

fractures discretized into 15 individual layers with on average five different conductivity panels. The actual number

of panels in each layer is not constant but depends on the range of conductivity values for that particular layer.

4.4 Flux Allocation

Next, the average fracture conductivity, 𝐶�̅�, of each panel is calculated based on the individual node values for Ck

and the number of nodes in that particular panel:

𝐶𝑘̅̅ ̅ =

∑ 𝐶𝑘𝑁𝑘=1

𝑁 (12)

where N is the number of nodes in the panel and ∑ 𝐶𝑘 is the sum of the conductivities of the individual nodes in the

panel. This approach is followed for all panels in all 15 layers for all 5 fractures in our modeling of Stage 2 in this

well. From this we propose a conductivity-based flux algorithm:

𝑞𝑘(𝑡) = 𝑍(1 + 𝑊𝑂𝑅) · 𝑞𝑤𝑒𝑙𝑙(𝑡) · 𝑆 ·𝐶𝑘̅̅̅̅ .𝐻𝑘.𝑋𝑓,𝑘

∑ 𝐶𝑘̅̅̅̅ ·𝐻𝑘·𝑋𝑓,𝑘𝑛𝑘

(13)

The algorithm takes into account the fracture panel conductive surface area when allocating flow into the individual

fractures. A conversion factor Z = 5.61 accounts for conversion of input units of ( )wellq t in STB/day into output

units of ( )kq t in ft3/day. Scaling factor S in Eq. (13) depends on the allocated production for the stage as determined

from the tracer data. Tracer data (Table 1) allow us to allocate total production to each fracture stage. Stage 2 is part

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of the traced segment “5-2" (Stages 2-5), which shows a contributing percentage of 13.1% from normalized oil-

soluble tracer flowback. Based on this percentage of flow over these four stages we can average the portion of the

production allocated to Stage 2 as 3.28% of total well production.

Fig 13 - Snapshot of evolved fractures of the Stage 3 well 46 with effective conductivity indicated by the color bar.

Fig. 14 - Discretized Fracture front view; warmer colors indicate higher conductivity.

Table 1 – Oil soluble tracer data for fracture stages. Source: Service company report.

Conductive fracture

height (Hf )

Conductive fracture half-

length (Xf )

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5. Drainage Visualization

The rock volume drained by the five fractures of Stage 2 in Well 46H has been reconstructed after quantifying the

flux allocations for 15 horizontal layers in the stage. For the creation of a 3D envelope of the drained rock volume

(DRV), we stack the individual 2D drainage shapes for each layer in the z-direction to visually represent the area

drained out by the fracture stage. Hydraulic fractures are modeled as line sinks with varying strengths to visualize

fluid flow near the fractures, pressure depletion and the velocity field in 2D flow planes based on the complex

analysis. The drained rock volume (DRV) can be computed based on the corresponding time-of-flight contours from

the particle tracking of streamlines. The 3D fracture model discretized each fracture into individual flow layers (Fig.

15), which intersect all fractures in each plane. By combining the drainage areas per layer, we can create a 3D

visualization of the drainage envelope for Stage 2.

Fig. 15 - Schematic of discretization of 3D fracture into layers for modeling.

5.1 Flow Visualization and Pressure Change Realization

With calculated total well output and the algorithm for flow allocation, we can now visualize flow based on the

prorated flux into discretized fracture layers using our method of complex potential. The velocities

contours |𝑉(𝑧, 𝑡)|, for a specific time t and layer l of the discretized hydraulic fracture, are plotted using the

equation:

𝑉(𝑧, 𝑡) = ∑𝑚𝑘(𝑡)

4𝜋𝑋𝑓,𝑘𝑒−𝑖𝛽𝑘𝑁

𝑘=1 · (log[𝑒−𝑖𝛽𝑘( 𝑧 − 𝑧𝑐,𝑘) + 𝑋𝑓,𝑘] − log[𝑒−𝑖𝛽𝑘(𝑧 − 𝑧𝑐,𝑘) − 𝑋𝑓,𝑘 ]) (14)

The calculated 𝑞𝑘(𝑡) accounts for the strength of flow near the fractures in our model layer of thickness Hk by

adjusting for formation volume factor (FVF) and reservoir porosity (PORO) as follows:

𝑚𝑘(𝑡) = 𝐹𝑉𝐹 · 𝑞𝑘(𝑡)

𝐻𝑘 · 𝑃𝑂𝑅𝑂

(15)

