Potential Benefits of Horizontal Wells for CO₂ Injection to Enhance Storage Security and Reduce Leakage Risks

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This work suggests that horizontal injectors are a safe way to keep CO₂ trapped in the storage site and reduce/prevent any unexpected event associated with leakage through the caprock since the horizontal well minimizes or avoids CO₂ contact with the caprock.

Abstract

This study used numerical simulations of CO₂ storage to identify the benefits of horizontal wells for geological carbon storage, such as enhancing CO₂ trapped in porous media due to relative permeability and capillary hysteresis. Two injection schemes were tested: one using a vertical injector and the other employing a horizontal well. The results revealed two main findings. Firstly, the horizontal injection well effectively prevented or minimized CO₂ penetration into the caprock across various sensitivity scenarios and over a thousand years of CO₂ redistribution. Secondly, horizontal wells provided a safe approach to trapping CO₂, increasing its entrapment as a residual phase by up to 19% within the storage site. This, in turn, reduced or prevented any unexpected events associated with CO₂ leakage through the caprock. Additionally, the paper proposes a practical method for designing the optimal length of a horizontal well. This method considers a combination of two parameters: the additional CO₂ that can be trapped using a horizontal well and the gravity number. In the case of the reservoir model of this study, a horizontal branch with a length of 2000 m was found to be the most effective design in enhancing CO₂ entrapment and reducing CO₂ buoyancy.

1. Introduction

Scenarios considered by international entities such as the International Agency (IEA) point out the complexity of actions needed to achieve goals established for reducing emissions of greenhouse gases in the coming decades, simultaneously with the desired transformation in energy generation sources. The report “World Energy Outlook 2022” [1] emphasizes that multiple technologies and energy sources will play an essential joint role in providing energy resources for the planet in a more sustainable scenario. Among the various options for reducing CO₂ emissions, Carbon Capture and Storage (CCS) presents itself as a technology with significant potential to reduce CO₂ emissions in a (probable) scenario of continued use of fossil fuels in the coming decades.

A CCS project involves CO₂ capture from high-emission industries and injecting it into geological formations such as aquifers and depleted hydrocarbon reservoirs. One of the most critical barriers to long-term and large-volume CO₂ storage in geological formations is the proof of safe and reliable storage. For that, CO₂ can take advantage of different trapping mechanisms in porous media [2,3,4,5]; for example, free CO₂ migration is controlled by the structural and stratigraphic trapping exerted by the caprock during the short term encompassing the injection time, known as a primary mechanism. During this stage, the caprock plays an essential role in the security of the CCS operation due to CO₂ buoyancy which can move it up to the surface or the seafloor in the case of offshore storage sites. In the Frio CO₂ field demonstration project conducted in the U.S. [6], CO₂ was injected in a deeper zone below several well-known shale seals. However, some authors [7] are currently reviewing the need for a caprock to control the plume rise because of the following reasons: (i) there is no prescriptive regulation concerning geologic seals; and (ii) the concept of the composite confining system is introduced, as a set of discontinuous barriers which create long and tortuous paths that attenuate mobile CO₂ rise.

During the mid- and long term, part of mobile CO₂ will be dissolved in water (solubility trapping), as time passes, especially in low-salinity brine under high-pressure and low-temperature conditions [8,9]. Saturation changes caused by the rising plume can lead to more CO₂ being trapped as a residual phase due to relative permeability and capillary hysteresis [10,11,12]. Beyond that, in few cases, some CO₂ can be trapped as minerals because of the resulting pH of the brine and the mineralogy of the rock [13,14]. Therefore, those additional mechanisms increase storage security, when the buoyant CO₂ is immobile in the pore space or no longer exists as a free phase (generally as super-critical CO₂).

Modeling CO₂ retention in porous media depends on the rock properties, such as porosity and permeability, and intrinsic parameters related to each trapping mechanism mentioned beforehand [15]. In this study, the entrapment of CO₂ in porous media will be rigorously modeled to allow a fair evaluation between two well geometries to inject CO₂: vertical and horizontal wells. The hypothesis to be investigated is related to CO₂ spreading around the well. With vertical wells, CO₂ is concentrated nearby with a limited spread due to the dominance of gravitational forces. However, with horizontal wells, CO₂ is broadly spread in porous media, developing a larger swept area, and it is thus likely to become trapped in that area due to hysteresis as a residual phase. Besides that, there is a possibility of contacting poor CO₂-saturated brine, enhancing the solubility and ionic entrapment. This analysis will be addressed during this comparison, as well as the better equilibrium between gravity and viscous forces provided by horizontal wells due to the main contribution of vertical permeability for the flow, reducing the buoyancy CO₂ flux.

