Academic literature on the topic 'Reservoirs – Mathematical models'
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Journal articles on the topic "Reservoirs – Mathematical models"
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Vieira, J. M. P., J. L. S. Pinho, N. Dias, D. Schwanenberg, and H. F. P. van den Boogaard. "Parameter estimation for eutrophication models in reservoirs." Water Science and Technology 68, no. 2 (July 1, 2013): 319–27. http://dx.doi.org/10.2166/wst.2013.248.
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Excessive eutrophication is a major water quality issue in lakes and reservoirs worldwide. This complex biological process can lead to serious water quality problems. Although it can be adequately addressed by applying sophisticated mathematical models, the application of these tools in a reservoir management context requires significant amounts of data and large computation times. This work presents a simple primary production model and a calibration procedure that can efficiently be used in operational reservoir management frameworks. It considers four state variables: herbivorous zooplankton, algae (measured as chlorophyll-a pigment), phosphorous and nitrogen. The model was applied to a set of Portuguese reservoirs. We apply the model to 23 Portuguese reservoirs in two different calibration settings. This research work presents the results of the estimation of model parameters.
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Ziemińska-Stolarska, Aleksandra, and Jerzy Skrzypski. "Review of Mathematical Models of Water Quality." Ecological Chemistry and Engineering S 19, no. 2 (January 1, 2012): 197–211. http://dx.doi.org/10.2478/v10216-011-0015-x.
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Review of Mathematical Models of Water Quality Water is one of the main elements of the environment which determine the existence of life on the Earth, affect the climate and limit the development of civilization. Water resources management requires constant monitoring in terms of its qualitative-quantitative values. Proper assessment of the degree of water pollution is the basis for conservation and rational utilization of water resources. Water quality in lakes and dams is undergoing continuous degradation caused by natural processes resulting from eutrophication and due to anthropogenic reasons. One of the tools that are used to solve problems of surface water pollution is modelling of changes which take place in lake waters and associated water quality changes. In the last thirty years a rapid development of mathematical modelling of water resources quality has been observed. A number of computer models have been designed which are successfully applied in practice in many countries, including Poland. This paper presents an overview of mathematical models for assessment of water quality in dam reservoirs. Description of the WASP program which will be used for modelling water quality in the Sulejow Reservoir was the focal point.
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Zhang, Bo-ning, Xiao-gang Li, Yu-long Zhao, Cheng Chang, and Jian Zheng. "A Review of Gas Flow and Its Mathematical Models in Shale Gas Reservoirs." Geofluids 2020 (November 30, 2020): 1–19. http://dx.doi.org/10.1155/2020/8877777.
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The application of horizontal wells with multistage hydraulic fracturing technologies has made the development of shale gas reservoirs become a worldwide economical hotspot in recent years. The gas transport mechanisms in shale gas reservoirs are complicated, due to the multiple types of pores with complex pore structure and special process of gas accumulation and transport. Although there have been many attempts to come up with a suitable and practical mathematical model to characterize the shale gas flow process, no unified model has yet been accepted by academia. In this paper, a comprehensive literature review on the mathematical models developed in recent years for describing gas flow in shale gas reservoirs is summarized. Five models incorporating different transport mechanisms are reviewed, including gas viscous flow in natural fractures or macropores, gas ad-desorption on shale organic, gas slippage, diffusion (Knudsen diffusion, Fick diffusion, and surface diffusion), stress dependence, real gas effect, and adsorption layer effect in the nanoshale matrix system, which is quite different from conventional gas reservoir. This review is very helpful to understand the complex gas flow behaviors in shale gas reservoirs and guide the efficient development of shale gas. In addition to the model description, we depicted the type curves of fractured horizontal well with different seepage models. From the review, it can be found that there is some misunderstanding about the essence of Knudsen/Fick diffusion and slippage, which makes different scholars adopt different weighting methods to consider them. Besides, the contribution of each mechanism on the transport mechanisms is still controversial, which needs further in-depth study in the future.
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Madgazin, R. J., and S. S. Orlova. "Mathematical models of hydrothermal regime of the reservoirs-coolers." Agrarian Scientific Journal, no. 2 (February 20, 2017): 59–63. http://dx.doi.org/10.28983/asj.v0i2.34.
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Mercado Sierra, Diana Patricia, Samuel Fernando Muñoz Navarro, and Aníbal Ordóñez Rodríguez. "DEVELOPMENT OF AN ANALYTICAL MODEL FOR STEAMFLOOD IN STRATIFIED RESERVOIRS OF HEAVY OIL." CT&F - Ciencia, Tecnología y Futuro 3, no. 5 (December 31, 2009): 19–34. http://dx.doi.org/10.29047/01225383.447.
