We demonstrate the use of Ensemble Kalman Inversion (EKI) for building three-dimensional, multi-fault, kinematically restorable structural geologic models, by means of a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modeled. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. Two modeling approaches are tested: restoration from the deformed state, and forward modeling from the restored state. We first test these methods on a synthetic model involving a single fault, and then apply them to a real-field example involving five faults. Models are prone to ensemble collapse, which results in underestimation of uncertainty at small ensemble sizes, but localization and covariance inflation can mitigate this issue. With these methods, EKI can recover the true parameter values in the synthetic case and produce a solution consistent with the data in the real case, as well as quantify uncertainty in both cases. EKI, therefore, shows promise as a tool for building complex, restorable structural geologic models, and it holds the potential for integration of fault kinematics with other ensemble-based subsurface modelling workflows.

Structural restoration using kinematic principles of fault-related folding is a valuable tool in building realistic geological models. Models are, however, typically uncertain and non-unique. While data inversion methods can be employed to find a best-fit model and estimate uncertainty, their use is limited to relatively simple models involving a single fault in two dimensions. In this work, we employ an iterative form of the Ensemble Kalman Filter (EnKF) together with a kinematic model for deformation around normal faults to build and restore three-dimensional structural geologic models. The EnKF is ideally suited to data inversion problems that involve large numbers of model parameters and is frequently used in reservoir simulations, which often do not consider uncertainty in geologic structure. We develop a workflow in which fault geometry, the distribution of slip on a fault, and the geometry of folded horizons are all modelled using the EnKF. The models are constrained by observations of faults and horizons in the present deformed state together with the expectation that horizons should restore flat. We test two modelling approaches: a restoration-based approach in which the model is built in the deformed state and then restored, and a forward modelling-based approach in which the model is built in the restored state and then forward modelled to match present-day data. We test these methods first on a synthetic model involving a single fault and then on a real-world example involving five faults. Both the restoration- and forward modelling-based methods work well for the synthetic model, but forward modelling works best for the more complex real-world case study. The EnKF method provides not only a best-fit model but also an estimate of model uncertainty. The estimation of uncertainty is, however, hindered by the phenomenon of ensemble collapse, which results in underestimation of the uncertainty in model parameters at small ensemble sizes. We employ bootstrap-based localization and covariance inflation to help mitigate this issue and use a dummy parameter to identify whether significant ensemble collapse has occurred. While ensemble collapse remains a challenge in some cases, the EnKF nonetheless shows considerable promise as a tool for building complex many-parameter structural models that are kinematically restorable, and it holds the potential for future integration of structural modelling with other EnKF-based workflows in subsurface modelling.

Subseismic faults are small faults or fractures that may be difficult to determine but can have large consequences for fluid flow and pressure communication in the subsurface. Thus, knowing their distributions may be important in several subsurface applications, such as hydrocarbon exploration and exploitation, geothermal energy production, and subsurface CO2 injection. The aim of this work is to use a stochastic model to populate a three-dimensional structural model of the subsurface with subseismic faults. The novelty of the proposed method is the conditioning of the stochastic model to input maps describing displacement and stress orientation along subsurface horizons. Hence, the resulting structural model will be consistent with these maps. The maps can originate from a variety of sources, for example, predictions of a geomechanical model or (indirect) measurements of subsurface displacements and stresses. The model uses simulated annealing as the optimization algorithm, where the residual between the displacement of the modeled subseismic faults and the input displacement map is minimized through an iterative process. Each subseismic fault is modeled with a three-dimensional displacement field around the fault slip plane, enabling comparisons with the input displacement map along a horizon. An example of how the model distributes the subseismic faults around larger known faults, using a synthetically created displacement map, is provided. The result shows that the model quickly converges towards a set of subseismic faults, giving total displacement and strike orientation close to the input maps.

