Directional Dependence of Gas Dispersion in Carbonates and Sandstones

Abstract

This study investigates the directional dependence of gas dispersion in porous media with varying lithology and macroscopic heterogeneity. Eight rock samples, including three carbonates and five sandstones, were examined through CH₄–CO₂ core-flooding experiments at 300 psi and 65 °C. Each core was first flooded with CO₂ displacing CH₄, then the core was inverted 180° to quantify the dispersion coefficient in both core orientations. Across most samples, gas dispersion showed directional dependence, with fitted K_L values differing by up to 60%. The directional difference depended on the sequence in which the gas mixing front encountered visible heterogeneity. Carbonates exhibited higher dispersion coefficients and smaller directional differences than most sandstone samples, whereas visibly layered sandstones showed larger directional differences. Directional differences decreased with increasing permeability for homogeneous cores but showed no consistent trend in heterogeneous ones, where macroscopic structure dominated flow behavior. Rocks with pronounced macroscopic heterogeneity, such as the Nugget sandstone, experienced the greatest directional differences. These findings indicate that dispersion directionality is governed by a hierarchy of controls, in which lithology, macroscopic heterogeneity, and permeability influence the extent of gas mixing. Rock-dependent in situ fluid mixing can therefore have important implications for subsurface systems engineering in geologic gas storage, particularly in well placement and operational strategy design.

1. Introduction

Gas dispersion in porous media governs how gases mix and redistribute during subsurface processes such as geological CO₂ storage, underground hydrogen storage, natural gas storage, and gas-enhanced hydrocarbon recovery. Dispersion arises from the combined effects of molecular diffusion and mechanical spreading caused by pore-scale velocity variations. To quantify this behavior, the longitudinal dispersion coefficient, K_L , provides the continuum-scale representation of these processes and links pore-scale transport behavior to macroscopic flow predictions. − Extensive theoretical, experimental, and numerical studies have established that dispersion depends on pore geometry, velocity distribution, and flow rate. In heterogeneous porous media, correlated velocity fields, tortuosity, and connectivity strongly influence mixing and solute spreading. − Recent pore-scale simulations further demonstrate that dispersion evolves dynamically as fluid elements stretch and sample different velocity domains, resulting in time-dependent effective dispersion coefficients. −

In natural rocks, variations in grain size, cementation, depositional layering, and compositional contrasts introduce macroscopic heterogeneity that reorganizes velocity fields at both pore and core scales. ,− Carbonates often exhibit complex interconnected pore systems and high coordination numbers that broaden velocity distributions and enhance mechanical dispersion, ,, whereas sandstones typically display narrower pore-throat distributions and more localized preferential pathways. − Stratified or layered media can therefore produce anisotropic flow behavior, and experimental and numerical studies have shown that inverting orientations may activate distinct velocity structures and yield directional mixing responses. , Despite this recognition of heterogeneity-induced variability, most laboratory studies treat the longitudinal dispersion coefficient as an intrinsic scalar property that is independent of flow direction and core orientation. Numerical models commonly assume isotropic or direction-independent dispersion tensors. However, if flow encounters heterogeneity in a different sequence when the core orientation is inverted, the velocity field may reorganize and potentially produce a different cumulative dispersion response. , Previous works have investigated dispersion directionality using a “dispersion echo” technique, in which tracer is injected and subsequently pumped back through the porous medium. − In homogeneous materials, the echo dispersion coefficient matches the transmission coefficient at all Péclet numbers, indicating directionally independent dispersion. In heterogeneous materials, however, directionally dependent dispersion behavior has been observed, with echo curves exhibiting lower effective dispersion coefficients than transmission experiments. These studies attribute directional dependence to the combined effects of geometric disorder in the velocity field and molecular diffusion. While the dispersion echo framework provides important insight into fundamental transport directionality, it has primarily been applied to tracer systems and idealized porous media. Its implications for gravity-stable single-phase gas–gas displacement across natural rock lithologies have not been systematically examined. This gap is especially relevant for cyclic subsurface operations, where injection and withdrawal repeatedly reverse the flow direction.