We apply the principle of flow reversal, and local pressures are calculated relative to an initial reference reservoir

pressure P0 at the time of injection (Weijermars et al. 2017b):

𝑃(𝑧, 𝑡) = 𝑃0 + ∆𝑃(𝑧, 𝑡) = 𝑃0 − ∅(𝑧, 𝑡)𝜇

𝑘

(16)

Where µ is fluid viscosity, k is the reservoir permeability, and ∅(𝑧, 𝑡) is the potential function representing pressure

change ∆P. We can model the flow of fluid into the hydraulically fractured well, and the corresponding pressure

declines due to the drainage by the producing well. For drainage contours visualization we assume the following:

PORO = 5%, k = 1 mD, FVF = 1.05 RB/STB, µ = 1 cP, and WOR = 4.6.

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5.2 Results of Visualization

This section shows the flow modeling results for Stage 2 taking into account the spatial variation in conductivity

along each hydraulic fracture discretized into 15 individual layers (Fig. 16). The drained region for each layer is

determined from the time-of-flight contours over the productive life of the well. We present the 2D drainage areas as

well as velocity and pressure contour plots for key individual layers (Layers 4, 6, 8, 10, 12 and 14). From our results

(Fig. 16 and Fig. 17) it is clear just how much of the actual fracture length is unproductive. In fact, regions drained

after 40 years are still confined to the proximity of the fracture surfaces.

Pressures in the model are calculated using Eq. (16) with the potential function representing the pressure change

based on the initial reservoir pressure as the reference pressure P0. The potential function is scaled by the fluid

viscosity (µ), and reservoir permeability (k), and ∆P(z, t) is quantified, efficiently rescaling initial reservoir pressure

P0=0. Actual reservoir pressure can be obtained at all times by adding back in P0 = 5,850 psi (based on vertical

pressure gradient, see Section 2.2). Assuming a reservoir permeability of 1mD after fracturing, the potential function

of Eq. (16) associated with the flow rates near the hydraulic fractures give pressure changes ∆P(z, t) on the order of

102 psi. The pressure contour plots (Fig. 16, right column) are scaled with the absolute pressure change ∆P, which

represents the pressure drawdown of the fractured well. Velocity peaks in each layer of the model coincide with

regions where pressure contour spacing is narrowest. Pressure drawdown is highest near the central region of the

fractures. By comparison, the velocity contours show the highest velocities of the fluid occur at the fracture tips and

particularly at the outer fractures where there is less flow interference between fractures.

The permeability used in the flow model of 1mD to match the actual reservoir production with realistic pressure

changes differs four orders of magnitude from the matrix permeability used in the initial fracture propagation model,

which has a mean permeability of 100 nD (Fig. 3). The low pre-frac permeability of 100 nD cannot be reconciled

with the productivity and corresponding pressure depletion rate in history matching, which requires the use of 1 mD

in the flow model. A possible explanation for the inferred difference in matrix permeability before and after the frac

treatment could be the existence and/or creation of secondary fracture systems near the main hydraulic fractures

(enhanced permeability region).

The time of flight contours (Fig. 16, middle column) outline the area drained after 40 years of production.

Commonly, pressure depletion plots are used as a proxy for drainage. Indeed, pressure plots in our study indicate

where the fluid is moving fastest in the reservoir due to a pressure gradient, namely where pressure contour spacing

is tightest. However, not all moving fluid will reach the fractures within the time scale of the well. Time-of-flight

contours give a more accurate estimation of the drained reservoir region as visualized by the CAM model.

Therefore, we conclude that in unconventional, ultra-low permeability reservoirs, pressure plots are less reliable for

representing the drained rock volume.

For the first time, we are able to visualize the 3D drained rock volume (DRV) for Stage 2 after 40 years of

production (Fig. 18). Between the fractures, there are still undrained regions that can be targeted for refracturing.

One observation is that the lower layers have a larger drained area than the upper layers of the fractured zone

showing the non-uniform flow from the reservoir into the fracture at different depths. Outer fractures have higher

hydraulic conductivities and therefore drain the adjacent matrix region more effectively. Additionally, the external

fractures in Stage 2 show hydraulic conductivities increasing from the top to the bottom layer, which is why the

drained region is the largest accordingly near the bottom of the outer fracs.