We have developed an efficient methodology for Bayesian prediction of lithology and pore fluid, and layer-bounding horizons, in which we include and use spatial geologic prior knowledge such as vertical ordering of stratigraphic layers, possible lithologies and fluids within each stratigraphic layer, and layer thicknesses. The solution includes probabilities for lithologies and fluids and horizons and their associated uncertainties. The computational cost related to the inversion of large-scale, spatially coupled models is a severe challenge. Our approach is to evaluate all possible lithology and fluid configurations within a local neighborhood around each sample point and combine these into a consistent result for the complete trace. We use a one-step nonstationary Markov prior model for lithology and fluid probabilities. This enables prediction of horizon times, which we couple laterally to decrease the uncertainty. We have tested the algorithm on a synthetic case, in which we compare the inverted lithology and fluid probabilities to results from other algorithms. We have also run the algorithm on a real case, in which we find that we can make high-resolution predictions of horizons, even for horizons within tuning distance from each other. The methodology gives accurate predictions and has a performance making it suitable for full-field inversions.

Summary Sedimentary rocks often obey vertical transvers isotropy due to the nature of the sedimentation process or the inherent orientation of rock grain minerals (e.g. clay platelets). Despite several documented cases in the literature, the effect of anisotropy is often neglected in seismic AVO inversion. We study the effect of transverse isotropy in shale encasing isotropic sand using probabilistic AVO inversion. The inversion algorithm is inverting seismic pre-stack data to lithology and fluid probabilities. A synthetic case demonstrates how anisotropy in shale may lead to wrong interpretation of fluid content in underlying sand. A field case in the northern North Sea shows that accounting for anisotropy in shale may improve the discrimination between good and poor sand of an Oxfordian turbidite reservoir. The results are encouraging and consistent with observations of sandy intervals in the wells and the depositional system of the study area. Our results clearly demonstrate that transverse anisotropy in sediments may give a significant contribution to the AVO gradient that otherwise could be misinterpreted. In the study area it becomes especially important, since there is a lack of contrast in acoustic impedance between the encasing shale and the target sand.

SummaryWe present stochastic simulations of sub-seismic faults conditioned on displacement intensity and stress orientation maps generated from a geomechanical model. The simulations are performed in an iterative process where new faults are proposed and have a high probability of being accepted if the contribution of the new fault gives a better match with the input displacement intensity map. The algorithm is demonstrated on a synthetic test case and shows that displacement field and strike orientation of the simulated sub-seismic faults matches the pattern of the displacement intensity map and the orientation of the maximum horizontal stress from a geomechanical model.