Recent studies have also evaluated density-driven dispersion, where buoyancy-induced convection enhances mixing beyond mechanical spreading. This mechanism is particularly important in gas–liquid systems, such as CO₂ dissolution into brine, where density contrasts trigger convective instabilities and fingering that amplify effective dispersion and mass transfer. − In these systems, dispersion becomes coupled to gravitational instability, phase behavior, and time-dependent density evolution. ,,, It is important to distinguish these gas–liquid systems from the gravity-stable single-phase gas–gas displacements considered in this study. In CH₄–CO₂ mixing under moderate reservoir conditions, the flow remains single phase, density contrasts are comparatively small, and no interfacial or capillary effects are present. Therefore, dispersion is governed primarily by molecular diffusion and mechanical spreading induced by velocity heterogeneity and structural anisotropy. ,,− Consequently, conclusions drawn from multiphase gas–liquid systems cannot be directly extended to single-phase gas–gas transport. An experimental evaluation is required to isolate mechanical dispersion effects and assess directional behavior under gravity-stable gas–gas conditions.

This study directly evaluates the directionality of dispersion in both macroscopically homogeneous and heterogeneous porous media, which is important in numerous subsurface applications such as cyclic injection for energy storage (e.g., hydrogen storage, natural gas storage, compressed air storage), and gas huff-and-puff for enhanced hydrocarbon recovery in shales. The specific objectives are to experimentally quantify the longitudinal dispersion coefficient in End 1-to-End 2 and End 2-to-End 1 core orientations during CH₄–CO₂ displacement, differentiate lithological controls on dispersion magnitude, evaluate the influence of heterogeneity on directionality, and assess the role of permeability in both homogeneous and heterogeneous systems. To address these objectives, eight rock samples, including three carbonates and five sandstones, were subjected to CH₄–CO₂ core-flooding experiments at 300 psi and 65 °C. Directional differences in dispersion coefficients were measured for each rock type under identical operating conditions. By isolating gravity-stable single-phase gas–gas transport, this work provides the first systematic experimental evaluation of gas dispersion directionality for a wide range of sedimentary rocks.

The remainder of this manuscript is organized as follows. Section describes the experimental materials, core-flooding apparatus, and analytical methodology used to determine the longitudinal dispersion coefficient. Section presents structural observations of macro-heterogeneity, evaluates directional and permeability effects on dispersion, and discusses the mechanistic implications for transport modeling and cyclic subsurface gas operations. Section summarizes the principal findings and outlines future research directions.

2. Experimental Methods

This section outlines the gas dispersion experiments, which describe the materials, core-flooding apparatus, and experimental procedure. The materials subsection presents the rock samples and gases used in the study. The apparatus subsection details the core-flooding system, including components for pressure control, flow regulation, and effluent analysis. The procedure subsection explains the experimental workflow, covering sample preparation, flooding operations, and data acquisition and processing.

2.1. Materials

The experiments were conducted on eight rock samples, including three carbonates and five sandstones. These were chosen to represent a wide range of pore structures and macroscopic heterogeneity. The experiments were conducted on cylindrical cores with a physical diameter of 0.038 m and a total length of 0.3048 m. The images shown in Figure represent 0.1016 m-long sections of the full cores. Table summarizes the average brine porosity and directional brine permeability values measured from three companion core plugs obtained from the same outcrop block as the cores utilized in the dispersion experiments. The procedures for measuring porosity and permeability of core plugs are briefly outlined as follows. The core plugs were dried to a constant mass before testing. Porosity, ϕ, was determined by calculating the ratio of pore volume, V_p , to total bulk volume, V_b by vacuum-saturating the dry core with brine and measuring the weight gain. Permeability, k, was measured by loading the core plug into a high-pressure core holder under representative confining stress, pumping brine through the plug at dynamic flow rates, q, and recording the stable pressure drop, ΔP, across its length, L. Applying Darcy’s Law converts these dynamic variables into absolute permeability, $k=\frac{q·\mu ·L}{A·\mathrm{\Delta }P}$ , where μ is brine viscosity and A is core cross-sectional area. The differences in measured permeabilities in both flow directions (End 1-to-End 2 and End 2-to-End 1) were negligible. The working gases, CO₂ and CH₄, were supplied by Praxair. Methane was of ultrahigh purity (mole fraction = 0.999), and liquid CO₂ had a purity greater than 0.999 mole fraction. All cores were oven-dried before the experiments to remove residual moisture that could affect gas flow.