The idea that the mass of residually trapped CO₂ is enhanced, when the plume migrates in the lateral direction was observed numerically by Han et al. [16], who investigated different levels of vertical and horizontal permeabilities in a model with a source point of injection. In the conclusion section of this work, the authors postulated that horizontal wells can be a likely means to increase the lateral extension of CO₂ plumes, taking advantage of the residual trapping mechanism. However, they did not simulate cases with horizontal wells, as is in the goals of our current study. In addition to that, our paper aims to expand the study by Okwen et al. [17]. They compared vertical and horizontal wells to store CO₂ in saline aquifers but did not consider the effect of hysteresis as a trapping mechanism, because their investigation was focused only on the injection time (50 years), where the system only underwent the drainage path. In other words, our work intends to evaluate the long-term CO₂ storage, modeling all of the trapping mechanisms that can occur.

Therefore, the innovative aspects of our work are summarized below:

• Providing technical arguments in favor of using horizontal wells in low- and mid-permeability targets (average less than 100–200 mD), considering the greater mass of CO₂ trapped as a residual fluid and the better equilibrium between gravity and viscous forces to control the CO₂ buoyancy, evaluating long-term storage (thousands of years of redistribution);
• Proposing a practical way to design the horizontal well length to maximize the CO₂ entrapment and make the flow less gravity-driven;
• Evaluating the impact of both strategies (vertical and horizontal injectors) on the risk of CO₂ penetration into the caprock, considering adsorption, diffusion, and the Darcy reactive flow.

The horizontal wells are applied in actual operating CCS projects worldwide. Sleipner in the North Sea and In Salah in the Sahara Desert are examples of storage sites with horizontal injectors [18]. Therefore, the broader impact of this research is intrinsically related to better control of the CO₂ plume redistribution, which has the following advantages:

• Preventing an unexpected and undesired interaction with the caprock, mainly related to the risk of CO₂ leakage due to fault/fracture activation or the creation of new fractures when the injection exceeds the minimum rock strength [19,20]. In addition, related to the geochemical reactions among the CO₂−brine−mineral system, which can affect the integrity of caprock and its sealing capacity with alteration in its petrophysical properties induced by mineral changes [21];
• Better control and monitoring of the CO₂ plume propagation to the CCS project evaluation with data from the injection or observation/monitoring wells, besides geophysical data, such as time-lapse seismic, vertical-seismic profiles (VSPs), and micro-seismic [5];
• Providing insights into the CO₂ storage in depleted oil/gas reservoirs where it is possible to use existing horizontal and multilateral wells.

The following conditions are outside the scope of this paper:

• Consideration of impurities and free water content in CO₂ stream injected;
• Modeling the dry-out effect due to water vaporization with CO₂ injection or another injectivity issue, which can be found in Machado et al. [22];
• CO₂ leakage through wells with poor cement jobs, as pointed out by Gholami et al. [23], can be the most important reason behind the migration and leakage;
• Drilling design planning and stability concerns for horizontal well construction;
• Investigation of solutions with horizontal branches to inject CO₂ and produce brine to relieve pressure buildup [24,25];
• Economic evaluation of vertical and horizontal wells. This specific evaluation would depend on factors such as the environment (onshore or offshore), well depth and length, and location of the operation.

2. Petrophysical Modeling for Sandstone and Shale

This study considered two sandstone geological models: homogeneous and heterogeneous saline aquifers (Figure 1). The caprock was modeled as a water-saturated shale, assuming homogeneous properties in both cases. The homogeneous model (Figure 1A) was 1000 m in width and 1200 m in thickness, of which 1000 m was the shale caprock. The gridblock size was 10 × 10 m² horizontally and 1 m thick.

Figure 1B shows the heterogeneous model with 7000 m in width and 2500 m in thickness (including the thickness of the shale caprock of about 1500 m). This latter model represented part of an actual sandstone aquifer, and it was built with seismic and well data from three wells drilled in that area, located at the Campos basin, Rio de Janeiro state in Brazil. This sector model had a pore volume of about 160 million m³; the gridblock size was 100 × 100 m² horizontally and 5 m thick. A grid refinement was performed around the injector to reduce the gridblock size from 100 m to 25 m, using the workflow proposed by Machado et al. [26].

Table 1. Summary of the main petrophysical properties used in the geological models.

	Homogeneous Model		Heterogeneous Model
	Sandstone	Shale	Sandstone	Shale
porosity (φ)	0.15	0.10	0.21 (mean)	0.10
permeability (k)	100 mD	0.001 mD	140 mD (mean)	0.001 mD
kv/kh ratio	0.1	0.1	0.1	0.1
pore compressibility	5.8 × 10−7 kPa−1	5 × 10−8 kPa−1	5.8 × 10−7 kPa−1	5 × 10−8 kPa−1
relative permeability	Figure 2	Figure 3	Figure 2	Figure 3
capillary pressure	Figure 2	Figure 3	Figure 2	Figure 3

summarizes the key petrophysical properties assigned to both models.

