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Conference paperSalinas P, Pavlidis D, Xie Z, et al., 2016,
Dynamic unstructured mesh adaptivity for improved simulation of nearwellbore flow in reservoir scale models
, 15th European Conference on the Mathematics of Oil Recovery, Publisher: EAGEIt is well known that the pressure gradient into a production well increases with decreasing distanceto the well and may cause downwards coning of the gaswater interface, or upwards coning ofwateroil interface, into oil production wells; it can also cause downwards coning of the water table,or upwards coning of a saline interface, into water abstraction wells. To properly capture the localpressure drawdown into the well, and its effect on coning, requires high grid or mesh resolution innumerical models; moreover, the location of the well must be captured accurately. In conventionalsimulation models, the user must interact with the model to modify grid resolution around wells ofinterest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of nearwellbore flow in reservoirscale modelsthrough the use of dynamic unstructured adaptive meshing. The method is novel for two reasons.First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of thewell is specified via a line vector. Mesh nodes are placed along the line vector, so the geometry ofthe mesh conforms to the well trajectory. The well location is therefore accurately captured, and theapproach allows complex well trajectories and wells with many laterals to be modelled. Second,the mesh automatically adapts during a simulation to key solution fields of interest such as pressureand/or saturation, placing higher resolution where required to reduce an error metric based on theHessian of the field. This allows the local pressure drawdown and associated coning to be capturedwithout userdriven modification of the mesh. We demonstrate that the method has wideapplication in reservoirscale models of oil and gas fields, and regional models of groundwaterresources.
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Journal articleJackson MD, Vinogradov J, Hamon G, et al., 2016,
Evidence, mechanisms and improved understanding of controlled salinity waterflooding part 1: Sandstones
, FUEL, Vol: 185, Pages: 772-793, ISSN: 0016-2361 -
Journal articleGomes JLMA, Pavlidis D, Salinas P, et al., 2016,
A force-balanced control volume finite element method for multi-phase porous media flow modelling
, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 431-445, ISSN: 1097-0363A novel method for simulating multi-phase flow in porous media is presented. The approach is based on acontrol volume finite element mixed formulation and new force-balanced finite element pairs. The novelty ofthe method lies in: (a) permitting both continuous and discontinuous description of pressure and saturationbetween elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocityand (c) the use of high-order flux-limited methods in space and to time avoid introducing non-physicaloscillations while achieving high-order accuracy where and when possible. The model is initially validatedfor two-phase flow. Results are in good agreement with analytically obtained solutions and experimentalresults. The potential of this method is demonstrated by simulating flow in a realistic geometry composed ofhighly permeable meandering channels.
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Journal articleAdam A, Pavlidis D, Percival J, et al., 2016,
Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity
, Journal of Computational Physics, Vol: 321, Pages: 512-531, ISSN: 1090-2716A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
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Journal articleMassart BYG, Jackson MD, Hampson GJ, et al., 2016,
Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 1. Surface-based modeling
, AAPG Bulletin, Vol: 100, Pages: 697-721, ISSN: 0149-1423Tidal heterolithic sandstones are commonly characterized by millimeter- to centimeter-scale intercalations of mudstone and sandstone. Consequently, their effective flow properties are poorly predicted by (1) data that do not sample a representative volume or (2) models that fail to capture the complex three-dimensional architecture of sandstone and mudstone layers. We present a modeling approach in which surfaces are used to represent all geologic heterogeneities that control the spatial distribution of reservoir rock properties (surface-based modeling). The workflow uses template surfaces to represent heterogeneities classified by geometry instead of length scale. The topology of the template surfaces is described mathematically by a small number of geometric input parameters, and models are constructed stochastically. The methodology has been applied to generate generic, three-dimensional minimodels (9 m3 volume) of cross-bedded heterolithic sandstones representing trough and tabular cross-bedding with differing proportions of sandstone and mudstone, using conditioning data from two outcrop analogs from a tide-dominated deltaic deposit. The minimodels capture the cross-stratified architectures observed in outcrop and are suitable for flow simulation, allowing computation of effective permeability values for use in larger-scale models. We show that mudstone drapes in cross-bedded heterolithic sandstones significantly reduce effective permeability and also impart permeability anisotropy in the horizontal as well as vertical flow directions. The workflow can be used with subsurface data, supplemented by outcrop analog observations, to generate effective permeability values to be derived for use in larger-scale reservoir models. The methodology could be applied to the characterization and modeling of heterogeneities in other types of sandstone reservoirs.
