Modeling of methane migration from gas wellbores into shallow groundwater at basin scale

We build a generic basin-scale two-dimensional numerical model, Fig. 1, comprising three horizontal layers. The conceptual model is built based on permeability and stratigraphy data compilations of North America and Europe implemented by Taherdangkoo et al. (2018) and Potter van Loon (2016). We applied median values reported for the domain length, recharge, claystone thickness, and claystone depth. A thin (21 m) continuous claystone is assumed at shallow depth (171 m) overlain by coarse sediments. The model spans across a domain of 10 km length and 1.8 km depth.

A large section of the top boundary, i.e., 95% of the model length, is defined as a constant recharge boundary intersecting a discharge boundary (5% of the model length). The groundwater recharge rate amounts to 0.05 m/year. The discharge is modeled as a constant hydraulic head boundary (Taherdangkoo et al. 2018). The lateral sides of the domain are set to no-flow boundaries.

It is common in the oil and gas industry to temporarily shut-in a well because of operational and economic reasons. The pressure in the gas reservoir does not decrease during the shut-in period. For this type of condition, should the well annulus intersect with a fracture/fracture system connecting the gas reservoir with the overburden, considerable leakage may occur (Reagan et al. 2015; Moortgat et al. 2018; Tatomir et al. 2018). The leakage rate depends on various factors such as reservoir pressure, reservoir gas saturation, in situ, and relative permeability (Reagan et al. 2015; Nowamooz et al. 2015). Kissinger et al. (2013) modeled constant leakage of methane from the reservoir into the overburden for 100 years. The authors emphasized that the constant escape of gas is regarded as “a conservative” assumption. Reagan et al. (2015) suggested that incidents of gas leakage from the reservoir are likely to be limited in time. Moortgat et al. (2018) considered a high methane inflow rate during the shut-in period, followed by a lower rate during the production.

The conceptual model considered here assumes fracture propagation into overlying formations during a hydraulic fracturing treatment (Kissinger et al. 2013; Reagan et al. 2015; Moortgat et al. 2018; Tatomir et al. 2018). The model assumes that during shut-in gas leaks into the overburden at a high flow rate, followed by a much lower rate once the production is resumed. We applied leakage rates published in Moortgat et al. (2018) as, similar to this study, they assumed methane leakage from a natural gas well into overlying formations. However, the geological setting, rock types, and tectonics are different from those considered here.

The leakage is assumed to occur at the top of the gas reservoir through the fracture system intersecting the overburden; thus, instead of explicitly considering the reservoir in the model, it is included as a boundary condition. The gas entering the domain is assumed to be pure methane and the presence of other thermogenic gases is neglected (Nowamooz et al. 2015; Roy et al. 2016; Rice et al. 2018a). The leakage source measures 100 m in length and it is situated at the bottom of the domain at 40% of the model length (\(3950\le x\le 4050\)) for all subsequent simulations. The remaining of the lower boundary is set to no-flow condition. The methane leakage rate is estimated based on the production rate from the borehole. A typical production rate of 300 MSCFD (million standard ft³/day) (Moortgat et al. 2018) (35,680 m³/day at reservoir condition) is assumed for the base-case model. Methane leaks into the overburden at a high inflow rate of 8920 m³/day, i.e., 25% of the production during the 7 days of the shut-in period, followed by an inflow rate of 892 m³/day, i.e., 10% of the initial leakage rate, for the next 2 years. The upward migration of methane and brine is monitored for 25 years of simulation time.

The low-permeability unit, i.e., claystone, is a laterally extensive single layer overlying the entire basin which might contain discontinuities. Moreover, multi-layered systems where low-permeability units are interbedded within permeable sediments may exist. Each field configuration could lead to a different contamination distribution in the subsurface based on its unique stratigraphic, geophysical, and hydrodynamic characteristics (Sauter et al. 2012; Lange et al. 2013). Herein, we first assume a single continuous claystone across the entire model length to obtain the first-order information on the influence of low-permeability sediments on methane migration. We then consider different configurations to explore the impact of claystone integrity and multi-layered clay systems.