2.

Representative photographs of 0.1016 m-long sections from the full cylindrical cores, which had a physical length of 0.3048 m and physical diameter of 0.038 m. ILS: Indiana limestone. SD: Silurian dolomite. BS: Berea sandstone. CTS: Carbon Tan sandstone. NS: Nugget sandstone. BENS: Bentheimer sandstone.

1. A Summary of Core Samples Used in This Study.

Rock name	Porosity (%)	Brine permeability (m2)	Brine permeability (mD)
Indiana limestone 1 (ILS1)	15 ± 0.5	4.93 × 10–15 ± 2.47 × 10–16	5.00 ± 0.25
Indiana limestone 2 (ILS2)	19 ± 0.5	4.93 × 10–14 ± 2.47 × 10–15	50.0 ± 2.50
Silurian dolomite 1 (SD)	15 ± 0.5	5.03 × 10–15 ± 2.52 × 10–16	5.10 ± 0.26
Berea sandstone 1 (BS1)	25 ± 0.5	4.93 × 10–14 ± 2.47 × 10–15	50.0 ± 2.50
Berea sandstone 2 (BS2)	25 ± 0.5	1.25 × 10–13 ± 6.23 × 10–15	127 ± 6.3
Carbon Tan sandstone (CTS)	11 ± 0.5	9.87 × 10–15 ± 4.94 × 10–16	10.0 ± 0.50
Nugget sandstone (NS)	11 ± 0.5	4.93 × 10–15 ± 2.47 × 10–16	5.00 ± 0.25
Bentheimer sandstone (BENS)	24 ± 0.5	1.97 × 10–12 ± 9.85 × 10–14	2000 ± 100

2.2. Experimental Setup and Procedure

The gas dispersion experiments were conducted using a core-flooding setup as shown in Figure . Experiments were conducted at a core temperature of 65 °C as the representative temperature for moderate-temperature subsurface reservoirs, with the core outlet pressure maintained at 300 psi throughout all experiments using a back-pressure regulator. To ensure the preservation of both methane (CH₄) and carbon dioxide (CO₂) in a gaseous state, with a specific emphasis on the influence of rock properties on gas dispersion in single-phase flow, the intentionally reduced pressure of 300 psi was selected. Although this pressure is below the typical subsurface reservoir pressures, the utilization of liquid or supercritical CO₂ at elevated pressure is beyond the scope of this work. Absolute pressure transducers were installed at the inlet and outlet of the core holder, and the pressure drop across the core was determined by calculating the difference between these two measurements. The measured pressure drop ranged from approximately 0.5 to 2 psi, contingent upon the flow rate. The confining pressure was maintained at 500 psi. Furthermore, the core holder was oriented vertically, and CO₂ was injected from the bottom upward. The experimental procedure began with core preparation, where each rock sample was oven-dried at 100 °C for at least 24 h to remove residual moisture and establish single-phase gas conditions. The dried core was then placed inside a flexible rubber sleeve within a stainless-steel core holder, and confining oil was applied at 200 psi above the system pressure to prevent bypass flow. Before gas injection, the core was vacuumed for 1 h to remove any remaining air.

1.

Core-flooding experimental setup. The core outlet pressure is maintained at 300 psi by BPR 3 and BPR 4.