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Journal articleAlroudhan A, Vinogradov J, Jackson MD, 2016,
Zeta potential of intact natural limestone: Impact of potential-determining ions Ca, Mg and SO4
, Colloids and Surfaces A - Physicochemical and Engineering Aspects, Vol: 493, Pages: 83-98, ISSN: 0927-7757We report measurements of the zeta potential on intact limestone samples obtained using the streaming potential method (SPM), supplemented by the more ubiquitous electrophoretic mobility method (EPM). The effect of the potential-determining ions (PDI) Ca, Mg and SO4, and the total ionic strength controlled by NaCl concentration, is investigated over the range typical of natural brines. We find that the zeta potential varies identically and linearly with calcium and magnesium concentration expressed as pCa or pMg. The zeta potential also varies linearly with pSO4. The sensitivity of the zeta potential to PDI concentration, and the IEP expressed as pCa or pMg, both decrease with increasing NaCl concentration. We report considerably lower values of IEP than most previous studies, and the first observed IEP expressed as pMg. The sensitivity of the zeta potential to PDI concentration is lower when measured using the SPM compared to the EPM, owing to the differing location of the shear plane at which the zeta potential is defined. SPM measurements are more appropriate in natural porous samples because they reflect the mineral surfaces that predominantly interact with the adjacent fluids. We demonstrate that special cleaning procedures are required to return samples to a pristine zeta potential after exposure to PDIs. We apply our results to an engineering process: the use of modified injection brine composition to increase oil recovery from carbonate reservoirs. We find a correlation between an increasingly negative zeta potential and increased oil recovery.
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Journal articleMassart BYG, Jackson MD, Hampson GJ, et al., 2016,
Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 2. Flow simulation
, AAPG Bulletin, Vol: 100, Pages: 723-742, ISSN: 0149-1423Tidal heterolithic sandstone reservoirs are heterogeneous at the sub-meter scale, due to the ubiquitous presence of intercalated sandstone and mudstone laminae. Core-plug permeability measurements fail to sample a representative volume of this heterogeneity. Here we investigate the impact of mudstone drape distribution on the effective permeability of heterolithic, cross-bedded tidal sandstones using three-dimensional (3D) surface-based “mini-models” that capture the geometry of cross-beds at an appropriate scale. The impact of seven geometric parameters has been determined: (1) mudstone fraction, (2) sandstone laminae thickness, (3) mudstone drape continuity, (4) toeset dip, (5) climb angle of foreset-toeset surfaces, (6) proportion of foresets to toesets, and (7) trough or tabular geometry of the cross-beds.We begin by identifying a representative elementary volume (REV) of 1 m3, confirming that the model volume of 9 m3 yields representative permeability values. Effective permeability decreases as the mudstone fraction increases, and is highly anisotropic: vertical permeability falls to c. 0.5% of the sandstone permeability at a mudstone fraction of 25%, while the horizontal permeability falls to c. 5% and c. 50% of the sandstone value in the dip (across mudstone drapes) and strike (parallel to mudstone drapes) directions, respectively. There is considerable spread around these values, because each parameter investigated can significantly impact effective permeability, with the impact depending upon the flow direction and mudstone fraction. The results yield improved estimates of effective permeability in heterolithic, cross-bedded sandstones, which can be used to populate reservoir-scale model grid blocks using estimates of mudstone fraction and geometrical parameters obtained from core and outcrop-analog data.
