Linear Reservoir Model Research Articles

Physics-Aware Degradation Model of Lithium-ion Battery Energy Storage for Techno-Economic Studies in Power Systems

Power system operation and planning decisions for lithium-ion battery energy storage systems are mainly derived using their simplified linear models. While these models are computationally simple, they have limitations in how they estimate battery degradation, either using the energy throughput or the Rainflow method. This paper proposes a hybrid approach for lithium-ion battery system modeling suitable for use in power system studies that enhances representation of battery degradation at a reasonable computational cost. The proposed hybrid model combines a physics-based model for improved degradation estimates with a simple and linear energy reservoir model commonly used to represent a battery storage system. The advantage of constructing the battery model with this vision is that it allows its smooth integration into the mixed-integer optimization frameworks. The proposed model is evaluated using both power- and energy-based use cases from the electrical grid. The simulations demonstrate that degradation could be reduced by 45% compared to other modeling strategies while generating the same level of operation profits. The net result of using the proposed hybrid model could be an extended lifespan through better informed planning and operating decisions for energy storage assets.

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.

Comparing Master Recession Curve Shapes Between Linear and Exponential Reservoir Models

The behaviour of river flows during periods of recession can be better identified than in other periods. The Master Recession Curve (MRC) approach is a technical approach that is quite effective and efficient in modelling baseflow. This study aims to compare the shape of the MRC between linear and exponential reservoir models. The research method uses two linear reservoir models, the Depuit-Boussinesq equation and an exponential model based on exponential hydraulic conductivity. The results showed that the combination of recession parameters (initial recession discharge, constant and coefficients) for MRC manually linear and exponential reservoir models, and hybridization of genetic algorithm processes, showed that MRC visualization for linear reservoir models was more optimal compared to exponential reservoir models. These results are closely related to the slope of the MRC, where the linear reservoir model is gentler, and the exponential reservoir model is relatively steeper. The slope of the MRC for both reservoir models relates to the storage capabilities of the baseflow and the hydraulic conductivity properties of the study area. The gentle slope of the MRC has the properties of relatively slow storage and is relatively long stored. In contrast, the steep slope of the MRC determines the somewhat wasteful nature of storage.

Filtration studies on cores and sand packed tubes from the Urengoy field for determining the efficiency of simultaneous water and gas injection on formation when extracting condensate from low-pressure reservoirs and oil from oil rims

Oil rims as well as gas condensate reservoirs of Russia's largest Urengoy field are developed by depletion drive without formation pressure maintenance, which has led to serious complications in production of oil, gas and condensate. In addition, field development by depletion drive results in low values of oil and condensate recovery. These problems are also relevant for other oil and gas condensate fields. One of the possible solutions is simultaneous water and gas injection. Rational values of gas content in the mixture for affecting gas condensate fields and oil rims of oil and gas condensate fields should be selected using the data of filtration studies on core models. The article presents the results of filtration experiments on displacement of condensate and oil by water, gas and water-gas mixtures when simulating the conditions of the Urengoy field. Simultaneous water and gas injection showed good results in the experiments on displacement of condensate, residual gas and oil. It has been ascertained that water-gas mixtures with low gas content (10-20 %) have a better oil-displacement ability (9.5-13.5 % higher) than water. An experiment using a composite linear reservoir model from cemented core material, as regards the main characteristics of oil displacement, gave the same results as filtration experiments with sand packed tubes and demonstrated a high efficiency of simultaneous water and gas injection as a method of increasing oil recovery at oil and gas condensate fields.

Computational and experimental studies of unstable isothermal filtration of methane–n-pentane gas-condensate mixture

During the operation of gas-condensate fields, reservoir pressure gradually decreases. When the pressure drops below the dew point, a retrograde fluid with low mobility is formed, which significantly reduces the well flow rate. Under certain conditions (pressure drop, yield point of the liquid phase, and absolute permeability of the reservoir), unstable filtration modes may occur, including those that block fluid flow. Determination of these conditions is necessary for planning a gas-condensate production strategy and developing methods for influencing the reservoir system to increase the flow rate of valuable hydrocarbon feedstock.This paper presents the results of computational and experimental studies of the isothermal filtration process of a model methane–n-pentane mixture in a porous medium. The studies were carried out on a linear bulk reservoir model at supercritical inlet pressures and variations in the composition of the supplied mixture and pressure at the model outlet. As a result of numerical and laboratory experiments, it was shown that there is a region of parameters (composition of the mixture, pressure drop, and yield point of the liquid phase) in which flow modes can be unstable, including those with periodic blocking of the fluid flow. The conditions for the appearance of unstable flow modes are discussed.

