Rapid desorption of radium isotopes from black shale during hydraulic fracturing. 2. A model
reconciling radium extraction with Marcellus wastewater production.
Joshua D. Landis, Mukul Sharma*, and Devon Renock
Department of Earth Sciences, Dartmouth College, Hanover NH 03755
*correspondence to [email protected]
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Radium in hydraulic fracturing wastewaters derives from two isotopically distinct end-‐ members in the shale, labile 228Ra phase hosted by mineral surfaces (226Ra/228Ra atom ratio ~250) and exchangeable 226Ra hosted by organic surfaces (226Ra/228Ra ~10,000). Here we use mass balance and isotope mixing models to reconcile extraction of Ra from these phases with mechanisms of Marcellus wastewater production. Radium isotopic mass balance requires that the characteristic water-‐rock ratio between wastewater and shale is exceedingly low, on the order of 0.04, and that this ratio decreases with time during wastewater production. An evolving water-‐rock interaction drives increasing Ra concentration (=[Ra]) and 226Ra/228Ra ratios during wastewater production, mediated by increasing [Ca2+] that favors desorption of 226 Ra from organics. Our observations and models of Ra isotope geochemistry are best reconciled with observations of water and salinity mass balance, δ 18O, Na-‐Br-‐Cl, and 87Sr/86Sr if wastewater is produced by mixing of injected fluids with a limited volume of pore brine (on the order of 13% by volume), accompanied by contemporaneous extraction of excess alkaline earth elements by water-‐rock exchange. Validated using Ra isotope data, this model attributes the extreme salinity and [Ra] in wastewaters to the progressive, hydrologic enrichment of injected fluids during hydraulic fracturing.
Keywords: radium, isotope,
sorption, exchange, water, rock
Ra, shale, Marcellus, wastewater, produced water,
hydraulic fracturing wastewater
organic surface, 1-15Å
nic pore orga
water-rock ratio [Ca2+]/Na+] [Ra2+] 226 Ra/228Ra
water-rock ratio [Ca2+]/Na+] [Ra2+] 226 Ra/228Ra
Hypersaline wastewaters * generated during hydraulic fracturing of Marcellus Shale have
extraordinary Ra concentrations and require handling, regulation and disposal as hazardous
waste. Understanding wastewater is necessary for managing its future production, but faces
two outstanding puzzles– the deficit of water and excess of salt in Marcellus wastewaters, the
‘salinity dilemma’ (Engelder et al. 2014). Hydraulic fracturing requires on the order of 6x106
liters of water to be injected into the well, but just 10-‐40% of this volume returns to the well-‐
head during the course of gas production. Conversely, total salinity and concentrations of
alkaline elements, including Ra, increase dramatically and continuously in wastewater recovered
over the lifetime of production (Hayes 2009, Rowan et al. 2015). Due to a distinctive 226Ra/228Ra
isotopic composition shared between Marcellus wastewaters and Marcellus Shale, and half-‐life
restrictions on both
wastewaters reflects sources within the shale and processes that regulate their release during
fracturing. We sought to reconcile Marcellus Shale Ra source and isotope geochemistry
described in our companion work (Landis et al. 2018) with mechanisms of wastewater
Three mechanisms have been proposed for the generation of hydraulic fracturing wastewater,
based on existing geochemical and geophysical data. These are not mutually exclusive, but
might contribute to differing degrees for different elements,
Ra (half-‐life 1600 years) and
Ra (half-‐life 5.8 years), the Ra in
(I) replacement of injected water by large-‐volume brines, i.e. basin brines, sequestered in
fracture networks or isolated facies exogenous to the shale matrix (Engle and Rowan 2014,
Rowan et al. 2015, Stewart et al. 2015, Kondash et al. 2017). This mechanism is consistent with
a common genetic Na-‐Br-‐Cl signature among Marcellus wastewaters and other Appalachian
Brines (Engle and Rowan 2014, Rowan et al. 2015), with temporal trends in δ 18O data that
suggest the mixing of different water sources (Rowan et al. 2015), and with differing major
cation ratios between experimental shale leachates and wastewaters that could indicate
production of wastewaters outside the shale (Stewart et al. 2015).
*Hydraulic fracturing industry describes these waters as flowback when recovered before gas
production commences, and produced water after production; collectively we term them wastewaters as they cannot be discharged to the environment or waste facilities without substantial treatment.
(II) diffusion of salts from ubiquitous, endogenous formation water within the Marcellus
Shale nanopore network into the injected fluid volume (Balashov et al. 2015). This mechanism
is consistent with the lack of free water in the Marcellus Shale that could contribute to
wastewater volume (Engelder 2012, Engelder et al. 2014), but also accommodates a brine
geochemical signature in wastewaters by invoking the presence of a labile, capillary-‐bound ‘pore
brine’. This brine would share Na-‐Br-‐Cl signature common to other Appalachian Brines due to a
shared marine origin and basinal geologic history, but would also have acquired distinctive
Marcellus 87Sr/86Sr (Chapman et al. 2012, Capo et al. 2014, Warner et al. 2012), Li (Phan et al.
