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  • Journal article
    Onyenanu G, Hampson GJ, Fitch P, Jackson MDet al., 2019,

    Effects of erosional scours on reservoir properties of heterolithic, distal lower shoreface sandstones

    , Petroleum Geoscience, Vol: 25, Pages: 235-248, ISSN: 1354-0793

    Distal intervals of interbedded sandstones and mudstones in shallow-marine, wave-dominated shoreface and deltaic reservoirs may contain significant hydrocarbon resources, but their reservoir properties are difficult to predict. Relatively small-scale (200 × 100 × 20 m) three-dimensional object-based reservoir models, conditioned to outcrop analogue data, have been used to investigate the controls on the proportion of sandstone, the proportion of sandstone beds that are connected by sandstone-filled erosional scours and the effective vertical-to-horizontal permeability ratio (kv/kh) of such intervals. The proportion of sandstone is controlled by sandstone-bed and mudstone-interbed thickness, and by parameters that describe the geometry, dimensions and lateral-stacking density of sandstone-filled scours. Sandstone-bed connectivity is controlled by the interplay between the thickness of mudstone interbeds and sandstone-filled erosional scours. Effective kv/kh is controlled by the proportion of sandstone, which represents the effects of variable distributions and dimensions of mudstones produced by scour erosion, provided that scour thickness is greater than mudstone-interbed thickness. These modelling results provide a means of estimating the effective kv/kh at the scale of typical reservoir-model grid cells using values of mudstone-interbed thickness and the proportion of sandstone that can potentially be provided by core data.

  • Journal article
    Sparks RSJ, Annen C, Blundy JD, Cashman KV, Rust AC, Jackson MDet al., 2019,

    Formation and dynamics of magma reservoirs

    , PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 377, ISSN: 1364-503X
  • Journal article
    Edmonds M, Cashman KV, Holness M, Jackson MDet al., 2019,

    Architecture and dynamics of magma reservoirs

    , PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 377, ISSN: 1364-503X
  • Journal article
    Abdul Hamid SA, Adam A, Jackson MD, Muggeridge AHet al., 2019,

    Impact of truncation error and numerical scheme on the simulation of the early time growth of viscous fingering

    , International Journal for Numerical Methods in Fluids, Vol: 89, Pages: 1-15, ISSN: 0271-2091

    The truncation error associated with different numerical schemes (first order finite volume, second order finite difference, control volume finite element) and meshes (fixed Cartesian, fixed structured triangular, fixed unstructured triangular and dynamically adapting unstructured triangular) is quantified in terms of apparent longitudinal and transverse diffusivity in tracer displacements and in terms of the early time growth rate of immiscible viscous fingers. The change in apparent numerical longitudinal diffusivity with element size agrees well with the predictions of Taylor series analysis of truncation error but the apparent, numerical transverse diffusivity is much lower than the longitudinal diffusivity in all cases. Truncation error reduces the growth rate of immiscible viscous fingers for wavenumbers greater than 1 in all cases but does not affect the growth rate of higher wavenumber fingers as much as would be seen if capillary pressure were present. The dynamically adapting mesh in the control volume finite element model gave similar levels of truncation error to much more computationally intensive fine resolution fixed meshes, confirming that these approaches have the potential to significantly reduce the computational effort required to model viscous fingering.

  • Journal article
    Jacquemyn C, Jackson MD, Hampson GJ, 2019,

    Surface-based geological reservoir modelling using grid-free NURBS curves and surfaces

    , Mathematical Geosciences, Vol: 51, Pages: 1-28, ISSN: 1874-8953

    Building geometrically realistic representations of geological heterogeneity in reservoir models is a challenging task that is limited by the inflexibility of pre-defined pillar or cornerpoint grids. Surface-based modelling workflow uses grid-free surfaces that allows efficient creation of geological models without the limitations of pre-defined grids. Surface-based reservoir modelling uses a boundary representation approach in which all heterogeneity of interest (structural, stratigraphic, sedimentological, diagenetic) is modelled by its bounding surfaces, independent of any grid. Volumes bounded by these surfaces are internally homogeneous and thus no additional facies or petrophysical modelling is performed within these geological domains and no grid or mesh discretization is needed during modelling. Any heterogeneity to be modelled within such volumes is incorporated by adding surfaces. Surfaces and curves are modelled using a parametric NURBS (non-uniform rational B-splines) description. These surfaces are efficient to generate and manipulate, and allow fast creation of multiple realizations of geometrically realistic reservoir models. Multiple levels of surface hierarchy are introduced to allow modelling of all features of interest at the required level of detail; surfaces at one hierarchical level are constructed so as to truncate or conform to surfaces of a higher hierarchical level. This procedure requires joining, terminating and stacking of surfaces to ensure that models contain “watertight” surface-bounded volumes. NURBS curves are used to represent well trajectories accurately, including multi-laterals or side-tracks. Once all surfaces and wells have been generated, they are combined into a reservoir model that takes into account geological relationships between surfaces and preserves realistic geometries.