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Conference paperMelnikova Y, Jacquemyn C, Osman H, et al., 2016,
Reservoir modelling using parametric surfaces and dynamically adaptive fully unstructured grids
Geologic heterogeneities play a key role in reservoir performance. Surface based geologic modeling (SBGM) offers an alternative approach to conventional grid-based methods and allows multi-scale geologic features to be captured throughout the modeling process. In SBGM, all geologic features that impact the distribution of material properties, such as porosity and permeability, are modeled as a set of volumes bounded by surfaces. Within these volumes, the material properties are constant. The surfaces have parametric, grid-free representation, which, in principle, allows for unlimited complexity, since no resolution is implied at the stage of modeling and features of any scale can be included. Surface based models are discretized only when required for numerical analysis. We report here a new automated and integrated workflow for creating and meshing stochastic, surfacebased models. Surfaces are represented through non-uniform rational B-splines (NURBS). Multiple relations between surfaces are captured through geologic rules that are translated into Boolean operations (intersection, union, subtraction). Finally, models are discretized using fully unstructured tetrahedral meshes coupled with a geometry-Adaptive sizing function that efficiently approximate complex geometries. We demonstrate the new workflow via examples of multiple erosional channelized geobodies, fault models and a fracture network. We also show finite element flow simulations of the resulting geologic models, using the Imperial College Finite Element Reservoir Simulator (IC-FERST) that features dynamic adaptive mesh optimization. Mesh adaptivity allows us to focus computational effort on the areas of interest, such as the location of water saturation front. The new approach has broad application in modeling subsurface flow.
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Conference paperJacquemyn C, Melnikova Y, Jackson MD, et al., 2016,
Geologic modelling using parametric NURBS surfaces
Most reservoir modelling/simulation workflows represent geological heterogeneity on a pillar-grid defined early in the modelling process. However, it is challenging to represent many common geological features using pillar grids: Examples include intersecting faults, recumbent folds, slumps, and non-monotonic injection structures such as salt diapirs. It is also challenging to represent multi-scale features, because the same number of pillars must be present in all layers so there is little flexibility to adjust the areal grid resolution. We present a surface-based geological modelling (SBGM) workflow that uses NURBS (Non-Uniform Rational B-Splines) surfaces to represent geological heterogeneities without reference to a pre-defined grid. The NURBS surfaces represent a broad range of heterogeneity types, including faults, fractures, stratigraphic surfaces across a range of length-scales, and boundaries between different facies or lithologies. The geological model is constructed using the NURBS surfaces and a mesh created only when required for flow simulation or other calculations. The mesh preserves the geometry of the modelled surfaces. NURBS surfaces are an efficient and flexible tool to model complex geometries and are common in many modelling and engineering disciplines; however, they are rarely used in reservoir modelling. Complex surfaces can be created using a small number of control points; modelling with NURBS surfaces is therefore computationally efficient. We report here a variety of new stochastic approaches to create geological NURBS surfaces, including (1) extrusion of spatially variable cross-sections, (2) parametric 3D geometry templates, and (3) perturbation of control points to yield similar results to some pixel-based geostatistical methods. Surface interactions, such as erosion, stacking or conforming, are enforced to ensure geological relationships are preserved and the boundary representation is watertight. We illustrate our NURBS SBGM approach
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Journal articleAbushaikha AS, Blunt MJ, Gosselin OR, et al., 2015,
Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs
, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 298, Pages: 41-61, ISSN: 0021-9991- Author Web Link
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- Citations: 32
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Journal articleVinogradov J, Jackson MD, 2015,
Zeta potential in intact natural sandstones at elevated temperatures
, Geophysical Research Letters, Vol: 42, Pages: 6287-6294, ISSN: 1944-8007We report measurements of the zeta potential of natural sandstones saturated with NaCl electrolytes of varying ionic strengths at temperatures up to 150°C. The zeta potential is always negative but decreases in magnitude with increasing temperature at low ionic strength (0.01 M) and is independent of temperature at high ionic strength (0.5 M). The pH also decreases with increasing temperature at low ionic strength but remains constant at high ionic strength. The temperature dependence of the zeta potential can be explained by the temperature dependence of the pH. Our findings are consistent with published models of the zeta potential, so long as the temperature dependence of the pH at low ionic strength is accounted for and can explain the hitherto contradictory results reported in previous studies.
