Geological reservoirs can be extensively fractured but the well-test signatures observed in the wells may not show a pressure transient response that is representative of naturally fractured reservoirs (NFRs): for example, one that indicates two distinct pore systems (i.e. the mobile fractures and immobile matrix). Yet, the production behaviour may still be influenced by these fractures. To improve the exploitation of hydrocarbons from NFRs, we therefore need to improve our understanding of fluid-flow behaviour in fractures.

Multiple techniques are used to detect the presence and extent of fractures in a reservoir. Of particular interest to this work is the analysis of well-test data in order to interpret the flow behaviour in an NFR. An important concept for interpreting well-test data from an NFR is the theory of dual-porosity model. However, several studies pointed out that the dual-porosity model may not be appropriate for interpreting well tests from all fractured reservoirs.

This paper therefore uses geological well-testing insights to explore the limitations of the characteristic flow behaviour inherent to the dual-porosity model in interpreting well-test data from Type II and III NFRs of Nelson's classification. To achieve this, we apply a geoengineering workflow with discrete fracture matrix (DFM) modelling techniques and unstructured-grid reservoir simulations to generate synthetic pressure transient data in both idealized fracture geometries and real fracture networks mapped in an outcrop of the Jandaira Formation. We also present key reservoir features that account for the classic V-shape pressure derivative response in NFRs. These include effects of fracture skin, a very tight matrix permeability and wells intersecting a minor, unconnected fracture close to a large fracture or fracture network. Our findings apply to both connected and disconnected fracture networks.@en

Fracture networks are heterogeneous systems creating anisotropic flow patterns, though field-scale flow models of fractured reservoirs use up-scaling of the fracture network to effective properties to model flow. We study the impact of upscaling aperture from a realistic aperture model, where aperture is defined by a stress-aperture relation that considers aperture variations within single fractures, to an arithmetically averaged distribution. This analysis is done through calculation of the equivalent permeability tensor of a discrete fracture and matrix flow model, taking into account different contrasts between fracture and matrix permeability. Results show that a strong equivalent permeability anisotropy emerges for a low matrix permeability, and that accurate representation of fracture aperture is as important as the fracture topology, particularly when the fracture matrix permeability ratio is large. The orientation of the permeability tensor varies with varying rock matrix permeability, reflecting anisotropy of the permeability that is impossible to extract from the fracture patterns itself. The results also highlight that utilizing a constant aperture for the fracture network may not reproduce the true anisotropy of the permeability. Utilizing an equivalent aperture in flow simulations introduces errors in both the direction and magnitude of principal permeabilities and the equivalent permeability anisotropy.

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Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do.

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Regional natural fracture networks often show variations on a scale below that captured by seismic reflection data. This variability is not considered in most reservoir models, but likely impacts uncertainties in permeability. We quantify this uncertainty using a database of 13,000 fractures in nine outcrops digitised in the carbonate Jandaíra Formation (Potiguar basin, Brazil). Distance between outcrops is on average 11 km, with a minimum of 300 m, which is comparable to the distance between wells in naturally fractured reservoirs. In between outcrops, significant variations exist in orientation, intensity, length and topology. Using discrete fracture-matrix flow models, we model the permeability of each deterministic pattern and find that small changes in geometry and topology result in permeability variations that are not captured by connectivity-based analyses such as percolation probabilities, particularly when the matrix is permeable. The permeability variations associated with subseismic-scale fracture variability are not captured in conventional stochastic models, but can be captured using deterministic outcrop models with flow through discrete fractures. The deterministic models provide a permeability range associated with subseismic fracture variability, that can be assigned to grid cells of fractured reservoir flow models, as an alternative to assuming constant permeability in the absence of subseismic-scale deformation.@en

The shallow-marine carbonate rocks of the Jandaíra Formation have been subject to significant permeability variations through time due to various events of fracturing and calcite cementation. As a consequence, the Jandaíra Formation accommodated fluid flow only during specific moments in time. We reconstructed these episodes of fluid flow based on isotope characterizations and microscope characteristics of calcite veins and host rock cements. The Jandaíra Formation, which belongs to the post-rift sequence of the Potiguar Basin in northeast Brazil, was deposited from the Turonian onward until a marine regression exposed it in the Campanian. Due to the subaerial exposure, meteoric waters flushed out marine connate waters, leading to an event of early diagenesis and full cementation of the Jandaíra Formation. Fluid flow through the resulting impermeable carbonate formation appears to be closely related to fracturing. Fracturing in the Late Cretaceous induced a drastic increase in permeability, giving rise to extensive fluid circulation. Host rock dissolution associated to the circulating fluids led to calcite vein cementation within the fracture network, causing it to regain an impermeable and sealing character. In the research area, fluid flow occurred during early burial of the Jandaíra Formation at estimated depths of 400–900 m. This study documents the first application of fluid inclusion isotope analysis on vein precipitates, which allowed full isotopic characterization of the paleo-fluids responsible for calcite vein cementation. The fluid inclusion isotope data indicate that upwelling of groundwater from the underlying Açu sandstones provided the fluids to the fracture network. In Miocene times, renewed tectonic compression of a lower intensity created a secondary fracture network in the Jandaíra Formation. The density of this fracture network, however, was too low to induce a new episode of fluid circulation. As a result, this tectonic event is associated with the development of barren extensional fractures.

