Unstructured Cut-Cell Grids for Modeling Complex Reservoirs

SPE Journal ◽  
2014 ◽  
Vol 19 (02) ◽  
pp. 340-352 ◽  
Author(s):  
Brad Mallison ◽  
Charles Sword ◽  
Thomas Viard ◽  
William Milliken ◽  
Amy Cheng
Keyword(s):  
Unstructured Grids ◽  
Simulation Models ◽  
Small Cells ◽  
Tetrahedral Mesh ◽  
Reservoir Modeling ◽  
Normal Faults ◽  
Numerical Representation ◽  
Cut Cell ◽  
Earth Models ◽  
Geologic Model

Summary Effective workflows for translating Earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cut-cell gridding tools that address these needs and improve the integration of our overall reservoir-modeling workflows. The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding uses a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial because of the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process. In practice, simulation grids are often constructed at coarser resolutions than Earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and to preserve critical geologic features. Because the simulation grid and the geologic model are constructed by use of the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate the accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a field-sector model, show the suitability of cut-cell grids for simulation.

scholarly journals Stimulated Reservoir Volume Characterization and Optimum Lateral Well Spacing Study of Two-Well Pad: Midland Basin Case Study

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jaeyoung Park ◽  
Candra Janova
Keyword(s):  
History Matching ◽  
Flow Simulation ◽  
Population Based ◽  
Reservoir Modeling ◽  
Target Area ◽  
Well Performance ◽  
Stimulated Reservoir Volume ◽  
Midland Basin ◽  
Well Spacing ◽  
Geologic Model

This paper introduces a flow simulation-based reservoir modeling study of a two-well pad with long production history and identical completion parameters in the Midland Basin. The study includes building geologic model, history matching, well performance prediction, and finding optimum lateral well spacing in terms of oil volume and economic metrics. The reservoir model was constructed based on a geologic model, integrating well logs, and core data near the target area. Next, a sensitivity analysis was performed on the reservoir simulation model to better understand influential parameters on simulation results. The following history matching was conducted with the satisfactory quality, less than 10% of global error, and after the model calibration ranges of history matching parameters have substantially reduced. The population-based history matching algorithm provides the ensemble of the history-matched model, and the top 50 history-matched models were selected to predict the range of Estimate Ultimate Recovery (EUR), showing that P50 of oil EUR is within the acceptable range of the deterministic EUR estimates. With the best history-matched model, we investigated lateral well spacing sensitivity of the pad in terms of the maximum recovery volume and economic benefit. The results show that, given the current completion design, the well spacing tighter than the current practice in the area is less effective regarding the oil volume recovery. However, economic metrics suggest that the additional monetary value can be realized with 150% of current development assumption. The presented workflow provides a systematic approach to find the optimum lateral well spacing in terms of volume and economic metrics per one section given economic assumptions, and the workflow can be readily repeated to evaluate spacing optimization in other acreage.

scholarly journals ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach

2014 ◽  
Vol 7 (4) ◽  
pp. 4463-4525 ◽  
Author(s):  
M. Jähn ◽  
O. Knoth ◽  
M. König ◽  
U. Vogelsberg
Keyword(s):  
Atmospheric Model ◽  
Sensitivity Study ◽  
Surface Fluxes ◽  
Small Cells ◽  
Scale Model ◽  
Implicit Time ◽  
Integration Scheme ◽  
Convective Boundary ◽  
Microphysics Scheme ◽  
Cut Cell

Abstract. In this work, the fully compressible, nonhydrostatic atmospheric model ASAM is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. An implicit time integration scheme ensures numerical stability around small cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid scale model, a two-moment bulk microphysics scheme, precipitation and vertical surface fluxes by a constant flux layer or a more complex soil model are implemented. Results for three benchmark test cases from the literature are shown. A sensitivity study regarding the development of a convective boundary layer together with island effects at Barbados is carried out to show the capability to perform real case simulations with ASAM.

Depogrid: Next Generation Unstructured Grids for Accurate Reservoir Modeling and Simulation (Russian)

2018 ◽  
Author(s):  
Samita Santoshini ◽  
Simon Harris ◽  
Sheleem Kashem ◽  
Arnaud Levannier ◽  
Azeddine Benabbou ◽  
...  
Keyword(s):  
Modeling And Simulation ◽  
Unstructured Grids ◽  
Reservoir Modeling ◽  
Next Generation

scholarly journals Specifying Quality of a Tight Oil Reservoir through 3-D Reservoir Modeling

2020 ◽  
pp. 3252-3265
Author(s):  
Nagham Jasim ◽  
Sameera M. Hamd-Allah ◽  
Hazim Abass
Keyword(s):  
History Matching ◽  
Simulation Models ◽  
Static Model ◽  
Model Construction ◽  
Reservoir Modeling ◽  
Oil Reservoir ◽  
Main Challenge ◽  
Static Modeling ◽  
Porosity And Permeability ◽  
Log Interpretation