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Fig. 16 - Top to bottom: Flow data for Layers 4 (top panel), 6, 8, 10, 12, and 14 (bottom panel). Left column - Velocity contour plots

(ft/month); Middle column - Drained area after 40 years production outlined by red time of flight contours. Streamlines in blue and

fracture segments with variable conductivity marked by alternating blue and green line segments, Right column - Pressure contour

plots (pressure values are scaled by (-103) psi, due to drawdown). Velocity and pressure plots shown after one-month production.

Fig. 16 - Top to bottom: Flow data for Layers 4 (top panel), 6, 8, 10, 12, and 14 (bottom panel). Left column -

Velocity contour plots (ft/month); Middle column - Drained area after 40 years production outlined by red time of

flight contours. Streamlines in blue and fracture segments with variable conductivity marked by alternating blue and

green line segments; Right column - Pressure contour plots (scale given as drawdown from initial pressure by 102

psi). Velocity and pressure plots are shown after one-month production. Length scale is in ft.

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Fig. 17 - Zoom on Layer 8 for velocity contour plot, drained area, and pressure contour plot. Length scale is in ft.

Fig. 18 - Drained Rock Volumes (DRVs) for five clusters for Stage 2. DRVs after 40 years of production are in red shades;

idealized fracture planes are in blue. Length scale is in ft.

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5.3 Fracture Interference

Above we demonstrated our discretization method on a single stage case (Stage 2). However, the well has 29 active

stages and as such flow interference between stages is to be expected. While full intensive modeling of each stage

by the discretization method to observe flow visualization is outside the scope of this paper, a simple scenario is

modeled to investigate flow interference effects between the toe stages (Fig. 19). From the modeled results for

Stages 2 to 9 (Fig. 20), the extreme ends of fracture stages appear to have higher velocities, due to less interference

with adjacent fractures.

The highest velocities are confined to the near-axial region of the wellbore, again emphasizing how much of the

created fracture length away from the near-wellbore area is unproductive. The pressure plot (Fig. 20) suggests a

large depletion region, while the time-of-flight contours after 40 years of production show the actual area drained is

very small when compared to the areas that show marked pressure changes. Actual areas drained are much smaller

than inferred from pressure contour plots, which concurs with previous work (Weijermars et al., 2017b).

Fig. 19 - Side view of well, showing Stages 2 to 9 crossed by the Layer 8 flow plane (Fig. 20). The slope of the well is negligible

and appears steep due to horizontal length being compressed by a factor of 30.

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6 Discussion

6.1 Microseismic Monitoring

The wells stacked around our study Well 46H (Fig. 1a) were monitored for micro-seismic response in the rock

volume near the treated frac stages. The operator used two horizontal sets of geophones in the monitoring Well 47H

(Fig. 21). Distances between the stimulated stages and the geophones varied from 790 ft (Stage 2) to 2,634 ft (Stage

15). This configuration allowed the monitoring of microseismic response from Stages 2-15, with the highest quality

data collected for Stages 3-8.

Fig. 21 – Microseismic monitoring configuration. Each stage is color-coded and has 5 clusters. Two sets of geophones are placed

in Well 47H. Source: modified from service company MS report.

Depth views and map views of the filtered data are shown in Fig. 22 and Fig. 23, respectively. The microseismic

results show most response occurs in the rock volume of the previous stage. The effect is discernable by carefully

comparing color-coded perf locations of each stage with the microseismic response clouds in both depth and map

views (Fig. 22 and Fig. 23). For example, the microseismic cloud of Well 46H of Stage 6 in Fig. 22 (top right) is

adjacent to Stage 5 perforations, and Stage 4 response cloud is largely overlapping with Stage 3 perforations. Similar

shifts in response clouds and perforation locations are seen in well 45H (Fig. 22, middle row), but less so in well

44H (Fig. 22, bottom row).

One interpretation of the mismatch between perforation locations and microseismic response clouds is that the

fracture treatment of the previous stages weakens the rock and is prone to microseismic slip when the next stage is

treated. More specifically, one could postulate based on Well 45H depth views (closest to the monitoring well, see

Fig. 1a), that frac fluid is injected into the matrix principally from the toe-end perf clusters (Fig. 23, middle row).

This is counter to observations in Canadian shale wells, for which a strong bias for flow into heel-end perforations

was reported (Azad et al. 2017; Somanchi et al. 2017).

