Nonlinear Reservoir Research Articles

Reservoir structure optimization of echo state networks: A detrended multiple cross-correlation pruning perspective

Reservoir structure optimization of echo state networks (ESN) is an important enabler for improving network performance. In this regard, pruning provides an effective means to optimize reservoir structure by removing redundant components in the network. Existing studies achieve reservoir pruning by removing insignificant neuronal connections. However, such processing causes the optimized neurons to still remain in the reservoir and thus hinder network inference by participating in computations, leading to suboptimal utilization of pruning benefits by the network. To solve this problem, this paper proposes an adaptive pruning algorithm for ESN within the detrended multiple cross-correlation (DMC2) framework, i.e., DMAP. On the whole, it contains two main functional parts: DMC2 measure of reservoir neurons and reservoir pruning. Specifically, the former is used to quantify the correlation among neurons. Based on this, the latter can remove neurons with high correlation from the reservoir completely, and finally obtain the optimal network structure by retraining the output weights. Experiment results show that DMAP-ESN outperforms its competitors in nonlinear approximation capability and reservoir stability.

Multi-scale nonlinear reservoir flow simulation based on digital core reconstruction

During the exploitation of oil and gas reservoirs, changes in reservoir physical or fluid properties will lead to alterations in formation seepage capacity, subsequently impacting the productivity of oil and gas wells. Therefore, it is crucial to evaluate the variations in reservoir physical and fluid properties as well as their influence on oil and gas well productivity during reservoir exploitation.It employs a descriptive approach to investigate cross-scale (i.e., micro-scale → small-scale → large-scale) fluid seepage phenomena in water flooding. By leveraging digital core reconstruction technology and focusing on micro-pore network simulation, it establishes an analytical framework for studying cross-scale seepage fields, facilitating the exploration of the micro-seepage mechanism that governs non-homogeneous water flooding's impact on liquid production capacity within a reservoir. Integrating constraints from micro-pore network simulation and small-scale core displacement test data, while considering macro-heterogeneity near wellbore areas as flow unit divisions and superposition bases within large-scale reservoirs, it reveals the nonlinear flow characteristics of changes in liquid production capacity in water-flooding oil reservoirs based on microscopic digital core analysis. This approach aligns with findings from small-scale core testing and sweep coefficient correction while also addressing the non-uniform distribution characteristics of physical parameters within large-scale reservoirs.By integrating permeability field characteristics at three levels, this approach optimizes its technical advantages in describing dynamic permeability fields at each level, thereby facilitating precise prediction of water drive oil development effects.

Volatile and Nonvolatile Programmable Iontronic Memristor with Lithium Imbued TiOx for Neuromorphic Computing Applications.

We demonstrate a lithium (Li) imbued TiOx iontronic device that exhibits synapse-like short-term plasticity behavior without requiring a forming process beforehand or a compliance current during switching. A solid-state electrolyte lithium phosphorus oxynitride (LiPON) behaves as the ion source, and the embedding and releasing of Li ions inside the cathodic like TiOx renders volatile conductance responses from the device and offers a natural platform for hardware simulating neuron functionalities. Besides, these devices possess high uniformity and great endurance as no conductive filaments are present. Different short-term pulse-based phenomena, including paired pulse facilitation, post-tetanic potentiation, and spike rate-dependent plasticity, were observed with self-relaxation characteristics. Based on the voltage excitation period, the time scale of the volatile memory can be tuned. Temperature measurement reveals the ion displacement-induced conductance channels become frozen below 220 K. In addition, the volatile analog devices can be configured into nonvolatile memory units with multibit storage capabilities after an electroforming process. Therefore, on the same platform, we can configure volatile units as nonlinear dynamic reservoirs for performing neuromorphic training and the nonvolatile units as the weight storage layer. We proceed to use voice recognition as an example with the tunable time constant relationship and obtain 94.4% accuracy with a minimal training data set. Thus, this iontronic platform can effectively process and update temporal information for reservoir and neuromorphic computing paradigms.