  • Journal article
    Jackson MD, Blundy J, Sparks RSJ, 2018,

    Chemical differentiation, cold storage and remobilization of magma in the Earth's crust

    , Nature, Vol: 564, Pages: 405-409+, ISSN: 0028-0836

    The formation, storage and chemical differentiation of magma in the Earth’s crust is of fundamental importance in igneous geology and volcanology. Recent data are challenging the high-melt-fraction ‘magma chamber’ paradigm that has underpinned models of crustal magmatism for over a century, suggesting instead that magma is normally stored in low-melt-fraction ‘mush reservoirs’1,2,3,4,5,6,7,8,9. A mush reservoir comprises a porous and permeable framework of closely packed crystals with melt present in the pore space1,10. However, many common features of crustal magmatism have not yet been explained by either the ‘chamber’ or ‘mush reservoir’ concepts1,11. Here we show that reactive melt flow is a critical, but hitherto neglected, process in crustal mush reservoirs, caused by buoyant melt percolating upwards through, and reacting with, the crystals10. Reactive melt flow in mush reservoirs produces the low-crystallinity, chemically differentiated (silicic) magmas that ascend to form shallower intrusions or erupt to the surface11,12,13. These magmas can host much older crystals, stored at low and even sub-solidus temperatures, consistent with crystal chemistry data6,7,8,9. Changes in local bulk composition caused by reactive melt flow, rather than large increases in temperature, produce the rapid increase in melt fraction that remobilizes these cool- or cold-stored crystals. Reactive flow can also produce bimodality in magma compositions sourced from mid- to lower-crustal reservoirs14,15. Trace-element profiles generated by reactive flow are similar to those observed in a well studied reservoir now exposed at the surface16. We propose that magma storage and differentiation primarily occurs by reactive melt flow in long-lived mush reservoirs, rather than by the commonly invoked process of fractional crystallization in magma chambers[14].

  • Journal article
    Li S, Collini H, Jackson MD, 2018,

    Anomalous Zeta Potential Trends in Natural Sandstones

    , GEOPHYSICAL RESEARCH LETTERS, Vol: 45, Pages: 11068-11073, ISSN: 0094-8276
  • Journal article
    Lei Q, Xie Z, Pavlidis D, Salinas P, Veltin J, Matar O, Pain C, Muggeridge A, Gyllensten A, Jackson Met al., 2018,

    The shape and motion of gas bubbles in a liquid flowing through a thin annulus

    , Journal of Fluid Mechanics, Vol: 285, Pages: 1017-1039, ISSN: 0022-1120

    We study the shape and motion of gas bubbles in a liquid flowing through a horizontal or slightly inclined thin annulus. Experimental data show that in the horizontal annulus, bubbles develop a unique ‘tadpole-like’ shape with a semi-circular cap and a highly stretched tail. As the annulus is inclined, the bubble tail tends to vanish, resulting in a significant decrease of bubble length. To model the bubble evolution, the thin annulus is conceptualised as a ‘Hele-Shaw’ cell in a curvilinear space. The three-dimensional flow within the cell is represented by a gap-averaged, two-dimensional model, which achieved a close match to the experimental data. The numerical model is further used to investigate the effects of gap thickness and pipe diameter on the bubble behaviour. The mechanism for the semi-circular cap formation is interpreted based on an analogous irrotational flow field around a circular cylinder, based on which a theoretical solution to the bubble velocity is derived. The bubble motion and cap geometry is mainly controlled by the gravitational component perpendicular to the flow direction. The bubble elongation in the horizontal annulus is caused by the buoyancy that moves the bubble to the top of the annulus. However, as the annulus is inclined, the gravitational component parallel to the flow direction becomes important, causing bubble separation at the tail and reduction in bubble length.