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Journal articleVinogradov J, Jackson MD,
Zeta potential in intact natural sandstones at elevated temperatures
, Geophysical Research Letters, ISSN: 1944-8007 -
Journal articleGraham GH, Jackson MD, Hampson GJ, 2015,
Three-dimensional modeling of clinoforms in shallow-marine reservoirs: Part 1. Concepts and application
, AAPG Bulletin, Vol: 99, Pages: 1013-1047, ISSN: 0149-1423Clinoform surfaces control aspects of facies architecture within shallow-marine parasequences and can also act as barriers or baffles to flow where they are lined by low-permeability lithologies, such as cements or mudstones. Current reservoir modeling techniques are not well suited to capturing clinoforms, particularly if they are numerous, below seismic resolution, and/or difficult to correlate between wells. At present, there are no modeling tools available to automate the generation of multiple three-dimensional clinoform surfaces using a small number of input parameters. Consequently, clinoforms are rarely incorporated in models of shallow-marine reservoirs, even when their potential impact on fluid flow is recognized.A numerical algorithm that generates multiple clinoforms within a volume defined by two bounding surfaces, such as a delta-lobe deposit or shoreface parasequence, is developed. A geometric approach is taken to construct the shape of a clinoform, combining its height relative to the bounding surfaces with a mathematical function that describes clinoform geometry. The method is flexible, allowing the user to define the progradation direction and the parameters that control the geometry and distribution of individual clinoforms. The algorithm is validated via construction of surface-based three-dimensional reservoir models of (1) fluvial-dominated delta-lobe deposits exposed at the outcrop (Cretaceous Ferron Sandstone Member, Utah), and (2) a sparse subsurface data set from a deltaic reservoir (Jurassic Sognefjord Formation, Troll Field, Norwegian North Sea). Resulting flow simulation results demonstrate the value of including algorithm-generated clinoforms in reservoir models, because they may significantly impact hydrocarbon recovery when associated with areally extensive barriers to flow.
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Journal articleGraham GH, Jackson MD, Hampson GJ, 2015,
Three-dimensional modeling of clinoforms in shallow-marine reservoirs: Part 2. Impact on fluid flow and hydrocarbon recovery in fluvial-dominated deltaic reservoirs
, AAPG Bulletin, Vol: 99, Pages: 1049-1080, ISSN: 0149-1423Permeability contrasts associated with clinoforms have been identified as an important control on fluid flow and hydrocarbon recovery in fluvial-dominated deltaic parasequences. However, they are typically neglected in subsurface reservoir models or considered in isolation in reservoir simulation experiments because clinoforms are difficult to capture using current modeling tools. A suite of three-dimensional reservoir models constructed with a novel, stochastic, surface-based clinoform-modeling algorithm and outcrop analog data (Upper Cretaceous Ferron Sandstone Member, Utah) have been used here to quantify the impact of clinoforms on fluid flow in the context of (1) uncertainties in reservoir characterization, such as the presence of channelized fluvial sandbodies and the impact of bed-scale heterogeneity on vertical permeability, and (2) reservoir engineering decisions, including oil production rate. The proportion and distribution of barriers to flow along clinoforms exert the greatest influence on hydrocarbon recovery; equivalent models that neglect these barriers overpredict recovery by up to 35%. Continuity of channelized sandbodies that cut across clinoform tops and vertical permeability within distal delta-front facies influence sweep within clinothems bounded by barriers. Sweep efficiency is reduced when producing at higher rates over shorter periods, because oil is bypassed at the toe of each clinothem. Clinoforms are difficult to detect using production data, but our results indicate that they significantly influence hydrocarbon recovery and their impact is typically larger than that of other geologic heterogeneities regardless of reservoir engineering decisions. Clinoforms should therefore be included in models of fluvial-dominated deltaic reservoirs to accurately predict hydrocarbon recovery and drainage patterns.