Quantitative characterization and application of deep learning carbonate reservoir

Abstract Quantitative reservoir characterization is an important research task in carbonate reservoir development. At present, the comprehensive evaluation of drilling, logging, seismic, and productivity testing data is usually used, which requires a large number of test data and tedious manual data collation. Deep learning technology can independently learn complex reservoir characteristics, has a strong ability for high-dimensional data structure mining, and has a strong advantage in solving complex nonlinear reservoir description problems closely related to various geological characteristics. Therefore, this paper applies deep learning technology to reservoir characterization. First, a deep neural network model is constructed, and then seven characteristic parameters such as fracture density, fracture opening, fracture porosity, matrix porosity, total porosity, effective thickness, and specific oil production index are taken as input variables. After model training and verification, the effective permeability distribution map of the reservoir in the target area can be automatically generated. The results show that the deep learning method has strong adaptability and practicability for the quantitative characterization of complex reservoirs, and provides a new way of thinking for the quantitative characterization of reservoirs.

An improved dynamic bidirectional coupled hydrologic–hydrodynamic model for efficient flood inundation prediction

Abstract. To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction.

A dual-reciprocity boundary element method based transient seepage model with nonlinear distributed point source dual-porosity gas reservoir

As a result of advancements in gas reservoir development technologies and a deeper understanding of seepage theory, numerous nonlinear seepage problems have emerged. Consequently, conventional analytical solution models are no longer applicable. Moreover, existing semi-analytical and numerical solution models suffer from issues like high computational complexity and limited flexibility, significantly constraining their practical utility. For this purpose, a gas reservoir transient seepage model is established based on the dual-reciprocity boundary element method (DRBEM). This model couples the wellbore storage coefficients with skin factor and introduces a novel dual-porosity transient interporosity seepage algorithm, enabling the resolution of transient seepage problems in dual-porosity gas reservoirs with nonlinear point source distributions. Additionally, it investigates the dynamic behavior of bottomhole pressure during the early production stage of gas wells, while capturing the dynamic pressure distribution within the seepage field. This approach offers the advantages of semi-analyticity, meshless, and eliminates the need for Laplace transforms, resulting in a significant reduction in computational complexity. Ultimately, the application of our model to well-pattern production with the production system transition issues, in conjunction with the log-log type curves of bottomhole pressure, and the dynamics of gas reservoir pressure, enables the analysis of interference characteristics between injection-production wells. This showcases the practical advantages of the model's application. The findings of this study provide valuable assistance for modeling and solving transient seepage problems in dual-porosity oil and gas reservoirs production. The application of DRBEM in unsteady-state diffusion, heat conduction, stress fields, and other potential field problems is relevant for reference.

Quantum-state engineering in cavity magnomechanics formed by two-dimensional magnetic materials

Cavity magnomechanics has become an ideal platform to explore macroscopic quantum effects. Bringing together magnons, phonons, and photons in a system, it opens many opportunities for quantum technologies. It was conventionally realized by an yttrium iron garnet, which exhibits a parametric magnon–phonon coupling mˆ†mˆ(bˆ†+bˆ) , with mˆ and bˆ being the magnon and phonon modes. Inspired by the recent realization of two-dimensional (2D) magnets, we propose a cavity magnomechanical system using a 2D magnetic material with both optical and magnetic drivings. It features the coexisting photon–phonon radiation-pressure coupling and quadratic magnon–phonon coupling mˆ†mˆ(bˆ†+bˆ)2 induced by the magnetostrictive interaction. A stable squeezing of the phonon and bi- and tri-partite entanglements among the three modes are generated in the regimes with a suppressed phonon number. Compared with previous schemes, ours does not require any extra nonlinear interaction and reservoir engineering and is robust against the thermal fluctuation. Enriching the realization of cavity magnomechanics, our system exhibits its superiority in quantum-state engineering due to the versatile interactions enabled by its 2D feature.