  • Journal article
    Onyenanu G, Hampson G, Fitch P, Jackson Met al., 2018,

    Characterisation of effective permeability in heterolithic, distal lower shoreface sandstone reservoirs: Rannoch Formation, Brent Group, UK North Sea

    , Petroleum Geoscience, ISSN: 1354-0793

    The reservoir properties of distal lower-shoreface and distal wave-dominated delta-front deposits, which consist of sandstone beds with locally scoured bases and mudstone interbeds, are poorly understood. The lower Rannoch Formation (Middle Jurassic Brent Group) forms an interval of such heterolithic sandstones in many North Sea reservoirs, and is used to illustrate a workflow for rapid estimation of reservoir properties and their sensitivity to key parameters. Mudstone-interbed thickness distributions in cored reservoir successions are compared to the thickness distribution of sandstone scour-fills in an outcrop analogue(s) in order to identify mudstones with the potential to form laterally extensive barriers to vertical flow. Effective kv/kh at the scale of several typical reservoir-model grid cells (200 × 100 × 20 m) is estimated in intervals bounded by these mudstone barriers via a simple analytical technique that is calibrated to previously documented reservoir-modelling experiments, using values of sandstone proportion measured in cored reservoir successions. Using data from the G2 parasequence (Grassy Member, Blackhawk Formation, east-central Utah, USA) outcrop analogue, mudstones bounding 3–8 m-thick, upwards-coarsening successions in the lower Rannoch Formation may define separate stratigraphic compartments in which grid-cell-scale effective kv/kh is estimated to be 0.0001–0.001 using a streamline-based analytical method.

  • Journal article
    Salinas P, Pavlidis D, Xie Z, Osman H, Pain C, Jackson Met al., 2018,

    A robust mesh optimisation method for multiphase porous media flows

    , Computational Geosciences, Vol: 22, Pages: 1389-1401, ISSN: 1420-0597

    Flows of multiple fluid phases are common in many subsurface reservoirs. Numerical simulation of these flows can bechallenging and computationally expensive. Dynamic adaptive mesh optimisation and related approaches, such as adaptivegrid refinement can increase solution accuracy at reduced computational cost. However, in models or parts of the modeldomain, where the local Courant number is large, the solution may propagate beyond the region in which the mesh isrefined, resulting in reduced solution accuracy, which can never be recovered. A methodology is presented here to modifythe mesh within the non-linear solver. The method allows efficient application of dynamic mesh adaptivity techniques evenwith high Courant numbers. These high Courant numbers may not be desired but a consequence of the heterogeneity of thedomain. Therefore, the method presented can be considered as a more robust and accurate version of the standard dynamicmesh adaptivity techniques.

  • Journal article
    Vinogradov J, Jackson MD, Chamerois M, 2018,

    Zeta potential in sandpacks: Effect of temperature, electrolyte pH, ionic strength and divalent cations

    , Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol: 553, Pages: 259-271, ISSN: 0927-7757

    Rocks in many subsurface settings are at elevated temperature and are saturated with brines of high ionic strength (high salinity) containing divalent ions. Yet most laboratory measurements of zeta potential in earth materials are obtained at room temperature using simple monovalent electrolytes at low ionic strength. Consequently, the zeta potential at conditions relevant to many subsurface settings is not known. We report experimental measurements of the temperature dependence of the zeta potential in well characterised, natural quartz sandpacks over the temperature range 23–120 °C saturated with electrolytes containing divalent ions at a range of concentrations relevant to natural systems. We find that the key control on zeta potential in these unbuffered experiments is pH, which varies in response to temperature and electrolyte composition. The zeta potential is negative irrespective of sample or electrolyte, but its magnitude is strongly correlated to pH, which varies both with temperature and the concentration of divalent ions. The pH decreases with increasing temperature at low ionic strength, but is independent of temperature at high ionic strength. The pH is also typically lower in the presence of divalent ions, irrespective of the total ionic strength. The zeta potential increases in magnitude with increasing pH. Different relationships between zeta potential, temperature and concentration of divalent ions could be obtained in buffered experiments where the pH is fixed at a given value.

