Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells

Accepted Manuscript Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells

Reza Taherdangkoo, Alexandru Tatomir, Tega Anighoro, Martin Sauter PII: DOI: Reference:

S0169-7722(18)30239-0 https://doi.org/10.1016/j.jconhyd.2018.12.003 CONHYD 3449

To appear in:

Journal of Contaminant Hydrology

Received date: Revised date: Accepted date:

3 August 2018 5 November 2018 19 December 2018

Please cite this article as: Reza Taherdangkoo, Alexandru Tatomir, Tega Anighoro, Martin Sauter , Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells. Conhyd (2018), https://doi.org/10.1016/j.jconhyd.2018.12.003

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ACCEPTED MANUSCRIPT Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells

Reza Taherdangkoo*, Alexandru Tatomir, Tega Anighoro, Martin Sauter Department of Applied Geology, Geosciences Center, University of Goettingen, Goldschmidtstr. 3, D-37077

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Göttingen, Germany

*Corresponding author

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Email: [email protected]

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Tel.: +49-1573-9533348

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ACCEPTED MANUSCRIPT Abstract Hydraulic fracturing in shale/tight gas reservoirs creates fracture network systems that can intersect pre-existing subsurface flow pathways, e.g. fractures, faults or abandoned wells. This way, hydraulic fracturing operations could possibly pose environmental risks to shallow groundwater systems. This paper explores the long-term (> 30 years) flow and transport of fracturing fluids into overburden lay-

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ers and groundwater aquifers through a leaky abandoned well, using the geological setting of North German Basin as a case study. The three-dimensional model consists of 15 sedimentary layers with

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three hydrostratigraphic units representing the hydrocarbon reservoir, overburden, and the aquifer

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itself. The model considers one perforation location at the first section of the horizontal part of the well, and a discrete hydraulic fracture intersecting an abandoned well. A sensitivity analysis is carried

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out to quantify and understand the influence of a broad spectrum of field constellations (reservoir properties, abandoned well properties and its proximity to hydraulic fractures) on the transport of

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contaminants to shallower permeable strata. The modeling results indicate the abandoned well spatial properties and its distance from the hydraulic fracture are the most important factors influencing the

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transport of fracturing fluids to the shallow aquifer. It is observed that even for different field settings,

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only a limited amount fracturing fluid can reach the aquifer in a long-term period.

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Keywords: fracturing fluid; hydraulic fracturing; abandoned well; numerical modeling; North Ger-

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man Basin; groundwater contamination.

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ACCEPTED MANUSCRIPT 1 Introduction Unconventional hydrocarbon reservoirs such as shale/tight gas reservoirs are characterized by low permeabilities and even natural fractures do not provide efficient pathways for fluid flow from reservoir to production wells [1]. The development of unconventional reservoirs requires stimulation techniques such as hydraulic fracturing (HF) aimed at creating artificial fracture networks and increasing

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local permeability [2]. The process of hydraulic fracturing is characterized by injecting fracturing fluid through perforated locations in a wellbore at a bottom-hole pressure higher than the minimum

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principal stress [3]. Hydraulic fracturing enhances local permeability by creating new fractures, im-

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proving fracture-fracture interaction, re-opening and further propagation of pre-existing fractures [4].

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Hydraulic fracturing operations may possibly imply a variety of environmental risks [5]. One of the common concerns is the upward migration of contaminants (e.g. HF fluid, and formation fluids) from

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hydrocarbon bearing formations towards shallow aquifers [2,5]. However, the upward migration of contaminants is generally constrained by the sedimentary basin properties such as thickness of low permeable overburden and a low vertical hydraulic gradient, the driving force. Furthermore, the verti-

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cal migration of contaminants is bounded by the density of formation fluids and the limits of hydrau-

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lic fracturing (e.g. injection pressure, and operation duration), this in turn affects fracture aperture

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growth, fracture propagation, pressure propagation and stimulated volume of the reservoir [6–8]. The presence of natural preferential pathways such as faults and fractures or anthropogenic pathways such

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as leaky wells and a driving force are important components that will inadvertently affect the upward migration of fluids [8].

The majority of unconventional oil and gas fields have a long history of conventional hydrocarbon production and exploration (e.g. Pennsylvania) [9]. In mature sedimentary basins (e.g. Texas) [10] with a high density of production wells, hydraulic fractures may intercept aged abandoned wells or their vicinity (frac hit) [9,11]. The possibility of frac hit primarily depends on depth of the horizontal well, its location and the extent of hydraulic fractures [12]. If frac hit materializes, depending on the well hydraulic characteristics, rapid vertical transport of fluids to surface or groundwater resources may occur [1,13]. 3

ACCEPTED MANUSCRIPT In hydrocarbon field development, the wells are abandoned either immediately after drilling due to unsuccessful operation or they are abandoned after reservoir depletion [14]. The standard practice employed in well abandonment procedure includes; emplacing cement plugs in the wellbore above several zones to isolate different intervals including water and hydrocarbon bearing zones. The wellbore barrier system comprises the cement sheath located along the annulus between the outer casing

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and host rock, cement-outer casing bond, and cement-host rock bond [15–17]. Note that wellbore integrity could be defected by poor well construction (i.e. improper cementing and completion), ce-

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ment degradation, casing failure, and formation damage around the wellbore. The outside of the cas-

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ing could also be fractured or damaged due to production and injection activities during the lifetime of the well. All of the above failure scenarios could provide pathways for vertical fluid flow into overly-

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ing layers [15,18]. However, the most probable source of contaminant transport is through permeable flow paths outside the casing [19].

