Fine-grid Model Research Articles

Development of 3D flow diagnostic numerical simulator and rock property modelling for a homogeneous faulted reservoir

Research has shown that faults, especially sealing faults, have become a barrier to flow. Flow diagnostics, on the other hand, are straightforward and controlled numerical flow experiments that are performed to examine a reservoir model, build links and offer rudimentary volume estimates as well as to quickly produce a qualitative representation of the reservoir’s flow patterns. To evaluate, assess, and validate reservoir models and production scenarios, the ’diagnostics’ module in the Matlab Reservoir Simulation Toolbox (MRST) provides a computationally less expensive alternative to running fully featured multiphase simulations. This is done to determine qualitatively regions for well placement to maximize hydrocarbon recovery. Monitoring flow fields, timelines, and tracers—neutral particles in the fluid that flow with the fluid—are all part of flow diagnostics. These techniques are used to determine volumetric communication between a pair of injector-producer wells, as well as flow patterns between injection-production wells and the arrival time between them. To create the grid, the simulation schedule, the wells, upscaling, arrival time computation, and flow diagnostics (drainage and sweep regions) were all done using the Matlab reservoir simulation toolbox (MRST) package by “Makemodel 3” on the data obtained from “SPE 10th comparative solution project” on the MRST package. This was done for a homogeneous anisotropic faulted porous medium. The simulation runs for about 473,739 milliseconds on a fine grid having 20040 active cells while in the coarse model with faster computational time of about 200 seconds, 112 milliseconds. At the early stages of the reservoir bottom-hole pressure for injector I1(about 7000psia) and three producers P1, P2 and P3 remains constant over time (about 3600psia) thanks to pressure support by I1. The extent of residence time after 10 years for the fine, coarse and more coarser model is that fluid element find it easier to transverse through the fault line from I1 to P1, P2 then P3 which takes lesser time than crossing across two intersecting faults, It can also be seen that the sweep efficiency of the fine grid is more effective than the coarse grid. Finally, it has been seen clearly that the fine grid model gives more accurate details but slower computational time while the coarse model which is less accurate but with faster computational time.

The Influence of Terrain Smoothing on Simulated Convective Boundary-Layer Depths in Mountainous Terrain

Many applications rely on a correct estimation of the convective boundary layer (CBL) depth over mountainous terrain, but often these applications use numerical model simulations. Although models inevitably smooth terrain, the amount of smoothing depends on grid spacing. We investigate the behavior of the CBL in coarse- and fine-grid models applied to mountainous terrain by using output from an operational mesoscale modeling system and by performing quasi-idealized simulations. We investigate different areas in different climate zones using different CBL top derivation methods, grid spacing ratios, planetary boundary layer (PBL) schemes, and terrain smoothing. We find that when compared to fine-grid simulations, CBL depths are systematically larger in coarse domains over mountaintops, and to a lesser extent in valleys. On average, differences between coarse- and fine-domains over mountaintops could reach around 10%. In certain locations, differences could be as high as 25%. We attribute the result to terrain smoothing. Similarly, when using a coarse-grid CBL height (relative to mean sea level) interpolated using fine-grid terrain information, there is good agreement with fine-grid CBL depths over mountaintops and less agreement in valleys. Our results have implications for applications that use output from coarse model grids in mountainous terrain. These include inverse modeling studies (e.g., greenhouse gas budget estimations or integrated water vapor transport), PBL evaluation studies, climate research, air quality applications, planning and executing prescribed burns, and studies associated with precipitation over mountainous terrain.

A Practical and Innovative Workflow to Support the Numerical Simulation of CO2 Storage in Large Field-Scale Models