Copula-based modeling of hydraulic structures using a nonlinear reservoir model

Abstract Multivariate flood frequency analysis has been widely used in the design and risk assessment of hydraulic structures. However, analytical solutions are often obtained based on an idealized linear reservoir model in which a linear routing process is assumed, and consequently, the flood risk is likely to be over- or underestimated. The present study proposes a nonlinear reservoir model in which the relationships of reservoir water level with reservoir volume and discharge are assumed to be nonlinear in order to more accurately describe the routing process as it takes into consideration the interactions between hydrological loading and different discharge structures. The structure return period is calculated based on the copula function and compared with that based on the linear reservoir model and the bivariate return period based on the Kendall distribution function. The results show that the structure return period based on the linear model leads to an underestimation of the flood risk under the conditions of high reservoir water level. For the same reservoir, linear and nonlinear reservoir models give quite different reservoir volume-water level and discharge-water level curves; therefore, they differ substantially in the sensitivity to flood events with different combinations of flood peak and volume. We also analyze the effects of the parameters involved in the reservoir volume-water level and discharge-water level relationships on the maximum water level at different return periods in order to better understand the applicability and effectiveness of the proposed method for different hydraulic projects.

Storage-Discharge Relationships under Forest Cover Change in Ethiopian Highlands

Detecting the impacts of forest cover changes on hydrology is challenging given uncertainties in how changes will manifest in observed streamflow. Considering changes in the rate of change of observed streamflow (e.g., recession characteristics) may offer insights to hydrological shifts driven by forest cover change that are not seen when considering absolute changes of streamflow itself. This study assesses the impacts of forest cover changes on the storage–discharge relationships in three meso-scale watersheds in the highlands of Ethiopia based on a 30-year hydro-climatic and land cover change dataset. We analyze streamflow recessions and fitted parameters of a linear reservoir model to depict fundamental shifts in the storage–discharge relation for these watersheds. Our analysis shows that recession slopes and the total storages increase as natural forest covers decrease in the 273 km2 Woshi-Dimbira and 1980 km2 Upper-Didesa watersheds. The linear reservoir model storage coefficient parameter shows an increasing trend with time for the 41 km2 Sokoru watershed which is afforested, indicating faster drainage and reduction in storage. Our work highlights that considering storage–discharge relationships may be useful for assessing the impacts of forest cover change on water resources in regions where land use change is active and rapid.

Derivation of instantaneous unit hydrographs using linear reservoir models

Abstract In this research, a new conceptual model for producing instantaneous unit hydrographs (IUHs) is introduced by a linear combination of the Nash model, which assumes that the discharge from a reservoir is a linear function of its storage, and a model called inter-connected linear reservoir model (ICLRM), which assumes that the discharge from a reservoir is a linear function of the difference of its storage and its adjacent downstream reservoir. By employing these assumptions, a system of first-order linear differential equations with three degrees of freedom (storage coefficient, number of reservoirs, and weighting coefficient) is obtained as the governing equation for the proposed model. This model may be considered as the general form of the two models and is therefore capable of simulating IUHs laying between these two models. To show the capabilities of the model, linear and curvilinear soil conservation service (SCS) hydrographs are simulated using dimensionless hydrographs obtained by this model. Moreover, several real hydrographs were simulated by the proposed model and compared with hydrographs obtained by Nash, ICLRM, and SCS models. The results show that the model yields more accurate results compared to other studied models and may be considered as a new model for simulating IUHs.

Characterizing River Baseflow Recession Using Linear Reservoir Model in Alang Watershed, Central Java, Indonesia

Alang is a sub-watershed emptying into the Gajah Mungkur Reservoir in Wonogiri, Central Java Indonesia, with an area of 51.01 km2 and lithology composed of Baturetno Formation and Wonosari Formation. Baseflow is a major component of river flow during the dry season. Hence, the characterization of its recession becomes necessary, and it can be performed with innovation in baseflow hydrological modeling, that is, the recession curve. This study was designed to describe the distinctive features of baseflow recession using a linear reservoir model, which is depicted in individual and master recession curves. The baseflow recession in AlangSubwatershed was represented by a combination of varying initial recession discharge (Q0), α, and recession constants (Krb). The individual recession curves were typified by Q0=0.19-9.11, α= 0.089-0.243, and Krb=0.7843-0.9148. As for the master recession curve, it had Q0=9.99, α=0.085, and Krb=0.928. These results signify a sloping recession curve, meaning that the water storage and aquifer characteristics that store and transmit water in Alang Subwatershed are in good condition.