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Well abandonment practice varies from well to well and depends on several factors such as well depth, well diameter, casing condition, casing material, hydrological setting, local regulations, etc

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[20,21]. A detailed description of well completion and abandonment must be taken into account to

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properly evaluate the probability of contaminant leakage through the abandoned well. Data needed for

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such evaluation could be provided from field and laboratory experiments [22]. Many wells in mature sedimentary basins were drilled and abandoned before today's rigor-

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ous plugging standards [14,23]. In addition, quite a number of old abandoned wells remain unplugged [24,25], and adequate documentation on their locations and spatial characteristics are rarely available [14]. Unplugged or improperly plugged abandoned wells provide preferential pathways for transport of fluids to the overlying aquifers and this poses threats to groundwater systems [1,21,26]. A couple of research projects have investigated groundwater contamination scenarios from shale gas development. However, a few studies addressed the potential contamination transport through leaky abandoned wells (e.g. Reagan et al. [1]; Brownlow et al. [10]). The objective of this study is to build a three-dimensional field-scale generic model to explore the long-term transport of HF fluid through a leaky abandoned well when it is affected by fracturing operation (Fig. 1). A comparison 4

ACCEPTED MANUSCRIPT study is performed to select the proper modeling approach for representing the abandoned well. The studied reservoir is the Posidonia Shale in the North German Basin. A parametric study is designed to explore a wide range of field configurations and rank the significance of key parameters such as abandoned well permeability and its proximity to induced fractures on vertical transport of HF fluid

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through an abandoned well.

Fig. 1. A schematic of frac hit to an abandoned well.

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2 The North German Basin

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The reservoir of interest is situated within the North German Basin (NGB) which is part of intracontinental Central European Basin system [27]. The development of the NGB system was initiated in the

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Late Carboniferous to Permian, owing to rifting, subsidence, and associated volcanism subsequent to

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the Variscan Orogenesis [28,29]. The reservoir is the organic-rich Lower Jurassic Posidonia Shale [30]. The domain consists of 15 layers of varying thickness. The 15 layers include three hydrostratigraphic zones representing the hydrocarbon reservoir, overburden, and aquifer. The depth information and hydraulic parameters for each layer are listed in Table 1 [31]. Table 1. Summary of basic parameters used in the model [31]. Layer no. 1 2 3 4 5 6 7

Lithostratigraphic units Quaternary sand Tertiary fine sand Tertiary Rupelian clay Tertiary silt/clay E. Cretaceous claystone E. Cretaceous Wealden M. Jurassic claystone 1

Thickness (𝑚) 50 50 50 50 450 350 100

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Vertical permeability (𝑚2 ) 5 × 10 −12 5 × 10 −13 1 × 10 −17 1 × 10 −15 1 × 10 −17 1 × 10 −16 1 × 10 −15

Porosity 0.3 0.2 0.1 0.1 0.1 0.1 0.1

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1 × 10 −14 1 × 10 −15 1 × 10 −17 1 × 10 −14 1 × 10 −17 1 × 10 −14 1 × 10 −17 1 × 10 −19

200 50 100 30 70 30 120 35

M. Jurassic sandstone L. Jurassic marlstone 2 M. Jurassic claystone 1 M. Jurassic claystone 1 M. Jurassic claystone 2 M. Jurassic claystone 2 M. Jurassic claystone 3 Posidonia shale

0.15 0.1 0.05 0.15 0.05 0.15 0.05 0.01

3 Conceptual model descriptions

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A three-dimensional model with a vertical dimension of 1735 𝑚, lateral extent of 2500 𝑚, and width

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of 1200 𝑚 is constructed. The sedimentary layers are assumed as homogeneous. The depth-varying

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relationships were applied to calculate temperature and salinity throughout the domain to better reflect the uniqueness of the study area. The average ground temperature in Germany is 8.2 °𝐶 [32], assum-

ences in fluid density thus

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ing an average geothermal gradient of 0.04 ℃/𝑚 [33,34]. The temperature gradient induces differdriving groundwater flow [35]. The following equation is used to com-

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bine the geothermal gradient with the depth information [34]: 𝑇𝑑𝑒𝑝𝑡ℎ = 𝑇0 + (∇𝑇 × 𝑑𝑒𝑝𝑡ℎ)

(1)

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where 𝑇𝑑𝑒𝑝𝑡ℎ is temperature at a specific depth, 𝑇0 is the ground temperature, ∇𝑇 is the average geothermal gradient. The average vertical salinity gradient of 0.15 𝑔/𝑙, which is in the range reported for

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the NGB [34,36–39], is considered in the entire domain. We do not take into account the lateral variation of salinity; therefore, any regional or local change in salinity gradients is ignored. The depth-

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dependent salinity is calculated by the following equation [34]: 𝑆𝑑𝑒𝑝𝑡ℎ = ∇𝑆 × 𝑑𝑒𝑝𝑡ℎ

(2)

A constant-head pressure boundary calculated from hydrostatic pressure and reservoir pressure gradient is imposed along the lateral sides of the domain. The atmospheric pressure is assigned at the top boundary. The initial steady-state condition in the overburden and reservoir layer is calculated in the same manner as the side pressure boundary conditions. A no-flow boundary is set at bottom of the domain thus preventing fracturing fluid from leaving the system. Overpressure is a common feature of shale gas formations which is mainly due to the combination of very low permeability and the genera6

ACCEPTED MANUSCRIPT tion of significant internal gas [40], hence the shale is considered overpressurized with a pressure gradient equal to 13 𝑘𝑃𝑎/𝑚 [41]. The overburden and reservoir pore fluid properties (e.g. density and viscosity) depend upon certain factors such as temperature, pressure, and fluid composition (e.g. salt concentration in the water phase). The density (function of P, T, salinity) and dynamic viscosity (function of T, salinity) of the brine are then calculated using Batzle and Wang [42] equations. Fluid

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density increases with an increase in pressure and salinity and it has an inverse relationship with temperature. In our model, brine density increases linearly with depth and is equal to 1215 𝑘𝑔 ⁄𝑚3 at

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bottom of the reservoir.