  • Journal article
    Deveugle PEK, Jackson MD, Hampson GJ,

    A comparative study of reservoir modeling techniques and their impact on predicted performance of fluvial-dominated deltaic reservoirs: reply

    , AAPG Bulletin, Vol: 102, Pages: 1664-1667, ISSN: 0149-1423
  • Journal article
    Onyenanu GI, Jacquemyn CEMM, Graham GH, Hampson GJ, Fitch PJR, Jackson MDet al., 2018,

    Geometry, distribution and fill of erosional scours in a heterolithic, distal lower shoreface sandstone reservoir analogue: Grassy Member, Blackhawk Formation, Book Cliffs, Utah, USA

    , Sedimentology, Vol: 65, Pages: 1731-1760, ISSN: 0037-0746

    Many shoreface sandstone reservoirs host significant hydrocarbon volumes within distal intervals of interbedded sandstones and mudstones. Hydrocarbon production from these reservoir intervals depends on the abundance and proportion of sandstone beds that are connected by erosional scours, and on the lateral extent and continuity of interbedded mudstones. Cliff‐face exposures of the Campanian ‘G2’ parasequence, Grassy Member, Blackhawk Formation in the Book Cliffs of east‐central Utah, USA, allow detailed characterization of 128 erosional scours within such interbedded sandstones and mudstones in a volume of 148 m length, 94 m width and 15 m height. The erosional scours have depths of up to 1·1 m, apparent widths of up to 15·1 m and steep sides (up to 35°) that strike approximately perpendicular (N099 ± 36°) to the local north–south palaeoshoreline trend. The scours have limited lateral continuity along strike and down dip, and a relatively narrow range of apparent aspect ratio (apparent width/depth), implying that their three‐dimensional geometry is similar to non‐channelized pot casts. There is no systematic variation in scour dimensions, but ‘scour density’ is greater in amalgamated (conjoined) sandstone beds over 0·5 m thick, and increases upward within vertical successions of upward‐thickening conjoined sandstone beds. There is no apparent organization of the overall lateral distribution of scours, although localized clustering implies that some scours were re‐occupied during multiple erosional events. Scour occurrence is also associated with locally increased amplitude and laminaset thickness of hummocky cross‐stratification in sandstone beds. The geometry, distribution and infill character of the scours imply that they were formed by storm‐generated currents coincident with riverine sediment influx (‘storm floods’). The erosional scours increase the vertical and lateral connectivity

  • Journal article
    Malcolm G, Jackson M, MacAllister DJ, Vinogradov J, Butler APet al., 2018,

    Self-potential as a predictor of seawater intrusion in coastal groundwater boreholes

    , Water Resources Research, ISSN: 0043-1397

    Monitoring of self‐potentials (SP) in the Chalk of England has shown that a consistent electrical potential gradient exists within a coastal groundwater borehole previously affected by seawater intrusion (SI) and that this gradient is absent in boreholes further inland. Furthermore, a small but characteristic reduction in this gradient was observed several days prior to SI occurring. We present results from a combined hydrodynamic and electrodynamic model, which matches the observed phenomena for the first time and sheds light on the source mechanisms for the spatial and temporal distribution of SP. The model predictions are highly sensitive to the relative contribution of electrochemical exclusion and diffusion potentials, the ‘exclusion efficiency’, in different rock strata. Geoelectric heterogeneity, largely due to marls and hardgrounds with a relatively high exclusion efficiency, was the key factor in controlling the magnitude of the modelled SP gradient ahead of the saline front and its evolution prior to breakthrough. The model results suggest that, where sufficient geoelectric heterogeneity exists, borehole SP may be used as an early warning mechanism for SI.

  • Journal article
    Jacquemyn C, Jackson MD, Hampson GJ, John CM, Cantrell DL, Zűhlke R, AbuBshait AJ, Lindsay RF, Monsen Ret al., 2018,

    Geometry, spatial arrangement and origin of carbonate grain-dominated, scour-fill and event-bed deposits: Late Jurassic Jubaila Formation and Arab-D Member, Saudi Arabia