Summary Numerical simulation of the CO2 storage process in porous media, such as in hydrocarbon (gas or oil) depleted reservoirs and in saline aquifers, has been the most indicated tool due to its ability to represent CO2 capacity and the different trapping mechanisms that retain CO2 in the subsurface. Given the complexity of the physicochemical phenomena involved, the modeling needs to incorporate multiphase flow, complex representation of fluids, rock, and rock-fluid interaction properties. These include CO2 reactions with aqueous species and with reservoir rock minerals, in addition to the structural and stratigraphic aspects of the reservoir heterogeneity. These phenomena need to be represented on suitable temporal and spatial scales for accurate predictions of their impacts. Currently, many studies are focused on simulating submodels or sectors of the reservoir, where using finer grids is still practical. This level of grid refinement can be prohibitive, in terms of simulation times, for modeling the entire reservoir. To address this challenge, we propose a new and practical workflow to simulate CO2 storage projects in large field-scale models. When the proposed workflow is applied in both synthetic and real field cases, simulation time is reduced by up to 96% compared to that of the fine-grid model, preserving the same results in representing the aforementioned mechanisms. The workflow is based on classical and standard approaches to handle the high simulation time, but in this study, they are structured and sequenced in three steps. The first one considers the most relevant mechanisms for CO2 storage, ranked from a high-resolution sector model. With the mechanisms prioritized in the previous step, a single-phase upscaling of petrophysical properties can be applied in the field-scale model, followed by adopting a grid with dynamic sizing. The proposed methodology is applied to saline aquifer models in this study, but it can be extended for storage in depleted hydrocarbon reservoirs.

Geological understanding of permeability upscaling in mixed carbonate siliciclastic reservoirs: An outcrop approach, Miocene Dam formation, eastern Saudi Arabia

In reservoir modeling and simulation, upscaling a fine-grid model (scale of millions of cells), which includes numerous geological details to a coarser grid model (scale of thousands of cells), is indispensable to reduce unachievably high computational time and costs. The upscaling process usually results in losing essential details of the fine-scale model and may introduce overestimating or underestimating reservoir properties. Although numerous mathematical approaches have been developed to reduce such limitations, linking upscaling process to the conceptual understanding of sedimentary geology is less well addressed. Such linkage is critical to establishing a predictive conceptual model of factors that affect the upscaling process, such as heterogeneity and connectivity of reservoir rocks. This study generated several upscaling scenarios and performed multiple runs of fluid flow simulation for three-dimensional porosity and permeability models of carbonate strata deposited in a tidal flat setting (the Miocene Dam Formation, eastern Saudi Arabia). The objective was to understand porosity and permeability upscaling in tidal flat carbonate reservoirs based on lithological distribution and mainly answer questions related to the impact of increasing cell size on the distribution of petrophysical properties and the effect of averaging methods (harmonic, geometric, and arithmetic) on permeability upscaling of tidal flat carbonate. The results showed that porosity values in the tidal flat carbonate are sensitive to upscaling procedures. The mean of the porosity values increases substantially with increasing the cell size of the upscaled models and results in an overestimation of the volumetric parameters of the fine-grid model. A possible reason for such overestimation is the diminishing of the percentage of the cells representing the mud-dominated facies, which in the field occur as thin and interbedded layers. Upscaled permeability showed variation based on averaging methods, and the results from fluid flow simulation provide means to select the appropriate upscaled permeability based on lithofacies distribution. Collectively, these results suggested that a geological understanding of the lithofacies distribution is necessary for the upscaling process. Such knowledge helps to select the appropriate cell size and method for permeability averaging.

Experimental Investigations and Numerical Studies of Two-Phase Countercurrent Flow Limitation in a Pressurized Water Reactor: A Review

Gas–liquid two-phase countercurrent flow limitation (CCFL) phenomena widely exist in nuclear power plants. In particular, the gas–liquid countercurrent flow limitation phenomena in a pressurized water reactor (PWR) during a loss-of-coolant accident (LOCA) or a small-break loss-of-coolant accident (SBLOCA) play an important role in nuclear reactor safety research. Over several decades, a series of experimental investigations and numerical studies have been carried out to study the CCFL phenomena in a PWR. For the experimental investigations, numerous experiments have been conducted, and different CCFL mechanisms and CCFL characteristics have been obtained in various test facilities simulating different scenarios in a PWR. The CCFL phenomena are affected by many factors, such as geometrical characteristics, liquid flow rates, and fluid properties. For the numerical studies, more and more numerical models were presented and applied to the calculations of two-phase countercurrent flow over the past several decades. It is considered that the computational fluid dynamics (CFD) tools can simulate most of the two-phase flow configurations encountered in nuclear power plants. In this paper, the experimental investigations and the numerical studies on two-phase countercurrent flow limitation in a PWR are comprehensively reviewed. This review provides a further understanding of CCFL in a PWR and gives directions regarding future studies. It is found that relatively fewer investigations using steam–water under high system pressures are performed due to the limitation of the test facilities and test conditions. There are a number of numerical studies on countercurrent two-phase flow in a PWR hot leg geometry, but the simulations in other flow channels were relatively rare. In addition, almost all of the numerical simulations do not include heat and mass transfer. Thus, it is necessary to investigate the effects of heat and mass transfer experimentally and numerically. Furthermore, it is of significance to perform numerical simulations for countercurrent two-phase flow with a fine computational grid and suitable models to predict the formation of small waves and the details in two-phase flow.