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Herein, we do not model a stimulated reservoir volume (SRV); instead, a fully developed discrete fracture within the shale reservoir is considered. The fracture is modeled as a lower dimensional geo-

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metric object. The most commonly used two-dimensional models to approximate fracture propagation in the design of hydraulic fracturing treatments are the Perkins-Kern-Nordgren (PKN) and Khristia-

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novic-Geertsma-de Klerk (KGD) models [43]. PKN model assumes the fracture as confined within the pay zone with an elliptical cross section in the vertical plane. This model assumes that formation

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stiffness is concentrated in the vertical cross sections perpendicular to the fracture propagation direc-

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tion. The PKN model applies when the fracture length is much larger than its height [44,45]. In KGD

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model, the fracture has a constant and uniform height and a rectangular cross-section in the vertical plane. The KGD model assumes the formation stiffness to be concentrated in the horizontal cross

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sections perpendicular to the direction of fracture propagation. This assumption holds if the fracture height is much larger than its length [46–48]. The PKN model is considered for simulating the hydraulic fracture geometry. A straight planar height-fixed fracture, confined, and horizontally extending through the reservoir layer is assumed. The hydraulic fracture has a half elliptic cross-section, strike at 𝑁45°𝐸, a dip of 45° towards southwest, and 45° slope. The abandoned well hits the middle of the hydraulic fracture plane. The well is centered vertically in the domain, and modeled as having a circular cross section with a radius of 0.15 𝑚. Hydraulic fracturing is usually conducted in multiple stages to produce fracture networks. For each stage, a certain proportion of the well casing is perforated for connecting the well to the reservoir. The 7

ACCEPTED MANUSCRIPT highly pressurized fracturing fluid containing proppants, and other additives is then injected into the reservoir through the perforated area to create the fracture network [49]. This work, however does not aim at representing an actual fracking operation in terms of fracture propagation, dilatation and fracture network creation. The model assumes a perforation location at the first segment of the horizontal well from which, FH fluid is injected into the reservoir. The perforation location is directly connected

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to the fracture, and hence the fluid is only injected into the fracture. The consideration of a fully developed fracture prior to injection and HF fluid injection from a single perforation location can be

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seen as conservative assumptions. The graphical illustration of the conceptual model is presented in

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Fig. 2.

Fracturing fluid is a water-based chemical mixture comprising a base fluid (e.g. water / brine), friction

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reducers, scale inhibitors, corrosion inhibitors, surfactants, and other additives [50]. The model considers the HF fluid components as a pseudo-component (i.e. a conservative tracer) dissolved in the

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water phase. This means the model does not account for sorption and biological/chemical degradation processes. We acknowledge that modeling HF fluid as an inert tracer represents a conservative (less

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favorable) scenario and leads to an overestimation of contamination distribution in the aquifer [51].

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Note that our model takes into account buoyancy resulting from the density difference between the

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HF fluid and the brine. Schwartz [52] suggests that through a certain transport distance, the probability of simultaneous migration of liquid and methane gas is relatively low because of the contrast in

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their physical and chemical properties. Therefore, this study does not consider multiphase processes which require full representation of fluid and gas migration. The focus is solely on the transport of a water-based tracer in a fully saturated porous media.

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ACCEPTED MANUSCRIPT

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Fig. 2. Conceptual model setup. 3.1 Base case scenario

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The base case scenario considers geological setting of the North German Basin to systematically explore the leakage of contaminants from a shale gas reservoir through a leaky abandoned well into

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shallow aquifers. To realistically represent the lifetime of a typical horizontal well, each simulation comprises six different temporal periods namely: (1) reservoir initial condition prior to fracturing; (2)

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injection of HF fluid into the reservoir; (3) shut-in period; (4) first production period; (5) second pro-

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duction period; and (6) post-production period. The description of six simulation stages is presented in table 2. The first period models the steady state initial conditions through the system prior to opera-

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tion. Afterwards, the model utilizes the initial conditions generated from the first run to simulate the injection of HF fluid. During the injection period, fluid is injected into the reservoir from the perfora-

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tion location at a constant rate of 3.15 𝑚3 ⁄𝑚𝑖𝑛 for 2.5 days [53]. This is equivalent to injection volumes of 11356 𝑚3 [10]. Stage 3 represents a 5-day shut-in period, in which there is neither injection nor abstraction of fluid in the domain. Afterwards, first and second productions periods take place and last interruptedly for 2 and 13 years, respectively. During the first production period, the production rate is 16 𝑚3 ⁄𝑑 and it is lowered to 3.2 𝑚3 ⁄𝑑 in the second period. In stage 6, the production is stopped and no fluid enters or leaves the domain. This stage models the continued migration of HF fluid into the shallow aquifers until 15 years after the production period.

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ACCEPTED MANUSCRIPT Table 2. The different stage of simulations. No. 1 1 3 4 5 6

Stage Initial condition HF fluid injection Shut-in First production Second production Post-production

Duration 2.5 days 5 days 2 years 13 years 15 years

Description Reservoir condition prior to HF operation Injection of 11,356 𝑚3 HF fluid into the shale reservoir Relaxation time, pressure dissipation Production of 16 𝑚3 ⁄𝑑 from the horizontal well Production of 3.2 𝑚3 ⁄𝑑 from the horizontal well Well is plugged and abandoned

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The data needed for representing the abandoned well data (e.g., permeability) are collected from HF

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fluid, methane, and CO2 leakage modeling studies. The parameters values selected for the reference scenario are chosen to better understand the leakage of HF fluid through an abandoned well and may

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not realistically reflect an actual fracturing operation. Table 3 summarizes the input parameters for the

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numerical simulations. The parameters for sensitivity analysis were selected based on results from previous studies (e.g. Reagan et al. [1]; Taherdangkoo et al. [54, 55]; Birdsell et al. [53]) aimed at

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revealing the most influential factors determining upward migration of contaminants in the subsurface. Table 4 presents the base case parameters and their ranges of variations for the sensitivity study.

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Table 3. The general model input parameters.