Conduit fault zones and fault zones that can accommodate longdistance along-fault flow are well-documented phenomena. In reservoir simulation models, flow within these features is more correctly captured using volumetric representations of fault zones instead of employing standard two-dimensional fault planes. The present study demonstrates a method for generating fault envelope grids on full-field reservoir models, within which fault cores (i.e., regions where most of fault zone displacement is accommodated) are modeled. The modeled fault core elements are lenses and slip zones. They are defined as facies units andpopulated in the fault envelope grids using combined object-based simulation and deterministic techniques. Using the facies property, four reservoir simulation models are generated by modulating fault core thickness and slip zone type and permeability. Membrane slip zones (slip zones that act as partial barriers to fluid flow) cause the fault cores to form baffle–conduit systems. Along-strike positioned injector–producer pairs focus flow into the fault cores, decreasing sweep efficiency. In contrast, injected fluids of injector–producer pairs positioned to drain perpendicular to the fault cores are partitioned and distributed by the fault cores and therefore increase overall sweep efficiency. In reservoir models with conduit slip zones (slip zones that enhance flow along them and act as partial barriers toflow across them), the fault cores act as thief zones. Fluids preferentially move through the fault cores toward the nearby producers instead of through sedimentary layers with high permeability. Sweep efficiency in the reservoir models with conduit fault cores has less dependency on injector–producer configuration. Our study suggests that the improved realism added by incorporating volumetrically expressed fault cores substantially influences forecasts of field AUTHORS Muhammad Fachri ~ Uni Centre for Integrated Petroleum Research; Department of Earth Science, University of Bergen; present address: ARA Petroleum, P.O. Box 1127, Ruwi 112, Sultanate of Oman; muhammad.fachri@arapetroleum.com Muhammad Fachri is a senior geoscientist at ARA Petroleum. He received his B.Sc. degree in geophysics in 1999 and M.Sc. degree in structural geology in 2002 from the Institute Technology Bandung. In 2014 he received his Ph.D. in reservoirmodeling fromtheUniversity of Bergen. Before joining ARA Petroleum, he worked for Weatherford Petroleum Consultants and Statoil. His research interests include faults, their implementation in reservoir models, and fault zone fluid flow. Jan Tveranger ~ Uni Centre for Integrated Petroleum Research, P.O. Box 7810, N-5020 Bergen, Norway; Department of Earth Science, University of Bergen, Realfagbygget, Allégaten 41, N-5007 Bergen, Norway; jan. tveranger@uni.no Jan Tveranger received his Dr. Scient. from the University of Bergen in 1995. He worked for Saga Petroleum and later Norsk Hydro before becoming head of the geoscience group at the Centre for Integrated Petroleum Research. He currently holds an adjunct professorship of geomodeling at the Department of Earth Science, University of Bergen. Alvar Braathen ~ Uni Centre for Integrated Petroleum Research, P.O. Box 7810, N-5020 Bergen, Norway; Department of Geosciences, University of Oslo, P.O. Box 1072, Blindern, Oslo, Norway; alvar. braathen@geo.uio.no Alvar Braathen received his Dr. Scient. degree from the University of Tromsø, Norway, in 1994. Subsequently, he worked for the Geological Survey of Norway, the Centre for Integrated Petroleum Research at the University of Bergen, and the University Centre in Svalbard (UNIS), Norway, before being appointed professor in structural geology at the Department of Geosciences, University of Oslo. He holds an adjunct professorship at UNIS. Copyright ©2016. The American Association of Petroleum Geologists. All rights reserved. Gold Open Access. This paper is published under the terms of the CC-BY license. Manuscript received July 1, 2014; provisional acceptance March 2, 2015; revised manuscript received November 21, 2015; final acceptance February 1, 2016. DOI:10.1306/02011614118 AAPG Bulletin, v. 100, no. 5 (May 2016), pp. 795–817 795 Downloaded from https://pubs.geoscienceworld.org/aapgbull/article-pdf/3346185/BLTN14118.pdf by guest on 07 August 2019 behavior and consequently should be considered during oil and gas production planning.

Corner point grids is currently the standard grid representation for use in reservoir simulation. The cell faces in corner point grids are traditionally represented as bilinear surfaces where the edges between the corner points all are straight lines. This representation has the disadvantage that along faults with varying dip the cell faces on either side will not precisely match, giving overlapping cells or gaps between cells. We propose an alternative representation for the cell faces. The four vertical cell faces are still represented as bilinear surfaces, but instead of having linear edges between the cell corners along the top and bottom faces, we propose a representation of the vertical cell faces where any horizontal intersection will give a straight line, giving column faces whose shape is independent of the corner point locations of the individual grid cells. This ensures that the grid columns match up and that there are no gaps or overlapping volumes between grid cells. This representation gives a local parameterization for the whole grid column, and the top and bottom grid cell surfaces are modeled as bilinear using this parameterization. A set of local coordinates for the grid cell permits all the common grid operations like volume calculation, area calculation for cell faces, and blocking of well traces.

The internal structure and petrophysical property distribution of fault zones are commonly exceedingly complex compared to the surrounding host rock from which they are derived. This in turn produces highly complex fluid flow patterns which affect petroleum migration and trapping as well as reservoir behavior during production and injection. Detailed rendering and forecasting of fluid flow inside fault zones require high-resolution, explicit models of fault zone structure and properties. A fundamental requirement for achieving this is the ability to create volumetric grids in which modeling of fault zone structures and properties can be performed. Answering this need, a method for generating volumetric fault zone grids which can be seamlessly integrated into existing standard reservoir modeling tools is presented. The algorithm has been tested on a wide range of fault configurations of varying complexity, providing flexible modeling grids which in turn can be populated with fault zone structures and properties.

