Three-phase flow is a key process occurring in subsurface reservoirs, for example, during CO2 sequestration and enhanced oil recovery techniques such as water alternating gas (WAG) injection. Predicting three-phase flow processes, for example, the increase in oil recovery during WAG, requires a sound understanding of the fundamental flow physics in water- to oil-wet rocks to derive physically robust flow functions, i.e. relative permeability and capillary pressure. In this study, we use pore-network modelling, a reliable and physically based simulation tool, to predict the flow functions. We have developed a new pore-scale network model for rocks with variable wettability, from water- to oil-wet. It comprises a constrained set of parameters that mimic the wetting state of a reservoir. Unlike other models, it combines three main features: (1) A novel thermodynamic criterion for formation and collapse of oil layers. The new model hence captures wetting film and layer flow of oil adequately, which affects the oil relative permeability at low oil saturation and leads to accurate prediction of residual oil. (2) Multiple displacement chains, where injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows for the accurate modelling of the mobilisation of many disconnected phase clusters that arise, in particular, during higher order WAG floods. (3) The model takes realistic 3D pore-networks extracted from pore-space reconstruction methods and CT images as input, preserving both topology and pore shape of the sample. For water-wet systems, we have validated our model with available experimental data from core floods. For oil-wet systems, we validated our network model by comparing 2D network simulations with published data from WAG floods in oil-wet micromodels. This demonstrates the importance of film and layer flow for the continuity of the various phases during subsequent WAG cycles and for the residual oil saturations. A sensitivity analysis has been carried out with the full 3D model to predict three-phase relative permeabilities and residual oil saturations for WAG cycles under various wetting conditions with different flood end-points.@en

Naturally Fractured Reservoirs (NFR) contain a significant amount of remaining petroleum reserves and are now considered for Enhanced Oil Recovery (EOR) schemes that involve three-phase flow such as water-alternating-gas (WAG) injection. Reservoir simulation of three phase flow is challenging because a proper set of flow functions, i.e. relative permeability and capillary pressure functions, that describe the underlying physics of fluid displacement is vitally important to obtain reliable production forecasts but associated with high uncertainty. For NFR, another challenge is the upscaling of recovery processes, particularly fracture-matrix transfer during three-phase flow, to the reservoir scale using dual porosity or dual permeability models.In this work we approach a solution to these challenges by analysing three-phase flow during WAG injection at various scales, starting at the pore scale and then move on to an intermediate scale which is comparable to the scale of a single reservoir simulation grid block. At this scale, we represent fractures and matrix using a fine-grid model that employs empirical and pore-network modelling derived three-phase flow functions to study the effect of capillary and gravity forces on fracture-matrix transfer. We also consider different matrix wettabilities and permeabilities, as well as matrix block size distributions. We then perform an upscaling step that is typical for field-scale recovery simulations and use the dual porosity model to represent fracture-matrix transfer processes that were observed at the grid-block scale. This enables us to analyse and improve the accuracy of dual porosity models for three-phase displacement processes inherent to WAG in NFR.We find that different three-phase saturation profiles develop inside matrix blocks, which are strongly dependent on wettability of the matrix. These profiles have a profound impact on recovery during WAG injection. The classical dual porosity model fails to capture these saturation profiles and hence miscalculates recovery during early WAG cycles. We present a double block dual porosity model, i.e. a simple multiple continua model, which better matches the fine grid simulation results.@en