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Parameter Domain length Domain width Overburden thickness Reservoir thickness Abandoned well porosity Abandoned well radius Surface temperature Salinity gradient Geothermal gradient Hydraulic fracture half-length, 𝐿𝑓 Hydraulic fracture width, 𝑊𝑓 Hydraulic fracture permeability, 𝐾𝑓 Hydraulic fracture porosity, ∅𝑓 Hydraulic fracture height, ℎ𝑓 Molecular diffusivity of solutes in pure fluid Water compressibility Fracturing fluid density Longitudinal dispersivity Transverse dispersivity

Unit 𝑚 𝑚 𝑚 𝑚 𝑚 𝑚 ℃ 𝑔⁄ (𝑙. 𝑚) ℃/𝑚 𝑚 𝑚 𝑚2 𝑚 𝑚2 /𝑠 1/𝑃𝑎 𝑘𝑔/𝑚3 𝑚 𝑚

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Value 2500 1200 1600 35 0.15 0.15 8.2 0.15 0.04 150 8 1 × 10−11 0.3 35 1 × 10 −9 4.4 × 10−9 1000 10 1

Source

[31] [31] [56,57] [14,57–59] [32] [36] [33] [3,60,61] [3,61] [61] [3] [31] [31] [31,41] [31] [31]

ACCEPTED MANUSCRIPT Table 4. Model parameters and range. Parameter Abandoned well permeability, 𝐾𝑎 Reservoir permeability, 𝐾𝑅 Reservoir porosity, ∅𝑅 HF injection volume, 𝑉𝐹𝐹 Distance of fracture plane to well, 𝐷𝑤 Reservoir overpressure gradient, (𝑑𝑃/𝑑𝑧)𝑅

Unit 𝑚2 𝑚2 𝑚3 𝑚 𝐾𝑃𝑎/𝑚

value 1 × 10−12 1 × 10−19 0.01 11356 13

Variation 1 × 10 −17 − 1 × 10−11 1 × 10 −21 − 1 × 10−18 0.01 − 0.05 11000 − 15000 0 − 15 10 − 17

Reference [14,56–58,62–65] [1,10,66] [41,66–68] [10,53,69] [10,41,70]

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3.2 Conceptual modeling approaches for the abandoned well

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Modeling the leaky abandoned well as a three-dimensional sub-domain fully reflects its spatial properties and addresses the upward movement of fluids from the reservoir through the well with suffi-

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cient accuracy. However, three-dimensional simulation of the well implies a high degree of complexi-

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ty in the model and thus compromises its cost efficiency. A comparative study was carried out to select the proper modeling approach for representing the well. The comparison was implemented by

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considering the well as a three-dimensional object (case I) and a two-dimensional object (case II). For case I, the abandoned well with radius 0.15 𝑚 is modeled as a cylindrical porous medium with a

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higher permeability compared to the adjacent formation while for case II the well is defined as a pla-

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nar fracture, with rectangular cross section. For case II, the planar fracture has a width of 0.5 𝑚, thickness of 0.14 𝑚 corresponding to a circular cross section with radius of 0.15 𝑚. The same physi-

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cal properties (effective porosity and intrinsic permeability) are assigned in both cases.

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The domain used in this simulation is similar to the one used for the leakage scenario, but on a smaller scale with dimensions 100 × 100 × 100 𝑚. The model is composed of a single isotropic, homogeneous layer, one perforation location at the first segment of the horizontal well, a two-dimensional hydraulic fracture and an abandoned well. The two-dimensional discrete fracture is fully developed and placed at the center of the domain. The abandoned well intersects the middle of the fracture and is connected to the top boundary of the domain. The HF fluid is injected at the perforation location at a constant rate for a total period of 30 minutes. The following assumptions were made: The initial conditions in the domain include hydrostatic pressure and geothermal temperature distribution. The hydrostatic pressure is dependent upon brine density and the latter depends on the geother-

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ACCEPTED MANUSCRIPT mal gradient. The lateral boundaries of the domain are set to a hydrostatic pressure equal to the initial conditions. The top boundary is set to a constant pressure calculated from the hydrostatic pressure gradient. The top boundary is considered as the bottom of the freshwater aquifer. The domain fluid properties (density and viscosity) are assumed to be constant. 3.3 Parametric study

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A parametric study is designed for a wide spectrum of field configurations to examine the extent of

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contaminant (i.e. HF fluid) migration from a hydrocarbon bearing formation into the shallower permeable strata through a leaky well. Taherdangkoo et al. [54] studied the short-term upward transport

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of HF fluid from a hydrocarbon bearing formation into a shallow aquifer through a highly permeable

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fault zone intersecting the stimulated reservoir volume. The study incorporated a sensitivity analysis to rank the influence of several factors including reservoir depth, injection pressure, fault permeabil-

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ity, fault porosity, fault width, overburden permeability, overburden porosity, overburden anisotropy ratio, and basin salinity on upward migration of contaminants. Therefore, the parametric study conducted in this research is restricted to investigate the impact of injection rate, reservoir properties, and

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abandoned well properties. The parametric study applies one-at-a-time (OAT) method [71] in analyz-

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ing the influence of changing the values of each chosen parameter. OAT method has a limited use in

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exploratory modeling as it does not explore all the possible combinations between input variables, and it usually provides a local sensitivity measurement. However, OAT is a simple, easy to implement,

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and computationally cheap method, thus providing relevant observations as it exposes the independent effects of each parameter [72]. The North German Basin geology is considered as the baseline where each parameter is changed at a time. 3.3.1 Hydraulic fracturing injection rate The effectiveness of hydraulic fracturing treatment depends on several factors such as injection rate, injection depth, injection pressure, and HF fluid properties (e.g. viscosity). Wang et al. [4] concluded that fluid injection rate influences treating pressure, corresponding stimulated reservoir volume and hydrocarbon production. We changed injection rate to capture the full range of its potential influence

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ACCEPTED MANUSCRIPT on HF fluid flow. The HF fluid injection rate varies between 3.05 to 4.16 𝑚3 /𝑚𝑖𝑛, thus corresponding to a total injection volume of between 11000 and 15000 𝑚3 [10,53,69]. 3.3.2 Shale overpressure Overpressure occurs when pore fluid pressure is higher than normal hydrostatic fluid pressure at a specific depth [73]. Overpressure in subsurface rocks could be produced through three main mecha-

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nisms, namely: increase in compressive stress, change in pore fluid volume, and fluid buoyancy [74].

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Osborne and Swarbrick [74] concluded that disequilibrium compaction and gas generation are the most probable mechanisms for producing pressure anomalies in low permeable sediments. Disequilib-

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rium compaction is a common overpressuring mechanism in thick low permeable sequences (e.g.