Gridding Effects on CO2 Trapping in Deep Saline Aquifers

Three-dimensional numerical models of potential underground storage and compositional simulation are a way to study the feasibility of storing carbon dioxide in the existing geological formations. However, the results of the simulations are affected by many numerical parameters, and we proved that the refinement of the model grid is one of them. In this study, the impact of grid discretization on CO2 trapping when the CO2 is injected into a deep saline aquifer was investigated. Initially, the well bottom-hole pressure profiles during the CO2 injection were simulated using four different grids. As expected, the results confirmed that the overpressure reached during injection is strongly affected by gridding, with coarse grids leading to non-representative values unless a suitable ramp-up CO2 injection strategy is adopted. Then, the same grids were used to simulate the storage behavior after CO2 injection so as to assess whether space discretization would also affect the simulation of the quantity of CO2 trapped by the different mechanisms. A comparison of the obtained results showed that there is also a significant impact of the model gridding on the simulated amount of CO2 permanently trapped in the aquifer by residual and solubility trapping, especially during the few hundred years following injection. Conversely, stratigraphic/hydrodynamic trapping, initially confining the CO2 underground due to an impermeable caprock, does not depend on gridding, whereas significant mineral trapping would typically occur over a geological timescale. The conclusions are that a fine discretization, which is acknowledged to be needed for a reliable description of the pressure evolution during injection, is also highly recommended to obtain representative results when simulating CO2 trapping in the subsurface. However, the expedients on CO2 injection allow one to perform reliable simulations even when coarse grids are adopted. Permanently trapped CO2 would not be correctly quantified with coarse grids, but a reliable assessment can be performed on a small, fine-grid model, with the results then extended to the large, coarse-grid model. The issue is particularly relevant because storage safety is strictly connected to CO2 permanent trapping over time.

Grid edge classification method to enhance levee resolution in dual-grid flood inundation models

Dual-grid models address the computational bottlenecks of large-scale (>103 km2) urban flood modeling with solution updates on a coarse grid that are informed by topographic data on a fine grid. However, dual-grid models may poorly resolve levees, leading to loss of accuracy. Here we present a grid edge classification method whereby specific edges of the coarse grid are flagged to gather nearby topographic data from the fine grid and create a contiguous physical barrier. The method relies on levee location data in a polyline format, and does not require levee height data since that information is stored on the fine grid. Using a 6804 km2 model of the Los Angeles Metropolitan Region with 3 m topographic data and 987 km of levees, the proposed method is implemented and evaluated. Simulations using coarse grids of 15, 30 and 60 m capture flood extent consistent with fine-grid models based on a critical success index (CSI) of 90, 87 and 82%, respectively. Edge classification improves CSI up to 7 percentage points over a model with unclassified coarse grid edges, and reduces the false alarm ratio up to 10 percentage points. Differences in model performance across the study area are noted, including lower accuracy on urbanized alluvial fans. With compute costs that scale with the coarse grid, dual-grid models can efficiently realize more accurate large-scale models of urban flood hazards.

Fine grid model for the dielectric characteristics of ground‐penetrating radar in mixed media

ABSTRACTThe Fisher–Yates random shuffling algorithm combined with the finite‐difference time‐domain method is proposed to construct a fine grid model for the forward simulation of ground‐penetrating radar in mixed media. First, the finite‐difference time‐domain method was used to divide the coarse grid model into several fine grid models by conforming to the boundary conditions of different media, and the corresponding dielectric parameters were assigned to Yee cells in each fine grid model. Then, the Fisher–Yates random shuffling algorithm was used to randomly scramble all Yee cells with equal probability, and the array of scrambled Yee cells was recombined into a coarse grid model. Finally, the geoelectric model of mixed media was generated with the finite‐difference time‐domain method, and a ground‐penetrating radar image excited by electromagnetic wave pulses was obtained. To explore the characteristic signals and dielectric properties of the ground‐penetrating radar electromagnetic response in mixed media, image entropy theory was used to describe the ground‐penetrating radar image, and waveform analysis and wavelet transform mode maximum methods were used to analyse the single‐channel ground‐penetrating radar signal of the mixed media. The results showed that the Fisher–Yates random shuffling–finite‐difference time‐domain method can be used to construct a valid and stable fine grid model for simulating ground‐penetrating radar in mixed media. The model effectively inhibits electromagnetic attenuation and energy dissipation, and the wavelet transform mode maximum method explains the relative dielectric permittivity distribution of the mixed media. The findings of this study can be used as a theoretical basis for correcting radar parameters and interpreting images when ground‐penetrating radar is applied to mixed media.