The dominant physical and chemical processes for fluid migration are advection (viscous, buoyant, and capillary), dissolution, and diffusion (Nowamooz et al. 2015). Methane sorption is assumed to be negligible (Rice et al. 2018b). The flow and transport of fluids are simulated using both a miscible flow model and an immiscible flow model. The miscible flow model considers advection, diffusion, and dissolution processes, while the immiscible model considers migration via advection and diffusion.

All simulation runs are conducted with the open-source numerical simulator DuMu^X (Flemisch et al. 2011). For spatial discretization, the box method, a vertex (or node)-centered finite volume method based on a finite-element grid, is used. The grid resolution equals 500 cells in the x-direction and 180 cells in the y-direction, corresponding to finite volume element length of 20 m in x-direction, and 10 m in y-direction. A fully implicit Euler time discretization scheme using the Newton method is applied to solve the linearized system of non-linear partial differential equations (Helmig 1997). The first time-step size is set to 0.01 s and the maximum time-step is 1e6 s. The time-step size is controlled by the number of iterations required by the Newton method to achieve convergence for the last time integration (Flemisch et al. 2011; Koch et al. 2020).

We use 2P2C (two-phase, two-component) and 2P (two-phase) modules for simulating isothermal miscible and immiscible two-phase flow and transport of fluids in porous media, respectively. The binary diffusion and the diffusive mass fluxes in each phase are computed according to Fick’s law. The mass balance equation for a two-phase two-component model can be formulated for each k as follows (Helmig 1997; Dietrich et al. 2005):where the index α represents the wetting and non-wetting phases. The index κ represents the components brine and methane. φ is the effective porosity and \(\rho_{\alpha }\) is the density of phase α. \(X_{\alpha }^{k}\) is the mass fraction of component κ in the phase α, \(S_{\alpha }\) is the saturation, \(\mu_{\alpha }\) is the dynamic viscosity, and \(k_{r\alpha }\) is the relative permeability. \({\varvec{K}}\) is the intrinsic permeability tensor, \(P_{\alpha }\) is the phase pressure, g is the gravitational acceleration, and \(D_{Pm, \alpha }^{k}\) is the effective diffusion coefficient of the porous medium.

Methane can exist as a free-phase gas with a limited amount of water vapor or dissolved in the aqueous phase. The amount of water in the gas phase based on Duan et al. (1992a). Methane solubility varies over a wide range of temperatures, pressures, and brine compositions (Duan et al. 1992a; Duan and Mao 2006). Methane dissolution in the aqueous phase is assumed to occur at thermodynamic equilibrium and gas-phase saturations were simultaneously updated at each time-step to consider the mass loss to brine. Assuming methane at equilibrium with respect to water, methane solubility (mg/L) can be computed following the Duan et al. (1992a) approach as in:where \(m\) is the molality of CH₄ or salts in the liquid phase and \(x\) is the composition in the vapor phase. \(P\) is the total pressure and R is the universal gas constant. \(\mu_{{CH_{4} }}^{l\left( 0 \right)}\) is the standard chemical potential of CH₄ in the liquid phase and \(\emptyset\) is the fugacity coefficient. The index a and c are anion and cation, respectively. \(\lambda_{{CH_{4} - ion}}\) and \(\zeta_{{CH_{4} - c - a}}\) are interaction parameters. \(\frac{{\mu_{{CH_{4} }}^{l\left( 0 \right)} }}{RT}\) and the interaction parameters are calculated by Pitzer et al. (1984) method (Duan et al. 1992a).