The relative permeability curves for CO₂ and brine in sandstone and shale were obtained by Bennion and Bachu [27]. The CO₂—brine capillary pressure curves were obtained from a J-function fitted to the data from Abdoulghafour et al. [28] for the sandstone and from Bennion and Bachu [29] for the shale. As the mean ratio k/φ was the same in both models, the capillary pressure curve resulting from the J-function is also the same. Figure 2 and Figure 3 show the final drainage curves used in the simulation for the aquifer and the caprock, respectively. The imbibition curves will be generated according to the hysteresis model to be detailed in the next section.

The capillary pressure in the shale caprock exhibited a threshold of 318 kPa, as depicted in Figure 3. This threshold represented the minimum pressure required to exceed the capillary forces and enable free super-critical CO₂ migration into the caprock.

3. Modeling CO₂ Entrapment for Sandstone and Shale Formations

The sandstone saline aquifer and its shale caprock in the aforementioned models were numerically simulated using CMG-GEM [30]. CMG-GEM is known for its versatility and robustness in predicting and analyzing various thermodynamic properties and fluid behavior for CCS projects [2,3,11,22,26]. It is based on the discretization of component conservation and energy balance equations in space and time using finite volume and finite difference methods [31,32].

One of the key strengths of the CMG-GEM model lies in its accurate prediction of CO₂ phase behavior for wide ranges of pressure and temperature. It can effectively capture the transition of CO₂ from gaseous to liquid states, as well as its behavior in supercritical conditions, which is crucial for understanding and studying CO₂ storage. Overall, the CMG-GEM simulation model enables accurate prediction and analysis of CO₂ behavior and the following trapping mechanisms:

• CO₂ solubility in brine according to the method by Li and Nghiem [33] based on Henry’s law. This model is based on Henry’s constant calculation according to Equation (1) as a function of pressure and temperature. The effect of salt on the gas solubility in the aqueous phase is modeled by the salting-out coefficient [34].

  $$ln\left(H_i\right)=ln\left(H_i^{*}\right)+\frac{\overline{v_i}}{RT}\left(p-p^{*}\right)$$

  (1)

  where:
  • $H_i$ is Henry’s constant at current pressure (p) and temperature (T);
  • $H_i^{*}$ is Henry’s constant at reference pressure (p*) and temperature (T);
  • $\overline{v_i}$ is the partial molar volume at infinite dilution;
  • R is universal gas constant;
  • I is species dissolved in water (CO_2(aq) in this work).

The $H_i^{*}$ constant was computed considering the initial conditions of the models in

Table 2. Summary of the initial conditions of the reservoir models.

	Homogeneous Saline Aquifer	Heterogeneous Saline Aquifer
Initial pressure	11,800 kPa at 1000 m	7159 kPa at 730 m
Temperature	80 °C	70 °C
Salinity	50,000 ppm	70,000 ppm
$H_i^{*}$	5.66 × 105	6.44 × 105

.

• Solubility trapping in brine can be enhanced by diffusion. To model this effect, the diffusion coefficient (D) for super-critical CO₂ in brine is applied to compute the effective CO₂ diffusion (D_eff) considering tortuosity τ [35]:

  $$D_{eff}=\frac{D}{\tau }$$

  (2)

  In shales, where diffusion is a relevant mechanism due to lower permeability, the tortuosity value ranges approximately from 40 to 70 [36]. An effective diffusion equal to 2.8 × 10⁻⁷ cm²/s [37] was used in the simulations.
• Chemical trapping by adsorption of CO₂ in the gas phase was modeled using a Langmuir model [38], which is a widely accepted isotherm adsorption equation [39,40]. With data for shales [41,42] and sandstone [43], two isotherms were matched to model the adsorption. Table 3 summarizes Langmuir parameters (^BCO₂ and ^ωCO_2,max) obtained according to Equation (3), that is, the extended Langmuir isotherm for multicomponent adsorption [44,45]:

  $${\omega }_{{CO}_2}=\frac{{\omega }_{{CO}_2, max}{B}_{{CO}_2}{y}_{{CO}_2, g}p}{1+p{{\displaystyle \sum }}_j{B}_j{y}_{j, g}}$$

  (3)

  where
  • ^BCO₂ is the parameter for Langmuir isotherm relation;
  • ^BCO₂ is the moles of adsorbed CO₂ per unit mass of rock;
  • ^ωCO_2,max is the maximum moles of adsorbed CO₂ per unit mass of rock;
  • ^YCO_2,g is the molar fraction of adsorbed CO₂ in the gas phase.
    Table 3. Parameters of Langmuir isotherm to model the CO₂ adsorption.

    	Sandstone	Shale
    $B_{{CO}_2}$	0.00017 kPa−1	0.00017 kPa−1
    ${\omega }_{{CO}_2, max}$	0.07 gmol/kg	0.18 gmol/kg

    Table 3. Parameters of Langmuir isotherm to model the CO₂ adsorption.