Once prepared, CH₄ was injected into the core at 300 psi to fully saturate the pore space. After saturation, CO₂ was introduced at controlled interstitial velocities of 1.69 × 10^–4, 2.12 × 10^–4, and 3.39 × 10^–4 m/s using a high-precision Quizix dual-cylinder pump to displace the resident CH₄. For each velocity, CO₂ was injected for a duration of 2 pore volumes. Complete breakthrough was consistently achieved by 2 pore volumes, which served as the termination point for each experiment. The displacement is considered gravity stable because CO₂ as the denser, displacing phase is flowing upward. Pressure gauges at the inlet and outlet continuously monitored system stability and pressure drop across the core. The effluent gas was collected and analyzed using a PerkinElmer Clarus 400 gas chromatograph equipped with a thermal conductivity detector (TCD) to quantify CH₄ and CO₂ concentrations. These measurements were used to construct gas breakthrough curves for dispersion analysis.

After completing the initial End 1-to-End 2 displacement, the core was removed from the vertical holder, flipped 180°, and reinstalled to perform the “End 2-to-End 1 orientation” experiment under identical operating conditions, i.e., the flipped core was first resaturated with CH₄ at 300 psi, followed by upward CO₂ injection at the same set of flow velocities (1.69 × 10^–4, 2.12 × 10^–4, and 3.39 × 10^–4 m/s). Gas concentrations were monitored continuously using the gas chromatograph to obtain the breakthrough curve for the End 2-to-End 1 dispersion.

2.3. Data Processing and Analysis

The longitudinal dispersion coefficient, K_L , was determined for both the End 1-to-End 2 and End 2-to-End 1 orientations by fitting the analytical solution of the one-dimensional advection–dispersion flow model to the measured effluent concentration. This solution describes the combined effects of advection, representing the bulk transport of the solute by the fluid flow, and dispersion, which accounts for spreading due to velocity variations and molecular diffusion.

$$C_D=\frac{1}{2}\left[\mathrm{erfc}\left(\frac{x_D-t_D}{2{(\frac{t_D}{P_e})}^{\frac{1}{2}}}\right)\right]+\frac{1}{2}\exp (x_D{P}_e)\left[\mathrm{erfc}\left(\frac{x_D+t_D}{2{(\frac{t_D}{P_e})}^{\frac{1}{2}}}\right)\right]$$ 1

where C_D = C/C ₀ is the dimensionless concentration with C ₀ being the inlet concentration and C being the concentration at the given time at the outlet; x_D = x/L is the dimensionless length where L is the characteristic length; t_D = ut/L is the dimensionless time with the interstitial velocity u and the time t; P_e = uL/K_L is the fitted experimental Péclet number.

Initially, the core was saturated with methane (CH₄), resulting in a zero initial concentration of carbon dioxide (CO₂). Subsequently, CO₂ was continuously injected at a constant flow rate, and the gas chromatography (GC) system was employed to measure the composition of the effluent gas. The GC concentration measurement exhibited an uncertainty of approximately ±5%, as determined using a certified gas standard. Since replicate core-flood experiments were not conducted, this value represents the uncertainty in gas composition measurement rather than the total experimental uncertainty in dispersion coefficient (K _L). Core length, porosity, interstitial velocity, and inlet CO₂ concentration were considered fixed parameters, while K_L was the parameter that was fitted. The analytical solution was fitted to the normalized breakthrough data using the Generalized Reduced Gradient nonlinear algorithm, which minimized the difference between measured and modeled concentrations. GC sampling delay and system dead volume were determined experimentally, and the corresponding time correction was subtracted from the measured breakthrough times before data normalization and curve fitting. The reliability of the fitted K_L values was assessed using the goodness-of-fit between measured breakthrough curves and the analytical model. The fitted Péclet numbers and root-mean-square error (RMSE) values are presented in Tables S2–S9. The Péclet numbers reported in this study are experimental Péclet numbers obtained from breakthrough-curve analysis. Since the fitted longitudinal dispersion coefficient represents the combined contribution of mechanical dispersion and molecular diffusion, these Péclet numbers serve as comparative fitting parameters to evaluate the shape of breakthrough curves and the apparent directional transport behavior. The corresponding breakthrough profiles and model fits are depicted in Figures S1–S8, where symbols represent experimental measurements and lines represent model fits. GC concentration uncertainty was propagated through the nonlinear fitting procedure using 65,536 Sobol quasi–Monte Carlo realizations. For each realization, nonzero C _D values were independently perturbed using a uniform distribution within ±5% of the measured value, bounded between 0 and 1, and the breakthrough curve was refitted to obtain K_L . The directional difference, ΔK_L , was then recalculated. The 2.5th and 97.5th percentiles were reported as the propagated 95% uncertainty interval.