Three-phase flow in porous media is of great importance in enhanced oil recovery processes such as Water-Alternating-Gas (WAG) injection. In this work we use a new three-phase flow pore-network model, which fully captures the three-phase microscopic displacement processes, including accurate descriptions of oil films and layers, and which takes realistic 3D pore geometries extracted from pore-space images as an input. The pore-scale model is used to calculate physically robust relative permeability and capillary pressure functions for a range of realistic wettability scenarios. These three-phase flow functions have been used in a heterogeneous reservoir model with a range of equiprobable geological realisations of permeability and porosity distributions to demonstrate their impact on oil recovery after water, gas or WAG injection.Simulations at the pore-scale show that the residual oil saturations for a water-wet system are higher after water flooding compared to the corresponding residual oil saturations after gas injection. Residual oil saturations for oil-wet systems are significantly lower after both water and gas injection. This is due to the presence of stable oil wetting films, which provide hydraulic connectivity at low oil saturations.Simulations at the reservoir scale show that the lowest oil recovery for a water-wet case is obtained when a single fluid (gas or water) is injected; WAG injection yields significantly higher recovery factors. If the reservoir is oil-wet, however, pure gas injection results in the highest oil recovery. Overall, field-scale recovery predictions are very sensitive to the combination of both, different geological models and different three-phase relative permeability functions. Comparing recovery factors for network-derived and empirical relative permeability models demonstrates that the uncertainty in predicting oil recovery resulting from the choice of three-phase relative permeability models can be as large as the geological uncertainty present in a model that has been history matched using production data from a prolonged waterflood. This implies that the choice of three-phase flow functions directly affects the viability of WAG projects.@en

Carbonate reservoirs contain more than half of the world's remaining petroleum reserves and are increasingly becoming targets for water-alternating-gas (WAG) flooding as secondary or tertiary recovery. Heterogeneity in carbonate reservoirs spans from pore- to reservoir-scale. This is exacerbated by the presence of natural fractures and post-depositional dissolution. Furthermore, carbonate reservoirs tend to have variable wettability that impacts fluid flow which adds to reservoir uncertainty and renders managing WAG floods difficult. In this work, we examine the effect of rock and wettability heterogeneity on recovery profiles in naturally fractured carbonate reservoirs (NFCR). To simulate WAG flooding in NFCR with arbitrary wettability, we use saturation functions derived from a state-of-the-art pore network model to preserve multi-scale heterogeneities at the pore-scale. We study the interplay of capillary, gravity and viscous forces at an intermediate scale, then simulate WAG flooding in the presence of fractures in a heterogeneous carbonate ramp outcrop model. Adding the permeability and wettability heterogeneities impacts ultimate recoveries during water injection cycles by up to 6% and 14% absolute, respectively. Both heterogeneities affect the speed of recovery during gas injection cycles. Depending on its relation to permeability distribution, non-uniform wettability of matrix blocks can have a substantial impact on recovery during water injection cycles while recovery efficiency during the gas injection cycle can be reduced by a factor of 50%. Our work identifies the key factors that must be considered when modelling WAG floods in NFCR. We evaluate the reliability of conventional dual-porosity/dual- permeability numerical simulation approaches for NFCR by comparing results with multi-stage upscaled models through which we capture the fundamental controls on multi-phase flow. Hence, we can offer explanations for possible NFCR responses to WAG flooding and novel ways to improve the predictive ability of field-scale numerical simulation models.@en

Three-phase flow is a key to many EOR techniques such as Water Alternating Gas (WAG) injection. Predicting oil recovery during three-phase EOR in carbonates requires a sound understanding of the fundamental flow physics in mixed- to oil-wet rocks to derive physically robust flow functions, i.e. relative permeability and capil-lary pressure. In this work we use pore-network modelling, a reliable and physically-based simulation tool, to predict the flow functions. We have developed a new pore-scale network model for rocks with variable wettabil-ity, from mixed to oil-wet. It comprises a constrained set of parameters that mimic the wetting state of a reser-voir. Unlike other models, it combines three main features: (1) A novel thermodynamic criterion for formation and collapse of oil layers. The new model hence captures wetting film and layer flow of oil adequately, which affects the oil relative permeability at low oil saturation and leads to accurate prediction of residual oil. (2) Mul-tiple displacement chains, where injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows accurate modeling of the mobilization of many disconnected phase clusters that arise during higher order (WAG) floods. (3) The model takes realistic 3D pore-networks extracted from pore-space reconstruction methods and CT images as input, preserving both topology and pore shape of the rock. We validated our network model by comparing 2D network simulations with published data from WAG floods in oil-wet micromodels. This demonstrates the importance of film and layer flow for the continuity of the various phases during subsequent WAG cycles and for the residual oil saturations. A sensitivity analysis has been carried out with the full 3D model to predict three-phase relative permeabilities and residual oil saturations for WAG cycles under various wetting conditions with different flood end-points.@en