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shale, and clay) with continued rapid burial [74]. Overpressure is a transient phenomenon except when it is due to topography [74]. In our model, the overpressure is considered as an initial condition

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prior to fracturing [53]. We applied overpressure only within the shale, and not in neighboring formations. We acknowledge that the applied approach does not reflect the actual overpressure within the shale. The overpressure varies from 10 to 13 𝑘𝑃𝑎 /𝑚 [10,41,70] to understand its effect on migra-

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tion of HF fluid into shallow permeable layers. 3.3.3 Shale properties

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Shale gas formations possess specific features such as heterogeneity, low matrix porosity and perme-

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ability [75,76]. The formation characteristics play important roles in gas production from shale gas reservoirs. The shale effective porosity and permeability reduce during production periods due to pore pressure reduction within the reservoir. However, we consider constant values for reservoir porosity and permeability during the entire simulation period. We examined porosity and permeability of the rock matrix over a range reported in literature. The shale porosity and permeability variation range from 1 to 5 % and 1 × 10−21 to1 × 10 −18 𝑚2 , respectively. 3.3.4 Abandoned wellbore integrity There is limited information available on the integrity of the sealing materials used for old abandoned wells, and hence the hydraulic parameters (e.g. permeability) of the degraded barrier system is largely 13

ACCEPTED MANUSCRIPT unknown [62]. Previous modeling studies suggested different values of effective permeability for evaluating the vertical migration of fluids through a leaky wellbore [14,56–58,62–65]. Herein, the effective wellbore permeability is the primary parameter of interest and it averages the permeability of the entire fractured/degraded formation parallel to the casing. We consider a wide range of possible wellbore permeabilities based on the wellbore integrity of old wells that were drilled completed, and

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abandoned, using different technologies. The model is run to simulate a 30-year period under the assumption that wellbore properties of the abandoned well remained constant through the entire simula-

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tion period. An open wellbore shows permeabilities ranging between 2 × 10−13 and 1 × 10−11 𝑚2

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while in a properly sealed well permeabilities span between 1 × 10−17 to 1 × 10−13 𝑚2 . This wide span of wellbore permeabilities is believed to account for the parameter’s significance in contamina-

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tion distribution in aquifers in the defined failure scenario.

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3.3.5 Proximity of HF to abandoned well

In oil and gas fields with a high density of production wells, hydraulic fractures intersecting abandoned wells is commonly observed, and even multiple frac hits may occur [77]. However, the aban-

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doned well may not be affected by the operation. The abandoned well can be close or at large distance from the operation. Therefore, it is important to explore the influence of the abandoned well proximity

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to hydraulic fractures on the upward transport of fluids to shallower aquifers. The study is conducted by varying the lateral distance of the abandoned well from the fracture (0 − 15 𝑚).

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3.3.6 Influence of well production

A large amount of HF fluid can be removed from the subsurface during production from the reservoir. The influence of well production on the upward transport of HF fluid is explored through a scenario that ignores production. In this case, the HF fluid remains in the domain during the entire simulation period. The aim is to explore the long-term effect of well production on groundwater contamination distribution with a conservative approach. 4 Mathematical and numerical model

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ACCEPTED MANUSCRIPT The transport of HF fluid through the domain is calculated using the single phase version of Darcy’s law. The system contains a single phase flow of non-compressible fluids (e.g. brine) which consists of two components (i.e. brine and a tracer) with the exception of gas phase. The assumption of fully saturated conditions and Darcy flow lead to the following system of equations [78,79]:

𝜕𝑐 𝑖 𝜕𝑡

( 𝜌𝑤 𝜑) + ∇. 𝜌𝑤 [−

𝐊 𝜇𝑤

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𝜕𝑡

𝜇𝑤

(3)

(∇𝑝𝑤 + 𝜌𝑤 g)

(∇𝑝𝑤 + 𝜌𝑤 g)] = 0

𝑖 − ∇ ⋅ (𝐷𝑝𝑚 ∇𝑐𝑖 ) + 𝑢 ⋅ ∇𝑐𝑖 − 𝑅𝑖 = 0

(4)

(5)

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𝜕

−𝐊

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𝑢=

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where 𝐊 (𝑚2 ) represents intrinsic permeability tensor of the porous medium, 𝑢 (𝑚/𝑠) is fluid velocity, and 𝑝𝑤 (𝑃𝑎) is the pressure of fluid. 𝜇 𝑤 (𝑃𝑎. 𝑠) and 𝜌𝑤 (𝑃𝑎) are fluid dynamic viscosity and den-

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sity, respectively. 𝑔 (𝑚⁄𝑠 2 ) is the acceleration due to gravity; 𝑐𝑖 (𝑚𝑜𝑙/𝑚3 ) refers to the concentration 𝑖 of the chemical species 𝑖 (𝑚𝑜𝑙/𝑚3 ); 𝐷𝑝𝑚 (𝑚2 /𝑠) represents the diffusion coefficient of component 𝑖,

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and 𝑅𝑖 is the reaction rate and it is assumed to be zero. Therefore, the model neglects the interaction

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of HF fluid with the porous media. The fluid flow in the fracture is governed by a conservation equation, with a source term representing flow into the fracture from the matrix. Darcy’s law relates the

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tangential component of the averaged pressure gradient to the tangential component of the averaged

𝑞𝑓 = −

𝑘𝑓 𝜇

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Darcy velocity. The following form of Darcy’s law is solved in the fracture [78,80]: (6)

𝑑𝑓 (∇ 𝑇 𝑃 + 𝜌𝑔∇ 𝑇 𝐷 )

where subscript 𝑓 represents the fracture parameters, 𝑞𝑓 is the volumetric flow rate per unit length of the fracture, 𝑑𝑓 is the fracture aperture and subscript 𝑇 indicates that the gradient is measured on the tangential plane of the fracture. The numerical tool COMSOL Multiphysics 5.2a is utilized in developing and implementing the mathematical model [81]. COMSOL is based on a finite element approach in solving the partial differential equations, and thus it is applicable for representing and accommodating complexities of real reservoir 15

ACCEPTED MANUSCRIPT geometry and its geological objects realistically. The time dependent solution of the equations is accomplished through a fully coupled solution approach with small initial time steps. A complex, unstructured, free-triangular finite element grid was developed for discretization of the domain. The applied mesh influences the precision and computational scale, thus making it a vital component in the finite element modeling. In practice, the compatibility of the mesh density and

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computing capacity should be considered for the solution to satisfy the precision requirement. The abandoned well and its neighboring area were assigned a finer mesh to better simulate the upward

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movement of fluids through the permeable pathway and to avoid numerical problems due to large

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permeability contrasts. As determined by precision requirement, the mesh gets coarser towards boundaries of the model. The adopted mesh allowed explicitly the capture of distinctive fluid flow

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features in the domain.