Iterative ensemble smoothing scheme for reservoir history matching with unknown observation error covariance

Ensemble-based smoothers are well-known data assimilation tools in reservoir applications, including history matching and geophysical inversion. They entail the knowledge of the covariance of observation errors, which, however, is often poorly known in real applications and commonly estimated subjectively on the basis of a diagonal structure. This neglects the correlations within the observation errors, which may deteriorate the quality of the model estimates. Herein, we relaxed the independent observational error assumption by considering a nondiagonal structure for the covariance. Given that all the elements in the covariance matrix could not be estimated given a limited amount of data, which is typically the case in practice, we reduced the number of degrees of freedom by parameterizing this covariance with two scalar parameters, one for error variance and the other for error correlation length–scale. We then estimated these parameters together with the model variables using a hybrid algorithm that combined a variational Bayesian approach with particle filters and an ensemble-based smoother. The proposed approach was validated with a linear Gaussian model and a nonlinear reservoir flow model. The results clearly demonstrate the potential of the proposed method in effectively addressing the uncertainty of observations in the history-matching process.

Coexistence of short- and long-term memory in NbO$lt;SUB$gt;x$lt;/SUB$gt;-based memristor for a nonlinear reservoir computing system

Coexistence of short- and long-term memory in NbO$lt;SUB$gt;x$lt;/SUB$gt;-based memristor for a nonlinear reservoir computing system

Experimental surface runoff hydrographs from linear impervious subcatchments for rainfalls of extremely high intensity

This study focuses on lab-scale experimental runoff hydrographs from a linear completely impervious plane subcatchment. An improved method of surface runoff physical modelling was developed, allowing for expanded laboratory hydrograph simulations up to a linear scale of 10. Model rains of different intensities and durations were applied, and digital online data processing techniques were employed to ensure high time resolution and accurate flow rate determination. The experimental hydrographs were analyzed in a dimensionless form to facilitate generalization and comparison with widely used nonlinear reservoir method and unit hydrograph method. Wave-like fluctuations of the flow rate were observed in most experimental hydrographs as they approached the maximum runoff. The dimensionless phase time of the experimental hydrographs showed an increasing trend with higher rainfall intensity, and a power-law equation was derived to approximate this relationship. An averaged dimensionless runoff hydrograph was obtained by processing individual hydrographs, and it was approximated by the DR-Hill-Zerobackground model for the initial stage during the rainfall and by the Weibull model for the later stage, after the rainfall stopped. The findings of this study have significant implications for modelling surface runoff from small urban subcatchments, particularly under critical rainfall events with extremely high intensity.

Edge of Stability Echo State Network.

Echo state networks (ESNs) are time series processing models working under the echo state property (ESP) principle. The ESP is a notion of stability that imposes an asymptotic fading of the memory of the input. On the other hand, the resulting inherent architectural bias of ESNs may lead to an excessive loss of information, which in turn harms the performance in certain tasks with long short-term memory requirements. To bring together the fading memory property and the ability to retain as much memory as possible, in this article, we introduce a new ESN architecture called the Edge of Stability ESN (). The introduced model is based on defining the reservoir layer as a convex combination of a nonlinear reservoir (as in the standard ESN), and a linear reservoir that implements an orthogonal transformation. In virtue of a thorough mathematical analysis, we prove that the whole eigenspectrum of the Jacobian of the map can be contained in an annular neighborhood of a complex circle of controllable radius. This property is exploited to tune the 's dynamics close to the edge-of-chaos regime by design. Remarkably, our experimental analysis shows that model can reach the theoretical maximum short-term memory capacity (MC). At the same time, in comparison to conventional reservoir approaches, is shown to offer an excellent trade-off between memory and nonlinearity, as well as a significant improvement of performance in autoregressive nonlinear modeling and real-world time series modeling.