2017) and 226Ra/228Ra isotope ratios (Rowan et al. 2015) acquired through diagenesis over
geologic time scales as the brine equilibrates with adjacent mineral (clay) phases.
(III) contemporaneous water-‐rock interactions between injected fluids and the fractured
shale, which may include dissolution of soluble salts (Blauch et al. 2009) or cation exchange with
clay minerals (Renock et al. 2016); clay surfaces might be enriched in divalent alkaline elements
by membrane filtration (Engelder et al. 2014). Evidence for these interactions comes from
water and salt mass balance, indicating that pore brine alone cannot accommodate the total salt
extracted from the shale (Engelder et al. 2014); from excess divalent cations extracted during
Marcellus flowback (Barbot et al. 2013); from the rapid rate (hours to days) at which both
wastewaters and experimental shale leachates increase in salinity (Renock et al. 2016); and the
control of isovalent exchange reactions on cations that distinguish Marcellus wastewater
(Renock et al. 2016).
Experimental 226Ra/228Ra data indicate that contemporary water-‐rock reactions play a critical
role in the regulation of wastewater Ra chemistry. We proposed in a companion work that two
distinct end-‐members within the Marcellus Shale can contribute Ra to wastewaters (Landis et al.
2018). These are (1) labile 228Ra in a mineral phase with low 226Ra/228Ra (~250) that is accessible
to low ionic strength solutions such as surface waters. The 226Ra/228Ra ratio of this phase is
comparable to that of Appalachian brines, and like the pore brine described by Balashov et al.
(2015) is accessible to pure water leachates; for this reason we describe both as labile phases.
But while extraction of labile 228Ra is enhanced at high pressure, that of Na, Ca and Ba are not,
and 228Ra thus appears to be distinct from any brine per se. Importantly, neither labile 228Ra nor
any labile pore brine can reproduce high
Ra/228Ra ratios that distinguish Marcellus
The second Ra source within the Marcellus Shale is (2) exchangeable 226Ra from an organic
phase with very high 226Ra/228Ra (~104) and that is only accessible in very high [Ca2+] solutions.
The exchangeable 226Ra is physically isolated from both the mineral 228Ra source and any labile
pore brine present within the shale; this is consistent with hydrophobicity and poor water-‐
accessibility of organic pore networks (Gu et al. 2015, Zholfaghari et al. 2017). While 226Ra is
isolated from both 228Ra and pore brine, and is not accessible to low-‐ionic strength leachates, it
is rapidly released upon external additions of high [Ca2+]. In solutions of 1M Ca2+ over 10% of
total Ra can be leached from the shale in just hours. These experimental results are consistent
with the control of [Ca2+]/[Na+] on [Ra] and 226Ra/228Ra ratios observed in Marcellus wastewaters
(Landis et al. 2018). Taken together these observations indicate that contemporary water-‐rock
interactions and ion exchange processes control Marcellus wastewater Ra chemistry.
Radium in Marcellus wastewaters derives from within the shale itself, and 226Ra/228Ra ratios in
shale leachates distinguish Ra in wastewaters derived from brines and solid sources within the
shale. But the timing and mechanisms that generate extremely high [Ra] and 226Ra/228Ra ratios
in Marcellus wastewaters have not been described. Here we use isotope mass balance and
mixing models to reconcile Marcellus Ra geochemistry with the production of Marcellus
wastewater. We begin with a compilation of Ra data in Marcellus Shale and wastewaters in
order to provide a context for experimental data (Sections 4.1 and 4.2). We then apply a simple
mass balance model to describe the water-‐rock interaction between shale and wastewater
(Section 5), and an isotope mixing model to reproduce wastewater [Ra] versus 226Ra/228Ra
relationship (Section 6). We finish with a discussion of mechanisms contributing to wastewater
production in the context of Ra observations, models and water-‐rock interactions (Section 7).
The abundance of radium isotopes 226Ra (half-‐life 1600 years) and 228Ra (half-‐life 5.8 years)
reflects secular equilibrium with their respective U and Th parents, and provides insight into
processes operating over up to ca. 10 half-‐lives of each Ra daughter isotope (about 15,000 years
for 226Ra and 60 years for 228Ra). Radium thus does not record a genetic or diagenetic origin of
any brine, as might stable or long-‐lived isotope systems such as 7Li/6Li or 87Sr/86Sr. Instead 226Ra
and 228Ra concentrations in formation waters or brines reflect contemporary equilibrium of
decay, recoil and desorption with adjacent U and Th-‐bearing solid phases (Krishnaswami et al.