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5 Results and discussion 5.1 Comparison study for the abandoned well

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In this section, fluid flow through i) the fracture, ii) fracture-well interface, iii) along the well, and iv)

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at the bottom of the aquifer is monitored. The HF fluid concentration and pressure distribution are monitored at each location. This allows tracking of HF fluid migration towards the top boundary aqui-

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fer. The simulation results of case I are considered as the actual solution for modeling of fluid flow through the abandoned well. Fig. 3 presents the spatial distributions of the chemical concentration in

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the HF fluid and pressure in the y-z plane at 𝑥 = 50 𝑚, at the end of injection period. For both cases, the shape and vertical extent of the concentration plume towards the top boundary are largely similar. Case I and case II also reflect the same pressure spatial distribution through the domain. Fig. 4a shows that the spread of fluid within the hydraulic fracture and its ascent through the well is identical when considering the well as a cylindrical sub-domain and as a planar fracture. The HF fluid concentration at the fracture-well interface is 10 𝑘𝑔/𝑚3 , and it decreases with upward transport along the well. At the end of injection, HF fluid reaches a depth of 40 𝑚. Both cases represent the same pressure profile at the fracture-well interface and along the well. The simulation results demonstrate that representing the well in two dimensions is an adequate approach for modeling the upward migration of fracturing 16

ACCEPTED MANUSCRIPT fluid through a leaky abandoned well. Hence in this study, the leaky abandoned well is modeled as a two-dimensional fracture.

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a

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b

Fig. 3. Spatial distribution of fracturing fluid concentration and pressure at the end of the injection; (a)

b

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a

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case I; (b) case II. The cut plane is located at y-z direction at 𝑥 = 50 𝑚.

Fig. 4. (a) Fracturing fluid concentration; and (b) pressure profiles along the abandoned well in the y-z plane at the end of the injection. 5.2 Base case scenario

17

ACCEPTED MANUSCRIPT Fig. 5 (a-b) represents the spatial distribution of HF fluid plume in the y-z plane at 𝑥 = 1250 𝑚 at the end of injection and shut-in periods. The spread of HF fluid within the fracture, transport through the abandoned well, and its rise through the overburden layers is shown. The red arrows display the direction of total flux in the domain. Fig. 6 (a-b) compares HF fluid concentration distribution along the abandoned well at the end of each simulation period. During the first two periods, the Posidonia shale

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and its neighboring layer (i.e. M. Jurassic claystone 3 layer) host the bulk of fluid. The vertical migration of the fluid during these periods is relatively low and it is primarily due to the shale overpressure

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and fracturing pressure. The induced overpressure is dissipated in the reservoir during the shut-in

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period. However, the reservoir pressure still remains higher than the conditions prior to injection. As apparent from Fig. 5 (a-b), the total fluid flux direction is upward at the end of the injection period

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and it is mostly downward at the end of the shut-in period. The HF fluid reaches a maximum height of 252 𝑚 from fracture-well intersection (i.e. depth of 1468 𝑚 from the top) at the end of the injection

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period, and it increases to a height of 263 𝑚 (i.e. 1457 𝑚 depth) at the end of the shut-in period. The short-lived shut-in period has a minimal influence on the upward movement of fluids. The shape of

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HF fluid plume at the injection period is identical to that for the shut-in period (see Fig. 5). Therefore,

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in Fig. 6a, the iso-concentration lines belonging to these periods overlapped. Note that the transport of HF fluid plume in each layer depends on the layer physical properties (e.g. permeability). The fluid

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tends to spread more laterally in layers with high permeability. This phenomenon inhibits the upward

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migration of HF fluid through the abandoned well. a

b

Fig. 5. HF fluid concentration distribution in the y-z plane at 𝑥 = 1250 𝑚 at the end of (a) injection; (b) shut-in period. 18

ACCEPTED MANUSCRIPT b

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a

Fig. 6. HF fluid concentration distribution along the abandoned well in the y-z plane; (a) injection and

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shut-in periods; (b) first production, second production and post-production periods.

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The HF fluid is subject to upward buoyancy during the entire simulation which is due to the density differences between the injected fluid and brine. The induced overpressure is removed from the reser-

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voir with the start of production. The fluid could not enter the aquifers until the end of the first production period (see Fig. 7), and it reaches a maximum height of 1250 𝑚 from the fracture-well inter-

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section (i.e. depth of 470 𝑚 from the top) along the abandoned well. In Fig. 6b, HF fluid concentration along the abandoned well is displayed. At end of stage 3, HF fluid concentration at fracture-well

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interface is 10.5 𝑘𝑔/𝑚3 . This value is 6 times lower compared to the end of stage 2 which is due to

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the well production and upward fluid migration through the abandoned well. The location of HF fluid in the subsurface is illustrated in Fig. 8. This figure shows the vertical migration of HF fluid along the

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abandoned well, and its lateral movement in the overburden layers with different permeabilities.

Fig. 7. HF fluid flux along the abandoned well at the overburden-aquifer interface during production and post-production periods.

