Substituting of a Thermodynamic Simulation with a Metamodel in the Scope of Multiscale Modelling

2016 ◽  
Vol 879 ◽  
pp. 1207-1212 ◽  
Author(s):  
Piotr Macioł ◽  
Danuta Szeliga ◽  
Łukasz Sztangret
Keyword(s):  
Thermodynamic Simulation ◽  
Multiscale Simulation ◽  
Scale Model ◽  
Precipitation Kinetic ◽  
Fine Scale ◽  
Coarse Scale ◽  
Computational Point ◽  
Computing Power ◽  
Thermodynamic Computations ◽  
Scale Models

A typical multiscale simulation consists of numerous fine scale models, usually one for each computational point of a coarse scale model. One of possible ways of limiting computing power requirements is replacing fine scale models with some simplified and speeded up ersatz ones. In this paper, the authors attempt to develop a metamodel, replacing direct thermodynamic computations of precipitation kinetic with an advanced approximating model. MatCalc simulator has been used for thermodynamic modelling of precipitation kinetic. Typical heat treatment of P91 steel grade was examined. Selected variables were chosen to be modelled with approximating models. Several attempts with various approximation variants (interpolation algorithms and Artificial Neural Networks) have been investigated and its comparison is included in the paper.

Adaptive Local-Global Multiscale Simulation of the In-situ Conversion Process

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2112-2127 ◽  
Author(s):  
Faruk O. Alpak ◽  
Jeroen C. Vink
Keyword(s):  
Injection Rate ◽  
Multiscale Method ◽  
Scale Model ◽  
Fine Scale ◽  
Coarse Scale ◽  
Scale Models ◽  
Pattern Scale ◽  
Heat Injection ◽  
Coarse Grids

Summary Numerical modeling of the in-situ conversion process (ICP) is a challenging endeavor involving thermal multiphase flow, compositional pressure/volume/temperature (PVT) behavior, and chemical reactions that convert solid kerogen into light hydrocarbons and are tightly coupled to temperature propagation. Our investigations of grid-resolution effects on the accuracy and performance of ICP simulations demonstrated that ICP-simulation outcomes (e.g., oil/gas production rates and cumulative volumes) may exhibit relatively large errors on coarse grids, where “coarse” means a gridblock size of more than 3 to 5 m. On the other hand, coarse-scale models are attractive because they deliver favorable computational performance, especially for optimization and uncertainty quantification workflows that demand a large number of simulations. Furthermore, field-scale models become unmanageably large if gridblock sizes of 3 to 5 m or less have to be used. Therefore, there is a clear business need to accelerate the ICP simulations with minimal compromise of accuracy. We developed a novel multiscale-modeling method for ICP that reduces numerical-modeling errors and approximates the fine-scale simulation results on relatively coarse grids. The method uses a two-scale adaptive local-global solution technique. One global coarse-scale and multiple local fine-scale near-heater models are timestepped in a sequentially coupled fashion. At a given global timestep, the global-model solution provides accurate boundary conditions to the local near-heater models. These boundary conditions account for the global characteristics of the thermal-reactive flow and transport phenomena. In turn, fine-scale information about heater responses is upscaled from the local models, and used in the global coarse-scale model. These flow-based effective properties correct the thermal-reactive flow and transport in the global model either explicitly, by updating relevant coarse-grid properties for the next timestep, or implicitly, by repeatedly updating the properties through a convergent iterative scheme. Upon convergence, global coarse-scale and local fine-scale solutions are compatible with each other. We demonstrate the much-improved accuracy and efficiency delivered by the multiscale method by use of a 2D cross-section pattern-scale ICP simulation problem. The following conclusions are reached through numerical testing: (1) The multiscale method significantly improves the accuracy of the simulation results over conventionally upscaled models. The method is particularly effective in correcting the global coarse-scale model through the use of the fine-scale information about heater temperatures to regulate the heat-injection rate into the formation more accurately. The effective coarse-grid properties computed by the multiscale method at every timestep also enhance the accuracy of the ICP simulations, as demonstrated in a dedicated test case, in which a constant heat-injection rate is enforced across models of all investigated resolutions. (2) Multiscale ICP models result in accelerated simulations with a speed-up of four to 16 times with respect to fine-scale models “out of the box” without any special optimization effort. (3) Our multiscale method delivers high-resolution solutions in the vicinity of the heaters at a reduced computational cost. These fine-scale solutions can be used to better understand the evolution of the fluids and solids (e.g., kerogen conversion and coke deposition) in the vicinity of the heaters (several-feet-long spatial scale). Simultaneously, with the fine-scale near-heater solutions, the local-global coupled multiscale model provides key commercial ICP performance indicators at the pattern scale (several-hundred-feet-long spatial scale) such as production functions.