Carbonate reservoirs have structural heterogeneities at all length-scales (triple porosity: pore-vug-fracture) and tend to be mixed- To oil-wet. The interplay of structural and wettability heterogeneities impacts the sweep efficiency and oil recovery. The choice of an enhanced oil recovery process and the prediction of oil recovery require a sound understanding of the fundamental controls on fluid flow in mixed- To oil-wet carbonate rocks, as well as physically robust flow functions, i.e. relative permeability and capillary pressure functions. Obtaining these flow functions is a challenging task, especially when three fluid phases coexist, such as during water-alternating-gas injection (WAG). We have developed a new three-phase flow pore-network model, which comprises a novel thermodynamic criterion for formation and collapse of oil layers that strongly depends on the fluid spreading behaviour and the rock wettability. The criterion affects in particular the oil relative permeability at low oil saturations and the accurate prediction of residual oil saturations. Additionally, multiple displacement chains have been implemented, where injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows accurate modelling of the mobilization of the many disconnected phase clusters that arise during higher order WAG cycles. Pore-networks extracted from pore-space reconstruction methods and CT images are used as input for the pore-scale simulations and the model comprises a constrained set of parameters that can be tuned to mimic the wetting state of a given reservoir. Three-phase flow functions generated from networks with carbonate pore geometries and connectivities have been used in a heterogeneous carbonate reservoir model and we demonstrate their impact on the sweep efficiency after gas injection and WAG for a range of realistic wettability scenarios. We also show that the network generated flow functions give distinctly different recovery curves compared to recoveries for traditional three-phase flow relative permeability functions, such as Stone's.@en

Oil reservoirs have structural heterogeneities across multiple length scales and, particularly in carbonates, complexly distrib-uted wettabilities. The interplay of structural and wettability het-erogeneities is the fundamental control for sweep efficiency and oil recovery. This interplay must be captured in physically robust flow functions, such as relative permeability and capillary pressure functions. Such flow functions then allow us to choose the best improved-oil-recovery (IOR) or enhanced-oil-recovery (EOR) process and forecast oil recovery with adequate precision. Obtaining flow functions for reservoir rocks with varying wettability is a challenging task, especially when three fluid phases coexist. In this work, we use pore-network modeling, a reliable and physically based simulation tool, to predict three-phase flow functions. We have developed a new pore-scale network model for rocks with variable wettability. Unlike other models, this model combines three new and important features. (1) Our network model comprises a novel thermodynamic criterion for the formation and collapse of oil layers. This captures film/layer flow of oil adequately, which affects the oil relative permeability at low oil saturation. We can therefore predict residual oil more accurately. (2) We implemented multiple displacement chains, in which injection of one phase at the inlet triggers a chain of] interface displacements throughout the network. This allows us to accurately model the mobilization of disconnected phase clusters that arise during higher-order [water-alternating-gas (WAG)J floods. Again, this feature is key to a better prediction of residual oil saturation (ROS). (3) Our model takes realistic 3D pore networks extracted from pore-space reconstruction methods and X-ray computerized- tomography (CT) images as input. This preserves both topology and pore shape of the rock, providing better estimates of phase conductivities and relative permeability. We have validated our model by use of available experimental data for a range of wett-abilities and demonstrated the impact of single vs. multiple dis-placement on residual oil. We also used a proof-of-concept study in which we use flow functions for different wettabilities that have been computed with our model in field-scale reservoir simulations to forecast oil recovery during tertiary gas injection. These results are compared with predictions that used empirical flow functions. Flow functions computed by our network model gave higher oil recover)' than corresponding flow functions calculated by empirical models; oil recovery increases with decreasing water-wetness. This shows that the pore-scale physics encapsulated in our new network model leads to the right emergent behavior at the reservoir scale.@en