1982, Tricca et al. 2001).
Wastewater production and extraction of Ra during hydraulic fracturing is rapid relative to half-‐
lives of both 226Ra and 228Ra, consequently we ignore recoil and decay processes. Similarly,
decay of the long-‐lived Ra isotopes is very slow relative to desorption and this promotes a
correlation between [Ra] with total-‐dissolved-‐solids in saline aquifers (Sturchio 2001). Ra
extraction during the timeframe of hydraulic fracturing thus simplifies to a problem of dilution
and leaching (desorption plus dissolution), and the Ra isotopic composition of shale leachates
can be used to infer properties of host phases that regulate Ra release (Landis et al. 2018).
3. Experimental approach and methods.
Our experimental data are described in a companion paper (Landis et al. 2018). For these
experiments we selected three samples of Marcellus Shale that span a range of total-‐organic-‐
carbon content (TOC), Ra concentration and 226Ra/228Ra isotopic composition. These samples are
from Indiana County, Pennsylvania (2.0% TOC; undifferentiated Marcellus Shale); Chenango
County, New York (4.46% TOC; Lower Oatka Creek Mbr, Marcellus Shale); and Yates County,
New York (9.9% TOC; Upper Oatka Creek Mbr, Marcellus Shale). Thermal maturity of all rocks is
overmature and in the dry gas window. More detailed descriptions of these rocks are given in
Landis et al. (2018), Renock et al. (2016) and Niu et al. (2016). Experimental leachates of these
rocks include a pure water fraction (f1), 0.2M Ca2+ produced in situ by dissolution of carbonates
fraction (fX), and 1M CaCl2 (f2). Significant amounts of Na, Ca, Sr, Ba and S are released in pure
water, providing [Ca2+] around 0.01M (Renock et al. 2016). Analytical details are given in Landis
et al. (2018), with analysis of major elements by inductively-‐coupled plasma optical-‐emission
spectroscopy (ICPOES) and Ra isotopes by isotope-‐dilution thermal ionization mass
spectrometry (TIMS). A summary of descriptive data for these rocks is given in Table 1.
To provide a context for comparing experimental leachates to Marcellus wastewaters, we
compiled wastewater Ra data from the following sources, Rowan et al. (2011), Haluszczak et al.
(2012), Rowan et al. (2015), PADEP (2015). We report 226Ra/228Ra atom ratios, and all literature
activity data were converted using relation: N226/N228 = (A226/A228)·∙(λ228/λ 226), and λ228/λ226 ≈278,
where N specifies atom abundance, A radioactivity, and λ decay constant. We also compiled
bulk shale Ra data from reported U and Th concentrations (w/w) and calculated [226Ra] and
[228Ra] assuming secular equilibrium with [226Ra] = 3.40×10-‐7·∙[U] and [228Ra] = 4.01×10-‐10·∙[Th],
and the atom ratio 226Ra/228Ra = 840·∙(U/Th); half-‐lives of 226Ra = 1600 y, 238U = 4.47x109 y, 228Ra =
5.75 y, and 232Th = 14.05x109 y. Data sources include Leventhal et al. (1981), Lash and Blood
(2012), and Niu et al. (2016).
4.1 Comparing 226Ra/228Ra in wastewater and Marcellus Shale
Compiled data are presented in Figure 1. The Ra isotope ratios of Marcellus wastewaters (log-‐
normal distribution, with median 226Ra/228Ra = 1848; n = 79) are similar to those of compiled
Marcellus Shale measurements (226Ra/228Ra = 1507; n = 331). To estimate Ra composition of
Marcellus Shale we also used the correlation of organic matter content with 226Ra/228Ra ratios
(see Fig. 2 in Landis et al. 2018), as this approach avoids possible sampling bias towards organic-‐
rich facies (Wang and Carr 2013). Analysis of 18 wells in southwestern PA and northern VA by
Wang and Carr (2013) shows that Marcellus Shale subjected to hydraulic fracturing is typically
ca. 5% total-‐organic-‐carbon (TOC), which corresponds to a bulk rock 226Ra/228Ra atom ratio of ca.
1050. Facies with TOC > 6.5% are considered organic rich, with corresponding 226Ra/228Ra atom
In contrast to Marcellus Shale and its wastewaters, the 226Ra/228Ra composition of non-‐Marcellus
brines of the Appalachian basin is low (median = 250) and similar to that of the upper
continental crust (∼200; Wedepohl 1995; Figure 1). With some overlap in their distributions,
Marcellus wastewater Ra concentrations (median = 4550 pg L-‐1) are an order of magnitude
higher than those of Appalachian Basin brines (median = 450 pg L-‐1; Figure 1). The distinctive Ra
composition of Marcellus wastewater and its similarity to Marcellus Shale implies that
wastewater Ra is derived from solid phases of the shale with limited contributions from any
exogenous basin brines.