A Multiscale Adaptive Local-Global Method for Modeling Flow in Stratigraphically Complex Reservoirs

SPE Journal ◽  
2012 ◽  
Vol 17 (04) ◽  
pp. 1056-1070 ◽  
Author(s):  
Faruk O. Alpak ◽  
Mayur Pal ◽  
Knut-Andreas Lie
Keyword(s):  
Corner Point ◽  
Multiscale Simulation ◽  
Velocity Fields ◽  
Basis Functions ◽  
Fine Scale ◽  
Coarse Scale ◽  
Two Phase ◽  
Global Method ◽  
Flow Equations ◽  
Scale Models

Summary A robust and efficient simulation technique is developed on the basis of the extension of the mimetic finite-difference method (MFDM) to multiscale hierarchical-hexahedral (corner-point) grids by use of the multiscale mixed finite-element method (MsMFEM). The implementation of the mimetic subgrid-discretization method is compact and generic for a large class of grids and, thereby, is suitable for discretizations of reservoir models with complex geologic architecture. Flow equations are solved on a coarse grid where basis functions with subgrid resolution account accurately for subscale variations from an underlying fine-scale geomodel. The method relies on the construction of approximate velocity spaces that are adaptive to the local properties of the differential operator. A variant of the method for computing velocity basis functions is developed that uses an adaptive local-global (ALG) algorithm to compute multiscale velocity basis functions by capturing the principal characteristics of global flow. Both local and local-global methods generate subgrid-scale velocity fields that reproduce the impact of fine-scale stratigraphic architecture. By using multiscale basis functions to discretize the flow equations on a coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields on the underlying fine grid. The accuracy and efficacy of the multiscale method is compared with those of fine-scale models and of coarse-scale models with no subgrid treatment for several two-phase-flow scenarios. Numerical experiments involving two-phase incompressible flow and transport phenomena are carried out on high-resolution corner-point grids that represent explicitly example stratigraphic architectures found in real-life shallow-marine and turbidite reservoirs. The multiscale method is several times faster than the direct solution of the fine-scale problem and yields more accurate solutions than coarse-scale modeling techniques that resort to explicit effective properties. The accuracy of the multiscale simulation method with ALG-velocity basis functions is compared with that of the local velocity basis functions. The multiscale simulation results are consistently more accurate when the local-global method is employed for computing the velocity basis functions.

Survival analysis at multiple scales for the modeling of track geometry deterioration

2017 ◽  
Vol 232 (3) ◽  
pp. 842-850 ◽  
Author(s):  
Negin Alemazkoor ◽  
Conrad J Ruppert ◽  
Hadi Meidani
Keyword(s):  
Survival Analysis ◽  
Multiple Scales ◽  
Fine Scale ◽  
Coarse Scale ◽  
Track Geometry ◽  
Time Period ◽  
Scale Models ◽  
Optimal Maintenance ◽  
Maintenance Decisions

Defects in track geometry have a notable impact on the safety of rail transportation. In order to make the optimal maintenance decisions to ensure the safety and efficiency of railroads, it is necessary to analyze the track geometry defects and develop reliable defect deterioration models. In general, standard deterioration models are typically developed for a segment of track. As a result, these coarse-scale deterioration models may fail to predict whether the isolated defects in a segment will exceed the safety limits after a given time period or not. In this paper, survival analysis is used to model the probability of exceeding the safety limits of the isolated defects. These fine-scale models are then used to calculate the probability of whether each segment of the track will require maintenance after a given time period. The model validation results show that the prediction quality of the coarse-scale segment-based models can be improved by exploiting information from the fine-scale defect-based deterioration models.