    	Sandstone	Shale
    $B_{{CO}_2}$	0.00017 kPa−1	0.00017 kPa−1
    ${\omega }_{{CO}_2, max}$	0.07 gmol/kg	0.18 gmol/kg

• The residual CO₂ trapping due to the relative permeability and capillarity hysteresis with the saturation changes was modeled with the maximum gas trapped (S_gt) converted to the Land’s constant (C) [46] in the two-phase Carlson’s model [47], as recommended by Jarrell et al. [48], according to Equation (4):

  $$S_{gt}=\frac{S_{g max}}{1+C{S}_{g max}}$$

  (4)

  where S_{g max} is the maximum gas saturation.

Burnside and Naylor [49] obtained a S_gt distribution for sandstone, shale, and carbonates based on more than 30 published coreflood data for CO₂ and brine. The mean value for each lithology is presented in

Table 4. Maximum gas trapped due to hysteresis of relative permeabilities and capillarity.

	Sandstone	Shale
Sgt	0.25	0.35

.

• Ionic trapping due to acidic water reactions for bicarbonate and carbonate ions generation was modeled using kinetic parameters from the PHREEQC database [50,51].

  OH⁻ + H⁺ = H₂O

  (5)

  CO₂ + H₂O = H⁺ + HCO₃⁻

  (6)

  CO₃²⁻ + H⁺ = HCO₃⁻

  (7)

  The synthetic water composition is given in Table 5 for the homogeneous case [52] and the heterogeneous case (Personal communication with PETROBRAS. 2023. Rio de Janeiro-RJ, Brazil).
  Table 5. Ionic composition of formation brine.

  Ions	Molality Concentration (gmol/kgw)
  	Homogenous	Heterogeneous
  pH	8.8	6.8
  Ca2+	0.0475	0.027
  Na+	0.3234	1.272
  Cl−	0.551	1.3
  Mg2+	0.0084	0.028
  K+	0.0071	0.013
  SO42−	0.022	0.000085

  Table 5. Ionic composition of formation brine.

  Ions	Molality Concentration (gmol/kgw)
  	Homogenous	Heterogeneous
  pH	8.8	6.8
  Ca2+	0.0475	0.027
  Na+	0.3234	1.272
  Cl−	0.551	1.3
  Mg2+	0.0084	0.028
  K+	0.0071	0.013
  SO42−	0.022	0.000085

• The following mineralization reactions with primary minerals were modeled using kinetic parameters from PHREEQC for Transition State Theory (TST)-derived rate laws:

  Quartz [SiO₂] = SiO_{2 (aq)}

  (8)

  Kaolinite [Al₂Si₂O₅(OH)₄] + 6.0 H⁺ = 5.0 H₂O + 2 Al³⁺ + 2 SiO_{2 (aq)}

  (9)

  Calcite [CaCO₃] + H⁺ = Ca²⁺ + HCO₃⁻

  (10)

  Illite [K_0.6Mg_0.25Al_2.3Si_3.5O₁₀(OH)₂ + 11.2 H₂O = 3.5 H₄SiO₄ + 2.3 Al(OH)₄⁻ + 0.6 K⁺ + 0.25 Mg²⁺ + 1.2 H⁺

  (11)

  Albite [NaAlSi₃O₈] + 4 H⁺ = 3 SiO_{2 (aq)} + Al³⁺ + Na⁺ + 2 H₂O

  (12)

  Anorthite [CaAl2Si₂O₈] + 8 H₂O = 2 H₄SiO₄ + 2 Al(OH)₄⁻ + Ca²⁺

  (13)

  Chlorite [Mg₅Al₂Si₃O₁₀(OH)₈] + 16.0 H⁺ = 5.0 Mg²⁺ + 2.0 Al³⁺ + 3.0 H₄SiO₄ + 6.0 H₂O

  (14)

  Dolomite [CaMg(CO₃)₂] = 2 CO₃²⁻ + Mg²⁺ + Ca²⁺

  (15)

  Pyrite [FeS₂] + 2 H⁺ = 2 HS⁻ + Fe²⁺

  (16)

  The initial mineral compositions for the shale caprock [52] and for the sandstone [53] are summarized in Table 6. Illite is the most abundant clay mineral in the shale matrix, occurring in the sandstone matrix. The long-term exposure of clay minerals to Sc-CO₂ (super-critical CO₂) can generate strong CO₂ adsorption [54], justifying the modeling of this phenomenon to increase CO₂ storage capacity.
  Table 6. Mineral composition for the sandstone aquifer and the shale caprock.