The two flow orientations are referred to as End 1-to-End 2 and End 2-to-End 1 throughout the manuscript. These labels correspond to the fixed physical orientation of the core before and after inversion. The absolute value of the directional difference between the two flow orientations was calculated as

$$\mathrm{\Delta }{K}_L\%=100\times \frac{|K_{L,12}-K_{L,21}|}{\max (K_{L,12},K_{L,21})}$$ 2

3. Results and Discussion

The results begin with the representative images of rock samples to observe the extent and spatial distribution of macroscopic heterogeneity for each core. This is followed by an analysis of the impact of lithological differences on the magnitude of dispersion. The End 1-to-End 2 and End 2-to-End 1 dispersion coefficients obtained from the CH₄–CO₂ core-flooding experiments are compared to evaluate how heterogeneity and permeability affect the degree of dispersion directionality under identical conditions.

3.1. Observation of Rock Macroheterogeneity

Macroscopic heterogeneity refers to centimeter-scale spatial variations in rock structure, such as layering, banding, or compositional contrasts. − Unlike pore-scale heterogeneity, which governs local velocity distributions, macro-heterogeneity controls large-scale flow partitioning and the sequence in which the injected fluid encounters different structural domains. As a result, it can reorganize velocity fields during displacement and produce direction-dependent dispersion behavior. , High-resolution digital images were acquired for eight dry cores prior to gas-flooding experiments to observe large-scale heterogeneity. Each core was imaged under identical lighting conditions at 48 megapixels to document macroscopic features, including layering and vugs, as shown in Figure .

The limestone cores exhibit relatively uniform textures with minimal macroscopic heterogeneity. Indiana Limestone 1 (ILS1) and Indiana Limestone 2 (ILS2) demonstrate subtle grain-scale heterogeneity but lack persistent layering. Notably, ILS2 exhibits greater visual variability in cementation compared to ILS1. Silurian Dolomite (SD) contains a higher number of substantial vugs, although these features remain relatively continuous along the core length. These visible vugs are localized features and do not necessarily indicate high bulk porosity or permeability, particularly if they are sparse or poorly connected. Collectively, these observations suggest that the carbonate group (limestones and dolomite) is macroscopically homogeneous, characterized by the absence of pronounced layering.

Among the sandstones, Carbon Tan sandstone (CTS) exhibits a largely uniform texture with minimal visible layering, classifying it within the homogeneous group. Bentheimer sandstone (BENS) also displays a uniform texture with minimal layering, further supporting its classification. Berea sandstone 2 (BS2) exhibits weak layering oriented perpendicular to the flow axis, while Berea sandstone 1 (BS1) and Nugget sandstone (NS) display pronounced alternating light and dark bands associated with depositional compositional layering. These images demonstrate that the tested rocks encompass a wide range of macrostructural conditions, from macroscopically homogeneous limestones and dolomite to strongly layered sandstones. However, due to the classification being based solely on external photographs, internal permeability distribution, pore connectivity, tortuosity, and preferential flow pathways were not directly measured. Consequently, the visible structural features serve only as a basis for qualitative interpretation of potential directional transport behavior.

3.2. Directional Dispersion Behavior

Figure compares the fitted longitudinal dispersion coefficients, K_L , measured in the End 1-to-End 2 and End 2-to-End 1 orientations for all eight cores at three interstitial velocities. The corresponding values are summarized in Table S1 in the Supporting Information. The 1:1 reference indicates identical dispersion coefficients measured in the End 1-to-End 2 and End 2-to-End 1 core orientations. Figure presents the percentage change in dispersion coefficients across three increasing interstitial velocities, where the percentage change remains almost consistent across all velocities. This suggests that flow velocity has a limited impact on dispersion directionality in most rocks under the tested conditions.