A comparison with our estimation of stimulated zones from the fracture propagation model and the microseismic

clouds reveals a relatively poor spatial match. One explanation is that the outcome of the fracture propagation model

is very sensitive to input data and one realization may not reproduce a realistic result, only a proxy model of a

possible result given certain selected discrete inputs. Another possible explanation is that both outcomes, i.e.,

microseismic clouds and treatment fracture locations, are correct but represent physically different processes. The

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microseismic cloud picks up fault slip energy from the shear failure of fractures that are not necessarily connected to

the fluid treatment zone, whereas the hydraulic fracturing occurs by the tensile failure of intact rock.

According to Mohr-Coulomb criteria, shear failure in a Representative Element Volume (REV) may occur before

tensile failure in case of proper pressure perturbation. That is why analysis of clouds of Microseismic events (MS)

may provide an inflated perception of the volume of rock stimulated by fractures capable of taking proppant.

Fracture propagation models have already revealed that estimates of effective fracture length and height based on

micro-seismic tends to be vastly over-estimated by perhaps a factor of ten. The reason is that micro-seismic does not

differentiate the hydraulic fracture segments relevant for sufficient stimulation of the well productivity and may pick

up slip signals of reactivated natural fractures not connected to the wellbore and receiving no proppant load. In fact,

fracture models show that the propped segment of the hydraulic fracture is relatively short and confined to the near-

wellbore regions. Such banking and dunes migration of proppant is also predicted by proppant emplacement models

(Kou et al. 2018).

6.2 Well Interference and Productivity

The Wolfcamp Well 314H analyzed in our previous study of DRV (Weijermars et al. 2017b) has its wellhead

located only 3.5 miles due south from the wellhead of well 46H analyzed in our current study. The wells have their

toes pointing towards each other, with a horizontal separation of only 1.5 miles between their respective toes.

The Estimated Ultimate Recovery (EUR) based on history matching 3 years of historical production data with an

appropriate decline curves differs significantly for the two wells. Well 314H has a 30-year EUR=240,000 STB,

while Well 46H has a 30-year EUR=140,000 STB. Because the wells are located in the same landing zone, with toes

only 1.5 miles apart, differences in the organic content, original oil in place or variations in the thermal maturity are

less likely causes of the observed difference in the Wolfcamp well performance. What then can be the explanation

for differences in well productivity expressed as an EUR ratio 314H/46H of 1.71?

Marked differences occur on the engineering side. Well treatment of 314H had 33 stages and a total of 99 frac

clusters. Well 46H had 30 stages (stage 1 was abandoned) and a total of 143 frac clusters. The stages of 314H each

had 3 frac clusters 60 ft apart and were treated with 250,000 gallons and 200,000 lbs of proppant. Stages of 46H

each had 5 frac clusters (also 60 ft apart), treated with 304,000 gallons and 336,000 lbs of proppant load. The actual

fracture treatment pump rates for both wells were about 70 bpm. A distinguishing engineering factor is that ratio of

the fluid volume per frac cluster of Well 314H, and Well 46H was 1.37. The larger fluid load for the frac clusters in

Well 314H explains the more substantial seismic response of Well 314H and microseismic dimensions of fractures

much larger as compared to those of Well 46H.

Analysis of their respective microseismic dimensions shows that microseismic heights and lengths of Well 314H

average 400x1000 ft2, while Well 46H fractures average 400x590 ft

2. The resulting ratio of the seismically

determined frac areas for Wells 314H and 46H is 1.7. Recall that the EUR ratio 314H/46H was also 1.71. However,

any suggestion that the difference in frac dimension alone (due to the treatment of Well 46 with less fluid volume

per frac) would explain the difference in well performance neglects the considerable discrepancies in productive

length of the wells. We also note that the proppant load per perf cluster for wells 314H and 46H was nearly identical

(ratio of 0.99). The difference in performance of Well 314H and the nearby Wells 44H-47H most likely is due to the

much higher watercut of the latter wells (see the next section).

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Fig. 22 - Microseismic events projected on vertical reference planes (oriented S-N) for toe-end stages. Filtered signals are

shown in left column and inferred stimulated volumes are color shaded in right column. Individual stages are color-coded and

numbered. Top of the various Wolfcamp production units (A3, B1, B2, B3, C, and D) inferred from log data are also marked

in sections. Vertical offset between wells is 350 ft (Well 44H-45H) and 375 ft (Well 45H-46H). Lateral offset between wells is

shown in map projections of Fig. 23. Each grid block is 400x400 ft2. Source: modified from service company MS report.