Fractional Linear Reservoir Model as Elementary Hydrologic Response Function

This paper presents a fractional linear reservoir model as the elementary response function of hydrologic systems corresponding to the classical linear reservoir model and tests its applicability to rainfall–runoff modeling. To this end, we formulate a fractional linear reservoir model in terms of fractional calculus following the same procedure as the classical linear reservoir model and, at the simplest level, compare its performance of rainfall–runoff modeling with the linear and nonlinear reservoir models. The impulse response function of a fractional linear reservoir model, a probability density function (PDF) following the Mittag–Leffler distribution, shows nonlinearity due to its time-variant behavior compared to that of a linear reservoir model. In traditional linear hydrologic system theory, the lag and route version of a fractional linear reservoir model produces the fast-rising and slow-recession of runoff hydrographs, implying the mixed response of linear and nonlinear reservoir models to rainfall. So, a fractional linear reservoir model could be considered a fundamental tool to effectively reflect the nonlinearity of rainfall–runoff phenomena within the framework of the linear hydrologic system theory. In this respect, the fractional order of the storage relationship specifying a fractional linear reservoir model can be viewed as a kind of parameter to quantify the heterogeneity of runoff generation within a river basin.

Metalloborospherenes with a Stabilized Classical Fullerene-like Borospherene B40 Act as Nonlinear Optical Switches, Electron Reservoirs, Molecular Capacitors, and Molecular Reactors.

Using a new method of η5-Li and η6-Mg atoms capping the faces of the classical fullerene-like borospherene Td B40, we theoretically predict an exohedral metalloborospherene Td Mg10Li12&B40 molecule. Remarkably, a newfangled endoexo cage isomerism is proposed. Further, embedding Mg atoms in the Td B40 cage forms endohedral derivatives. Due to the intramolecular pull-push electron transfer relay, these obtained molecules possess unequal multilayered and alternant spherical charge distribution. The outer is an excess electron layer, bringing a molecular nonlinear switch character and an electron reservoir behavior with strong electron-donating and -accepting abilities. The middle (Mg2+)10(Li+)12 and the outer layers together constitute an electric double layer, presenting the behavior of a molecular capacitor where the electronic charge-discharge process occurs in the outer excess electron layer. The inner part is an empty cage B4026- with a strong negative electric field. The valence electrons of the embedded Mg atoms are transformed into new excess electrons and added in the outer excess electron layer, also exhibiting the charging behavior of the molecular capacitor. Considering the chemical reaction in the inner cage, the embedded Mg atom is ionized, forming an Mg2+ cation and 2e under the strong negative electric field; meanwhile, 2e is powerfully pushed into the outer excess electron layer. This chemical process shows a generalized Coulomb explosion, and thus the exohedral metalloborospherene molecules with cage B4026- may act as molecular reactors. The new species mark the genesis of classical fullerene-like borospherene chemistry and stimulate their applications in molecular nonlinear optical and nanoelectronics.

Development of a cellular automata-based distributed hydrological model for simulating urban surface runoff

The present study developed a distributed urban surface runoff model based on the cellular automata framework (CA-DUSRM) to simulate two-dimensional urban surface runoff processes. CA-DUSRM uses an improved nonlinear reservoir algorithm to simulate the generation of surface runoff outflow at grid cell scale and flow interactions among cells. The CA-DUSRM simulation results (total surface runoff and peak discharge) for an asphalt road sub-catchment during different rainfall events were in good agreement with actual measurements of both surface runoff and rainfall processes. The performance of CA-DUSRM was comprehensively and systematically analyzed under different rainfall–terrain scenarios. The results showed that increasing the temporal grain resulted in uncertain simulation results in relation to the rainfall intensity, slope, and terrain undulation employed; and significant spatial grain effects were mainly caused by large terrain undulation changes. Compared with the storm water management model (SWMM), CA-DUSRM performed better overall and was more sensitive to variation in terrain undulation and fluctuations in rainfall. Based on model structure and simulation mechanism perspectives, CA-DUSRM can present the influence of spatially heterogeneous underlying surface characteristics on the runoff processes and describe the lateral water exchanges, which makes the simulated processes closer to the actual processes when compared with SWMM. CA-DUSRM is potentially suitable for application in urban areas that have complex underlying surfaces.