Direct comparison between distributions of Marcellus Shale and wastewaters is sufficient to
demonstrate that wastewaters likely derive from within the shale (Rowan et al. 2015), and that
typical wastewater appears to have somewhat higher 226Ra/228Ra compositions than typical
shale. But more detailed inference is not possible and a modeling approach is required to
understand the relationship between Marcellus Shale and wastewaters due to (1) the relative
scales of rock and water samples, where individual rock measurements reflect tens to hundreds
of grams of shale, and individual wastewater measurements are likely to integrate many
thousands of liters of wastewater extracted from millions of cubic meters of shale formation; (2)
incongruent weathering, i.e. different susceptibilities of multiple host phases to Ra extraction
from the shale, and (3) the roles that evolving wastewater ionic strength, [Ca2+] and Ca/Na ratios
play in regulating release from these phases (Landis et al. 2018).
4.1.2 Signature of Ba(Ra)SO4 scaling in Marcellus wastes
In estimating median [Ra] of wastewaters we omitted samples that fall outside of the typical
field shown in Fig. 1 due to their likely modification by precipitation of radiobarite or co-‐
precipitation with calcite. We did not exclude them from estimating 226Ra/228Ra. To justify this,
we note that thermodynamic modeling of produced water chemistries reported in Haluszczak et
al. (2012) indicates that all produced water samples are saturated with respect to barite.
Whereas bulk Marcellus shale consists of several weight-‐percent sulfur, and laboratory leaching
of the shale demonstrates extraction of sulfur even in anoxic conditions (Renock et al. 2016,
Landis et al. 2018), wastewaters are depleted in sulfur. The reasonable conclusion is that
measured wastewater chemistries typically reflect some degree of sulfate precipitation as CaSO4
Radium isotopes, and radium versus barium, should not be fractionated from one another
(Porcelli et al. 2001) once solubilized in hydraulic fracturing wastewater. However, scaling of
(Ba,Ra)SO4 will reduce the concentration of both Ra and Ba in liquids versus unaltered
wastewaters, and necessarily increase their concentrations in waste solids versus bulk shale. Of
reported wastewaters compiled from Haluszczak et al. (2012), Rowan et al. (2011), Rowan et al.
(2015), PADEP (2015) and this study, 17% fall outside of this characteristic Ra field. In
comparison, 56% of recycled or treated wastewaters fall outside of the characteristic field (Fig.
2a). Considering solid waste materials, 78% of filter cake solids from wastewater treatment
facilities (PADEP 2015) fall outside the characteristic bulk shale field (Fig. 2b).
5. Radium (isotope) mass balance during water-‐rock interaction
5.1. Estimating a characteristic water-‐rock ratio during hydraulic fracturing
Shale leaching experiments can provide insight into the Ra chemistry of Marcellus wastewaters,
provided an understanding of the water-‐rock (W-‐R) ratio for the alteration of shale by fluid
interaction during hydraulic fracturing (Renock et al. 2016),
Here Crock is the Ra concentration in the bulk shale [pg kg-‐1], Cwater is the Ra concentration in the
wastewater [pg L-‐1], γ is the extraction efficiency of Ra from the rock, and W/R is the water-‐rock
ratio of the interaction [L kg-‐1]. For these long-‐lived Ra isotopes we ignore radioactive decay
(Krishnaswami et al. 1982, 1991), and Eq. 1 is thus equivalent to the mass balance approach
used for water-‐rock interactions in hydrothermal systems (Alt-‐Epping and Smith 2001) or for Ra
exchange in aquifer systems (Sturchio et al. 2001). In the latter case the behavior of Ra is
modeled according to instantaneous first-‐order exchange reactions, and it can be shown that γ
is equivalent to the inverse of the effective dimensionless partition coefficient K.
5.2. Water-‐Rock ratio and mixing of Ra source phases
The calculation of Eq. 1 provides an upper bounding limit on W-‐R ratio of fracturing, ignoring
radiobarite as a Ra sink. With median rock and wastewater concentrations as CR/ CW = 7141 pg
kg-‐1/4550 pg L-‐1, the maximum water-‐rock ratio of fracturing is ca. 1.6 L kg-‐1 if 100% of Ra were
extracted from the rock. The effect of scaling would be to bias the W-‐R estimate too high.
Experimental Ra extraction efficiencies from the shale are on the order of 10% (Landis et al.
2018), and the W-‐R ratio typical of hydraulic fracturing must thus be an order of magnitude
lower, or less than ca. 0.10 L kg-‐1.