3.

Comparison of K_L measured in the End 1-to-End 2 and End 2-to-End 1 orientations for eight rock samples at 300 psi and 65 °C. The dashed 1:1 line indicates directional independence.

4.

Percentage change in longitudinal dispersion coefficient (ΔK _L%) between End 1-to-End 2 and End 2-to-End 1 orientations for all rock samples at three different interstitial velocities.

Across all rock samples, K_L showed directional dependence. The two flow orientations differed by approximately 10–60%, which indicates that identical operating conditions can produce different apparent dispersion coefficients when the gas front enters the core from opposite ends. The fitted K_L values were also evaluated using RMSE values reported in Tables S2–S9 (in the Supporting Information) and breakthrough-curve fits shown in Figures S1–S8 (in the Supporting Information). The fitted experimental Péclet numbers further support the observed directional dependence in K_L . Lower fitted Péclet numbers correspond to broader breakthrough profiles and stronger apparent longitudinal dispersion, whereas higher fitted Péclet numbers indicate sharper breakthrough profiles and weaker dispersive spreading relative to advection. Since all the fitted Péclet numbers are higher than one, the primary transport mechanism is advection. Consequently, the dominant mixing mechanism between methane (CH₄) and carbon dioxide (CO₂) is mechanical dispersion, which serves as the focal point of this research. It is important to note that because these Péclet numbers are derived from the fitted breakthrough curves, they are interpreted as apparent transport parameters rather than direct measures of molecular diffusion versus advection. The directional differences in fitted Péclet number are therefore consistent with the directional differences in (K _L ), indicating that core inversion changes the apparent spreading behavior of the gas front.

The ± 5% GC concentration uncertainty was propagated through the breakthrough-curve fitting procedure to obtain 95% uncertainty intervals for the fitted K_L values and the corresponding directional differences, ΔK_L . Where the directional differences exceeded the propagated uncertainty, the results indicate that the directional dependence is unlikely to arise solely from GC measurement variability propagated through the curve-fitting procedure. Instead, the results suggest systematic flow reorganization induced by inverting the sequence of macroscopic heterogeneities encountered. This directional dependence reflects the changes in velocity fields when the core is inverted. It is hypothesized that the End 2-to-End 1 gas front encounters a new sequence of pore structures, potentially altering the activated flow pathways compared to the original orientation. Consequently, the velocity distribution and mixing length undergo changes, resulting in different dispersion coefficients. Therefore, dispersion in natural porous media should not be considered an intrinsic or purely scalar property. Instead, it may be influenced by the spatial order in which heterogeneities are encountered along the flow path. The subsequent sections will analyze how lithology, macroscopic heterogeneity, and permeability collectively control the magnitude of this directional dispersion behavior.

3.3. Influence of Lithology on the Magnitude of Dispersion

ILS1, SD, and NS were selected to compare samples with similar permeabilities, ranging from 4.93 × 10^–15 to 5.03 × 10^–15 m². The remaining samples were excluded from this comparison because their permeabilities differ substantially, which could confound lithological interpretation. These samples represent two rock types, carbonates and sandstones, to allow for a direct comparison of lithological effects while minimizing the influence of permeability. All tests were conducted under identical flow and pressure conditions to evaluate how lithology controls both the magnitude of the longitudinal dispersion coefficient. Figure shows the variation of the longitudinal dispersion coefficient, K_L , with interstitial velocity for the carbonate (ILS 1, SD) and sandstone (NS) samples. Across all tested velocities (1.69 × 10^–4 to 3.39 × 10^–4 m/s), the limestone and dolomite rocks show significantly higher K_L values (2.06 × 10^–6 and 6.46 × 10^–6 m² /s) than that for the Nugget sandstone sample (8.67 × 10^–7 to 3.34 × 10^–6 m² /s).

5.