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Pervasive fracture networks are common in many reservoir-scale carbonate bodies even in the absence of large deformation and exert a major impact on their mechanical and flow behaviour. The Upper Cretaceous Jandaíra Formation is a few hundred meters thick succession of shallow water carbonates deposited during the early post-rift stage of the Potiguar rift (NE Brazil). The Jandaíra Formation in the present onshore domain experienced <1.5 km thermal subsidence and, following Tertiary exhumation, forms outcrops over an area of >1000 km². The carbonates have a gentle, <5⁰, dip to the NE and are affected by few regional, low displacement faults or folds. Despite their simple tectonic history, carbonates display ubiquitous open fractures, sub-vertical veins, and sub-vertical as well as sub-horizontal stylolites. Combining structural analysis, drone imaging, isotope studies and mathematical modelling, we reconstruct the fracturing history of the Jandaíra Formation during and following subsidence and analyse the impact fractures had on coeval fluid flow. We find that Jandaíra carbonates, fully cemented after early diagenesis, experienced negligible deformation during the first few hundreds of meters of subsidence but were pervasively fractured when they reached depths >400-500 m. Deformation was accommodated by a dense network of sub-vertical mode I and hybrid fractures associated with sub-vertical stylolites developed in a stress field characterised by a sub-horizontal σ₁ and sub-vertical σ₂. The development of a network of hybrid fractures, rarely reported in the literature, activated the circulation of waters charged in the mountainous region, flowing along the porous Açu sandstone underlying the Jandaíra carbonates and rising to the surface through the fractured carbonates. With persisting subsidence, carbonates reached depths of 800-900 m entering a depth interval characterised by a sub-vertical σ₁. At this stage, sub-horizontal stylolites developed liberating calcite which sealed the sub-vertical open fractures transforming them in veins and preventing further flow. During Tertiary exhumation, several of the pre-existing veins and stylolites opened and became longer, and new fractures were created typically with the same directions of the older features. The simplicity of our model suggests that most rocks in passive margin settings might have followed a similar evolution and thus display similar structures. Basin Research

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Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling), and experiments (Barton-Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture-matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real-world large-scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton-Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton-Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low-permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

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Aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs. This uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical and diagenetic processes that control aperture. In the absence of cement bridges and high pore pressure, fractures in the subsurface are generally considered to be closed. However, experimental work, outcrop analyses and subsurface data show that some fractures remain open, and that aperture varies even along a single fracture. However, most fracture flow models consider constant apertures for fractures. We create a stress-dependent heterogeneous aperture by combining Finite Element modeling of discrete fracture networks with an empirical aperture model. Using a modeling approach that considers fractures explicitly, we quantify equivalent permeability, i.e. combined matrix and stress-dependent fracture flow. Fracture networks extracted from a large outcropping pavement form the basis of these models. The results show that the angle between fracture strike and σ₁ has a controlling impact on aperture and permeability, where hydraulic opening is maximum for an angle of 15°. At this angle, the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress. Averaging the heterogeneous aperture to scale up permeability probably results in an underestimation of flow, indicating the need to incorporate full aperture distributions rather than simplified aperture models in reservoir-scale flow models.

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We constrain fracture networks in flat-lying shallow water carbonates producing fracture models at scale from cm-to tens of meters over a large area of several tens of km2.Imaging is integrated with structural observation on the ground and isotope studies on the vein infill. Structures observed are sub-vertical mode I and hybrid veins displaying a conjugate pattern, sub-vertical stylolites and sub-horizontal stylolites. The structures formed during subsidence through a stress field characterized by the presence of a significant sub-horizontal tectonic stress. Little deformation occurred in the uppermost 400-500m. Wholesale fracturing affected the carbonates at depths between 500 and 800m resulting in a pervasive network of open fractures and stylolites. Increasing development of sub-horizontal stylolites generated the calcite which eventually sealed the fractures. Using the acquired fracture network, we test the impact of different aperture models on flow simulations @en

Geological well testing is a valuable tool that allows us to improve understanding of pressure transient behaviour in a fractured reservoir. However, not all wells in a fractured reservoir will show pressure transients that are expected for NFRs. Our findings demonstrate that high resolution models with proper grid refinement around the wells and fractures are required to model pressure transient behaviour adequately and produce a physically meaningful wellbore response for a fractured reservoir. The key concept for interpreting well test data from fractured reservoirs is the dual-porosity model. This model, originally developed by Warren and Root (1963) has been the industry standard for modelling NFRs and interpreting well-test data from NFRs for more than 50 years. Although there are a number of factors impacting the exact shape of the pressure transients, our results suggest that observing the classical “V-shape” in the pressure derivative, as expected from a dual-porosity model may be an exception, rather than a rule in NFR, even for well-connected fracture networks. Our work quantifies when and why the assumptions inherent to the dual-porosity model break down when interpreting well-test data from NFR. @en