  	Sandstone	Siliceous Shale
  Mineral	Normalized Volume Fraction	Normalized Volume Fraction
  quartz	0.614	0.277
  kaolinite	0.021	0.015
  calcite	0.020	0.073
  illite	0.011	0.374
  albite	0.210	0.063
  anorthite	0.076	0.115
  chlorite	0.048	0.038
  dolomite	0.000	0.021
  pyrite	0.000	0.023

  Table 6. Mineral composition for the sandstone aquifer and the shale caprock.

  	Sandstone	Siliceous Shale
  Mineral	Normalized Volume Fraction	Normalized Volume Fraction
  quartz	0.614	0.277
  kaolinite	0.021	0.015
  calcite	0.020	0.073
  illite	0.011	0.374
  albite	0.210	0.063
  anorthite	0.076	0.115
  chlorite	0.048	0.038
  dolomite	0.000	0.021
  pyrite	0.000	0.023

Permeability alteration due to mineral precipitation or dissolution was computed by applying the Kozeny−Carman equation with an exponent value of 3, recommended by Zeidouni et al. [55]:

$$k_k=k_n/rf$$

(17)

where

$$rf=r{f}_n{\left(\frac{{\phi }_n}{{\phi }_k}\right)}^3{\left(\frac{1-{\phi }_k}{1-{\phi }_n}\right)}^2,$$

(18)

where the resistance factor rf is modeled by the Kozeny−Carman equation or the power law relationship, and k_n and k_k refer to permeability at previous (n) and current (k) timesteps, respectively. The porosity, φ, in Equation (18) is calculated as follows:

$$\phi =\left[1+c_f\left(p-p^{*}\right)\right]\left[{\phi }^{*}-{{\displaystyle \sum }}_{j=1}^n\left(\frac{N_j}{{\rho }_{m,j}}-\frac{N_j^0}{{\rho }_{m,j}}\right)\right],$$

(19)

where φ* is the reference porosity for the case without mineral precipitation/dissolution, Nj is the total moles of mineral j per bulk volume at the current time, $N_j^0$ is the total moles of mineral j per bulk volume at the initial time, ρ_m,j is the mineral molar density, c_f is the rock compressibility, and p* is the reference pressure.

4. Potential Changes in the Caprock Integrity with a Vertical Injector

Figure 4 brings up the motivation for this study. It compares the injection of 7000 tonnes of CO₂ (3.5% of the initial pore volume) over 30 years through a vertical well perforated at the bottom of the aquifer (Figure 4A) and two cases with horizontal wells (400 m and 800 m in length indicated by L_w; Figure 4B,C), simulated in the homogeneous aquifer model. The horizontal wells were located at the same depth of the shallowest perforation of the vertical well at 1170 m. In this figure, the CO₂ in terms of global mole fraction, after 3000 years of redistribution, contacted and penetrated, mainly by diffusion, the caprock, when the injection well was vertical. On the other hand, the longer the horizontal well, the further away the CO₂ plume was from the caprock.

From Figure 4, in the vertical case, the upward movement of CO₂ was more prominent, leading to contact with the caprock, which had much lower permeability. This resulted in the CO₂ plume spreading extensively at the interface between the caprock and the host sandstone formation.

In contrast, in the horizontal well case, the CO₂ movement exhibited two distinct peaks, representing the toe and heel of the horizontal well. These peaks indicated areas of higher injectivity compared to other sections of the well, primarily due to the larger open area available for fluid flow. The presence of these peaks in the horizontal well configuration suggests that the CO₂ distribution and injectivity were not uniform along the entire length of the well.

A more significant CO₂ spreading with a horizontal well allowed more CO₂ to be trapped due to hysteresis. Figure 5 in the study illustrates the CO₂ inventory after a period of 3000 years of redistribution. The figure utilizes the following terminology to depict the different forms of the CO₂ inventory:

• % free Sc-CO₂: free CO₂ as a super-critical fluid;
• % CO₂ adsorbed: CO₂ adsorbed on the rock by chemical trapping;
• % CO₂ in water: dissolved CO₂ in aqueous phase, CO_{2 (aq)};
• % residual CO₂: CO₂ trapped as a residual gas due to relative permeability and capillarity hysteresis.

Figure 5 highlights the smaller percentage of free CO₂ as a supercritical fluid (1.6% of free Sc-CO₂ in purple) and the greater amount as a residual fluid (37% of residual CO₂ in yellow) provided when a horizontal injector well was used (Figure 5B). The free Sc-CO₂ increased to 13% with a vertical well, and the residual CO₂ reduced to 24% (Figure 5A). The CO₂ dissolution in the brine (% CO₂ in water in blue) was roughly the same in both cases (vertical and horizontal wells), in agreement with the conclusions from Okwen et al. [17] for short-term storage evaluations.