    , Sedimentology, Vol: 65, Pages: 1043-1066, ISSN: 0037-0746

    © 2017 The Authors. Sedimentology © 2017 International Association of Sedimentologists Outcrop analogues of the Late Jurassic lower Arab-D reservoir zone in Saudi Arabia expose a succession of fining-upward cycles deposited on a distal middle-ramp to outer-ramp setting. These cycles are interrupted by erosional scours that incise up to 1·8 m into underlying deposits and are infilled with intraclasts up to boulder size (1 m diameter). Scours of similar size and infill are not commonly observed on low-angle carbonate ramps. Outcrops have been used to characterize and quantify facies-body geometries and spatial relationships. The coarse grain size of scour-fills indicates scouring and boulder transport by debris or hyperconcentrated density flows strengthened by offshore-directed currents. Longitudinal and lateral flow transformation is invoked to produce the ‘pit and wing’ geometry of the scours. Scour pits and wings erode up to 1·8 m and 0·7 m deep, respectively, and are on average 50 m wide between wing tips. The flat bases of the scours and their lack of consistent aspect ratio indicate that erosion depth was limited by the presence of cemented firmgrounds in underlying cycles. Scours define slightly sinuous channels that are consistently oriented north–south, sub-parallel to the inferred regional depositional strike of the ramp, suggesting that local palaeobathymetry was more complex than commonly assumed. Weak lateral clustering of some scours indicates that they were underfilled and reoccupied by later scour incision and infill. Rudstone scour-fills required reworking of material from inner ramp by high-energy, offshore-directed flows, associated with storm action and the hydraulic gradient produced by coastal storm setup, to generate erosion and sustain transport of clasts that are generally associated with steeper slopes. Quantitative analysis indicates that these coarse-grained units ha

  • Journal article
    Magee C, Stevenson CTE, Ebmeier SK, Keir D, Hammond JOS, Gottsmann JH, Whaler KA, Schofield N, Jackson CA-L, Petronis MS, O'Driscoll B, Morgan J, Cruden A, Vollgger SA, Dering G, Micklethwaite S, Jackson MDet al., 2018,

    Magma Plumbing Systems: A Geophysical Perspective

    , JOURNAL OF PETROLOGY, Vol: 59, Pages: 1217-1251, ISSN: 0022-3530
  • Journal article
    Debbabi Y, Jackson M, Hampson G, Salinas Pet al., 2018,

    Impact of the buoyancy–viscous force balance on two-phase flow in layered porous media.

    , Transport in Porous Media, Vol: 2018, ISSN: 0169-3913

    Motivated by geological carbon storage and hydrocarbon recovery, the effect of buoyancy and viscous forces on the displacement of one fluid by a second immiscible fluid, along parallel and dipping layers of contrasting permeability, is characterized using five independent dimensionless numbers and a dimensionless storage or recovery efficiency. Application of simple dimensionless models shows that increased longitudinal buoyancy effects increase storage efficiency by reducing the distance between the leading edges of the injected phase in each layer and decreasing the residual displaced phase saturation behind the leading edge of the displacing phase. Increased transverse buoyancy crossflow increases storage efficiency if it competes with permeability layering effects, but reduces storage efficiency otherwise. When both longitudinal and transverse buoyancy effects are varied simultaneously, a purely geometrical dip angle group defines whether changes in storage efficiency are dominated by changes in the longitudinal or transverse buoyancy effects. In the limit of buoyancy-segregated flow, we report an equivalent, unidimensional flow model which allows rapid prediction of storage efficiency. The model presented accounts for both dip and layering, thereby generalizing earlier work which accounted for each of these but not both together. We suggest that the predicted storage efficiency can be used to compare and rank geostatistical realizations, and complements earlier heterogeneity measures which are applicable in the viscous limit.

  • Journal article
    Debbabi Y, Stern D, Hampson GJ, Jackson MDet al., 2018,

    Use of dimensionless scaling groups to interpret reservoir simulation results

    , Journal of Petroleum Science and Engineering, Vol: 163, Pages: 270-282, ISSN: 1873-4715

    In conducting studies to make reservoir management decisions, it is important to efficiently interpret results of reservoir simulations. An understanding of how and why predicted reservoir performance changes with model parameters guides evaluation of production strategies as well as exploration of the impact of uncertainty in reservoir description. The aim of this work is to demonstrate the use of dimensionless scaling groups to interpret and qualitatively predict simulation results of multiphase flow in subsurface reservoirs with a large number of wells. Dimensionless scaling groups which quantify the balance between the forces causing fluid flow were computed between well pairs to rationalize simulation results. The data required to partition the model according to injector-producer pairs and estimate the scaling groups were obtained within minutes using simplified, single-phase numerical experiments. We show that scaling groups can be used to classify multiphase flow behaviours observed over the field into a small set of flow regimes characterized by the combination of their dominant forces. Changes in fluid distribution and reservoir performance with the model parameters can be analyzed in terms of changes in the force balance, and qualitatively predicted using the scaling groups. Predictions made using scaling groups may guide, and thereby reduce the use of, time-consuming multiphase flow simulations to optimize field development plans, to improve the calibration of reservoir models to production data and interpreted subsurface heterogeneity, and to assess the impact of reservoir uncertainties on production.