Numerical Modeling of the Steam Chamber Ramp-Up Phase in Steam-Assisted Gravity Drainage

Due to the critical nature of the ramp-up phase of an efficient steam-assisted gravity drainage (SAGD) process, it is important to understand the physics of the steam chamber ramp-up phase in order to improve SAGD production performance. In conventional numerical simulation models, the dynamics of the steam chamber ramp-up phase are not fully resolved because of unclear steam–oil–water interactions during the vertical growth of the steam chamber and how its state changes as the reservoir parameters vary. This work provides an efficient approach for the numerical modeling of the steam chamber ramp-up phase in an SAGD operation. The steam chamber ramp-up phase was fully examined through the consideration of the effects of the temperature-dependent oil–water–gas multiphase flow system and the vertical countercurrent flow. The simulation results revealed that for the large temperature gradient of the mobile oil zone at the edge of the steam chamber, a delicate temperature-dependent multiphase flow system was essential for the reliable estimation of the SAGD ramp-up phase. The vertical countercurrent flows of oil–gas and oil–condensate were the dominant mechanisms over cocurrent flow, which significantly impacted the steam chamber ramp-up rate. The numerical model physically predicted the steam chamber ramp-up phase and could be used to efficiently compute a field-scale simulation using a dynamic gridding function that was based on a fine grid model.

Technology Focus: Heavy Oil (April 2022)

Heavy oils are characterized by high density, high viscosity, and high-heavy-fraction components. Because of high viscosity and lower API gravity than conventional crude oil, primary recovery of some of these crude oil types requires thermal stimulation of the reservoirs. Most of the technologies that deal with heavy oil need to address the mobility ratio or viscous forces before any flooding. In general, poor recovery is caused by physical reasons or geological reasons. Physical reasons can be categorized as capillary forces (existence of the interfacial tension between oil and water, wettability) or viscous forces (high mobility ratio between water and oil). Geological reasons are heterogeneities in reservoir rock and exist in all petroleum oil systems. In heavy oil reservoirs, enhanced oil recovery (EOR) intends to reduce the capillary forces and interfacial tension to improve microscopic displacement efficiency or improve the sweep efficiency (macroscopic) by reducing the mobility ratio between injected fluid and displaced fluid. Improving the mobility ratio is achieved by increasing the viscosity of water using polymers or by reducing the oil viscosity using heat. In general, all technologies need to address the capillary and viscous forces to improve oil recovery. Paper SPE 207361 discusses improving of the efficiency of the flood by near-wellbore conformance and improving the vertical sweep efficiency. The use of fiber-optic sensors, as addressed in paper SPE 199023, is intended to gather better data and avoid misinterpretation during falloff tests and injectivity tests. Traditionally, for heavy oil EOR simulation, because of the addition of chemical species or heat to the flow equations as well as the need for a finer grid resolution, the use of the full-field model in most cases was limited and the use of sector models and local grid refinement to obtain a reasonable accuracy has been applied in the industry. Sector modeling conditions must be satisfied to establish the reliability and the trade-off between accuracy (sector models) and computational expediency (full-field model). Recent development of hardware and software [graphics-processing-unit (GPU) -based simulators] has provided the industry with the tools to achieve a full-field model simulation in most fields by taking advantage of GPU solvers and using a fine-grid model to predict full-field performance. Recommended additional reading at OnePetro: www.onepetro.org. SPE 200279 - Field Application of the Autonomous Inflow Control Device for Optimized Heavy Oil Production in South Sultanate of Oman by Ali Al-Jumah, Petroleum Development Oman, et al. SPE 203012 - More Oil and Less Water: Autonomous Inflow Control Devices in New and Old Producers in Heavy Oil Fields From South of Oman by Ameera Al Harrasi, Petroleum Development Oman, et al. SPE 207684 - Game Changer in Dealing With Hard Scale Using a Slickline Torque Action Debris Breaker by Mahmoud Mohamed Koriesh, Dragon Oil, et al.