The variations in porosity and permeability are typically driven by changes in mineralogical composition, i.e., mineral grains and cement, depositional facies, burial depth, and post-depositional processes (Weibel et al. 2012). The mineral composition of the claystone comprises 50% kaolinite and 50% illite (Luijendijk and Gleeson 2015). Following Gleeson et al. (2011), we assumed that the shallow and overburden sediments contain 90% sand and 10% clay and obtained realistic permeability values. The permeability of sand is calculated using the Kozeny–Carman equation (Kozeny 1927; Carman 1937). The claystone permeability is determined using an empirical permeability-void ratio equation (Luijendijk and Gleeson 2015). The permeability of sediments is calculated following Luijendijk and Gleeson (2015). The porosity is calculated using lithology dependent exponential porosity-depth coefficients (Athy 1930; Sclater and Christie 1980). The estimated porosity and vertical permeability of claystone are 0.05 and 1.1 × 10^–20 m², respectively (Fig. 2). Permeability and porosity of shallow and overburden sediments in the y-direction vary approximately from 6.8 × 10^–14 to 2.6 × 10^–15 m² and from 0.3 to 0.12, respectively, as shown in Fig. 2. The anisotropy ratio (K_h/K_v) is set to 100 in the claystone and 10 in the surrounding sediments. The temperature at the top of the domain is 10 °C, with a vertical temperature gradient of 0.03 °C/m. The domain is initially water-saturated. The residual water saturation is set to 20% (Nowamooz et al. 2015; Rice et al. 2018b). In all simulations, we modeled a drainage-like process, because the gas saturation increases continuously with time. As gas cannot be trapped during the drainage, the residual gas saturation is assumed to be 0.01% (Rice et al. 2018b).

Methane is the predominant component in the gas mixture and small amounts of other components (e.g., N₂, CO₂, C₂, and C₃) have a negligible influence on the density and viscosity of the gas phase (Nowamooz et al. 2015). For simplification, the model considers the leaked gas as pure methane. Brine is modeled as a pseudo-component and represents pure water with a given salinity. Brine density and viscosity are calculated following Batzle and Wang (1992) equations. Methane density and viscosity are calculated based on Duan et al. (1992b, c) and (Daubert et al. 1998), respectively. The diffusion coefficient of water in the gas phase is calculated based on Fuller et al. (1966). Since the empirical equations for estimating the diffusion coefficient in infinite solution presented in Reid et al. (1987) all show a linear dependency on temperature, we simply scale the experimentally obtained diffusion coefficient of the dissolved methane in the water phase given in Kobayashi (2004) by temperature. Kobayashi (2004) suggested the diffusion coefficient of 3.55 × 10^–9 m²/s.

As methane leakage rates reported by Moortgat et al. (2018) are specified for surface conditions, a gas formation volume factor (B_g) of 0.0042 ft³/SCF is used to convert the values to reservoir conditions. The B_g is calculated using the averaged values reported by Edwards and Celia (2018). The model property values are presented in Table 1. The capillary pressure and the relative permeability are calculated as a function of saturation using Brooks and Corey (1964) equations as follows:where \(P_{d}\) is the entry pressure of the porous medium. The relative permeability functions, \(K_{r} \left( S \right)\), can be calculated by the following equations:

The effective saturation \({S}_{e}\) is defined using the following equation. \({S}_{wr}\) and \({S}_{gr}\) are irreducible saturation of liquid and gas phases, respectively:

The base-case models explore miscible and immiscible flow and transport of fluids to shallow layers for a period of 25 years. The temporal and spatial behavior of the plume in the subsurface and the change in volumetric flow rates to shallow groundwater of methane are observed. Moreover, methane and brine flow rates at various distances from the leaky gas well (ΔL = 2000, 3000, and 4000 m) are monitored. These locations can be interpreted as intersections of the aquifer with conductive permeable pathways such as faults and fractures, i.e., preferential flow paths for the transport of fluids in the upper crust. This choice allowed us to track the methane plume at various distances from the gas wellbore in basins with or without vertical permeable pathways.

A series of sensitivity analyses is designed to examine the roles of different geometric configurations and parameter combinations on the migration of fluids. Parameter selection is based on comprehensive features, events, and processes (FEPs) procedure highlighting the relevant importance of the key factors influencing the upward movement of contaminants (Tatomir et al. 2018). First, we explore the sensitivity of hydrodynamic properties (\({P}_{d}\), λ, and S_wr) of shallow and overburden sediments. The displacement or entry pressure \(({P}_{d})\) of the porous medium changes between 2 and 20 kPa and is set to 10 kPa in the base-case model. A large pore size distribution index (λ) indicates a comparatively uniform pore size distribution, while small values of λ describe a non-uniform distribution (Brooks and Corey 1964). λ varies from 2 to 6 and is set to 2 in the base-case model. These values are chosen to cover a wide range of values of pore size distribution index and entry pressure. Residual water saturation varies between 0.15 and 0.25 and equals to 2.0 in the base-case model (Class 2007; Nowamooz et al. 2015; Rice et al. 2018b).