Increasing hydrocarbon recovery from tight reservoirs is an essential goal of oil industry in the recent years. Building real dynamic simulation models and selecting and designing suitable development strategies for such reservoirs need basically to construct accurate structural static model construction. The uncertainties in building 3-D reservoir models are a real challenge for such micro to nano pore scale structure. Based on data from 24 wells distributed throughout the Sadi tight formation. An application of building a 3-D static model for a tight limestone oil reservoir in Iraq is presented in this study. The most common uncertainties confronted while building the model were illustrated. Such as accurate estimations of cut-off permeability and porosity values. These values directly affect the calculation of net pay thickness for each layer in the reservoir and consequently affect the target of estimating reservoir initial oil in place (IOIP). Also, the main challenge to the static modeling of such reservoirs is dealing with tight reservoir characteristics which cause major reservoir heterogeneity and complexities that are problematic to the process of modeling reservoir simulation. Twenty seven porosity and permeability measurements from Sadi/Tanuma reservoir were used to validate log interpretation data for model construction. The results of the history matching process of the constructed dynamic model is also presented in this paper, including data related to oil production, reservoir pressure, and well flowing pressure due to available production.

Upscaling and 3D Streamline Screening of Several Multimillion-Cell Earth Models for Flow Simulation

2006 ◽  
Vol 9 (01) ◽  
pp. 15-23 ◽  
Author(s):  
Ajay K. Samantray ◽  
Qasem M. Dashti ◽  
Eddie Ma ◽  
Pradeep S. Kumar
Keyword(s):  
History Matching ◽  
Flow Behavior ◽  
Flow Simulation ◽  
Field Performance ◽  
Fine Scale ◽  
Fractional Flow ◽  
Full Field ◽  
Earth Models ◽  
Geologic Model ◽  
And Performance

Summary Nine multimillion-cell geostatistical earth models of the Marrat reservoir in Magwa field, Kuwait, were upscaled for streamline (SL) screening and finite-difference (FD) flow simulation. The scaleup strategy consisted of (1) maintaining square areal blocks over the oil column, (2) upscaling to the largest areal-block size (200 x 200 m) compatible with 125-acre well spacing, (3) upscaling to less than 1 million gridblocks for SL screening, and (4) upscaling to less than 250,000 gridblocks for FD flow simulation. Chevron's in-house scaleup software program, SCP, was used for scaleup. SCP employs a single-phase flow-based process for upscaling nonuniform 3D grids. Several iterations of scaleup were made to optimize the result. Sensitivity tests suggest that a uniform scaled-up grid overestimates breakthrough time compared to the fine model, and the post-breakthrough fractional flow also remains higher than in the fine model. However, preserving high-flow-rate layers in a nonuniform scaled-up model was key to matching the front-tracking behavior of the fine model. The scaled-up model was coarsened in areas of low average layer flow because less refinement is needed in these areas to still match the flow behavior of the fine model. The final ratio of pre- to post-scaleup grid sizes was 6:1 for SL and 21:1 for FD simulation. Several checks were made to verify the accuracy of scaleup. These include comparison of pre- and post-scaleup fractional-flow curves in terms of breakthrough time and post-breakthrough curve shape, cross-sectional permeabilities, global porosity histograms, porosity/permeability clouds, visual comparison of heterogeneity, and earth-model and scaled-up volumetrics. The scaled-up models were screened using the 3D SL technique. The results helped in bracketing the flow behavior of different earth models and evaluating the model that better tracks the historical performance data. By initiating the full-field history-matching process with the geologic model that most closely matched the field performance in the screening stage, the amount of history matching was minimized, and the time and effort required were reduced. The application of unrealistic changes to the geologic model to match production history was also avoided. The study suggests that single realizations of "best-guess" geostatistical models are not guaranteed to offer the best history match and performance prediction. Multiple earth models must be built to capture the range of heterogeneity and assess its impact on reservoir flow behavior. Introduction The widespread use of geostatistics during the last decade has offered us both opportunities and challenges. It has been possible to capture vertical and areal heterogeneities measured by well logs and inferred by the depositional environments in a very fine scale with 0.1- to 0.3-m vertical and 20- to 100-m areal resolution (Hobbet et al. 2000; Dashti et al. 2002; Aly et al. 1999; Haldorsen and Damsleth 1990; Haldorsen and Damsleth 1993). It also has been possible to generate a large number of realizations to assess the uncertainty in reservoir descriptions and performance predictions (Sharif and MacDonald 2001). These multiple realizations variously account for uncertainties in structure, stratigraphy, and petrophysical properties. Although impressive, the fine-scale geological models usually run into several millions of cells, and current computing technology limits us from simulating such multimillion-cell models on practical time scales. This requires a translation of the detailed grids to a coarser, computationally manageable level without compromising the gross flow behavior of the original fine-scale model and the anticipated reservoir performance. This translation is commonly referred to as upscaling (Christie 1996; Durlofsky et al. 1996; Chawathe and Taggart 2001; Ates et al. 2003). The other challenge is to quantify the uncertainty while keeping the number of realizations manageable. This requires identifying uncertainties with the greatest potential impact and arriving at an optimal combination to capture the extremes. Further, these models require a screening and ranking process to assess their relative ability to track historical field performance and to help minimize the number of models that can be considered for comprehensive flow simulations (Milliken et al. 2001; Samier et al. 2002; Chakravarty et al. 2000; Lolomari et al. 2000; Albertão et al. 2001; Baker et al. 2001; Ates et al. 2003). In some situations, often a single realization of the best-guess geostatistical model is carried forward for conventional flow simulation and uncertainties are quantified with parametric techniques such as Monte Carlo evaluations (Hobbet et al. 2000; Dashti et al. 2002). Using the case study of this Middle Eastern carbonate reservoir, the paper describes the upscaling, uncertainty management, and SL screening process used to arrive at a single reference model that optimally combines the uncertainties and provides the best history match and performance forecast from full-field flow simulation. Fig. 1 presents the details of the workflow used.