Fault models are often based on interpretations of seismic data that are constrained by observations of faults and associated strata in wells. Because of uncertainties in depth migration, seismic interpretations and well data, there often is significant uncertainty in the geometry and position of the faults. Fault uncertainty impacts determinations of reservoir volume, flow properties and well planning. Stochastic simulation of the faults is important for quantifying the uncertainties and minimizing the impacts. In this paper, a framework for representing and modeling uncertainty in fault location and geometry is presented. This framework can be used for prediction and stochastic simulation of fault surfaces, visualization of fault location uncertainty, and assessments of the sensitivity of fault location on reservoir performance. The uncertainty in fault location is represented by a fault uncertainty envelope and a marginal probability distribution. To be able to use standard geostatistical methods, quantile mapping is employed to construct a transformation from the fault surface domain to a transformed domain. Well conditioning is undertaken in the transformed domain using kriging or conditional simulations. The final fault surface is obtained by transforming back to the fault surface domain. Fault location uncertainty can be visualized by transforming the surfaces associated with a given quantile back to the fault surface domain.

Traditionally fault seal calculations take place directly within the simulation grid. This approach works well for grids where all the faults are aligned along the grid pillars, but implementing an algorithm that works with stair-stepped representation of the faults has proven to be very difficult. Especially the calculation of the displacement field used both indirectly in the fault seal parameter calculation and directly in the calculation of fault zone permeability is challenging. It is hard to find where the different grid layers intersect the fault trace, and the layers are not always completely represented on both sides of the fault. We present a novel algorithm where the calculation of the fault zone permeability is carried out on a 2D plane representing the fault surface. The input parameters needed for calculating the fault zone permeability are resampled from the simulation grid onto the 2D plane, while the resulting fault zone permeability is resampled back into the simulation grid, prior to calculation of the fault transmissibility. The new approach is shown to generate good results both for pillar-faulted grids, and for grids with stair-stepped faults, and also works well near complex truncations.

In history matching and sensitivity analysis, flexibility in the structural modelling is of great importance. The ability to easily generate multiple realizations of the model will have impact both on the updating workflow in history matching and uncertainty studies based on Monte Carlo simulations. The main contribution to fault modelling by the work presented in this paper is a new algorithm for calculating a 3D displacement field applicable to a wide range of faults due to a flexible representation. This gives the possibility to apply this field to change the displacement and thereby moving horizons and fault lines. The fault is modelled by a parametric format where the fault has a reference plane defined by a centre point, dip and strike angles. The fault itself is represented as a surface defined by a function z = f (x, y), where x, y and z are coordinates local to the reference plane, with the z-axis being normal to the plane. The displacement associated with the fault outside the fault surface is described by a 3D vector field. The displacement on the fault surface can be found by identifying the intersection lines between horizons and the fault surface (fault lines), and using kriging techniques to fill in values at all points on the surface. Away from the fault surface the displacement field is defined by a monotonic decreasing function which ensures zero displacement at a specified distance from the fault. An algorithm is developed where the displacement can be increased or decreased according to user-defined parameters. This means that the whole displacement field is changed and points on horizons around the fault can be moved accordingly by applying the modified displacement field on them. The interaction between several faults influencing the same points is taken care of by truncation rules and the ordering of the faults. The method is demonstrated on a realistic synthetic case based on a real reservoir.

Faults are volumetric in nature and can cause complex fluid flow inside the fault zone because of its special fault zone architecture and different petrophysical properties from the host rock. Thus explicit fault zone modeling is important for capturing the fluid flow inside and through the fault zone precisely. Generation of a refined volumetric fault zone grid is the first step to perform explicit fault zone modeling. An algorithm for generating volumetric fault zones has already been implemented in Havana, however this algorithm failed to generate continuous top and bottom surfaces for the fault zone. This lead to internal discontinuities in the fault zone grid, and made it hard to run flow simulations on the grid. We now present an improved version of the algorithm that works well on complex faults and indicate the capability of explicit fault facies modelling of real field cases.

Abstract Fault geometry is modelled on basis of seismic data, but restricted by fault observations in wells. Due to uncertainties in depth migration, seismic interpretation and well data, there is a significant uncertainty in the geometry and position of the faults. Fault uncertainty impact reservoir volume, flow properties and well planning, and can be studied by stochastic simulation of faults. We have developed a method for stochastic simulation of fault surfaces and fault networks using standard geostatistical methods. This is made possible by the fault parameterization used, where the faults are modelled as tilted surfaces. This new method is more flexible and efficient compared to already existing algorithms due to a simpler parameterization. Conditioning to fault observations in wells is also made simpler. The fault is defined as a two-dimensional surface on a tilted reference plane. The uncertainty for a fault surface is bounded by a volume enclosing the fault surface. The smoothness of the simulated fault surfaces is controlled by variograms. The simulation is done by adding a simulated Gaussian residual. Well conditioning is done by kriging. Using the described method we can simulate a set of fault realizations where the simulated faults look realistic, are within the defined uncertainty volumes, and honour well observations. Technical contributions compared to previous work include efficient simulation of fault geometry, a flexible uncertainty model and well conditioning with no performance impact.