Modeling radial groundwater flow in fractured media using fracture continuum approach

Two modeling approaches are commonly utilized for simulating flow in fractured formations: the discrete fracture network (DFN) approach and the stochastic continuum (SC) approach. Although the DFN approach is the most accurate, it has computational and memory constraints. The SC approach ensures fast processing but results in system over-homogenization. The fracture continuum (FC) approach arises as an integrated technique that incorporates the merits of both approaches. The main objective of this research is to develop a computationally efficient technique based on the FC approach to simulate the radial groundwater flow towards wells through two-dimensional fractured media under both steady and transient conditions. A stochastic generation of the DFN is performed in a Monte Carlo framework taking into account wells positioning. The DFN flow system is solved by applying the mass balance equation at fracture intersections. Fracture segments are mapped onto grids of 1 × 1 m and 5 × 5 m resolution as conductivity and specific storage cells. The grid flow problem is solved via MODFLOW. Flow and head discrepancies between the proposed technique and the DFN approach (reference solution) are assessed in steady and transient conditions. A grid-conductivity correction is needed to preserve the DFN flow in the presence of wells. A porosity estimation is proposed to identify the grid-pressure transient response. Promising flow and head results are observed for fine and coarse grid models. Some of the studied cases show large discrepancies in the maximum drawdown obtained on the coarse grid model. Accordingly, a new technique is proposed to handle such discrepancies and is found efficient in transient simulations (e.g., 11% and 26.12% discrepancies are minimized to − 0.93% and − 1.03% for two studied cases). The adopted mapping technique is found efficient when the interest is to estimate the average drawdown over an aquifer as correlation coefficients of 0.89 and 0.97 are found for the coarse and fine grid models, respectively when compared to the DFN model. However, the technique has limitations in estimating the drawdown at locations of wells.

A Double-Scale method for near-well flow in reservoir simulation

Simulation of near-well flow around a single well in reservoirs is normally studied using radial logarithmic grids. A promising method for more complicated, multi-well cases is a combined approach of using a Cartesian and a radial grid. In this paper, a new method of overlapping grids is introduced in which a radial grid is overlapped on a coarse Cartesian grid in the area around a well. Connectivity between the two grids is established using an appropriate boundary condition. Five different algorithms of grids connectivity with internal boundary conditions are presented in which the data are transferred between the grids by interpolation pressure and saturations in each grid. This method is implemented in the open-source Matlab Reservoir Simulation Toolbox (MRST) using the modified black-oil model. The proposed approach is validated by simulation of a reference fine radial grid model on a gas-condensate reservoir. Comparing the results with the reference model indicates that the proposed Double-Scale method using a 21 × 21 coarse Cartesian grid is as accurate as a 1001 × 1001 simple Cartesian fine grid model. Then, a double-layer numerical problem with two production wells was simulated and sensitivity analysis was conducted to investigate the effect of critical condensate saturation and vertical permeability. Finally, the second SPE comparative solution project was simulated to compare the performance of the proposed method with the use of the perpendicular bisector (PEBI) grids around the well. Results showed that the accuracy of the PEBI grid and Double-Scale method are comparable. However, the proposed Double-Scale method is almost 2 times faster in this specific problem. • The new Double-Scale method is implemented in MRST toolbox. • The accuracy of results highly increases by using the Double-Scale method. • This method reduces the CPU time of simulation significantly. • The gravity drainage can be seen by monitoring vertical permeability variation. • The second SPE comparative solution project was simulated by the Double-Scale method.