We stress that, because wastewater Ra must be derived from the Marcellus Shale, the
extraordinarily high [Ra] that characterizes Marcellus wastewater can only be attained through
very low W-‐R values during the water-‐rock interaction. To obtain late-‐stage Marcellus
wastewaters with high [Ra] and 226Ra/228Ra compositions congruent with that of Marcellus
Shale, W-‐R ratios spanning ca. 0.025 to 0.15 are required as shown in Fig. 1b. Our calculation
using Ra indicates W-‐R ratios similar to those using Ba, Na or Sr (Balashov et al. 2015, Renock et
al. 2016), but ours is absolute because Ra is demonstrably derived from the Marcellus Shale
itself whereas the provenance of other elements cannot be guaranteed to exclude exogenous
Understanding the W-‐R ratio of hydraulic fracturing provides a critical basis for interpreting
mechanisms of wastewater production using experimental leachate data. Very low W-‐R ratios
are not achievable in the laboratory in static batch experiments. However, using Eq. 1 we solve
Cwater for all of our leachates to predict wastewater Ra composition from a given shale facies,
using measured rock Ra concentrations, and leachate Ra extraction yields and 226Ra/228Ra
compositions. Experimental leachates can then be compared directly to wastewater data, as
shown in Figure 3. Leachates appear as mixing trajectories where [Ra] vs. 226Ra/228Ra ratio
follows increasing [Ca2+]. Importantly, trajectories defined by leachates from the Chenango Co.
(with TOC and Ra composition typical of Marcellus Shale) approximate [Ra] vs. 226Ra/228Ra
compositions in basin-‐wide wastewater, provided a W-‐R ratio of 0.04 to 0.10 (Fig. 3a). Aggregate
trajectories from various leached shale domains, as represented by our test rocks with a range
of organic content, define the characteristic Ra signature of Marcellus wastewaters. These are
shown in Figure 3b.
Comparable trajectories in 226Ra/228Ra composition among leachates, rocks and wastewaters are
attributable to mixing within each between the same two principal Ra end-‐members, mineral
and organic, and to the control of organic carbon on total Ra abundance (Landis et al. 2018).
Isotopic disequilibrium between leachates and bulk Marcellus Shale is thus governed by (1) the
stronger effective partitioning of Ra in organic surface sites relative to that derived from mineral
sites, (2) increasing susceptibility of the 226Ra organic phase to exchange at higher leachate
[Ca2+], (3) the much larger reservoir of Ra associated with shale organic carbon.
5.3. Constraining the physical scale of reactive rock surfaces
Low W-‐R ratios are necessary to explain Ra mass balance and isotope mixing, but we require a
physical model that can accommodate W-‐R ratios on the order of 0.04. Such low ratios require
an extraordinary rock surface area that is ionically accessible to injected fluids. This is likely
achieved within the shale pore network where pores average ca. 3 nm diameter, or smaller for
pores within organic matter (Gu et al. 2015). If a pore is considered to be a fluid-‐filled sphere,
i.e. a single pore model, the rock enclosing the pore can be considered to have a reactive layer
subject to leaching. The thickness of this layer defines the effective water-‐rock (W-‐R) ratio for
the pore. A pore of diameter 3 nm has a volume of 14 nm3 calculated as 4/3πr3. A reactive layer
of thickness t has a volume of 4/3π(r’3-‐ r3), where r’ = r + t. This reactive rock volume is
converted to mass assuming a bulk density of 2.6 g cm3. A pore volume to reactive rock mass
ratio (W-‐R) of 0.04 requires a thickness of ca. 15 Å. Smaller pores require thinner reactive layers
to accommodate the W-‐R relationship.
In a dynamic diffusion model, Balashov et al. (2015) estimated that a volume of injected water
interacts with ca. 30x its volume in pore space to produce wastewater salinity. Balashov et al.
presume that the pore volume is filled with formation brine. Their estimated ratio (α) of
injectate to pore volume is 0.03, which is comparable to our volume-‐mass (W-‐R) estimates
based on Ra isotopes. Pore volume can be converted to a reactive rock volume using the
geometric relationship as above, where the volume ratio of pore to rock = r3 /(r’3-‐ r3). Rock
volume is again converted to mass using a density of 2.6 g cm-‐3. W-‐R can thus be calculated
from α as follows,
From this relation the reactive layer thickness (t=r’-‐r) can be estimated. Thickness of just 1.5 Å
provides a W-‐R ratio of 0.04.
In this estimate we have omitted any contribution to water volume from formation brines that
may be present in the pores. While in their model Balashov et al. (2015) presume that soluble
elements in the shale reflect pore volume that is filled with formation brine, our Ra leaching
data demonstrate that the bulk of wastewater Ra is not derived from a labile brine but instead
from organic surfaces; in this case our omission of the pore brine volume is valid if either
formation salts are not present as brine as assumed, or if Ra is extracted from additional pore
volume which is not water saturated. If we follow Balashov et al. in assuming that 2% of the
shale is water-‐saturated pore volume, and further assume that this water fully equilibrates with
injected fluids (which seems unlikely), the total water volume in the W-‐R interaction increases
by a factor of 30. This case provides an upper bounding limit on reactive rock thickness
= 𝛼 ∙
!! !!! !! !
necessary to provide a W-‐R ratio of 0.04 and converges to that of the single pore model, which
A reactive rock layer thickness between 1.5 and 15 Å approaches the order of a chemical bond
length and thickness of the Double-‐Electrical Layer at shale clay surfaces (Kwon et al. 2004),
suggesting that the physical constraints for W-‐R ratios on the order of 0.04 can be satisfied
within the ionic exchange environment of the shale. Future work might focus on reconciling
geophysical constraints with the chemical W-‐R estimated here using Ra.