Spatially distributed sensitivity of simulated global groundwater heads and flows to hydraulic conductivity, groundwater recharge, and surface water body parameterization

Abstract. In global hydrological models, groundwater storages and flows are generally simulated by linear reservoir models. Recently, the first global gradient-based groundwater models were developed in order to improve the representation of groundwater–surface-water interactions, capillary rise, lateral flows, and human water use impacts. However, the reliability of model outputs is limited by a lack of data and by uncertain model assumptions that are necessary due to the coarse spatial resolution. The impact of data quality is presented in this study by showing the sensitivity of a groundwater model to changes in the only available global hydraulic conductivity dataset. To better understand the sensitivity of model output to uncertain spatially distributed parameters, we present the first application of a global sensitivity method for a global-scale groundwater model using nearly 2000 steady-state model runs of the global gradient-based groundwater model G3M. By applying the Morris method in a novel domain decomposition approach that identifies global hydrological response units, spatially distributed parameter sensitivities are determined for a computationally expensive model. Results indicate that globally simulated hydraulic heads are equally sensitive to hydraulic conductivity, groundwater recharge, and surface water body elevation, though parameter sensitivities vary regionally. For large areas of the globe, rivers are simulated to be either losing or gaining, depending on the parameter combination, indicating a high uncertainty in simulating the direction of flow between the two compartments. Mountainous and dry regions show a high variance in simulated head due to numerical instabilities of the model, limiting the reliability of computed sensitivities in these regions. This is likely caused by the uncertainty in surface water body elevation. We conclude that maps of spatially distributed sensitivities can help to understand the complex behavior of models that incorporate data with varying spatial uncertainties. The findings support the selection of possible calibration parameters and help to anticipate challenges for a transient coupling of the model.

A systematic comparison of statistical and hydrological methods for design flood estimation

Abstract We compare statistical and hydrological methods to estimate design floods by proposing a framework that is based on assuming a synthetic scenario considered as ‘truth’ and use it as a benchmark for analysing results. To illustrate the framework, we used probability model selection and model averaging as statistical methods, while continuous simulations made with a simple and relatively complex rainfall–runoff model are used as hydrological methods. The results of our numerical exercise show that design floods estimated by using a simple rainfall–runoff model have small parameter uncertainty and limited errors, even for high return periods. Statistical methods perform better than the linear reservoir model in terms of median errors for high return periods, but their uncertainty (i.e., variance of the error) is larger. Moreover, selecting the best fitting probability distribution is associated with numerous outliers. On the contrary, using multiple probability distributions, regardless of their capability in fitting the data, leads to significantly fewer outliers, while keeping a similar accuracy. Thus, we find that, among the statistical methods, model averaging is a better option than model selection. Our results also show the relevance of the precautionary principle in design flood estimation, and thus help develop general recommendations for practitioners and experts involved in flood risk reduction.

Analytical River Routing with Alternative Methods to Estimate Seepage

Knowledge of flow exchange between surface and groundwater is of great importance for use of water resources. The determination of seepage between a stream and an underlying aquifer requires an accurate estimation of the river stage and of the head in the aquifer. An approach is presented to estimate analytically river flow and stage while using the SAFE conductance to calculate the seepage. A major contribution of this article lies in the methodology for river routing with its use of a modified Linear Reservoir model. The parameter C is related to discharge based on Manning’s equation. That relation breathes into an empirical model a dynamic character. A second major contribution is to show that it is possible to simultaneously calculate river stage and aquifer head in the aquifer cell that contains the river. As a result iteration is not necessary to estimate that river cell head as river stage changes, as opposed to what is usually done in most numerical groundwater models. Iteration is still needed for the adjacent cells to the river cell. Because the influence of a change in the adjacent cell head on the river cell head is much delayed and attenuated the iteration is not sensitive to that change. A goal of this document is to show how that method can be used within a simple physically based routing procedure [1] to estimate the river stage that has a definite influence on seepage.