  • Journal article
    MacAllister DJ, Jackson MD, Butler AP, Vinogradov Jet al., 2018,

    Remote detection of saline intrusion in a coastal aquifer using borehole measurements of self potential

    , Water Resources Research, Vol: 54, Pages: 1669-1687, ISSN: 0043-1397

    Two years of self‐potential (SP) measurements were made in a monitoring borehole in the coastal UK Chalk aquifer. The borehole SP data showed a persistent gradient with depth, and temporal variations with a tidal power spectrum consistent with ocean tides. No gradient with depth was observed at a second coastal monitoring borehole ca. 1 km further inland, and no gradient or tidal power spectrum were observed at an inland site ca. 80 km from the coast. Numerical modeling suggests that the SP gradient recorded in the coastal monitoring borehole is dominated by the exclusion‐diffusion potential, which arises from the concentration gradient across a saline front in close proximity to, but not intersecting, the base of the borehole. No such saline front is present at the two other monitoring sites. Modeling further suggests that the ocean tidal SP response in the borehole, measured prior to breakthrough of saline water, is dominated by the exclusion‐diffusion potential across the saline front, and that the SP fluctuations are due to the tidal movement of the remote front. The electrokinetic potential, caused by changes in hydraulic head across the tide, is one order of magnitude too small to explain the observed SP data. The results suggest that in coastal aquifers, the exclusion‐diffusion potential plays a dominant role in borehole SP when a saline front is nearby. The SP gradient with depth indicates the close proximity of the saline front to the borehole and changes in SP at the borehole reflect changes in the location of the saline front. Thus, SP monitoring can be used to facilitate more proactive management of abstraction and saline intrusion in coastal aquifers.

  • Journal article
    Zhang Z, Geiger S, Rood M, Jacquemyn C, Jackson M, Hampson G, De Carvalho FM, Marques Machado Silva CC, Machado Silva JD, Sousa MCet al., 2017,

    A Tracing Algorithm for Flow Diagnostics on Fully Unstructured Grids With Multipoint Flux Approximation

    , SPE Journal, Vol: 22, Pages: 1946-1962, ISSN: 1930-0220

    Flow diagnostics is a common way to rank and cluster ensembles of reservoir models depending on their approximate dynamic behavior before beginning full-physics reservoir simulation. Traditionally, they have been performed on corner-point grids inherent to geocellular models. The rapid-reservoir-modeling (RRM) concept aims at fast and intuitive prototyping of geologically realistic reservoir models. In RRM, complex reservoir heterogeneities are modeled as discrete volumes bounded by surfaces that are sketched in real time. The resulting reservoir models are discretized by use of fully unstructured tetrahedral meshes where the grid conforms to the reservoir geometry, hence preserving the original geological structures that have been modeled.This paper presents a computationally efficient work flow for flow diagnostics on fully unstructured grids. The control-volume finite-element method (CVFEM) is used to solve the elliptic pressure equation. The flux field is a multipoint flux approximation (MPFA). A new tracing algorithm is developed on a reduced monotone acyclic graph for the hyperbolic transport equations of time of flight (TOF) and tracer distributions. An optimal reordering technique is used to deal with each control volume locally such that the hyperbolic equations can be computed in an efficient node-by-node manner. This reordering algorithm scales linearly with the number of unknowns.The results of these computations allow us to estimate swept-reservoir volumes, injector/producer pairs, well-allocation factors, flow capacity, storage capacity, and dynamic Lorenz coefficients, which all help approximate the dynamic reservoir behavior. The total central-processing-unit (CPU) time, including grid generation and flow diagnostics, is typically a few seconds for meshes with O (100,000) unknowns. Such fast calculations provide, for the first time, real-time feedback in the dynamic reservoir behavior while models are prototyped.

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