19

ACCEPTED MANUSCRIPT The upward HF fluid flux to aquifer is negligible prior to 3 years of production (Fig. 7). The fluid reaches the shallow freshwater aquifer one year after the commencement of the secondary production. The fluid flux into the aquifer peaked during year ten, and afterwards experienced a steady decline. The HF fluid flux at overburden-aquifer interface is 0.08 𝑚3 /𝑦𝑟 at the end of production. Fig. 8b displays the graphical representation of HF fluid migration through the well and its lateral transport in

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overburden layers at the end of production periods. During 15 years of production, 67% of the injected fluid volume is removed from the domain. This plays an important role in decreasing HF fluid

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potential migration into the overburden layers and shallow aquifers. Pore pressure reduction occurs in

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the reservoir during the two stages of production. The upward buoyancy is an important mechanism for transport of fluids to overlying layers. The upward buoyancy force decreases over time due to

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mixing of HF fluid with brine during its transport. Fracturing fluid removal from the domain, its lateral spreading into the overburden layers and the decrease in the buoyancy force explain the decrease

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in the upward fluid flux along the abandoned well during production and post-production periods. b

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a

c

20

ACCEPTED MANUSCRIPT Fig. 8. Spatial distribution of HF fluid along the abandoned well and its neighboring area at the end of (a) first production; (b) second production; (c) post-production period. The cut plane is located at y-z direction at 𝑥 = 1250 𝑚. A halt in production results in pressure build-up in the Posidonia shale. The upward flow of HF fluid during the post-production period leads to an increase in chemical distribution in the shallow aquifers.

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Note that the transport of fracturing fluid through the abandoned well progresses at a much slower pace in shallow layers than in deeply seated layers. Over time the fluid flows more laterally into the

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overburden layers and hence the fluid flux into the aquifer decreases. This phenomenon is reflected in

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Fig. 7. At the end of the simulation, 67 % of HF fluid volume is discharged by well production, 33 % remained in the subsurface, and 0.02 % reached the shallow aquifer. Fig. 8c shows the transport of HF

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fluid into the overburden layers and overlying aquifers at the end of the simulation period (30 years). The fluid flux along the abandoned well at the overburden-aquifer interface is 0.07 𝑚3 /𝑦𝑟 at the end

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of simulation.

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5.3 Parametric study

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The sensitivity analysis is designed to examine field uncertainties and draw a meaningful conclusion for the defined failure scenario. A total of 22 simulations, aimed at assessing different field scenarios

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were ran by altering key parameter values. Fig. 9 (a-g) illustrates HF fluid flux at the overburdenaquifer interface during 30 years of simulation time. In the following, the influence of each studied

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parameter is described.

The total volume of HF fluid in the system correspondingly increases with the increase in the injection rate. Thus, a higher amount of fluid remains in the subsurface even after the end of production. A higher injection rate imposes a higher induced pressure gradient in the reservoir. Therefore, the pressure front propagates a greater distance into the formation. This increases the upward fluid flux through the abandoned well and consequently more fluid flows to shallower strata. Fig. 9a, presents HF fluid flux at the overburden-aquifer interface based on total injected fluid volume (𝑉𝐹𝐹 ). When the injection rate increases to 4.16 𝑚3 /𝑚𝑖𝑛 (fluid volume of 15000 𝑚3 ), the upward fluid flux into the aquifer is 1.75 times higher compared to the base case scenario (fluid volume of 11356 𝑚3 ). Model21

ACCEPTED MANUSCRIPT ing results indicate that higher injection rates lead to a slightly higher chemical concentration in the shallow aquifers. However, the long-term influence of injection rate on the upward movement of fluids to overlying layers is relatively low. The effect of reservoir overpressure on the vertical transport of HF fluid through the abandoned well is negligible. During the short-lived injection period, the reservoir overpressure and fracturing injec-

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tion pressure are the dominant forces for fluid transport. Thereafter, the induced pressure is removed quickly by production from the well and pressure drawdown occurs over time. Thus, the upward mi-

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gration of HF fluid through the abandoned well is not dependent on overpressure in the defined failure

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scenario. Fig. 9b shows that a change in the shale overpressure gradient from 10 to 17 𝑘𝑃𝑎 /𝑚 does not influence HF fluid flux at the overburden-aquifer interface. The results further indicate that the

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amount of HF fluid removed from the well during the production period is insensitive to the change in

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overpressure gradient.

The effect of shale properties on HF fluid transport are shown in Fig. 9 (c-d). The ascent of HF fluid through abandoned well decreases with an increase in shale permeability. This occurs because pres-

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sure dissipation across the abandoned well decreases with an increase in reservoir permeability. How-

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ever, it leads to slight changes in the vertical fluid flux at overburden-aquifer interface. A reduction in

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the shale porosity also decreases the upward fluid flux. It mirrors the same effect associated with an increase in reservoir permeability. Although reservoir physical properties affect the upward transport

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of HF fluid to shallower layers, they do not impose a significant influence in the long-term concentration pattern. The amount of removed HF fluid by the well decreases with the decrease in shale permeability. The corresponding volume is 76 % and 63 % for shale permeability of 1 × 10 −18 and 1 × 10−21 𝑚2 , respectively. It shows that contaminant flux into overlying aquifers decreases with the increase in HF fluid discharge. The changes in shale porosity have insignificant influence on discharge of HF fluid from the domain. The upward migration of HF fluid through the abandoned well strongly depends on the effective wellbore permeability. The fluid does not move upward for wellbore permeabilities equal to or lower than 1 × 10−13 𝑚2 . In this case, HF fluid does not reach the shallow aquifers even after a long time. 22

ACCEPTED MANUSCRIPT The amount of fluid removed by production is 75 % of the initially injected volume for a well permeability of 1 × 10−17 𝑚2 and 25 % of HF fluid volume remains in the subsurface without being able to move upward. Hence, abandoned wells with low permeabilities (i.e. high wellbore integrity) prevent upward HF fluid transport into overburden layers, a trivial result. Fig. 9e illustrates that a slight increase in wellbore permeability leads to higher fluid flux at the overburden-aquifer interface, thus

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resulting in an increase in concentration in the aquifer. For instance, if wellbore permeability increases to 2 × 10−12 𝑚2, the corresponding chemical flux at the overburden-aquifer interface is 3.6 times

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higher compared to the base case. The maximum fluid flux into the aquifer is observed for a well

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permeability of 1 × 10−11 𝑚2 which is 27.4 times higher than the base case. Here, 56 % of the injected fluid volume is discharged during production period, ca. 1% reached the aquifer, and 43% re-

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mained in the subsurface. The modeling results suggest that wellbore integrity controls the transport of contamination into the shallower strata and consequently the contamination distribution into the

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aquifer. The results indicate that the abandoned well has to fail to act as a permeable pathway for transport of fluids.