Analytical Upgridding Method To Preserve Dynamic Flow Behavior

2010 ◽  
Vol 13 (03) ◽  
pp. 473-484 ◽  
Author(s):  
Seyyed Abolfazl Hosseini ◽  
Mohan Kelkar
Keyword(s):  
Single Phase ◽  
Flow Behavior ◽  
Pressure Profile ◽  
Scale Model ◽  
Optimum Number ◽  
Fine Scale ◽  
Coarse Scale ◽  
Flow Process ◽  
Number Of Layers ◽  
Pressure Profiles

Summary A geocellular model contains millions of gridblocks and needs to be upscaled before the model can be used as an input for flow simulation. Available techniques for upgridding vary from simple methods such as proportional fractioning to more complicated methods such as maintaining heterogeneities through variance calculations. All these methods are independent of the flow process for which simulation is going to be used, and are independent of well configuration. We propose a new upgridding method that preserves the pressure profile at the upscaled level. It is well established that the more complex the flow process, the more detailed the level of heterogeneity needed in the simulation model. In general, ideal upscaling is the process that preserves the "pressure profile" from the fine-scale model under the applicable flow process. In our method, we upgrid the geological model using simple flow equations in porous media. However, it should be remembered that to obtain a better match between fine scale and coarse scale, we also need to use appropriate upscaling of the reservoir properties. The new method is currently developed for single-phase flow; however, we used it for both single-phase and two-phase flows for 2D and 3D cases. The method differs fundamentally from the other methods that try to preserve heterogeneities. In those methods, gridblocks are combined that have similar velocities (or other properties) by assuming constant pressure drop across the blocks. Instead, we combine the gridblocks that have similar pressure profiles, although to release some of our assumptions such as having constant velocities in gridblocks, we balance our equation with the K2 term. The procedure is analytical and, hence, very efficient, but preserves the pressure profile in the reservoir. The gridblocks (or layers) are combined in a way so that the difference between fine- and coarse-scale pressure profiles is minimized. In addition, we also propose two new criteria that allow us to choose the optimum number of layers more accurately so that a critical level of heterogeneity is preserved. These criteria provide insight into the overall level of heterogeneity in the reservoir and the effectiveness of the layering design. We compare the results of our method with proportional layering and the King et al. method (King et al. 2006) and show that, for the same number of layers, the proposed method captures the results of the fine-scale model better. We show that the layer merging not only depends on the variation in the permeability between the gridblocks (K2 term), but also on the relative magnitude of the permeability values by combining 1/K2 and K2 terms.

Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 304-316 ◽  
Author(s):  
Arild Lohne ◽  
George A. Virnovsky ◽  
Louis J. Durlofsky
Keyword(s):  
Capillary Pressure ◽  
Effective Properties ◽  
Absolute Permeability ◽  
Scale Model ◽  
Phase Flow ◽  
Fine Scale ◽  
Coarse Scale ◽  
Two Stage ◽  
Two Phase ◽  
Rate Dependent

Summary In the coarse-scale simulation of heterogeneous reservoirs, effective or upscaled flow functions (e.g., oil and water relative permeability and capillary pressure) can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geocellular model. However, if no subgeocellular-scale information is included, the potentially important effects of smaller-scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite-difference equations describing steady-state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. Accurate reproduction of the fine-grid solutions (simulated on 500'500 grids) is achieved on coarse grids of 10'10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate-dependent effective properties in the upscaling can significantly improve the accuracy of the coarse-scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.

scholarly journals Integrating coarse-scale uncertain soil moisture data into a fine-scale hydrological modelling scenario

2011 ◽  
Vol 8 (3) ◽  
pp. 6031-6067
Author(s):  
H. Vernieuwe ◽  
B. De Baets ◽  
J. Minet ◽  
V. R. N. Pauwels ◽  
S. Lambot ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Moisture Content ◽  
Soil Moisture Content ◽  
Epistemic Uncertainty ◽  
Hydrological Modelling ◽  
Scale Model ◽  
Fine Scale ◽  
Coarse Scale ◽  
Soil Moisture Data ◽  
External Data