The higher amount of CO₂ adsorbed (4.1% of CO₂ adsorbed in green) in Figure 5A with a vertical injector is due to the CO₂ penetration in the caprock, which contained 22% of the mass injected. As discussed before, adsorption was much more relevant in the shale rock compared to in the sandstone aquifer minerals, and this was confirmed by Figure 6, with the inventory for each region (caprock and aquifer). Figure 6B shows that almost 11% of CO₂ was adsorbed in the shale and that most of the CO₂ in the caprock penetrated it by diffusion since CO₂ dissolved in the brine was the highest amount (41.8%). Since there was no invasion of CO₂ to caprock for the case with the horizontal well, the adsorbed quantity was expected to be lower, as shown in Figure 5.

The mass of mineralized CO₂ was omitted from the previous graphs, because it was only 0.0005% of the total injected after 3000 years. It was mainly related to the calcite (83% in moles), dolomite (8% in moles), and pyrite (9% in moles) precipitation in the caprock with the vertical injector where CO₂ contacted the caprock. There was no evidence of mineralization inside the aquifer since mainly non-reactive minerals constitute the sandstone matrix. Thus, those reactions are more relevant for modeling the caprock.

To compute how horizontal wells can make the CO₂ flow less gravity-driven compared to vertical wells, the concept of the gravity number introduced by Zhou et al. [56] was applied, specified by Equation (20):

$$\frac{M{N}_{gv}}{1+M}$$

(20)

where

$N_{gv}=\frac{\Delta \rho gL{k}_v}{Hu{\mu }_{brine}}$, which is the characteristic time ratio for fluid to flow in the transverse direction due to gravity;

M is the mobility ratio;

$\Delta \rho$ is the density difference between the brine and CO₂;

g is the acceleration due to gravity;

L is the length of the aquifer;

H is the aquifer thickness;

k_v is the average vertical permeability;

u is the Darcy velocity (=interstitial velocity × φ);

${\mu }_{brine}$ is the brine viscosity.

The higher the gravity number (Equation (20)) is, the more gravity-dominant the flow becomes. In our comparison, a value of 200 was calculated for a vertical well, whereas it was 100 for a horizontal well with 800 m of length, reinforcing the buoyancy observation in Figure 4.

The invasion depth in caprock due to diffusion reached over 26 m after 3000 years using a vertical well (based on the values of CO₂ in the aqueous phase (CO_2(aq)). The CO₂ gas saturation plume (CO_2(g)) in Figure 7 was only 17 m thick, highlighting that the diffusive flow was more relevant than Darcy flow in the caprock, as concluded by Currenti et al. [57] during the numerical investigation of CO₂ leakage scenarios in shale caprock. Higher capillary pressure, critical water saturation typical of the shale (Figure 3), and lower permeability all inhibited the CO₂ convective flow through the caprock.

This computed upward CO₂ velocity of 26 m/3000 years had the same magnitude compared with other numerical studies, such as 3 m/100,000 years [36], 8 m/100,000 years [58], and 1 to 77 m/1000 years [57]. The numbers are unequal due to differences in the models’ properties and grid resolution and should be used only for qualitative comparison. In our case, a vertical refinement by a factor of 10 times was tested 50 m under and above the interface between sandstone and shale rocks using gridblocks of a 0.1 m thickness. With the finer gridblocks, the penetration was reduced by only 15% from the estimated penetration (22 m).

Those results show that CO₂ penetration in the caprock is possible (mainly by diffusion) and can generate leakage to the surface or other non-target zones when the migration is associated with flow through fault/fracture potentially activated by the pressure buildup [57]. Figure 8 compares the CO₂ propagation in terms of saturation and aqueous mole fraction when an open fracture with 10 mD of intrinsic permeability and an aperture of 0.00014 m was placed inside the caprock [57]. This represented a single natural fracture with a length of 1600 m which traversed the entire thickness of the caprock (it did not intersect the sandstone). It was characterized by the fixed intrinsic permeability and aperture for numerical flow simulation through it. As the dynamic and geomechanical behavior of the fracture (such as fracture propagation) was not considered in the modeling process, there was no requirement to specify the mechanical properties. The flow in the fracture was modeled using the Embedded Discrete Fracture Model (EDFM) [59,60,61,62] according to the procedure proposed by Machado et al. [63], which validated the EDFM application to reactive transport simulation in fractured media. In the current case, the dissolved CO₂ in brine diffused into caprock and rose through the fracture due to its higher permeability than that of the shale caprock. Therefore, the penetration of the CO_2(aq) (70 m) was also greater than by CO_2(g) (17 m), as observed in Figure 7, making the leakage more likely when there were active fractures or faults in the shale caprock. To prevent or minimize this risk, the application of horizontal wells will be investigated in a heterogeneous and more realistic aquifer model in the next section.

5. Sensitivity Analysis with a Horizontal Injector

In the previous section, some advantages emerged regarding horizontal wells for a CCS project. In summary, they are shown as follows:

• the wider lateral extension of the CO₂ plume in comparison to the vertical rise;
• more CO₂ trapped as a residual fluid as it spreads in the porous media;
• less gravity-dominant flow.