Technology Focus: Hydraulic Fracturing Modeling (November 2021)

In the past decades, the success of unconventional hydrocarbon resource development can be attributed primarily to the improved understanding of fracture systems, including both hydraulically induced fractures and natural fracture networks. To tackle the fracture characterization problem, several recent papers have provided novel insights into fracture modeling technique. Because of the complex nature and heterogeneity of rock discontinuity, fabric, and texture, the fracture-modeling process typically suffers from limited data availability. Research shows that modeling results reached without interrogation of high-resolution petrophysical and geomechanical data can mislead because the fluid flow is actually controlled by fine-scale rock properties. A more-reliable fracture geometry can be obtained from an enhanced modeling process that preserves the signature from high-frequency data. Advanced techniques to model fracturing processes with proppant transportation and thermodynamics require even more-sophisticated simulation and computation power. When the subsurface is too puzzling to be described by a physical model and existing data, machine learning and artificial intelligence can be adapted as a practical alternative to interpret complex fracture systems. Taking a discrete fracture network (DFN) as an example, a data-driven approach has been introduced to learn from outcrop, borehole imaging, core computed tomography scan, and seismic data to recognize stratigraphic bedding, faults, subseismic fractures, and hydraulic fractures. Input data can be collected by hand, 3D stereophotogrammetry, or drone. When upscaling DFN into a coarse grid for reservoir simulation, deep-learning techniques such as convolutional neuron networks can be used to populate fracture properties into a dual-porosity/dual-permeability model approved to yield high accuracy compared with a fine-grid model. Furthermore, the new techniques greatly extend the application of fracture modeling in the arena of the energy transition, such as in geothermal optimization. Recommended additional reading at OnePetro: www.onepetro.org. SPE 203927 - Numerical Simulation of Proppant Transport in Hydraulically Fractured Reservoirs by Seyhan Emre Gorucu, Computer Modelling Group, et al. SPE 202679 - Deep-Learning Approach To Predict Rheological Behavior of Supercritical CO2 Foam Fracturing Fluid Under Different Operating Conditions by Shehzad Ahmed, Khalifa University of Science and Technology, et al. SPE 203983 - A 3D Coupled Thermal/Hydraulic/Mechanical Model Using EDFM and XFEM for Hydraulic-Fracture-Dominated Geothermal Reservoirs by Xiangyu Yu, Colorado School of Mines, et al.

Contrasting lightning projection using the lightning potential index adapted in a convection-permitting regional climate model

Lightning climate change projections show large uncertainties caused by limited empirical knowledge and strong assumptions inherent to coarse-grid climate modeling. This study addresses the latter issue by implementing and applying the lightning potential index parameterization (LPI) into a fine-grid convection-permitting regional climate model (CPM). This setup takes advantage of the explicit representation of deep convection in CPMs and allows for process-oriented LPI inputs such as vertical velocity within convective cells and coexistence of microphysical hydrometeor types, which are known to contribute to charge separation mechanisms. The LPI output is compared to output from a simpler flash rate parameterization, namely the CAPE times PREC parameterization, applied in a non-CPM on a coarser grid. The LPI’s implementation into the regional climate model COSMO-CLM successfully reproduces the observed lightning climatology, including its latitudinal gradient, its daily and hourly probability distributions, and its diurnal and annual cycles. Besides, the simulated temperature dependence of lightning reflects the observed dependency. The LPI outperforms the CAPE times PREC parameterization in all applied diagnostics. Based on this satisfactory evaluation, we used the LPI to a climate change projection under the RCP8.5 scenario. For the domain under investigation centered over Germany, the LPI projects a decrease of 4.8% in flash rate by the end of the century, in opposition to a projected increase of 17.4% as projected using the CAPE times PREC parameterization. The future decrease of LPI occurs mostly during the summer afternoons and is related to (i) a change in convection occurrence and (ii) changes in the microphysical mixing. The two parameterizations differ because of different convection occurrences in the CPM and non-CPM and because of changes in the microphysical mixing, which is only represented in the LPI lightning parameterization.

Development of an effective design for a down-hole water sink to control water in oil production wells