Quantification and variation characteristics of baseflow nonpoint source pollution in Yiluo River Basin, China

Baseflow is an important component of runoff that is one of the essential mediums for groundwater pollution to migrate to runoff. Effective water-quality management requires full understanding of the nonpoint source (NPS) pollutants pathways. However, the contributions of baseflow and baseflow NPS pollutants at multiple scales are still challenging. In this study, the baseflow was quantified and compared by the nonlinear reservoir method, the digital filtering method and the Soil and water Assessment Tool (SWAT) in the Yiluo River, and SWAT model was used to simulate and quantify the NPS and baseflow NPS pollution. Then the scaling effect of baseflow NPS pollution was studied. The results indicated that the average annual baseflow of the basin outlet section and baseflow index of the whole basin was 38.07 m3/s and 0.58 during the studied years (2001–2017). The multiyear average baseflow pollution load for TN and TP was 4216.18 t/a and 293.33 t/a. The spatial distribution of the NPS pollution and baseflow NPS pollution showed higher in the northeast and lower in the southwest, and the baseflow NPS pollution contribution rate in most basins was more than 50 %. The spatial scale effects of NPS pollution load became more obvious with the increase of basin area, and the contribution of baseflow NPS pollution increased. The precipitation and temperature played important roles in baseflow pollution, especially baseflow TN load.

Baseflow estimation based on a self-adaptive non-linear reservoir algorithm in a rainy watershed of eastern China

Accurate baseflow estimation is critical for water resources evaluation and management, and non-point source pollution quantification. Nonlinear reservoir algorithm (NRA) has been increasingly applied to baseflow separation because of its good approximation to the real groundwater discharge (commonly dominated by the unconfined aquifer) in most watersheds. However, in the rainy regions, large uncertainties may remain in the traditional NRA-separated baseflow sequences due to its empirical transition function for the rising limb of discharge process, and the evident variations of baseflow recession in the initial period of the falling limb caused by the disturbance from surface flow or rainfall events. To improve the reliability of baseflow separation, a self-adaptive non-linear reservoir algorithm (SA-NRA) was developed in this study based on the NRA, a self-adaptive groundwater discharge modified parameter, and the Particle Swarm Optimization algorithm (PSO). The validation of SA-NRA in a rainy watershed of eastern China showed that SA-NRA could be the approach to provide a goodness-of-fit for baseflow recession behaviors in the rainy regions. The traditional NRA and Eckhardt's two-parameter recursive digital filter (ERDF), calibrated (or validated) only with the pure baseflow recession data, can hardly provide reliable baseflow predictions for the non-pure baseflow recession periods (including the rising limb and the falling limb with surface flow or rainfall disturbance) due to the apparent variations of baseflow recession behavior. Therefore, more attentions should be paid to the uncertainties of baseflow separation for the non-pure baseflow recession periods in the rainy regions.

Comparison of Nonlinear Reservoir and UH Algorithms for the Hydrological Modeling of a Real Urban Catchment with EPASWMM

This paper presents a comparative analysis of two hydrological models in the Storm Water Management Model (SWMM) software, namely, the non-linear reservoir (N-LR) and the unit hydrograph (UH), on the urban catchment of Cascina Scala, Pavia in Italy. The two models were applied for the simulation of the rainfall-runoff transformation in the 42 sub-catchments in Cascina Scala, while flow routing in the underground channels was simulated by means of the De Saint-Venant equations. A dataset of rainfall and runoff for 14 events from 2000 to 2003 was adopted for the calibration and validation of the models. The calibration was performed on 7 out of the 14 events by maximizing the fit of modeled-to-measured hydrographs in the final channel of the system. Prediction performance was assessed through different indices. Results from both models fit measured data well in terms of the total hydrograph. Whereas the time to peak was reliably predicted by both models, the N-LR was found to slightly outperform the UH in terms of total volume and peak flow prediction, though it requires a more detailed knowledge of the system for its implementation. Accordingly, the UH must be preferred in the case of a scarcity of data.