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- Citations: 30
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Journal articleMaes J, Muggeridge AH, Jackson MD, et al., 2015,
Modelling in-situ upgrading of heavy oil using operator splitting method
, Computational Geosciences, Vol: 20, Pages: 581-594, ISSN: 1573-1499The in-situ upgrading (ISU) of bitumen and oil shale is a very challenging process to model numerically because of the large number of components that need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Operator splitting methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as the splitting error. The best splitting method for modelling a given process minimises the splitting error whilst improving computational performance compared to a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to the modelling of ISU. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error. While this error has been extensively analysed for linear operators for a wide range of methods, the results cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. In this paper, we investigate the application of various operator splitting techniques to the modelling of the ISU of bitumen and oil shale. The techniques were tested on a simplified model of the physical system in which a solid or heavy liquid component is decomposed by pyrolysis into lighter liquid and gas components. The operator splitting techniques examined include the sequential split operator (SSO), the Strang-Marchuk split operator (SMSO) and the iterative split operator (ISO). They were evaluated on various test cases by considering the evolution of the discretization error as
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Journal articleJackson MD, Percival JR, Mostaghiml P, et al., 2015,
Reservoir modeling for flow simulation by use of surfaces, adaptive unstructured meshes, and an overlapping-control-volume finite-element method
, SPE Reservoir Evaluation and Engineering, Vol: 18, Pages: 115-132, ISSN: 1094-6470We present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional corner-point or unstructured grids.Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N +1) representation for pressure. This method exactly represents Darcy-force balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptive-mesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required.After valid
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Journal articleMostaghimi P, Percival JR, Pavlidis D, et al., 2015,
Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media
, MATHEMATICAL GEOSCIENCES, Vol: 47, Pages: 417-440, ISSN: 1874-8961- Author Web Link
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- Citations: 35
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Journal articleMaes J, Muggeridge AH, Jackson MD, et al., 2015,
Scaling heat and mass flow through porous media during pyrolysis
, HEAT AND MASS TRANSFER, Vol: 51, Pages: 313-334, ISSN: 0947-7411- Author Web Link
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- Citations: 7
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Conference paperSalinas P, Percival J, Pavlidis D, et al., 2015,
A discontinuous overlapping control volume finite element method for multi-phase porous media flow using dynamic unstructured mesh optimization
, SPE Reservoir Simulation Symposium -
Journal articleSu K, Latham J-P, Pavlidis D, et al., 2015,
Multiphase flow simulation through porous media with explicitly resolved fractures
, Geofluids, Vol: 15, Pages: 592-607, ISSN: 1468-8123Accurate simulation of multiphase flow in fractured porous media remains a challenge. An important problem is the representation of the discontinuous or near discontinuous behaviour of saturation in real geological formations. In the classical continuum approach, a refined mesh is required at the interface between fracture and porous media to capture the steep gradients in saturation and saturation-dependent transport properties. This dramatically increases the computational load when large numbers of fractures are present in the numerical model. A discontinuous finite element method is reported here to model flow in fractured porous media. The governing multiphase porous media flow equations are solved in the adaptive mesh computational fluid dynamics code IC-FERST on unstructured meshes. The method is based on a mixed control volume – discontinuous finite element formulation. This is combined with the PN+1DG-PNDG element pair, which has discontinuous (order N+1) representation for velocity and discontinuous (order N) representation for pressure. A number of test cases are used to evaluate the method's ability to model fracture flow. The first is used to verify the performance of the element pair on structured and unstructured meshes of different resolution. Multiphase flow is then modelled in a range of idealised and simple fracture patterns. Solutions with sharp saturation fronts and computational economy in terms of mesh size are illustrated.
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