Incorporating reservoir impacts into flood frequency distribution functions

Assessing flood frequency is pivotal for hydrology, with implications for many fields ranging from river science to the insurance industry. Reservoir regulation may alter the characteristics of the flood frequency distribution function. This paper incorporates reservoir impacts as an inherent variable to derive an analytical solution of outflow peaks and proposes new flood frequency distributions. Steps are as follows: (1) the original flood without reservoir impacts is assumed to follow a Pearson type III distribution, (2) linear and nonlinear reservoir models, including numerical integration and triangular area calculation methods, are proposed to simulate the relationships between inflow and outflow peaks, and (3) the flood frequency distributions resulting from reservoir impacts are derived. Derived equations are applied to the Shuibuya and Wuqiangxi reservoirs in China. Results show that: (1) although the numerical integration method with the nonlinear model is comparable with the reservoir flood routing, the triangle area calculation method with the nonlinear model is recommended for its accuracy and simplicity, (2) the reservoir regulation changes the flood frequency distribution function entirely in the nonlinear reservoir model, while only change the parameter in the linear reservoir model, and (3) downstream flood’s CV can be increased or decreased, which depends on the reservoir regulating capacity. It is indicated that altering the parameters of the flood frequency distribution is not sufficient to characterize watershed under reservoir control. This paper proposes the analytical solution about inflow and outflow peaks, which can point out the possible changes in the watershed with reservoir construction in plan.

Introducing a new conceptual instantaneous unit hydrograph model based on a hydraulic approach

ABSTRACTA novel approach is introduced for simulation of instantaneous unit hydrographs (IUHs). The model consists of a series of linear reservoirs that are connected to each other, and is referred to as the inter-connected linear reservoir model (ICLRM). By assuming the flow between two reservoirs is a linear function of the difference between the water levels in the reservoirs, a system of first-order linear differential equations is obtained as the ICLRM governing equation. By solving the equations, the discharge from the last reservoir is considered as an IUH. A small-scale laboratory device was constructed for the simulation of IUHs using the model. By studying four hydrographs extracted from the literature, and simulating them using both the ICLRM and the Nash model, it is concluded that the ICLRM can predict these hydrographs more accurately than the Nash model. Due to the simplicity of the construction and operation of the ICLRM and, more importantly, its visual aspect, the ICLRM may be considered as an effective educational tool for studying IUHs.

A Framework for Dry Period Low Flow Forecasting in Mediterranean Streams

The objective of this article is to provide a simple and effective tool for low flow forecasting up to six months ahead, with minimal data requirements, i.e. flow observations retrieved at the end of wet period (first half of April, for the Mediterranean region). The core of the methodological framework is the exponential decay function, while the typical split-sample approach for model calibration, which is known to suffer from the dependence on the selection of the calibration data set, is enhanced by introducing the so-called Randomly Selected Multiple Subsets (RSMS) calibration procedure. Moreover, we introduce and employ a modified efficiency metric, since in this modelling context the classical Nash-Sutcliffe efficiency yields unrealistically high performance. The proposed framework is evaluated at 25 Mediterranean rivers of different scales and flow dynamics, including streams with intermittent regime. Initially, signal processing and data smoothing techniques are applied to the raw hydrograph, in order to cut-off high flows that are due to flood events occurring in dry periods, and allow for keeping the decaying form of the baseflow component. We then employ the linear reservoir model to extract the annually varying recession coefficient, and, then, attempt to explain its median value (over a number of years) on the basis of typical hydrological indices and the catchment area. Next, we run the model in forecasting mode, by considering that the recession coefficient of each dry period ahead is a linear function of the observed flow at the end of the wet period. In most of the examined catchments, the model exhibits very satisfactory predictive capacity and is also robust, as indicated by the limited variability of the optimized model parameters across randomly selected calibration sets.

New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models

Water flows in the hydrosphere through a tangled and tortuous labyrinth of ways that is the hydrological cycle. Flow separation models are an attempt to group such complexity of paths into a few components of flow and storage so as to reflect the overall behaviour of a basin. A new method of analysis and separation of flow components, based on equations of dynamic relations between Linear Reservoirs connected in Parallel (PLR models), is developed in this article. A synthesis of models based on mathematical filter equations is carried out in order to make comparisons with the proposed model. Reference is also made to the methodology of adjustment and calibration of the PLR models based on the recession curves of the real hydrographs. The models are tested with the continuous register of a basin located in the northeast of Spain. The simulations are carried out with two reservoir models (2R models), three reservoirs (3R models) and with a mathematical filter model to compare the results. With the results of the models, flow duration curves (FDCs) and storage duration curves (SDCs) were elaborated, thus allowing assessment of the origin of the water resources of the basin, a guarantee of their regulation and availability, the dynamic storage in the catchment, residence times and other features.