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Increasing fracture-well distance influences HF fluid arrival at the aquifer base. The fluid reaches the

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shallow aquifer 4 years after production when the fracture-well distance is 5 𝑚. At the end of the sim-

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ulation, if the abandoned well is 5 𝑚 away from the fracture, the fluid flux at overburden–aquifer interface is 3.6 times lower compared to the base case. An increase in fracture-well distance to 10 𝑚

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reduces fluid flux to 0.01 𝑚3 ⁄𝑦𝑟 . This value is 7.2 times lower compared to the base case model. The removed HF fluid during well production is 74 % when the well is 5 𝑚 away from the hydraulic fracturing. This value remains constant for a fracture-well distance of 10 and 15 𝑚 which is due to the minimal effect of the hydraulic fracture to the abandoned well. If the leaky well is 15 𝑚 away from the fracture, HF fluid cannot be detected in the aquifer. The model results indicate that the proximity of hydraulic fracture to the abandoned well is the second most influential parameter on the vertical transport of fluids to shallower strata. When well-fracture distance is large enough, most of HF fluid is removed from the domain and the possibility of upward transport is minimal.

23

ACCEPTED MANUSCRIPT Ignoring the production leads to a higher contaminant concentration in the shallow aquifers (Fig. 9g). Here, the HF fluid flux into the aquifer is 10 times higher compared to the base case. This indicates the production from the reservoir reduces contamination treats to groundwater aquifers. The modeling results suggest that the wellbore integrity of the abandoned well and its distance from fracturing operation are the most and second most influential parameters determining the vertical

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transport of HF fluid through an abandoned well. The HF fluid injection rate and reservoir properties also have impacts on fluids transport towards shallow aquifers. The results for the upward flow

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through the abandoned well are within the range reported by Brownlow et al. [10] and Reagan et al.

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[1]. It is evident that HF fluid does not reach the aquifer within a short-time frame. The modeling results show limited vertical transport of fluids through the abandoned well under different field pos-

b

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d

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c

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a

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sibilities.

24

ACCEPTED MANUSCRIPT f

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e

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g

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Fig. 9 HF fluid flux along the abandoned well at the overburden-aquifer interface during production and post-production periods for the parametric sweep; (a) injection rate; (b) shale overpressure gradient; (c) shale permeability; (d) shale porosity; (e) abandoned well permeability; (f) well distance from

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the hydraulic fracture; (g) and case without production. 6 Conclusions

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This research focuses on the numerical simulation of fracturing fluid flow and transport of contami-

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nants from a hydrocarbon bearing formation towards shallow aquifers through an abandoned well. The models are based on permeability and stratigraphy data of the geological sequence in the North German Basin. We conducted a parametric study to examine the influence of key factors, such as reservoir properties, abandoned well permeability and its proximity to hydraulic fractures on the vertical transport of fracturing fluid through an abandoned well. Numerical modeling results revealed the following: 

During the injection period, fracturing pressure and reservoir overpressure are the main driving forces for vertical transport of HF fluid. During shut-in period, pressure dissipation occurs across the reservoir. Thereafter, the fracturing pressure is removed and reservoir pressure re-

25

ACCEPTED MANUSCRIPT duction occurs with production from the horizontal well. The upward buoyancy is an important mechanism for upward transport of fluids to shallower strata during production and post-production periods. 

Well production removes a significant amount of injected HF fluid (67% of total volume) from the domain thus reducing the probability of HF fluid transport to overlying layers. When

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production is ignored, HF fluid flux at the overburden-aquifer interface is 10 times higher compared to the base case. This indicates that neglecting the effect of well production leads to

The combined effect of well production and mixing of HF fluid with formation fluid signifi-

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

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the overestimation of contamination distribution in aquifers.

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cantly reduce buoyancy force. This decreases upward movement of HF fluid towards groundwater aquifers. We suggest that further modeling studies take into account these im-



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portant effects.

Most notably, increasing abandoned well permeability significantly increases the fluid flux to

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shallow aquifers. When well permeability is set at 1 × 10−11 𝑚2 , HF fluid flux at the over-

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burden-aquifer interface is 27.4 times higher compared to the base case. HF fluid could not reach the aquifers for wellbore permeability lower than 1 × 10−13 𝑚2 . Therefore, wellbore

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integrity is the most important factor controlling the leakage of fluids through an abandoned well. It is concluded that only a defected wellbore could act as a permeable pathway for



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movement of fluids to overlying layers. The proximity of fracturing to the abandoned well is the second most influential parameter influencing the upward transport of fluids. The HF fluid cannot be detected in the aquifer when the abandoned well is 15 𝑚 away from the hydraulic fracture. 

HF fluid tends to spread laterally in high permeable sediments. Therefore, the existence of such layers further decreases the upward transport of fluids leading to a lower contamination distribution in the aquifer.

26

ACCEPTED MANUSCRIPT 

Reservoir physical properties have minimal effects on vertical migration of fluids especially in the log-term frame. The results derived from varying shale overpressure were no different compared to the base case model.



The short-term probability of shallow aquifer contamination resulting from fracturing is negligible even in the presence of a leaky abandoned well. Model results show that HF fluid

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reaches the aquifer three years after production. The long-term simulation reveals that the risks hydraulic fracturing pose to shallow aquifers are low (i.e. 0.02% of injected fluid reach

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to the aquifer at the of simulation time).

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Acknowledgment

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We acknowledge the funding received from the European Union's Horizon 2020 Research and Innovation program. Project ''Furthering the knowledge Base for Reducing the Environmental Footprint of

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Shale Gas Development'' FRACRISK, grant agreement 636811. References

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ACCEPTED MANUSCRIPT Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells

Reza Taherdangkoo*, Alexandru Tatomir, Tega Anighoro, Martin Sauter Department of Applied Geology, Geosciences Center, University of Goettingen, Goldschmidtstr. 3, D-37077

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*Corresponding author

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The study investigates the upward flow of fracturing fluid through an abandoned well. The geological setting of the North German Basin is considered. The fracturing fluid does not reach to freshwater aquifers in a short-time period. A limited vertical flow of fracturing fluid through the abandoned well is observed.

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Email: [email protected], Tel.: +49-1573-9533348

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