We include simulations for sedimentary basins with dip angles of 0º, 1º, and 3º. We rotate the model coordinate system to tilt the geological geometric configuration. We keep the top of the domain at the same depth and increase the maximum depth by increasing the dip. Thereafter, the impact of methane leakage rate from the wellbore is explored. As an alternative to the high leakage with short duration, two low constant gas inflow rates of 60 and 120 m³/day for uninterrupted 25 years are considered.

The sensitivity analysis then considers a discontinuity, 10% of the model length, in the middle of the claystone to examine the role of low-permeability rocks on fluid flow and mass transport. Further simulations include the integration of a multi-layered claystone system with interbedded permeable rocks at shallow depth. We assume two different field settings by varying the geometry of the clay system, consisting of four clays with random horizontal position, depth, and integrity. All clays are embedded between 150 and 350 m depth and have the same thickness as the base-case value, 21 m. This sensitivity analysis is presented to examine how the migration of methane from a deep gas reservoir is impacted by sequences of low-permeability rocks.

The gas saturation and pressure profiles of methane leakage using the miscible flow model are shown in Figs. 3 and 4, respectively. In this model, methane exists as free and dissolved-phase gas in the aqueous phase. Methane migrates upward predominantly by buoyancy and reach the claystone after approximately 695 days. The strong vertical buoyancy controls the direction of methane migration; thus, the lateral spread is limited. The tube-shaped flow of gas is partially due to the consideration of a homogenous model domain. The diameter of the plume around the leakage source is approximately 320 m after 2 years and remains constant. The claystone overlying the overburden sediments constitutes an effective barrier to the upward movement of fluids. For this type of configuration, once methane reaches the claystone layer, the gas spreads laterally along the horizontally stratified layer due to the sustained pressure. As illustrated in Fig. 5, an important volume of gas phase accumulates at the claystone base after 25 years reaching eventually the aquifer. Permeable pathways, such as fractures, faults, and abandoned wells through barrier rocks, play an important role in fluid migration in the upper crust. In the context of hydraulic fracturing operations, the presence of these flow paths in the proximity of a leaky gas well could lead to the early occurrence of methane in groundwater (Darrah et al. 2014; Cahill et al. 2017; Moortgat et al. 2018).

For the time 25 years after the leakage, the dissolved methane (mg/L) in the aqueous phase is presented in Fig. 5b. The density of the gas phase and the composition of the aqueous phase strongly depend on pressure and temperature. Methane solubility in the aqueous phase is higher in deep formations due to the increase in pressure (Eq. 2), and thus, more methane is dissolved in brine before the appearance of the gas phase (Duan et al. 1992a; Duan and Mao 2006). Following the commencement of leakage, free-phase methane moves upward by buoyancy and progressively dissolves in brine. Dissolved methane is gradually transported by advection and diffusion. The high buoyancy force from density contrasts between methane (density > 110 kg/m³) and brine (density > 1100 kg/m³) controls the long-term upward migration of free-phase methane.

As illustrated by the pressure profiles (Fig. 4), the hydrostatic pressure is lower at shallow depth. The reduction of the hydrostatic pressure leads to a significant decrease in the density of the gas phase, and the release of some of the dissolved methane into the gas phase. Accordingly, more highly buoyant free-phase methane appears at shallow depths with the consequence of increasing the upward flow rate. For such conditions, large amounts of free-phase methane migrate to the groundwater system within a relatively short time.

The gas-phase saturation and pressure profiles of the immiscible flow model are shown in Figs. 6 and 7, respectively. Methane reaches the base of the claystone after approximately 660 days. The methane accumulation at the claystone is followed by the extensive horizontal spreading. Similar to the methane migration in the miscible flow model set-up, the diameter of the plume around the leakage source measures approximately 320 m after 2 years and remains unchanged. In both miscible and immiscible flow models, the lateral spread of the plume before reaching the claystone is limited, partially due to the assumption of a homogenous domain.