6. Isotope mixing models predict wastewater Ra composition
Based on an understanding of the physical scale of the shale-‐wastewater W-‐R interaction,
mixing between mineral 228Ra and organic 226Ra end-‐members, and the role of [Ca2+] in releasing
organic 226Ra, we constructed isotope-‐mixing models to see if we could reproduce the [Ra] vs.
predicted by the model is derived from standard isotope mixing as described in Appendix 1.
Briefly, Ra isotopic composition of a leachate is predicted by the following:
𝑄!"# = !
Here Qmix is the 226Ra/228Ra isotopic ratio (Quotient) of the leachate, γm is the extraction
efficiency of total rock 226Ra that is attributable to the m phase (mineral Ra atoms extracted per
kilogram rock), γo that of the organic phase, CR226 is the total concentration of 226Ra in the rock
[atoms kg-‐1]; the mass of rock subjected to leaching, R, is omitted as written for a unit mass of 1
Total [Ra] is predicted as a function of [Ca2+] as follows:
[𝐶𝑎 !! ] =
𝑦! = 𝑓 𝐶𝑎 !!
Ra/228Ra isotopic composition that characterizes Marcellus wastewaters. Radium composition
!! ∙!!!!" ∙!!! ∙!!!!" !!" !! ∙!!!!" ! ∙!! !! ! !!
!!!" ∙ !!" ! !
!! !!! !! !! ! !!
Coupling Eqs. 4 and 5, our model thus assumes that 226Ra yield of the organic phase (γo)
increases with decreasing W/R, but scaling between the two is a fitted parameter mediated by
increasing concentrations of Ca2+. We adjusted the mixing model to reproduce wastewater data
by assuming a range of [Ca2+] vs. γo relationships. Organic Ra yield (γo) is constrained at ca. 50%
in 1M [Ca2+] as derived by Landis et al. (2018). Total Ca2+ and Ra mineral yields (γm) might also
be adjusted as fitted parameters but here are assumed to be constant for all W/R. Ca2+ yield is
constrained at 5-‐10%, similar to observed yields in pure water and exchangeable fractions
(Renock et al. 2016, Stewart et al. 2015). Mineral Ra yield (γm) is constrained at 0.5-‐1%, similar
to those observed in pure water and deduced from CaCl2 leachates (similar amounts of mineral
Ra are extracted both in pure water at high pressure and in 1M CaCl2 at atmospheric pressure).
Within these constraints we considered a range of mixing scenarios (described in Table A1 and
Figure A1) instead of attempting a robust fit of the wastewater data since the relationship
between organic yield (γo) and [Ca2+] is not well known at the relevant scales and conditions.
Nonetheless, all scenarios reproduce wastewater Ra data as shown in Fig. 4. In all scenarios the
critical parameters [Ra], 226Ra/228Ra, [Ca2+] and ionic strength are comparable to wastewater
measurements, without requiring external sources of Ra or Ca as from basin brine. That is, all
wastewater data can be explained by the leaching of Ra from the fine shale fabric as evident in
the hand sample, and does not require invocation of large-‐scale features such as isolated facies,
fracture networks or basin brines. Isotope mixing model results suggest that the shale mineral
90% derived from organics by leaching (Table A1).
Wastewater time series data from Greene County, PA reported by Rowan et al. (2011) provide a
test case for assessing rapid water-‐rock interactions for a single fracture network. In this case
saline, Ra-‐enriched wastewater from a previous well was recycled as the fracturing fluid.
Salinity, [Ra] and 226Ra/228Ra ratio of wastewater increase with time beyond that of the injectate,
proceeding rapidly over days following initiation of flowback and continuing to increase for over
one year (Figure 4b; Rowan et al. 2011, Rowan et al. 2015). A three-‐member mixing scenario
between recycled injected fluid, extracted mineral and organic phases of the shale, and a
decreasing W-‐R ratio over this time period, can explain the observed evolution in wastewater Ra
composition as illustrated in Fig. 4b. In this scenario, the fraction of Ra derived from the
Ra phase likely contributes ca. 10% of total wastewater Ra (by mass) with the balance of ca.
injected fluid is ca. 47% on the first day of wastewater production, dropping to ca. 11% by the
end of one year. Radium contributions from mineral and organic phases of the shale evolve
from 6% and 48% on the first day, to 5% and 84% by day 438, respectively.