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The use of analytical models to predict reservoir behavior depends on the similarity between the mathematically modeled system and the reservoir. Currently, there are not any models available for the prediction of steamflood behavior in stratified reservoirs based on the characteristics of reservoirs found in the Colombian Middle Magdalena valley, because the existing analytical models describe homogenous or idealized reservoirs. Therefore, it is necessary to propose a new model that includes the presence of clay intercalation in zones submitted to steamflood. The new analytical model is founded on the principles describing heat flow in porous media presented in the models proposed by Marx and Langenheim (1959); Mandl and Volek (1967), and Closmann (1967). Then, a series of assumptions related to the producing and non-producing zones and steamflood were determined, thus defining the system to be modeled. Once the system is defined, the initial and boundary conditions were established to contribute to find specific solutions for the case described. A set of heat balancing procedures were proposed from which a series of integro-differential equations were found. These equations were solved by using the Laplace transform method. The mathematical expressions were defined for the calculation of parameters such as volume of the heated zone, the rate of instantaneous and cumulative heat losses, and the oil rate and recovery factor. We can find differences when comparing the model response with the simulation, because in the mathematical model, we cannot include phenomena such as drop pressure, relative permeability and the change of oil viscosity with temperature. However, the new analytical model describes approximately the steam zone behavior, when the heat flow in the clay intercalations is not in stationary state.
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Silva, Fabio Leandro da, Ângela Terumi Fushita, Marcela Bianchessi da Cunha-Santino, and Irineu Bianchini Júnior. "Advantages, disadvantages and methods of applying mathematical models to evaluate water quality in reservoirs: a systematic review." Ambiente e Agua - An Interdisciplinary Journal of Applied Science 17, no. 2 (April 12, 2022): 1–19. http://dx.doi.org/10.4136/ambi-agua.2804.
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Human activities are affecting reservoir water quality; consequently, methods are necessary to verify those impacts. Mathematical modeling improves the understanding of the anthropic impact on water quality, changes in limnological data, and helps formulate management strategies. However, it is necessary to consider the (dis)advantages as well as the methods used for water-quality assessment in reservoirs. This study conducted a systematic review in four databases: (i) PubMed/Medline; (ii) Scopus; (iii) Web of Science; and (iv) Wiley Online Library. We combined Boolean operators and words aiming to identify papers linked to the scope. Rayyan software allowed the initial screening of the found papers. Peer-reviewed papers and the use of mathematical models to assess reservoir water quality were the inclusion criteria. Exclusion criteria included articles in languages other than English, grey literature, and inaccessible articles. Our research found 169 articles, of which 39 were selected and only 13 were included in the review. Mathematical modeling has many benefits related to real-world problems, but the main disadvantages are process simplification, specific rules of the model, and lack of information or data monitoring. Kinetic equations, regression models, Monte Carlo analysis, finite segment models, modeling tools, zero-order rate equations, partial differential algebraic equations, and predictive analysis are the methods observed in mathematical modeling. This review provides information for unfamiliar managers who intend to use mathematical models to assess the water quality of reservoirs.
Keywords: limnologic tool, model inventory, water management.
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de Rooij, G. H. "Is the groundwater reservoir linear? A mathematical analysis of two limiting cases." Hydrology and Earth System Sciences Discussions 11, no. 1 (January 6, 2014): 83–108. http://dx.doi.org/10.5194/hessd-11-83-2014.
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Abstract. Storage–discharge relationships of the groundwater reservoirs of several catchments in a temperate-humid climate were reported in the literature to be seemingly non-linear. Once recharge was adequately accounted for during model calibration they turned out to be linear. The question was posed if this linearity was a fundamental property of groundwater reservoirs in general. A mathematical analysis based on analytical solutions for several cases involving parallel flow in horizontal aquifers shows that this is not the case when the surface water level is close to the aquifer bottom. When the aquifer is of constant thickness, linear-reservoir behaviour arises when the forcings remain constant for a sufficiently long time. This can range from a few weeks for aquifers with a dense drainage network of streams or ditches to years or centuries for large aquifers drained by rivers many kilometers apart. The characteristic time of the groundwater reservoir depends on whether or not the aquifer is leaky and recharge is non-zero. It is concluded that groundwater reservoirs can only be linear if their thickness can be assumed independent of the hydraulic head, and if they have a dense drainage network. Even then, they behave non-linearly up to several weeks after a change in recharge. Models that conceptualize the catchment as a configuration of coupled reservoirs will normally assign the groundwater discharge surplus generated because of the initially non-linear behaviour of the groundwater to their fast-responding reservoirs, thereby exaggerating the importance of fast-responding flow routes in a catchment.
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Klein, Rupert, Roya Ebrahimi Viand, Felix Höfling, and Luigi Delle Site. "Nonequilibrium Induced by Reservoirs: Physico‐Mathematical Models and Numerical Tests." Advanced Theory and Simulations 4, no. 7 (May 5, 2021): 2100071. http://dx.doi.org/10.1002/adts.202100071.
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Gao, Xiang, Tailu Li, Yao Zhang, Xiangfei Kong, and Nan Meng. "A Review of Simulation Models of Heat Extraction for a Geothermal Reservoir in an Enhanced Geothermal System." Energies 15, no. 19 (September 28, 2022): 7148. http://dx.doi.org/10.3390/en15197148.