Despite the scarcity of major deformation structures such as folds and faults, the flat-lying, post-rift shallow water carbonates of the Jandaira Formation (Potiguar Basin, NE Brazil) display well-organized fracture systems distributed of tens of km2. Structures observed in the outcropping carbonates are sub-vertical, generally N-S trending mode I and hybrid veins and barren fractures, sub-vertical roughly E-W trending stylolites and sub-horizontal stylolites. These features developed during subsidence in a simple and constant stress field characterized by, beside gravity, a significant horizontal stress probably of tectonic origin. The corresponding depth curves have different origin and slopes and, therefore, cross each other resulting in position of the principal stresses which change with depth. As a result, the type and amount of fractures affecting subsiding rocks change despite the fact that the far-field stresses remain constant. Following early diagenesis and porosity elimination in the first 100-200m depth, Jandaira carbonates experienced wholesale fracturing at depths of 400-800m resulting in a network of NNW-NE trending fractures partly organized in conjugate sets with a low interfault angle and a sub-vertical intersection, and sub-vertical stylolites roughly perpendicular to the fractures. Intense fluid circulation was activated as a consequence through the carbonates. With increasing subsidence, sub-horizontal stylolites formed providing calcite which precipitated in the open fractures transforming them in veins. The Jandaira formation lost thereby the permeability it had reached during the previous stage. Because of the lack of major deformation, the outcrops of the Jandaira Formation is an excellent analog for carbonate reservoirs in the Middle East, South Atlantic and elsewhere. @en

Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture geometry and aperture, which cannot be fully sampled from subsurface data. We quantify for a range of aperture-size scaling models and the Barton-Bandis conductive shear model the fractures that are critically stressed at in-situ stress conditions as defined by either Coulomb friction or Barton-Bandis peak shearing. These models are applied to realistic large-scale fracture networks. (Sub-)linear length scaling predicts the largest average aperture, and subsequent equivalent permeability exceeds 1 Darcy in a 10mD matrix. In contrast, Barton-Bandis aperture predicts an equivalent permeability of 60mD. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton-Bandis peak shear. The impact of the reactivated fracture network on equivalent permeability depends on the matrix properties, as in a low-permeable matrix, fracture connectivity controls equivalent permeability, while for a more permeable matrix, large absolute apertures are more important than network connectivity. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on fracture connectivity, controlled by aperture. @en

Unconventional shale reservoirs have practically no in-situ permeability, but they may be rich in natural fractures, which can positively or negatively impact hydraulic fracturing. We study a naturally fractured shale formation, with bed-perpendicular fractures, which are mostly cemented, fracture corridors and bedding-parallel calcite veins (beef). Microseismic indicates that the Stimulated Rock Volume (SRV) is heterogeneous and anisotropic, which is likely related to reactivation of the natural structural heterogeneities. At in-situ conditions, the shale is overpressured, but the pore pressure is below the required threshold to reactivate natural fractures. During hydraulic fracturing, fractures may be locally reactivated. The local reactivation is quantified using a coupled stress-fluid pressure Finite Element model, based on a discrete fracture network constructed around a pilot area with several horizontal and vertical wells. The models show that only a small part of the fracture network close to induced fractures is reactivated, creating an anisotropic SRV. Vertically, beef limits growth of induced fractures, while increasing the aperture and length. Furthermore, beef can generate horizontal high-permeability zones, increasing the SRV. These models, when accurately calibrated using pressure interference data, are useful to optimize well placement and completion strategies. @en

Outcrop fracture data sets can now be acquired with ever more accuracy using drone technology augmented by field observations. These models can be used to form realistic, deterministic models of fractured reservoirs. Fractured well test models are traditionally seen to be finite or infinite conductivity or double porosity - corresponding the fractures with or without matrix support. Using this simple field outcrop based geometrical model to generate typical well test responses for wells either intersecting fractures or well nearby fractures shows that such responses can occur in sequence as part as a diagnostic signature of naturally fractured reservoirs.@en

Geometries of 2 fracture families in a carbonate pavement. Lengths of the fractures have been digitized and stored. The data is collected as part of a fieldwork to characterize natural fracture systems in a folded carbonate formation, with the aim of studying the role between large-scale folding and small-scale fracturing. In addition, the specific data from this outcrop has been used in geomechanical and flow models, focusing on stress-driven aperture modelling and quantification of fluid flow. The data has been digitized using DigiFract software, developed at TU Delft (Hardebol & Bertotti, 2003, Computers & Geoscience)@en