Recently, cost, and adverse environmental impacts of wastewater treatment in oil and gas industries have been elevated. Due to several negative environmental consequences, the methods for decreasing this large amount of water production are essential. Such methods can remove or decrease application of water treatment and desalination, which cause numerous environmental consequences. Downhole water sink (DWS) production is one of the methods to control wastewater production. It produces water from the aquifer to prevent water movement to the underground oil production zone. Consequently, the application of desalination plants, and their environmental drawbacks become limited. The optimal design for DWS is important to provide an efficient process regarding technical and economic aspects. DWS modeling, sensitivity analysis, and optimization are investigated as the solutions in this work based on the simulation of a reliable published model following numerical validations. In this work, in a fair comparison, it is shown that, DWS is more beneficial than conventional production with respect to water cut and oil production rate, evidentially. The related NPV is considerably improved from 1.01E+07 [$] to 1.16E+07 [$]. In the sensitivity analysis of DWS, opening length and water drainage rate, as the effective variables, have been analyzed prior to optimization, showing high sensitivity of NPV to this variable. By analyzing the mesh resolution, it is concluded that although in the vertical direction, there was no sensitivity more the mentioned model, the NPV is sensitive to grid resolution in the radial direction. Accordingly, a coarsened model is prepared to accelerate calculation in optimization in addition the fine-grid model. Afterward, by adopting a stochastic optimization technique to DWS design, the NPV is improved from 2.17E+08 [$] to 4.67E+08 [$], and the resulted optimized variables are conformed with the sensitivity results. Moreover, the effect of anisotropy on reservoir production behavior is analyzed in DWS design. This study shows that by increasing the vertical to horizontal permeability, the water production increases and oil production decreases. Finally, to verify the optimization results, a comparison between non-optimized and optimized DWS reveals significant improvement from 6.50E+07 [$] to 4.67E+08 can be obtained.

An Improved Multicomponent Diffusion Model for Compositional Simulation of Fractured Unconventional Reservoirs

Summary Most simulators currently use the advection/diffusion model (ADM), where the total flux comprises Darcian advection and Fickian diffusion. However, significant errors can arise, especially for modeling diffusion processes in fractured unconventional reservoirs, if diffusion is modeled by the conventional Fick’s law using molar concentration. Hence, we propose an improved multicomponent diffusion model for fractured reservoirs to better quantify the multiphase multicomponent transport across the fracture/matrix interface. We first give a modified formulation of the Maxwell-Stefan (MS) equation to model the multicomponent diffusion driven by the chemical potential gradients. A physics-based modification is proposed for the ADM in fractured reservoirs, where fracture, matrix, and their interface are represented by three different yet interconnected flow domains to honor the flux continuity at the fracture/matrix interface. The added interface using a more representative fluid saturation and composition of the interface can hence better capture the transient mass fluxes between fracture and matrix. The proposed approach is also implemented in an in-house compositional simulator. The multicomponent diffusion model is validated with both intraphase and interphase diffusion experiments. Then, the improved model for fracture/matrix interaction is compared with a fine-grid model. The proposed multiple interacting continua (MINC) model with three continua (MINC3) can better match the fine-grid model’s result than the double-porosity (DP) model, which only obtains a fair match at an early time. Then, we simulate a gas huff ‘n’ puff (HnP) well in the Permian Basin to investigate the effect of diffusion within the fractured tight oil reservoir. The simulation reveals that diffusion has a minor effect on the performance of depletion when oil is the dominant phase. For gas HnP, the simulation neglecting diffusion will underestimate the oil recovery factor (RF) but overestimate the gas rate. The DP approach tends to overestimate the RF of heavy components but leads to a similar cumulative oil RF compared with MINC3. With the diffusion included in the simulation, gas HnP performance becomes more sensitive to the soaking time than the model without diffusion. Although increasing the soaking time will lead to a higher RF after considering diffusion, the incremental oil is not sufficiently large to justify a prolonged soaking time.

Infill well placement optimization in two-dimensional heterogeneous reservoirs under waterflooding using upscaling wavelet transform

Optimal location of infill wells is very important in the development strategies of any reservoir. It is even one of the most challenging tasks for waterflooding projects in heterogeneous reservoirs. The new infill wells have to be located based on optimum reservoir management practice taking into considerations several reservoir parameters. Usually, there are several potential locations of the new infill wells. Selecting and evaluating of all the possible candidate wells using fine scale models is neither computationally straightforward nor time efficient for geological models consisting of millions of grid cells. This paper presents a practical and cost effective method that minimizes the number of simulation runs and maximizes oil recovery by optimizing infill well location. The proposed method consists of upscaling the geological reservoir model from fine scale into a coarser scale while preserving the important characteristics of the fine scale model. The proposed approach uses wavelet transform as an upscaling technique. To illustrate its feasibility and effectiveness, the proposed method is applied to three synthetic cases of two-dimensional inverted five-spot heterogeneous reservoir models. Static Dykstra-Parsons coefficient of permeability variation is utilized to compute the degree of heterogeneity of each of the three models. Permeability distribution values are used to represent and construct the reservoir models. The permeability models are upscaled from the original fine grid model to coarser scale levels. A computationally efficient and extremely time saving three-dimensional streamline simulator is used to implement the proposed approach. This paper shows that the results obtained from the upscaled models are in excellent agreement with the fine scale models. More importantly, the results also illustrate that the proposed method extensively reduces the number of simulation runs required to find the optimum well location between 75% and 93% depending on the reservoir heterogeneity. The methodology presented in this paper provides a straightforward road map for upscaling several heterogeneous reservoir models using wavelet transform approach to determine the optimum infill well location.