Performance study of an innovative concept of hybrid constructed wetland-extensive green roof with growing media amended with recycled materials

Implementation of green roofs requires a large amount of primary material, especially for constructing the growing media layer. In addition, irrigation of green roofs with potable water is uneconomical and unsustainable. The novel hybrid green roof system proposed in this paper is in line with the principles of circular economy as it incorporates recycled materials into green roof growing media and greywater for irrigation. Two experimental beds were built to evaluate the concept of treating greywater in a constructed wetland prior to using it to irrigate a dual-layer extensive green roof. The growing media in both two extensive green roof beds contained ca. 37.5% by volume of recycled crushed building rubble containing a large proportion of brick. One of the two beds additionally contained 9.5% by volume of sewage sludge-based biochar. The concept of the hybrid roof and novel growing media was evaluated based on laboratory analysis of the growing media and on onsite measurements of hydraulic and thermal performance. The growing media amended with recycled materials developed in this study had hydrophysical properties comparable to commercially available growing media without recycled materials. Observations made during one vegetation season from June to October and a ten day-intensive water quality monitoring campaign during September 2020 showed that the constructed wetland significantly reduced total nitrogen and orthophosphate concentrations in pre-treated greywater. Due to the irrigation method employed, in which water flowed predominantly through drainage mats below the growing media, nutrient-leaching by the irrigation water was avoided. Concentrations of nutrients in the effluent were observed to increase only in response to precipitation. The temperature peak of the bottom green roof layer was shifted by almost 9 h from the peak in air temperature, and temperature fluctuations were significantly reduced. Vegetation on the bed amended with biochar demonstrated more vigorous growth due to available nutrients in the biochar which increased the rate of temperature-reducing evapotranspiration. More water evapotranspirated more water, which provided more water retention capacity confirmed by a lower runoff coefficient. Simple storage routing hydraulic modeling of hybrid green roof runoff using a nonlinear reservoir was performed.

Detecting Permafrost Active Layer Thickness Change From Nonlinear Baseflow Recession

AbstractPermafrost underlies about one fifth of the global land area and affects ground stability, freshwater runoff, soil chemistry, and surface‐atmosphere gas exchange. The depth of thawed ground overlying permafrost (active layer thickness) has broadly increased across the Arctic in recent decades, coincident with a period of increased streamflow, especially the lowest flows (baseflow). Mechanistic links between active layer thickness and baseflow have recently been explored using linear reservoir theory, but most watersheds behave as nonlinear reservoirs. We derive theoretical nonlinear relationships between long‐term average saturated soil thickness (proxy for active layer thickness) and long‐term average baseflow. When applied to 38 years of daily streamflow data for the Kuparuk River basin on the North Slope of Alaska, the theory predicts increased cm a−1 between 1983 and 2020 ( cm total). The rate of increase nearly doubled to cm a−1 between 1990 and 2020, during which time local field measurements from Circumpolar Active Layer Monitoring sites indicate the active layer increased cm a−1. The predicted rate of increase more than doubled again between 2002 and 2020, outpacing a near doubling of observed active layer thickening, consistent with trends in terrestrial water storage inferred from Gravity Recovery and Climate Experiment satellite gravimetry and Modern‐Era Retrospective Analysis for Research and Applications climate reanalysis. Overall, hydrologic change is accelerating in the Kuparuk River basin, and we provide a theoretical framework for estimating basin‐scale changes in active layer water storage from streamflow measurements.

Strange Properties of Linear Reservoirs in the Infinitely Large Limit for Prediction of Continuous-Time Signals

Large linear reservoirs, while not necessarily of practical utility, might provide insight to large nonlinear reservoirs. Our study of large linear reservoirs in the context of improving predictive capabilities suggests that: one desires to be near the edge of instability; and random matrix theory guarantees that the performance of large linear random matrices is only dependent on how weights in the weight matrix are chosen and not the individual weights. It also seems as though dynamic and static weights are quite different in performance. We comment on how these lessons may or may not apply to the large nonlinear reservoirs that are typically used for prediction applications.