7. Reconciling Ra isotope geochemistry with Marcellus wastewater production
Three mechanisms are proposed for wastewater production, (I) mixing with exogenous basin
brine, (II) diffusion from endogenous pore brine, or (III) contemporaneous water-‐rock reactions.
These are not mutually exclusive. However, because wastewater Ra must be derived from solid
phases within the Marcellus Shale itself, it provides an absolute tracer of physic-‐chemical water-‐
rock interactions that govern wastewater production and may thus help to discriminate
contributions from different mechanisms.
Radium isotope mass balance requires that the characteristic W-‐R ratio of hydraulic fracturing
must be on the order of 0.04. With ratios of this order, the extraction of endogeneous elements
in the shale matrix including Na, Ca, Ba and Sr, can reproduce wastewater salinity without
contributions from exogenous large-‐volume brines (I). This is an important observation because
Ra or Sr isotopes alone cannot rule out the role that fracture networks could play in transporting
exogenous fluids through the fracture network (e.g., Warner et al. 2012). The rapid rate at
which Sr and Ra can be leached from experimental shale samples suggests that any brine routed
through the Marcellus Shale would rapidly acquire a Marcellus signature irrespective of its
source. However, a low W-‐R ratio for the fluid-‐rock interaction and mass balance considerations
must still apply. Following are additional insights and considerations from Ra isotopes that
discriminate mechanisms of wastewater production.
7.1. Salt and water mass balance in Marcellus wastewater
The limited amount of water available within the Marcellus Shale (Engelder 2012, Engelder et al.
2014) and the small wastewater volume recovered at the well head, relative to the amount
injected, argue further against the role of exogenous brines (I) in wastewater production – the
system is water limited. Analysis of Marcellus well logs from New York shows that on average
the porosity of the shale ranges from 4.7% to 7.9% with a permeability of about one hundred
nano-‐Darcy. We determined averages of total porosity (=𝜙) and pore volume occupied by water
(=water saturation, Sw) in the Marcellus Shale using density, resistivity and gamma-‐ray logs for
three wells in New York (Advanced Resources International 2011) and used these data to
calculate the mass of water present per unit mass of the shale as follows:
where 𝜌 denotes density and subscripts ‘B’ and ‘R’ denote formation water and rock,
respectively. Assuming that the densities of the brine and shale are 1.1 g cm-‐3 and 2.73 g cm-‐3,
respectively, we find that ratio varies from 2 mg g-‐1 to 12 mg g-‐1 with an average of 5 mg g-‐1 or
With an estimated 0.5% of shale mass comprised of water and a hydraulic fracturing W-‐R ratio
of 0.04, the contribution of pore brine or formation water to wastewater volume is less than
13% (calculated as 1/(0.04÷0.005)). This assumes no additions of brine from isolated fractures
Following our assumptions, the balance and majority of wastewater volume is comprised of the
original injected fluid rather than formation water. Given this, late stage produced water cannot
represent pure brine as proposed by Kondash et al. (2017). With TDS exceeding 200,000 mg L-‐1,
the dilution of this wastewater by a factor of ca. 10 implies a brine with impossibly high
concentrations exceeding 200% by weight. Engelder et al. 2014 described this as the ‘salinity
dilemma’. Water and salinity mass balance in wastewaters are not satisfied strictly by
extraction of brines, and additional mechanisms must be invoked.
7.2. Geochemical tracers of labile brine versus water-‐rock interactions
7.2.1 Na-‐Br-‐Cl and δ18O
The contribution of endogenous pore brines (II) to wastewater salinity is necessary to explain
some geochemical tracers and their evolution during wastewater recovery, but insufficient to
explain others. Contributions of brine are necessary to reconcile wastewater Na-‐Br-‐Cl signature,
which is derived from paleo seawater and requires contributions from a liquid brine rather
dissolution of soluble salts (Engle and Rowan 2014, Rowan et al. 2015). Similarly, δ18O trends in
wastewaters reported by Rowan et al. (2015) suggest that mixing of liquid end-‐members within
the shale is dominated by a brine component. However, in the Rowan et al. data recycled
wastewaters were reinjected for fracturing and the wastewater signature is approximately
uniformly depleted in δ18O, about -‐3 to -‐1 (Rowan et al. 2015); the apparent degree of mixing
between injected fluids and endogenous brine is limited, as the endmember brine δ18O
signature is unknown. Conventional brine δ18O values measured by Dresel and Rose (2010) span
-‐6 to +2, but are highly sensitive to alteration by depleted groundwaters with δ18O compositions
lying on the meteoric water line. Rowan et al. (2015) conclude that salinity and not δ18O is the
strongest argument for mixing between distinct fluids in the generation of wastewaters.