The mass flow rates of methane and brine are obtained from the total non-wetting phase and wetting phase flow rates calculated from advection, diffusion, and dissolution processes. Figure 8a, b represents methane and brine volumetric flow rates at 2000, 3000, and 4000 m distances to the gas well, respectively. Methane reaches the monitoring locations during the extensive lateral spreading at the claystone base. The methane flow rate increases rapidly to its maximum value and then shows a continuous decrease with time (Fig. 8a). The flow rates of fluids corresponding to the miscible model are slightly lower compared to the immiscible model, indicating the effect of gas dissolution on transport. Similar to the observations of Tatomir et al. (2018), the methane flow rate is higher where the conductive feature, e.g., fault, is closer to the leakage location. However, leakage continues to be active for much longer time periods when the conductive features are further located.

The pressure gradient created by the gas influx causes brine to slowly migrate in the subsurface (Fig. 8b). Brine flow rate at the measuring locations increases during the leakage and declines sharply after the drop-in pressure. The first peak value corresponds to the end of the shut-in period and the second peak corresponds to the end of leakage. Brine flow changes in the direction of regional groundwater flow after approximately 5 years due to the combined influence of regional hydraulic gradient, cease of gas leakage, and negative buoyancy. Although brine flows towards the monitoring locations (i.e., highly permeable pathways), the probability of deep brine reaching shallow groundwater is low (Osborn et al. 2011; Gassiat et al. 2013; Pfunt et al. 2016; Taherdangkoo et al. 2019) due to the absence of significant driving forces.

As illustrated by Figs. 3, 4, 5, 6, 7, and 8, using miscible and immiscible flow models results in slightly different methane plume sizes and travel times to groundwater. This is due to the low solubility of methane in the ambient water, particularly at shallow depths. The influence of methane solubility on gas transport becomes less significant once the plume spreads at shallow groundwater.

The sensitivity analysis is conducted employing the miscible flow model. First, the influence of key parameters including Brooks–Corey parameters, residual water saturation, tilted geometries, and methane leakage rates are examined. Then, the impacts of the claystone integrity and multi-layered claystone systems on the spatial distribution of the methane plume in the subsurface and the arrival time to shallow groundwater are discussed.

The occurrence of thermogenic methane in groundwater may indicate that the gas has migrated upward from a hydrocarbon reservoir into the shallow subsurface. The presence of connective permeable pathways, e.g., faults, interconnected bedding planes, and fractures, in the vicinity of the leaky gas well could result in an early manifestation of methane in groundwater wells (Gorody 2012; Darrah et al. 2014; Cahill et al. 2017). For the leaked methane encountering low-permeability layers, methane preferentially flows along higher permeability sediments, either up-dip (Fig. 9d) or in the direction of groundwater flow (Fig. 10b, c) (Steelman et al. 2017). For such conditions, methane can reach distances of hundreds of meters from the leaky well, delaying the breakthrough to the shallow aquifer system.

Elevated levels of methane concentrations have been observed in groundwater wells within approximately 1 km distance to hydrocarbon wells (Osborn et al. 2011; Jackson et al. 2013; Darrah et al. 2014; Brantley et al. 2014; Heilweil et al. 2015). Our results show that methane can be manifested even at distances of larger than 1 km from the leaky well because of the flow deviation along low-permeability rocks.

The temporal and spatial behavior of the methane plume in the subsurface highly depends on the geological and hydrogeological characteristics of the formations overlying the gas reservoir (Steelman et al. 2017; Rice et al. 2018b). The results indicate that methane can migrate to large distances from the source of leakage and, thus, the concentration of the methane in groundwater wells (if at all) can vary considerably with both time and space. Some observational studies (Molofsky et al. 2013; Li and Carlson 2014; Siegel et al. 2015; McMahon et al. 2017; Nicot et al. 2017; Botner et al. 2018) found no correlation between thermogenic methane in water samples from groundwater wells and just the distance to hydrocarbon wells corroborating our findings.