Carbonate reservoirs have structural heterogeneities (triple porosity: pore-vug-fracture) and are mixed- to oil-wet. The interplay of structural and wettability heterogeneities impacts the sweep efficiency and oil recovery. The choice of an IOR or EOR process and the prediction of oil recovery requires a sound understanding of the fundamental controls on fluid flow in mixed- to oil-wet carbonate rocks and physically robust flow functions, i.e. relative permeability and capillary pressure functions. Obtaining these flow functions is a challenging task, especially when three fluid phases coexist. In this work we use pore-network modelling, a reliable and physically-based simulation tool, to predict three-phase flow functions. We have developed a new pore-scale network model for rocks with variable wettability. Unlike other models, this model comprises a novel thermodynamic criterion for formation and collapse of oil layers. The new model hence captures film/layer flow of oil adequately which impacts the oil relative permeability at low oil saturation and hence the accurate prediction of residual oil. Pore-networks extracted from pore-space reconstruction methods and CT images have been used as input for our simulations and the model comprises a constrained set of parameters that can be tuned to mimic the wetting state of a given reservoir. We have validated our model with available experimental data for a range of wettabilities. A sensitivity analysis has been carried out to investigate the dependency of relative permeabilities on layer collapse and film/layer flow under various wetting conditions. Additionally, WAG injection has been simulated with different lengths of so-called multi-displacement chains and different flood end-points. The flow functions generated by our model can be passed to the next scales (upscaling) to predict the oil recovery at the reservoir scale and we demonstrate this using a proof-of-concept study.@en

Carbonate reservoirs have textural heterogeneities at all length-scales (triple porosity pore-vug-fracture) and tend to be mixed- to oil-wet The choice of an enhanced oil recovery process and the prediction of oil recovery require a sound understanding of the fundamental controls on fluid flow in mixed- to oil-wet carbonate rocks, as well as physically robust flow functions, i e relative permeability and capillary pressure functions Obtaining these flow functions is a challenging task, especially when three fluid phases coexist, such as during water-alternating-gas injection (WAG) We have recently developed a method for integration of pore-networks derived from micro CT images at different length-scales, thus capturing pore structures from different types of porosity The network integration method honours the connectivity between different pore types, including micro-fractures, and their spatial distribution In this work, we use these multi-scale networks as input for our three-phase flow pore-network model, which comprises a novel thermodynamic criterion for formation and collapse of oil layers that strongly depends on the fluid spreading behaviour and the rock wettability The criterion affects in particular the oil relative permeability at low oil saturations and the accurate prediction of residual oil saturations We generate three-phase flow functions for gas injection and WAG from networks with carbonate pore geometries and connectivities and we demonstrate the impact on residual saturations of the different types of porosity and the interaction with different realistic wettability scenarios We also show that the network generated three-phase flow relative permeabilities are distinctly different from traditional models, such as Stone's The flow functions will be used in a heterogeneous carbonate reservoir model and to demonstrate their impact on the sweep efficiency.@en

Naturally Fractured Reservoirs (NFR) contain a significant amount of remaining petroleum reserves and are now being considered for water-alternating-gas (WAG) flooding as secondary or tertiary recovery. Reservoir simulation of WAG is very challenging even in non-fractured reservoirs because a proper set of saturation functions that describe the underlying physics is vitally important but associated with high uncertainty. For NFRs, another challenge is the upscaling of recovery processes, particularly the fracture-matrix transfer during three-phase flow, to the reservoir scale using dual-porosity or dual-permeability models. In this work, we approach a solution to this challenge by building models at various scales, starting from pore-scale to an intermediate scale then to the reservoir scale. We show how pore-network modelling and fine grid modelling where the fractures and matrix are represented explicitly can be used to increase the accuracy of numerical simulations at the field-scale in order to predict recoveries for NFR during WAG. We study the sensitivity to WAG design parameters as well as the impact of matrix wettability on recovery. We also compare the fine grid model with an equivalent dual-porosity model. Simulation at an intermediate scale showed at least 10% absolute change in recovery due to the choice of the empirical three-phase relative permeability model. In fine grid simulation with physically consistent pore-network derived three-phase relative permeability and capillary pressure, injected water and gas are predicted to displace each other, leaving oil behind, therefore reducing WAG efficiency. For this case, empirical models over-estimate recovery by 25%. Classical dual-porosity model over-estimates recovery during the early WAG cycles, and fails to adequately match recovery of the fine grid simulation. Our multi-scale simulation approach identifies important factors and uncertainties when considering WAG flooding in NFR. It provides a methodology through which WAG recovery can be estimated using available technology while preserving the pore-scale physics for three-phase flow, which are crucial to making reliable forecasts at the reservoir scale.@en