Comparative analysis of the effectiveness of the conceptual rainfall-runoff hydrological models on the selected rivers in Odra and Vistula basins

Identification of physical processes occurred in the watershed is one of the main tasks in hydrology. Currently the most efficient hydrological processes describing and forecasting tool are mathematical models. They can be defined as a mathematical description of relations between specified attributes of analysed object. It can be presented by: graphs, arrays, equations describing functioning of the object etc. With reference to watershed a mathematical model is commonly defined as a mathematical and logical relations, which evaluate quantitative dependencies between runoff characteristics and factors, which create it. Many rainfall-runoff linear reservoirs conceptual models have been developed over the years. The comparison of effectiveness of Single Linear Reservoir model, Nash model, Diskin model and Wackermann model is presented in this article.

Derivation of low flow frequency distributions under human activities and its implications

Low flow, refers to a minimum streamflow in dry seasons, is crucial to water supply, agricultural irrigation and navigation. Human activities, such as groundwater pumping, influence low flow severely. In order to derive the low flow frequency distribution functions under human activities, this study incorporates groundwater pumping and return flow as variables in the recession process. Steps are as follows: (1) the original low flow without human activities is assumed to follow a Pearson type three distribution, (2) the probability distribution of climatic dry spell periods is derived based on a base flow recession model, (3) the base flow recession model is updated under human activities, and (4) the low flow distribution under human activities is obtained based on the derived probability distribution of dry spell periods and the updated base flow recession model. Linear and nonlinear reservoir models are used to describe the base flow recession, respectively. The Wudinghe basin is chosen for the case study, with daily streamflow observations during 1958–2000. Results show that human activities change the location parameter of the low flow frequency curve for the linear reservoir model, while alter the frequency distribution function for the nonlinear one. It is indicated that alter the parameters of the low flow frequency distribution is not always feasible to tackle the changing environment.

KAJIAN KEBERLANJUTAN ALIRAN DASAR SUNGAI MELALUI ANALISIS KURVA RESESI HIDROGRAF PADA DAS KEDUANG KABUPATEN WONOGIRI PROVINSI JAWA TENGAH

The streamflow hydrograph recession curve notes that behavior of the relationship between the aquifer structure and dependencies with the groundwater outflow towards river basin channel. The recession behavior of river basin hydrographs will investigate to understand the hydrology processes of the river basin in the future. This research was conducted with the aim: to analyze the characteristics of the baseflow recession based on the parameters and coefficients of the recession, and the shape of the individual recession curve and the master recession curves both manually and through the processing of genetic algorithms using a linear reservoir model of hydrooffice software package recession curve (RC) 4.0.
 The results of the visualization of the recession curve shape of the watershed of the research shows there is a very interesting trend in the watershed storage process.The characteristics of the baseflow recession to research watershed with the recession curve slope describe the baseflow recession conditions, especially excellent water storage. The river basin of Keduang have the form of a relatively sloping recession curves, both individual and master recession curve with relatively high recession constant ranged between 0,80 – 0,90 have baseflow recession characteristic is excellent, i.e. the watershed water storage which is the higher volume of water storage.

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

High quality on-line flow forecasts are useful for real-time operation of urban drainage systems and wastewater treatment plants. This requires computationally efficient models, which are continuously updated with observed data to provide good initial conditions for the forecasts. This paper presents a way of updating conceptual rainfall-runoff models using Maximum a Posteriori estimation to determine the most likely parameter constellation at the current point in time. This is done by combining information from prior parameter distributions and the model goodness of fit over a predefined period of time that precedes the forecast. The method is illustrated for an urban catchment, where flow forecasts of 0–4 h are generated by applying a lumped linear reservoir model with three cascading reservoirs. Radar rainfall observations are used as input to the model. The effects of different prior standard deviations and lengths of the auto-calibration period on the resulting flow forecast performance are evaluated. We were able to demonstrate that, if properly tuned, the method leads to a significant increase in forecasting performance compared to a model without continuous auto-calibration. Delayed responses and erratic behaviour in the parameter variations are, however, observed and the choice of prior distributions and length of auto-calibration period is not straightforward.