Tectonic evolution of shallow water carbonates: the Lastoni di Formin platform (Dolomites - Italy)

2020 ◽  
Author(s):  
Riccardo Inama ◽  
Niccolò Menegoni ◽  
Cesare Perotti
Keyword(s):  
Carbon Dioxide Sequestration ◽  
Field Measurements ◽  
Fracture Pattern ◽  
Strike Slip ◽  
Hydrocarbon Exploration ◽  
Reservoir Modeling ◽  
Normal Faults ◽  
The Matrix ◽  
Porosity And Permeability ◽  
Seismic Scale

<p>Carbonate rocks are among the most important targets for hydrocarbon exploration, and are considered of particular interest also for gas storage and carbon dioxide sequestration. The development of complex fracture networks in carbonates have a significant influence in fluid circulation, enhancing porosity and permeability and, therefore, modifying their storage capacity. The middle-Triassic Lastoni di Formin platform (Italian Dolomites) was studied by combining field measurements and photogrammetric techniques. The reconstruction of the Digital Model of the buildup allowed the analysis at the outcrop scale with a resolution of 5-10 cm, and gave the opportunity to focus on the behavior of sub-seismic (<10 m) structural elements. Even though their influence on the reservoir quality has been documented, heterogeneities of this order of dimensions are considered as part of the matrix properties in reservoir modeling: outcrop analogues represents a very good source of data that can help to fill this resolution gap. Many generations of fractures and faults can be distinguished at seismic and sub-seismic scale in the present-day fracture pattern of Lastoni di Formin, that is the result of different successive deformational events. In particular, the outcrop records the presence of two different tectonic phases: an E-W extension (Jurassic), that generate N-S trending joints and normal faults, and the Alpine compression (Neogene), that forms conjugate strike slip faults and flower structures. Moreover, an early fracturing gravitational event can be observed: is represented by opening-mode fractures and extensional faults sub-orthogonal to the direction of progradation of the buildup. The presence of platform-derived materials (oncoids) in the fracture fills allows to time-constrain the genesis of these fractures shortly after the deposition. Bed-perpendicular diffuse fractures, which are often strata-bound or terminate on bed-parallel stilolythes, were also detected. Both the margin-parallel early fractures and the Jurassic structures underwent strike-slip reactivations during the Alpine orogeny, which indicates a N-S to NNW-SSE shortening. Evidence of these movements can be inferred from riedel structures, en-chelon arrays, splays and fault jogs that can be observed at different scale. Reactivation of early structures can indicate that they influenced the distribution of subsequent faults and fractures affecting the platform.</p><p> </p>

scholarly journals ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach

2015 ◽  
Vol 8 (2) ◽  
pp. 317-340 ◽  
Author(s):  
M. Jähn ◽  
O. Knoth ◽  
M. König ◽  
U. Vogelsberg
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Atmospheric Model ◽  
Surface Fluxes ◽  
Small Cells ◽  
Scale Model ◽  
Integration Scheme ◽  
Test Cases ◽  
Cut Cell ◽  
Orographic Clouds

Abstract. In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM) is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat–long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.

scholarly journals NOTE ON THE NATURE OF THE CURRENT OF INJURY IN TISSUES

1929 ◽  
Vol 13 (1) ◽  
pp. 47-56 ◽  
Author(s):  
W. J. V. Osterhout ◽  
E. S. Harris
Keyword(s):  
Single Cell ◽  
Intact Cell ◽  
Single Cells ◽  
The Other ◽  
Small Cells ◽  
Neighboring Cell ◽  
Negative Current ◽  
Cut Cell

Leading off from two places on the same cell (of Nitella) with 0.001 M KCl we observe that a cut produces only a temporary negative current of injury. If we lead off with 0.001 M KCl from any cell to a neighboring cell we find that when sap comes out from the cut cell and reaches the neighboring intact cell a lasting negative "current of injury" is produced. This depends on the fact that the intact cell is in contact with sap at one point and with 0.001 M KCl at the other (this applies also to tissues composed of small cells). If we employ 0.1 M KCl in place of 0.001 M the current of injury with a single cell is positive (and is more lasting when a neighboring cell is present). Divergent results obtained with tissues and single cells may be due in part to these factors.

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