Dispersion coefficient (K_L ) versus interstitial velocity for carbonate (ILS 1, SD) and sandstone (NS) samples with similar permeabilities for End 1-to-End 2 and End 2-to-End 1 orientation.

Carbonates may possess complex pore networks with irregular pore bodies, high coordination numbers, and extensive interconnections. ,, These features allow for a broader velocity distribution and result in stronger mechanical dispersion and higher K_L . However, their pore systems are well connected and relatively isotropic. If such pore systems represent the carbonates utilized in this study, the velocity field would be more comparable after core inversion, resulting in a restricted directional change in K _L . Sandstones, in contrast, exhibit simpler grain frameworks and narrower pore-throat size distributions. , Their flow pathways may be more localized, and preferential channels tend to form along the dominant displacement direction. Therefore, it may be hypothesized that when the core is flipped, these paths are not reactivated identically, leading to larger differences in measured K_L . Similar lithology-dependent dispersion behavior has been observed in pore-scale imaging and modeling studies, where carbonates show broader velocity distribution and stronger mechanical mixing than sandstones with uniform grain packing. ,,,,,,

While lithology can be used to characterize the magnitude of dispersion behavior, it cannot fully account for the variability in directional differences observed. For example, CTS exhibits a relatively high dispersion coefficient, but a higher degree of directional differences compared with other sandstones of similar permeability. This indicates that even within a single lithological group, dispersion behavior can vary significantly. Such variation implies that large-scale structural attributes, including visible layering and compositional contrasts, exert additional control on flow symmetry. The next section explores how these macroscopic heterogeneities influence the extent of dispersion directionality.

3.4. Effect of Macroscopic Heterogeneity on Dispersion Directionality

To qualitatively evaluate how visible macroscopic heterogeneity may influence dispersion directionality, CTS, BS1, and NS were compared because they exhibit progressively stronger differences in visible layering. The results shown in Figure indicate that the directional difference increases with visible heterogeneity. Imaging from Section indicates that CTS is macroscopically homogeneous, BS1 exhibits weak but continuous lamination, and NS shows strong layering with alternating density bands. Consistent with these observations, CTS, which lacks visible layering, exhibits minimal, but significant directional change of less than 20%. BS1, characterized by subtle lamination, displays an intermediate difference of 40%. NS, the most highly layered sample, shows the largest directional change of 57%. This trend suggests that macroscopic heterogeneity amplifies the directional dependence of dispersion, even under comparable flow conditions.

Additionally, the visible layering in the full 0.3048 m-long Nugget sandstone core suggests that the gas front may encounter a different sequence of structural features depending on flow orientation, as shown in Figure . This sequence dependence may contribute to the larger directional differences observed for Nugget sandstone compared with the less visibly layered samples. However, because the internal permeability distribution was not directly measured, this explanation is proposed as a possible mechanism rather than a direct observation. Hence, directional dependence was greatest in the strongly layered NS core, intermediate in the weakly laminated BS1 core. Remarkably, it is also quite significant in macroscopically homogeneous rocks such as CTS. While heterogeneity dictates how flow paths vary during core inversion, the extent to which this persists also depends on the rock’s permeability, which is explored in the next section.

6.

Macro-heterogeneity sequence for (a) End 1-to-End 2 displacement and (b) End 2-to-End 1 gas displacement.

3.5. Effect of Permeability on Dispersion Directionality

Permeability may influence the balance between advective spreading and diffusive mixing, as well as the velocity distribution within the pore network. To examine this, the percentage change in dispersion coefficient ΔK_L % across all flow rates was analyzed as a function of permeability for two structural categories: macroscopically homogeneous and heterogeneous rocks. Although SD lacks pronounced layering and was classified as macroscopically homogeneous based on external imaging, its visible vugs distinguish it from the more macroscopically uniform samples included in the permeability-trend analysis. SD was therefore excluded from this analysis.