Abstract. In a hydrological modelling scenario, often the modeller is confronted with external data, such as remotely-sensed soil moisture observations, that become available to update the model output. However, the scale triplet (spacing, extent and support) of these data is often inconsistent with that of the model. Furthermore, the external data can be cursed with epistemic uncertainty. Hence, a method is needed that not only integrates the external data into the model, but that also takes into account the difference in scale and the uncertainty of the observations. In this paper, a synthetic hydrological modelling scenario is set up in which a high-resolution distributed hydrological model is run over an agricultural field. At regular time steps, coarse-scale field-averaged soil moisture data, described by means of possibility distributions (epistemic uncertainty), are retrieved by synthetic aperture radar and assimilated into the model. A method is presented that allows to integrate the coarse-scale possibility distribution of soil moisture content data with the fine-scale model-based soil moisture data. To this end, a scaling relationship between field-averaged soil moisture content data and its corresponding standard deviation is employed.

scholarly journals Modeling the past, present, and future distributions of endangered white abalone (Haliotis sorenseni) to inform recovery efforts in California

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259716
Author(s):  
Jordan DiNardo ◽  
Kevin L. Stierhoff ◽  
Brice X. Semmens
Keyword(s):  
Population Monitoring ◽  
Independent Data ◽  
Fine Scale ◽  
Coarse Scale ◽  
California Department ◽  
Climate Conditions ◽  
Point Conception ◽  
Scale Models ◽  
In Captivity ◽  
National Marine Fisheries Service

White abalone (Haliotis sorenseni) was once commonly found in coastal waters of the Southern California Bight (SCB) and south to Punta Abreojos, Baja California, Mexico. During the 1970s, white abalone supported a commercial fishery, which reduced the population and resulted in the closure of the fishery in 1996. When population levels continued to decline, National Marine Fisheries Service (NMFS) listed the species as endangered under the Endangered Species Act. The California Department of Fish and Wildlife and NMFS began surveying the wild populations, propagating specimens in captivity, and protecting its seabed habitat. We modeled coarse-scale (17 x 17 km) historical (using fishery-dependent data [1955–1996]) and contemporary (using fishery-independent data [1996–2017]) distributions of white abalone throughout its historical domain using random forests and maximum entropy (MaxEnt), respectively, and its fine-scale (10 x 10 m) contemporary distribution (fishery-independent data) using MaxEnt. We also investigated potential outplanting habitat farther north under two scenarios of future climate conditions. The coarse-scale models identified potential regions to focus outplanting efforts within SCB while fine-scale models can inform population monitoring and outplanting activities in these particular areas. These models predict that areas north of Point Conception may become candidate outplant sites as seawater temperatures continue to rise in the future due to climate change. Collectively, these results provide guidance on the design and potential locations for experimental outplanting at such locations to ultimately improve methods and success of recovery efforts.

Downscaling seismic tomography models

2021 ◽  
Author(s):  
Navid Hedjazian ◽  
Thomas Bodin ◽  
Yann Capdeville
Keyword(s):  
Seismic Imaging ◽  
Waveform Inversion ◽  
Effective Medium ◽  
Scale Model ◽  
Multiscale Approach ◽  
Full Waveform Inversion ◽  
Fine Scale ◽  
Full Waveform ◽  
Macro Scale ◽  
Scale Models

<p>Seismic imaging techniques such as elastic full waveform inversion (FWI) have their spatial resolution limited by the maximum frequency present in the observed waveforms. Scales smaller than a fraction of the minimum wavelength cannot be resolved, only a smoothed version of the true underlying medium can be recovered. Application of FWI to media containing small and strong heterogeneities therefore remains problematic. This smooth tomographic image is related to the effective elastic properties, which can be exposed with the homogenization theory of wave propagation. We study how this theory can be used in the FWI context. The seismic imaging problem is broken down in a two-stage multiscale approach. In the first step, called homogenized full waveform inversion (HFWI), observed waveforms are inverted for a macro-scale, fully anisotropic effective medium, smooth at the scale of the shortest wavelength present in the wavefield. The solution being an effective medium, it is difficult to directly interpret it. It requires a second step, called downscaling, where the macro-scale image is used as data, and the goal is to recover micro-scale parameters. All the information contained in the waveforms is extracted in the HFWI step. The solution of the downscaling step is highly non-unique as many fine-scale models may share the same long wavelength effective properties. We therefore rely on the introduction of external a priori information. In this step, the forward theory is the homogenization itself. It is computationally cheap, allowing to consider geological models with more complexity.</p><p>In a first approach to downscaling, the ensemble of potential fine-scale models is described with an object-based parametrization, and explored with a MCMC algorithm. We illustrate the method with a synthetic cavity detection problem. In a second approach, the prior information is introduced by the means of a training image, and the fine-scale model is recovered with a multi-point statistics algorithm. We apply this method on a subsurface synthetic problem, where the goal is to recover geological facies.</p><p> </p>