7.2.2. alkaline earth elements
Consistent with the extraction of divalent cations from an exchangeable phase, Barbot et al.
(2013) demonstrate non-‐conservative behavior of divalent cations versus Br and Cl during
flowback. Unlike conventional brines, low salinity wastewaters are depleted in alkaline earth
elements relative to Br and Cl. Over time the cations Mg, Ca, Sr, and Ba become more enriched
in wastewaters relative to Br or Cl. As the divalent elements increase but both SO4 and CO3
decrease with time (Barbot et al 2013), this trend might be interpreted as the continued
extraction of alkaline cations from the rock in late wastewaters rather than their loss to scaling
in early water as Barbot et al. imply.
In the data of Rowan et al. (2015) we also see that while Na-‐Br-‐Cl may increase by a factor of ~2-‐
3 during wastewater production, Mg, Ca, and Sr increase by a greater amount, and Ba and Ra
may increase by factors up to 10 over the same time period. Ba and Ra are principally derived
from the shale by ion exchange reactions, from clays (Renock et al. 2016) and organics,
respectively (Landis et al. 2018), and thus provide sensitive indicators of water-‐rock interaction.
Both [Ba] and [Ra] increase most rapidly in wastewaters among all cations. Critically, 226Ra/228Ra
also increases while Ba/Ra remains about constant, suggesting that the increase in [Ba] and [Ra]
is attributable to their enhanced extraction as wastewater salinity increases, rather than to
exhaustion of sulfate and cessation of radiobarite precipitation; the latter processes would
affect both Ra isotopes identically.
Both the occurrence of scaling and isovalent exchange with other alkaline earth elements likely
contribute to incongruence of major element ratios, e.g., Ca/Na, between experimental
leachates and wastewaters as observed by Stewart et al. (2015).
7.2.3. lithium and strontium isotopes
Both Li and Sr isotopes in wastewaters bear an isotopic signature attributed to Marcellus clay
mineral diagenesis (Phan et al. 2016, Chapman et al. 2012), acquired during brine emplacement
and residence in the shale, and distinct from other Appalachian brines (Warner et al. 2012).
Water soluble, NH4-‐exchangeable and clay interlayer (HCl-‐extractable) fractions extracted from
shale all show Sr isotope ratios (0.709-‐0.711) consistent with (or slightly lower than) wastewater
0.75; Stewart et al. 2015; Balashov et la. 2015). Thus, while experimental shale extractions are
compatible with wastewater composition, Sr isotopes do not discriminate between
contributions from any labile brine and Sr extracted from clays by water-‐rock reactions, and thus
do not offer insights into the mechanisms or timescale of extraction.
7.2.4. radium isotopes
Radium isotopes distinguish leachable phases in the shale. The 226Ra/228Ra ratios of water
leachates are low (~250) at both low and high pressure, demonstrating that labile brine cannot
generate the distinctive 226Ra/228Ra signature of Marcellus wastewaters (Landis et al. 2018).
Additional processes must be invoked to explain wastewater 226Ra/228Ra. Moreover, if water-‐
extractable salts reported here and elsewhere (Stewart et al. 2015, Balashov et al. 2015, Renock
et al. 2016) are attributed to pore brine within the shale matrix as Balashov et al. have done,
corresponding concentrations of Na and Ca in the brine would exceed 1M and would be
sufficient to extract organic-‐derived Ra with high 226Ra/228Ra composition, if this solution were in
contact with 226Ra-‐bearing phases. This does not appear to be the case. The high 226Ra/228Ra
ratios and high [Ra] that distinguish Marcellus wastewaters can only be extracted from the
Marcellus Shale by physical modification of the shale, as we have done experimentally with
additions of high [Ca2+] (Landis et al. 2018) and as must occur during hydraulic fracturing.
7.3. A mechanistic model reconciling geochemical and geophysical data
Sr/86Sr ratios (0.710-‐0.712). The remaining refractory fractions are highly radiogenic (0.73-‐
We have shown that the 226Ra/228Ra ratios of Marcellus wastewater can be attributed to mixing
of distinct end-‐members within the shale, regulated by water-‐rock reactions and proceeding
over a timescale of days, consistent with the duration of flowback recovery. The evolution in
mineral and exchangeable, organic phases within the shale matrix. The source of Ca2+ in
wastewater is likely a mixture of contributions from salts, carbonate dissolution, clay surface
exchange, and endogenous pore brine. Around 5% of total Ca in the shale is water-‐soluble
(Renock et al. 2016, Stewart et al. 2015) and consistent with a labile pore brine component, with
another 10-‐20% exchangeable from clays (Stewart et al. 2015). Carbonate dissolution likely
constitutes only a minor source of Ca2+ to wastewaters -‐-‐ injected fluids with pH ~2 have only
enough free acidity to dissolve