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Fig. 23 - Microseismic events projected on horizontal reference planes (oriented with N directed to the right, W is up,

and E is down) for toe-end stages of multi-fracing wellbores. Filtered signals are shown in left column and inferred

stimulated rock volumes are color shaded in right column. Well spacing in horizontal projection varies from 200 to

600 ft. Each grid block is 400x400 ft2. Source: modified from service company MS report.

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6.3 Impact of Water Flux on Well Productivity

We believe that well interference is a negligible factor in the depressed productivity of Wells 44H-47H. However, a

major factor is that the water saturations and evolution of water-to-oil ratios (WOR) in Wolfcamp wells are high

(WOR=4, water cut = 80%). This WOR is higher than the average of 2.6-2.8, reported for unconventional wells in

the Midland Basin (Scanlon et al. 2017). In general, the water cut in Wolfcamp wells is much higher than, for

example, Eagle Ford wells (the subject of other studies in our group):

Eagle Ford wells in the oil window typically have WOR=1.2 or higher at the onset of the first production. The

flowback water component is still high in the first production month, but quickly drops to WOR=0.2 after the

first month of production, and slowly continues to decline further to WOR=0.1 within about 2 years of

production and then stabilizes. The GORs of Wolfcamp and Eagle Ford wells in oil window are about the

same.

However, in the Wolfcamp wells, we see a different WOR trend: For Well 314H, the WOR is around 4.5 in

the first month, again due to flowback of frac water, then rapidly declines to WOR = 0.4 after four months of

production. But unlike in the Eagle Ford wells, the WOR goes starts to rise again over the next three years of

production from WOR=0.55 at the end of year two, WOR = 0.75 end of year 3, WOR = 1.9 end of year 4.

For Wells 44H-47H, we see water cuts of 80% and WOR = 4 without any drop even after four years of

production, which means most of the reservoir pressure is used to pump water rather than oil.

In the Eagle Ford wells, we studied lateral fracture hits occur between wells as far as 4,000 ft apart. These hits likely

close mostly (no water in Eagle Ford, although some from overlying Austin Chalk may seep in). The decline seen in

the Eagle Ford wells are taken as a “normal” production trend in dry, ultra-low permeability reservoirs unconnected

to water resources via any discrete fracture network.

What then could be the possible explanation(s) for the high watercut in Wolfcamp wells? Plausible explanations of

high water production could be the high initial content of mobile water or special shape of relative permeability

curves in the formation. There is still a place for debate here. However, another possible explanation relates to

waterflooding programs and produced water disposal. The Spraberry Trend Area (Upper Spraberry and JoMill

formations) which is 500 - 1,000 feet above the Wolfcamp was heavily waterflooded over decades since the 1960s.

There are literally billions of barrels of injected water in the formerly under-pressured Spraberry that overlies the

over-pressured Wolfcamp. Schechter (2002) and colleagues (Lorenz et al. 2002) performed intensive

characterization of the Spraberry intervals and concluded that fractures are pervasive throughout the Upper and

Lower Spraberry intervals. Horizontal core clearly demonstrated that the intensive, multiple systems of natural

fractures dominate all aspects of fluid flow. Also, the injection of produced water has been ramped up in recent

years, particularly in the Spraberry Trend Area (Scanlon et al. 2017). When massive hydraulic fracturing is

conducted, the Wolfcamp and Lower Spraberry may establish direct fluid communication with water injected over

decades. Any frac-to-water hits from the Wolfcamp to the Spraberry may start gravity drainage once overpressure

drops due to production-related pressure depletion in Wolfcamp wells, and progressive seepage of Spraberry water

into the wells may occur when there is fracture communication. Micro-seismic data for offset wells drilled in

Wolfcamp A and B units show MS cloud height sufficient to reach the Spraberry siltstones. Permeability

enhancement in the stimulated volume together with fracture communication may allow the injection water in the

overlying Spraberry to appear in Wolfcamp production wells: a new kind of fracture hits, we coin here as “frac-to-

water hits.”

7. Conclusions

Hydraulic fracturing in unconventional reservoirs is a process that is still not adequately understood to the extent

where we can have total reliance on the accuracy of our reservoir models. As such without this crucial

understanding, we are not able to adequately predict the behavior of these reservoirs. In this paper, we track fluid

flow into hydraulically fractured wells based on a Complex Analysis Method (CAM).