Faults in nature commonly affect surrounding rock volumes and can as such be described as fault envelopes with a given internal geometry and architecture. Modeling techniques currently employed when modeling faults in petroleum reservoirs are mostly two-dimensional (2-D); hence, a need is present for more accurate and realistic description and quantification of deformational architectures and properties to accurately predict fluid flow in fault zones.Fault facies (FF) modeling is a concept for three-dimensional (3-D) fault zone characterization, facies modeling of fault rocks and fluid flow simulation, which is presented here and demonstrated by the use of a synthetic fault model. FF modeling is performed by first generating a 3-D grid of the fault envelope, which includes the conventional fault plane. Second, a kinematic strain calculation is executed in the FF grid. The strain parameter is used to calculate a fault product distribution factor (FPDF), which describes the fault displacement in the fault envelope. This parameter together with strain distribution is subsequently used to condition the fault model for facies modeling. Finally, FF modeling is executed. To achieve adequate flexibility and realism, pixel-based modeling is combined with object-based modeling methods to populate the FF grid with facies.This synthetic model shows that it is possible to honor structural outcrop observations in fault zones, and FF modeling is able to produce realistic looking fault zone deformation structures in 3-D. It is possible to implement faults with varying width and displacement, although the FF grid itself has a regular fixed width. This is highly advantageous as compared to controlling the fault geometry with the grid itself. We propose that FF modeling can improve fault zone characterization and also capture fluid flow uncertainty in fault zones in a more realistic way than is possible with 2-D methods.

This article describes an algorithm to compute finite strain in faulted corner point grids using the software Havana. The algorithm is based on a simple fault displacement formula, and a volumetric computation of strain in the grid's deformed configuration. The volumetric computation of strain is tested by comparing the finite strain of a 3D trishear model calculated by this method, with that calculated by the tetrahedrons method. The agreement between both methods confirms the validity of the volumetric strain computation. The algorithm is applied to synthetic models of one and three intersecting normal faults, and to a real model with seven faults, the Emerald Field. In all cases the computed finite strain is consistent with the fault network and with the variation of slip along the faults. There is one parameter that affects the computation significantly: the drag radius ( r d ) or extent of folding across a fault. Low r d models yield high finite strain and strain gradients but limited fault interaction, and vice versa. Using empirical relations between fault throw and damage zone width, r d can be narrowed down and further constrained by evaluating the quality of the grid's restoration. The strain algorithm can be integrated easily into a reservoir modelling workflow and in stochastic modelling. The algorithm provides criteria for conditioning the distribution of deformational features within the reservoir zones affected by faulting, based on the magnitude of finite strain.