Analysis of the impacts of relative permeability and mobility ratio on heterogeneity loss error during upscaling of geological models

The detailed geological fine grids are upscaled to create reliably sized simulation coarse models to solve flow equations in a more efficient way. Any upscaling process results in a loss of accuracy, along with an increase of errors. Numerical dispersion, heterogeneity loss, and connectivity misrepresentation are responsible for the upscaling errors. Recognizing the source of each error, and the behavior of influential factors through upscaling process could provide an optimum level of upscaling and an evaluation of upscaling methods’ accuracy. Despite the importance of upscaling error, little attention has been paid to this subject. This paper represents a rigorous analysis of the heterogeneity loss behavior associated with the relative permeability contrast and the mobility ratio under a waterflooding process. For this purpose, heterogeneous fine grid models are constructed by the fractional Brownian motion process. The models are upscaled by three upscaling factors. The models achieved are implemented to eliminate the impact of numerical error among upscaling errors in order to focus strictly on heterogeneity loss. Water–oil displacement simulation is then performed on fine and corresponding refined upscaled models at three different ratios of relative permeabilities and mobility ratios. In the next stage, the relation between flow performance error and heterogeneity loss is investigated by the heterogeneity loss plot. The slope of this plot provides the reservoir engineer an insight to evaluate the performance of upscaling methods and the behavior of the influential factors on upscaling errors. Moreover, by using the heterogeneity loss plot for each ratio, a limit of coarsening is presented. Based on the results, the heterogeneity loss error is affected more by the mobility ratio contrast than the relative permeability difference. Also, it is demonstrated that water-wet reservoirs with light oil are more sensitive to the level of upscaling.

LARGE-SCALE AIR POLLUTION MODELING IN EUROPE UNDER DIFFERENT CLIMATIC SCENARIOS

The treatment of large-scale air pollution models is not only important for modern society, but also an extremely difficult task. Five important physical and chemical processes: (1) horizontal advection, (2) horizontal diffusion, (3) vertical exchange, (4) emission of different pollutants and (5) dry and wet deposition have to be united and handled together. This leads to huge computational problems which have to be treated on modern high-speed parallel architectures by using advanced numerical methods. The computational difficulties are vastly increased when such models are used in the investigation of the impact of climatic changes on high pollution levels that are often exceeding certain critical concentrations and, therefore, are becoming harmful for plants, animals and human beings. There are two major reasons for the great increase in computational difficulties: (a) it is necessary to run the discretized data on fine spatial grid models over very long time-periods consisting of many consecutive years and (b) different scenarios are to be used in order to investigate the sensitivity of the pollution levels to systematic variations of several carefully selected key parameters. How the major difficulties can be resolved is explained here. Furthermore, many results are presented in order to demonstrate the ability of the model to handle successfully the huge computational tasks by using fine space and time discretization and by applying a chemical scheme with many chemical species participating in several hundred chemical reactions. Our results indicate that the climatic changes will often lead to some increases in the pollution levels.

Nonlocal multicontinuum (NLMC) upscaling of mixed dimensional coupled flow problem for embedded and discrete fracture models

In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of equations. For fine grid discretization, we use a conservative finite-volume approximation. We construct an upscaled model using the non-local multicontinuum (NLMC) method for the coupled system. The proposed upscaled model is based on a set of simplified multiscale basis functions for the auxiliary space and a constraint energy minimization principle for the construction of multiscale basis functions. Using the constructed NLMC-multiscale basis functions, we obtain an accurate coarse grid upscaled model. We present numerical results for both fine-grid models and upscaled coarse-grid models using our NLMC method. We consider model problems with (1) discrete fracture fine grid model with low and high permeable fractures; (2) embedded fine grid model for two types of geometries with differnet fracture networks and (3) embedded fracture fine grid model with heterogeneous permeability. The simulations using the upscaled model provide very accurate solutions with significant reduction in the dimension of the problem.