Consequently, the risk of contacting the caprock can be reduced, preventing leakage by diffusion or flow through geological features in the shale, such as fractures or faults.

To evaluate those points better, a thorough sensitivity analysis will be conducted in the heterogeneous aquifer model to compare the horizontal well performance and a vertical injector. As our goal mainly focuses on the flow inside the aquifer and preventing flow in the caprock, heterogeneity is more critical in the sandstone layers. Table 1 provides the base case properties for the heterogeneous aquifer, keeping the caprock permeability homogeneous. The pore volume injected (PVI) will be 6.5% over 25 years.

5.1. Sensitivity to the Horizontal Well Length (L_w)

Figure 9 brings the intuitive conclusion from the previous discussion on the lateral spreading of CO₂ when a horizontal well was used. In this case, this lateral spreading became wider for a longer horizontal well. From L_w = 2000 m, after 3000 years of redistribution, there was no CO₂ in contact with the caprock in terms of global mole fraction, which accounted for the total CO₂ concentration in both brine and gas phases. Hence, the case with L_w = 2000 m was further considered in the base case with a horizontal well. This case showed no invasion of CO₂ into the caprock, while the equivalent vertical injector had 2% brine with dissolved CO₂ diffused into the caprock.

5.2. Sensitivity to the Injection Rate

The base case injected 6.5% PV at 350,000 metric tonnes/year as a typical field project injection rate. The CO₂ mass injected was kept the same for these cases (~6.5% PVI), but the injection rate was varied. Figure 10 shows that the CO₂ distribution was insensitive to the injection rate for long-duration evaluation since the total mass injected was the same and the long-term entrapment is a function of petrophysical and trapping parameters, which remained unchanged.

5.3. Sensitivity to the Horizontal Permeability

The permeability of the aquifer was increased by a factor of 10, keeping the ratio of k_v/k_h equal to 0.1. In both cases, the CO₂ plume reached the caprock (Figure 11), emphasizing the main advantage of horizontal wells over vertical wells is in low- to mid-permeability reservoirs.

5.4. Sensitivity to the k_v/k_h Ratio

Assuming the properties of the base case (Table 1), the ratio of vertical to horizontal permeability was changed between 0.01 and 0.6. The results in Figure 12 confirm the lower risk of contacting the shale caprock when a horizontal well was used with a broad range of k_v/k_h ratios.

5.5. Sensitivity to the Natural Water Flow

Aquifers typically receive groundwater recharge, generating a natural flux in porous media. For the specific target represented by the heterogeneous base model, the natural water flow velocity was assumed to be 0.0015 ft/d [64]. To model this effect, two open boundary conditions were imposed on the lateral edges of the aquifer, coupled with an analytical function to calculate the water influx to the aquifer using the Carter−Tracy method [65]. The left edge was modeled as the source, and the right edge was modeled as the sink, as represented in Figure 13. Calibrating the analytical aquifer permeability, it was possible to calculate a similar velocity of 0.0015 ft/d (yellow region in Figure 13).

Despite the low velocity, this flux affected the CO₂ plume propagation. Increased plume spreading makes the monitoring more challenging and impossible to prevent contact with the caprock even with a horizontal well.

Table 7. Lateral CO₂ plume extension in the aquifer, thickness in the caprock and the diffused mass of brine mass saturated with CO₂.

	Aquifer CO2 Plume Spread (m)	Caprock CO2 Plume Thickness (m)	Brine in the Caprock (% in Mass)
vertical injector	2980–5510	36−6	2.0−1.1
horizontal injector with a 2000 m length	0–1440	0–6	0.0–0.26

shows the lateral spread of the CO_2(g) plume and the thickness inside the shale from Figure 14 and the percentage of brine mass with CO_2(aq) inside the caprock from Figure 15.

It is clear that the natural water flux contributed to expanding the CO₂ lateral extension, limiting its vertical migration, e.g., reducing the leakage risk but making it more difficult for plume monitoring with observation wells due to its spread over thousands of meters and with seismic methods due to its small thickness (the thickness of less than 10 m was challenging due to the seismic vertical resolution).

However, this contact with the shale overburden using the vertical well case was still more pronounced compared to that using the horizontal well, which further increased the risk of flowing via existing or activated fractures and faults in the caprock.

5.6. Sensitivity to the Time of Redistribution

All of the previous analyses show that horizontal wells were more resilient than vertical ones in preventing contact with the caprock and consequently avoided CO₂ leakage through paths that existed or could be created inside the shale. Figure 16B expands the timeframe of the base case over 20,000 years and confirms no contact with the caprock when a horizontal well with L_w = 2000 m was considered in the base case. The equivalent plot for the vertical well in Figure 16A shows that the CO₂ diffusion into the caprock reached 3% of the mass of the brine with CO_2(aq) at 20,000 years, against 2% at 3000 years.