scholarly journals A Near–Far-Field Model for Bubbles Influenced by External Electrical Fields

2019 ◽  
Vol 9 (21) ◽  
pp. 4722
Author(s):  
Juergen Geiser ◽  
Paul Mertin
Keyword(s):  
Field Model ◽  
Transport Model ◽  
Near Field ◽  
Bubble Formation ◽  
Dielectric Liquid ◽  
Scale Model ◽  
Far Field ◽  
Fine Scale ◽  
Coarse Scale ◽  
Carrier Fluid

In this paper, we present a model that is based on near–far-field charged bubble formation and transportation in an underlying dielectric liquid. The bubbles are controlled by the dielectric liquid, which is influenced by an external electrical field. This allows us to control the shape and volume of the bubbles in the dielectric liquid, such as water. These simulations are important to close the gap between the formation of charged bubbles, which is a fine-scale model and their transport in the underlying liquid, which is a coarse-scale model. In the fine-scale model, the formation of the bubbles and their influence of the electric-stress is approached by a near-field model, which is done by the Young–Laplace equation plus additional force-terms. In the coarse-scale model, the transport of the bubbles is approached by a far-field model, which is done with a convection-diffusion equation. The models are coupled with a bubble in cell scheme, which interpolates between the fine and coarse scales of the different models. Such a scale-dependent approach allows us to apply optimal numerical solvers for the different fine and coarse time and space scales and help to foresee the fluctuations of the charged bubbles in the E-field. We discuss the modeling approaches, numerical solver methods and we present the numerical results for the near–far-field bubble formation and transport model in a dielectric carrier fluid.

Equation-Free/Galerkin-Free Reduced-Order Modeling of the Shallow Water Equations Based on Proper Orthogonal Decomposition

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Vahid Esfahanian ◽  
Khosro Ashrafi
Keyword(s):  
Shallow Water ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Scale Model ◽  
Fine Scale ◽  
Coarse Scale ◽  
Reduced Order ◽  
Shallow Water Flows ◽  
The One ◽  
Proper Orthogonal

In this paper, two categories of reduced-order modeling (ROM) of the shallow water equations (SWEs) based on the proper orthogonal decomposition (POD) are presented. First, the traditional Galerkin-projection POD/ROM is applied to the one-dimensional (1D) SWEs. The result indicates that although the Galerkin-projection POD/ROM is suitable for describing the physical properties of flows (during the POD basis functions’ construction time), it cannot predict that the dynamics of the shallow water flows properly as it was expected, especially with complex initial conditions. Then, the study is extended to applying the equation-free/Galerkin-free POD/ROM to both 1D and 2D SWEs. In the equation-free/Galerkin-free framework, the numerical simulation switches between a fine-scale model, which provides data for construction of the POD basis functions, and a coarse-scale model, which is designed for the coarse-grained computational study of complex, multiscale problems like SWEs. In the present work, the Beam & Warming and semi-implicit time integration schemes are applied to the 1D and 2D SWEs, respectively, as fine-scale models and the coefficients of a few POD basis functions (reduced-order model) are considered as a coarse-scale model. Projective integration is applied to the coarse-scale model in an equation-free framework with a time step grater than the one used for a fine-scale model. It is demonstrated that equation-free/Galerkin-free POD/ROM can resolve the dynamics of the complex shallow water flows. Moreover, the computational cost of the approach is less than the one for a fine-scale model.

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