This method allowed us to model flow near to the fractured wells at high resolution and was used to generate flow

velocity field solutions, pressure depletion plots and visualize the Drained Rock Volume (DRV) near to the

fractures. The method allocates flow of individual fractures using fracture properties determined by a planar-3D

fracturing simulation, which takes into account stress shadowing on the fracture propagation and also rock

permeability enhancement. The results reinforce the notion that pressure plots are poor proxies for the DRV,

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because the drained volume remains very limited (and much smaller than suggested by the pressure plots) even after

40 years of production.

Another critical insight gathered from our modeling is the unevenness in the drainage volumes around each

hydraulic fracture in Stage 2 (Fig. 18). The lower layers (13, 14, and 15) of the fractures have the highest drained

regions and correspondingly also the highest fracture conductivities, which may be a direct result of proppant

settling, as while pumping, more proppant settles into the lower layers creating higher proppant placement and thus

higher conductivity nearer to the base of the fractures. From the estimated DRV, we seek to provide a schedule for

refracturing that targets undrained regions to improve the overall recovery of the wells.

Further recommendations are summarized below:

1. Based on results of the fracture propagation and CAM models, a significant section of the distal fracture

length has hydraulic conductivity so low that no significant contribution is made to the DRV.

2. The outer fractures of modeled Stage 2 have the highest hydraulic conductivity and therefore greater

DRVs.

3. However, all DRVs remain quite narrow when visualized using the time of flight contours.

4. Hydraulic fractures in low permeability reservoirs with strong pressure-dependent leakoff (Nolte 1986)

created by hybrid treatment (slick water and crosslink gel) overstimulate the pad size (relative to proppant

placement region) and increase the risk of fracture hits without any measurable benefits for the main

fracture conductivity.

5. There is an opportunity to redesign the “stairstep” proppant pump schedule and reduce the slick water pad

size to the technical minimum. Such pad reduction mitigates the risk of fracture hits, lowers the cost of the

pumping job, and improves the effective conductivity and final drained rock volume (DRV).

6. Given the risk of premature watering out of the Wolfcamp wells, one should use a fracture treatment plan

with conservative height growth, which favors the gel treatment with a small volume of slick water to avoid

any frac-to-water hits from the Wolfcamp to the Spraberry.

Acknowledgments - This project was sponsored by the Crisman-Berg Hughes consortium and startup funds from

the Texas A&M Engineering Experiment Station (TEES). The field data for our study came from University Lands

leases, operated by Pioneer Natural Resources and were made available for further research in a research

collaboration between the Texas Oil and Gas Institute and the Crisman Institute, Texas A&M University. Dr.

Aaditya Khanal and Dr. Jihoon Wang provided generous support by helping troubleshoot coding issues.

Nomenclature

EUR = Estimated Ultimate Recovery

FVF = Formation Volume Factor, RB/STB

MS = microseismic events

PR = Poisson’s Ratio (static), unitless

PORO = porosity, unitless

TVD = True Vertical Depth, ft

WOR = Water to Oil Ratio

YMS = Young’s Modulus (Static), psi

𝐴𝜑 = faulting regime parameter, unitless

a and m = fitting parameters of Duong’s decline model

𝐶𝑘̅̅ ̅ = average fracture conductivity, mD·ft

𝐻𝑘 = conductive fracture height for node k (equals to 5ft), ft

k = permeability, D 𝑚𝑘(𝑡) = strength of the interval source for node k, ft

2/day

𝑁 = total number of nodes, unitless

𝑁𝑝(𝑡) = cumulative oil production, STB

𝑃𝑐 = closure pressure, psi 𝑃0 = initial reservoir pressure, psi S = scaling factor, unitless

ΔS = horizontal stress anisotropy magnitude, psi

𝑆𝑡 = regional tectonic stress, psi

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𝑆𝑉 = total vertical stress, psi 𝑃𝑝 = pore pressure, psi

( )kq t = total fluid flow in node k, ft

3/day

𝑞𝑤𝑒𝑙𝑙(𝑡) = well oil production, STB/day 𝑋𝑓,𝑘 = conductive fracture half-length of node k, ft.

𝑉(𝑧, 𝑡) = fluid velocity potential, ft/month Z = unit conversion factor of 5.615, ft

3/STB

𝑧𝑐,𝑘 = center of interval-source k

𝛼 = vertical Biot’s poroelastic constant, unitless

𝛽𝑘 = angle of the interval-source k 𝜀 = regional horizontal strain, microstrain µ = viscosity, cP ∅(𝑧, 𝑡) = potential function representing pressure change ∆P

𝜑 = stress ratio, unitless

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