for the fourteenth SPE Bergen One Day seminar 18th April 2007 Session: Geoscience and reservoir engineering Faults in reservoir models – unwanted surprises and new methods for avoiding them Tveranger, J.*, Braathen, A.**, Cardozo, N.*, Espedal, M.*, Fredman, N.*, Fossen, H.**, Nøttveit, H.*, Røe, P.***, Skorstad, A.***, Soleng, H.*** and Syversveen, A-R.*** * Center for Intergrated Petroleum Research (CIPR), University of Bergen, Allègaten 41, N-5007 Bergen, Norway ** The University Centre in Svalbard, P.O. Box 156, N-9171 Longyearbyen , Norway *** The Norwegian Computing Centre, Gaustadallèen 23 P.O. box 114, Blindern N-0214 Oslo, Norway Standard reservoir modelling techniques routinely incorporate faults as simple offsets along grid splits. The impact of faults on reservoir fluid flow is thereby captured by the combined effect of stratigraphic displacement and transmissibility modifiers attached to the cell surfaces bordering the grid split. These transmissibility modifiers can be derived either from specialised tools calculating expected transmissibility from combining information on reservoir lithology with fault throw, or by ad hoc history matching of the simulation model. However, this approach disregards the fact that fault impact in reservoirs is commonly not limited to a single, clear-cut fault plane but affects a volume of host rock thereby creating a complex 3D architecture. By failing to incorporate the presence of often extensive fault damage zones and fault core architectures into the reservoir model actual 3D flow inside and through fault zones is not captured in-place volumes are overestimated fault sealing (including capillary seals) is highly simplified communication along faults can not be forecast model uncertainty cannot be properly evaluated as fault features critical for reservoir behaviour are not included in the model hazardous areas for drilling can not be reliably predicted The Fault Facies project addresses this problem by a concerted research effort involving structural geologists, mathematicians, modellers, programmers and reservoir engineers. The project has developed a practical methodology that allows volumetric gridding of fault zones on reservoir scale models and populating the resulting fault envelopes with realistic fault architectural elements and petrophysical properties. Models are built using a standard reservoir modelling tool (Irap RMS) employing a customised gridding algorithm in HAVANA. Architecture and petrophysical properties of the fault zones are modelled by adapting facies model tools developed for object based modelling of sedimentary facies and employing volumetric strain as a conditioning parameter for the resulting fault zone architecture and petrophysical properties. The new method is fully integrated with existing modelling workflows and can be added onto existing models with no need to build new models from scratch. Although still under development the Fault Facies method offers a practical solution to evaluation of fault impact on reservoir fluid flow in realistic detail.

Although faults traditionally have been modelled as membrane-like surfaces, the flow pattern through a fault is affected in a volumetric region. The physical properties of the fault rock will be different from what they were prior to the faulting process. Defining specific Fault Facies only present in the close vicinity of a fault gives a possibility to model the flow through faults more detailed than by conventional modelling. The Fault Facies will depend on both the pre-faulted facies, and the strain affecting the rocks when faults are created. A workflow has been created which demonstrates that the concept can be utilized in realistic reservoir modelling, starting from a conventional reservoir model where the fault is defined as a surface. A fault zone is defined in a small volume around the fault surface. It has a finer grid than the original model. First, all Fault Facies are modelled, followed by petrophysical modelling accounting for the fact that the greatest deformation occurs near the centre of the fault zone. The suggested concept produces direct modelling of vertical flow in the faults, making the unphysical non-neighbouring connections obsolete.

There is an increasing demand to discuss diagnostic images and reports of difficult cases with experienced staff. A possible solution besides physically transporting patients and material is to use high-speed communication networks to transfer images and reports electronically. With the web application PACSflow we have developed a solution to transfer images, reports, and messages as a single package in a one-step procedure. The PACSflow is an interoperable and standard compliant web-based application, which gives clinicians a user-friendly interface for their work on a daily basis. The solution assumes that the diagnostic images are compatible with the digital imaging and communications in medicine (DICOM) format. The Department of Cardiology at the Rikshospitalet University Hospital in Oslo, Norway, and the Department of Internal Medicine at the Soslashrlandet Sykehus in Arendal, Norway, are making clinical use of the system. Initial tests indicate that use of PACSflow has reduced the time required to prepare and transfer data by a factor of 3

Faults significantly influence fluid flow in reservoirs. In standard reservoir flow-simulator grids, faults are represented as surfaces or planes. However, outcrop studies show that faults often must be regarded as volumetric elements. Inside such fault zones, the facies characteristics differ significantly from those in the rest of the reservoir. In a fault facies reservoir model faults are represented as volumes populated with facies with properties derived from their origin and faulting history. In this paper, we compare fluid flow performance of a fault facies model and a conventional fault model. The uncertainties attached to the fault zone properties and architecture included in the fault facies model produce a straightforward effect on the range of simulation outcomes and uncertainty of production parameters. In the conventional model, similar effects can only be reproduced ad hoc using poorly determined random fudge factors. We also look at the effect of upscaling the fault zone. Results show that the flow properties in the fault facies model differ from the conventional model with regard to both water cut and total oil production. As expected, upscaling may introduce a significant bias in the cumulative oil production.