6. Horizontal Well Design

The study identified two primary findings associated with the use of horizontal wells in CO₂ storage:

• Horizontal injection wells effectively prevent or minimize CO₂ penetration into the caprock across various sensitivity scenarios. This finding is closely linked with the buoyancy effect, which can be modeled by the gravity number introduced in Equation (20). Consequently, the gravity number is one of the variables used to determine the optimal length of horizontal wells;
• Horizontal wells offer a safer approach to trapping CO₂ by increasing its entrapment as a residual phase compared to the use of vertical wells as injectors. In this context, the additional CO₂ trapped as a residual phase becomes a crucial variable.

Therefore, the ideal length for a horizontal well would be one that maximizes CO₂ entrapment while minimizing buoyancy effects.

To confirm our hypothesis that the wider the lateral CO₂ spreading, the more the residual entrapment, Figure 17 brings the evolution of the residual CO₂ trapped by hysteresis for the cases considered in Figure 9. Figure 17 shows that a longer L_w increased residual saturations as the plume contacted new permeability regions of the aquifer. However, the residual CO₂ mass developed a plateau after 1500 years for all these cases, which represented the optimum value. For instance, from L_w = 2000 m, there was no additional entrapment for longer horizontal branches. Therefore, L_w = 2000 m seems to be an optimum length for the entrapment.

Figure 18 combines two parameters plotted against the length of the horizontal well:

• On the left: the difference between the CO₂ saturation trapped as a residual phase (∆CO₂ residual) obtained with the vertical well minus the one with the horizontal well after 1500 years, corresponding to the time of plateau in Figure 17;
• On the right: the gravity numbers according to Equation (20) for different well lengths.

Due to the permeability heterogeneity, a well length of L_w = 2000 m had more access to higher permeability regions (i.e., concentrated in the middle of this model). Hence, it developed higher z-transverse velocities (u in Equation (20)), causing a lower gravity number for the well length of 2000 m (Figure 18).

This combination allows setting an optimum horizontal well length to enhance the CO₂ entrapment and to control the rise of the CO₂ plume, preventing its contact with the caprock and mitigating the associated risks. In this case, the optimum considering both purposes was L_w = 2000 m, which is technically possible according to actual CCS field projects [18,25].

Figure 18. The difference between the residual trapped CO₂ for vertical and horizontal wells (axis on the left) and the gravity number (axis on the right) against the well length after 1500 years.

Figure 18. The difference between the residual trapped CO₂ for vertical and horizontal wells (axis on the left) and the gravity number (axis on the right) against the well length after 1500 years.

7. Conclusions

The main conclusions are summarized below:

• The CO₂ intrusion into the caprock was mainly dominated by diffusion of the dissolved CO₂ in the brine. This can become more critical, if this solution accesses active faults and fractures of the shale caprock;
• The impact of mineral precipitation in the caprock and its integrity was negligible, with only an insignificant precipitation of about 0.0005% of the total injected CO₂ after 3000 years. Therefore, considering reservoir parameters such as mineralogy, pH, injection rate, pressure, and temperature, there was a small risk for caprock integrity due to mineralization/dissolution;
• Horizontal wells were more effective in controlling the CO₂ buoyancy due to two mechanisms:

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  enhancement of the CO₂ entrapment as a residual phase by up to 19% due to relative permeability/capillary pressure hysteresis where the more spread plume contacted new portions of the aquifer pore volume;

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  the better balance between gravity and viscous forces provided by horizontal wells compared to by vertical wells, with up to an 18% reduction in this balance compared to the vertical well case. The conclusion was based on simulations of homogeneous and heterogeneous sandstone saline aquifers over thousands of years.

• A sensitivity test showed the following results:

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  hypothesis was mainly valid for low- and mid-permeability aquifers (<200 mD);

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  for long-term evaluation, there was no significant impact on the injection rate for the same CO₂ mass injected;

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  the natural flux in aquifers can affect the plume propagation, triggering its contact with the caprock even with horizontal wells; and

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  these conclusions regarding horizontal wells persisted over tens of thousands of years.

• A practical method was proposed to design the optimum length for horizontal wells, combining the maximum CO₂ saturation trapped as the residual phase and the gravity number.

These results present an exciting opportunity to further enhance CO₂ entrapment in CCS projects. The study’s findings provide a basis for exploring alternative project options. These alternatives may involve optimizing well geometry, considering uncertainties in trapping properties and exploring different geological realizations.

By incorporating well geometry optimization techniques and accounting for uncertainties, it is possible to improve CO₂ entrapment and storage efficiency. This approach allows for a more comprehensive assessment of potential benefits and risks associated and opens up promising perspectives for advancing CCS projects.