Pore-network representations of permeable media provide the framework for explicit simulation of capillary-driven immiscible displacement governed by invasion-percolation theory. The most demanding task of a pore-network flow simulation is the identification of trapped defending phase clusters at every displacement step, i.e. the phase connectivity problem. Instead of employing the conventional adjacency list we represent the connectivity of a phase cluster as a tree accompanied by a set of adjacent non-tree edges. In this graph representation, a decrease in phase connectivity due to a pore displacement event corresponds to deletion of either a tree or a non-tree edge. Deletion of a tree edge invokes a computationally intensive search for a possible reconnection of the resulting subtrees by an adjacent non-tree edge. The tree representation facilitates a highly efficient execution of the reconnection search. Invasion-percolation simulations of secondary water floods under different wetting conditions in pore-networks of different origin and size confirm the efficiency of the proposed phase connectivity algorithm. Moreover, a systematic simulation study of runtime growth with increasing model size on regular lattice networks demonstrates a consistent orders-of-magnitude speed-up compared to conventional simulations. Consequently, the proposed algorithm proves to be a powerful tool for invasion-percolation simulations on large multi-scale networks and for extensive stochastic analysis of typical single-scale pore-networks.

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The relationship between flow properties and chemical reactions is the key to modeling subsurface reactive transport. This study develops closed-form equations to describe the effects of mineral precipitation and dissolution on multi-phase flow properties (capillary pressure and relative permeabilities) of porous media. The model accounts for the fact that precipitation/dissolution only takes place in the water-filled part of pore space. The capillary tube concept was used to connect pore-scale changes to macroscopic hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and consequently in the pore size distribution. The updated pore size distribution is converted back to a new capillary pressure–water saturation relation from which the new relative permeabilities are calculated. Pore network modeling is conducted on a Berea sandstone to validate the new continuum-scale relations. The pore network modeling results are satisfactorily predicted by the new closed-form equations.@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.

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A multiscale network integration approach introduced by Jiang et al. (2013) is used to generate a representative pore-network for a carbonate rock with a pore size distribution across several orders of magnitude. We predict the macroscopic flow parameters of the rock utilising (i) 3-D images captured by X-ray computed microtomography and (ii) pore-network flow simulations. To capture the multiscale pore size distribution of the rock, we imaged four different rock samples at different resolutions and integrated the data to produce a pore-network model that combines information at several length-scales that cannot be recovered from a single tomographic image. A workflow for selection of the number and length-scale of the required input networks for the network integration process, as well as fine tuning the model parameters is presented. Mercury injection capillary-pressure data were used to evaluate independently the multiscale networks. We explore single-scale, two-scale, and three-scale network models and discuss their representativeness by comparing simulated capillary-pressure versus saturation curves with laboratory measurements. We demonstrate that for carbonate rocks with wide pore size distributions, it may be required to integrate networks extracted from two or three discrete tomographic data sets in order to simulate macroscopic flow parameters.

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Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid-fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces.

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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

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

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.

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Pore-network modelling, or digital petrophysics, is an emerging technology which allows computing physically consistent two- and three-phase flow functions such as relative permeability and capillary pressure curves at arbitrary wettability. Considering the difficulty in measuring these functions reliably in the laboratory, pore-network modelling is increasingly used to guide and complement costly and time-consuming SCAL programmes. Although pore-network modelling is now well-established for clastic reservoirs, applying it to carbonate rocks is significantly more challenging due to their complex and multi-scale pore structure, comprising micro- and macro-pores as well as cracks and fractures. We have hence developed a novel method to integrate pore-networks, which have been extracted at multiple scales directly from CT images at different resolutions, into a single pore-network model that can be used in subsequent calculations of two- and three-phase flow functions. This method has been validated by comparing computed two-phase relative permeability and capillary pressure curves for a multiscale network to the corresponding laboratory measurements. However, in this approach it is important to accurately consider the impact of the spatial distribution of fine network elements, which are extracted from high-resolution images. We therefore show the impact of the spatial correlation of high-resolution porosity on single- and two-phase fluid flow and propose a model that allows us to simulate the spatial correlation between coarse-scale pores and fine-scale porosity in the absence of a suitable CT image that segments the rock into three phases (pores, sub-resolution matrix porosity, and solid). We demonstrate the impact of the spatial correlation of microporosity on absolute and relative permeabilities by applying this model to various datasets, including CT images of an off-shore carbonate reservoir. This demonstrates that the spatial correlation of microporosity is one of the key factors controlling recovery from carbonate reservoirs and that our new method allows us to quantify it.@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.

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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 (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

When regions of three-phase flow arise in an oil reservoir, each of the flow parameters, i. e. capillary pressures and relative permeabilities, are generally functions of two phase saturations and depend on the wettability state. The idea of this work is to generate consistent pore-scale based three-phase capillary pressures and relative permeabilities. These are then used as input to a 1-D continuum core- or reservoir-scale simulator. The pore-scale model comprises a bundle of cylindrical capillary tubes, which has a distribution of radii and a prescribed wettability state. Contrary to a full pore-network model, the bundle model allows us to obtain the flow functions for the saturations produced at the continuum-scale iteratively. Hence, the complex dependencies of relative permeability and capillary pressure on saturation are directly taken care of. Simulations of gas injection are performed for different initial water and oil saturations, with and without capillary pressures, to demonstrate how the wettability state, incorporated in the pore-scale based flow functions, affects the continuum-scale displacement patterns and saturation profiles. In general, wettability has a major impact on the displacements, even when capillary pressure is suppressed. Moreover, displacement paths produced at the pore-scale and at the continuum-scale models are similar, but they never completely coincide.

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