Figure shows the relationship between ΔK_L % and permeability for the macroscopically homogeneous cores (ILS1, ILS2, CTS, and BENS) across all flow rates, where ΔK_L % ranges from approximately 2 to 30%. Within this group, directional differences decrease with increasing permeability. The low permeability sample ILS1 exhibits moderate directional differences, whereas the highly permeable BENS displays nearly symmetric transport with ΔK_L % values below 10%. This trend suggests that the velocity field becomes more similar after the core is inverted, limiting directional asymmetry and maintaining consistent mixing behavior.

7.

Percentage change in dispersion coefficient (ΔK_L %) as a function of permeability for both macroscopically homogeneous samples (ILS 1, ILS 2, CTS, BENS) and heterogeneous samples (NS, BS1, and BS2).

In contrast, the macroscopically heterogeneous samples (BS1, BS2, and NS) exhibit substantially larger directional differences, with ΔK_L % ranging from approximately 35 to 58%. Unlike the homogeneous group, no systematic relationship between permeability and directionality is observed. All heterogeneous samples show ΔK_L % values exceeding 40%, regardless of permeability. The absence of a clear correlation suggests that structural heterogeneity exerts a stronger control on dispersion directionality than permeability in these systems. In layered or anisotropic media, contrasts between high- and low-permeability bands dominate flow redistribution during inversion, overriding the influence of bulk permeability.

4. Conclusions

This study experimentally quantified the directionality of gas dispersion in porous media by conducting CH₄–CO₂ core-flooding experiments at 300 psi and 65 °C. Eight rock samples, including three carbonates and five sandstones, were used in both End 1-to-End 2 and End 2-to-End 1 orientation experiments to evaluate how lithology, macroscopic heterogeneity, and permeability affect the longitudinal dispersion. The fitted K_L values showed directional dependence across the tested samples. End 1-to-End 2 and End 2-to-End 1 dispersion coefficient values differed significantly even for macroscopically homogeneous rocks. Macroscopic heterogeneity, such as layering, was associated with larger directional differences in K_L , with differences reaching up to approximately 60%.

Carbonates exhibited higher dispersion coefficients and smaller directional differences than most sandstone samples. Macroscopically heterogeneous samples, such as NS and BS2, displayed the largest directional dependence, while homogeneous, high permeability rocks such as BENS and ILS2 showed nearly symmetric dispersion. This important observation indicates that permeability correlates with directional differences only in macroscopically homogeneous samples, while structural layering dominated flow reorganization in heterogeneous systems.

These findings have direct implications for modeling, upscaling, and predicting gas transport in subsurface processes such as enhanced gas recovery and underground energy storage. As such, assuming directionally independent dispersion in layered or anisotropic reservoirs can lead to inaccurate predictions of recovery/storage efficiency and produced fluid composition. Incorporating direction-dependent dispersion terms or structure-informed transport parameters can significantly improve the accuracy of large-scale subsurface models used for developing cyclic injection and withdrawal scenarios and dynamic optimal control of the subsurface processes.

The current research is confined to steady, single-phase gas flow under moderate pressure conditions. The experiments also do not directly replicate repeated cyclic injection and withdrawal because the CH₄-saturated initial condition was reestablished before each directional test. In actual cyclic operations, residual mixing, compositional history, and successive flow reversals may further influence gas dispersion. The observed dispersion behaviors in this work occur at pressures lower than those typically encountered in subsurface reservoirs. At 65 °C and elevated pressures exceeding 1100 psi, commonly encountered in subsurface reservoirs, carbon dioxide exists in a supercritical state. This state significantly influences mass transfer processes, including molecular diffusion and the local distribution of fluid velocity driven by buoyancy. Such influence can impact the role of rock properties on directional mechanical dispersion. Therefore, future research should expand upon this framework to address higher-pressure conditions, cyclic flow, multiphase systems, and internal rock characterization through computed tomography (CT) imaging or spatial permeability assessments.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c05136.

• Dispersion coefficient and the directionality metric, ΔK_L %, for eight rock samples; Péclet numbers and root mean square error (RMSE) for all rocks; breakthrough curves for all rocks (PDF)

The authors declare no competing financial interest.