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This paper reviews the heat transfer model for geothermal reservoirs, the fracture network in reservoirs, and the numerical model of hydraulic fracturing. The first section reviews the heat transfer models, which contain the single-porosity model, the dual-porosity model, and the multi-porosity model; meanwhile the mathematical equations of the porosity model are summarized. Then, this paper introduces the fracture network model in reservoirs and the numerical method of computational heat transfer. In the second section, on the basis of the conventional fracture theory, the PKN (Perkins–Kern–Nordgren) model and KGD (Khristianovic–Geertsma–De Klerk) model are reviewed. Meanwhile, the DFN (discrete fracture network) model, P3D (pseudo-3D) model, and PL3D (planar 3D) model are reviewed. The results show that the stimulated reservoir volume method has advantages in describing the fracture network. However, stimulated reservoir volume methods need more computational resources than conventional fracture methods. The third section reviews the numerical models of hydraulic fracturing, which contains the finite element method (FEM), the discrete element method (DEM), and the boundary element method (BEM). The comparison of these methods shows that the FEM can reduce the computational resources when calculating the fluid flow, heat transfer and fracture propagations in a reservoir. Thus, a mature model for geothermal reservoirs can be developed by coupling the processes of heat transfer, fluid flow and fracture propagation.
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Mańko, Robert, and Norbert Laskowski. "Comparative analysis of the effectiveness of the conceptual rainfall-runoff hydrological models on the selected rivers in Odra and Vistula basins." ITM Web of Conferences 23 (2018): 00025. http://dx.doi.org/10.1051/itmconf/20182300025.
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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.
Dissertations / Theses on the topic "Reservoirs – Mathematical models"
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Yeates, Peter Stafford. "Deep mixing in stratified lakes and reservoirs." University of Western Australia. Centre for Water Research, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0046.
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The onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.
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Estalrich-Lopez, Juan. "Short-term operation of surface reservoirs within long-term goals." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184854.
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A stochastic dynamic programming model (called P.B.S.D.P.) based on the consideration of peak discharge and time between peaks as two stochastic variables has been used to model and to solve a reservoir operation problem. This conceptualization of the physical reality allows to solve, in this order, the tactical and strategic operation of surface reservoirs. This P.B.S.D.P. model has been applied to the Sau reservoir in the Northeastern corner of Spain. The results showed a significant improvement over the currently used operation procedure, yielding values of yearly average electricity production that are somewhat under 6% of what could have been the maximum electricity production.
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Ugbo, Justin Petroleum Engineering Faculty of Engineering UNSW. "A new model for evaluating water saturation in shaly sand reservoirs using quantitative x-ray diffraction and cation exchange capacity cliff head field, Western Australia." Awarded by:University of New South Wales. Petroleum Engineering, 2007. http://handle.unsw.edu.au/1959.4/40443.
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Interpretation problems are commonly associated with calculating water saturation in nonhomogenous shaly sand reservoirs. Redefining petrophysical properties based on well logs in shaly sand reservoirs by using fundamental geologic attributes is an important tool in developing subsurface hydrocarbon resources. Studies of the electrical anisotropy of shaly sands have shown that the level of our understanding and our ability to correctly evaluate low resistivity and low contrast pay can be greatly improved. The model developed in this thesis is similar in form to the shaly sand Dual Water model by Clavier et al. (1984). It is an experiment based model designed to directly assess and quantify the mineralogical and electrical effects of clay minerals in heterogeneous reservoirs. Clay minerals usually have multiple effects on petrophysical properties obtained from geophysical well log measurements. The total expansible clay model evaluates these effects via direct measurement of independent mineralogy and conductivity of clay minerals within reservoir sands. This model integrates the following as an effective basis for characterizing shaly sand reservoirs: ??? Rietveld based Siroquant assay for quantitative X-ray diffraction, used in determining mineral percentages from standard XRD trace patterns, ??? Cation exchange capacity, used to determine the quantity of cations involved in the exchange at the shale-water interface, ??? Porosity, permeability, density and resistivity measurements, ??? Thin section petrography, used in identifying mineral patterns, visible porosity and reservoir quality. Overall, application of correlations drawn from the model yields improved results for water saturation which appeared consistent with those earlier calculated using known water saturation models (Clavier et al Dual Water model, 1984, Juhasz, 1981). A total of twenty three samples from two wells in the Cliff Head fIeld were analyzed for this study.
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García, Iturbe Selma L. "Simulation of physical and chemical processes in reservoirs: Two case studies." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4968/.
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Managing water quality aspects requires the use of integrative tools that allow a holistic approach to this problem. Water quality models coupled to hydrodynamic models are these tools. This study presents the application of the water quality model WASP coupled to the hydrodynamic model DYNHYD for two distinct reservoirs: Lake Texoma and Tocoma Reservoir. Modeling the former included simulations of water velocities, water level, and four chemical and physical compounds: chlorides, dissolved oxygen (DO), biochemical oxygen demand (BOD), and total suspended solids (TSS); and validation of the results by comparing with observed values during March - May, 1997. The latter is still under project status and the simulation was performed in a prospective way. The analysis included simulations of water velocities under current and for expected conditions, DO and BOD. Both models, DYNHYD and WASP, fitted pretty well to observed conditions for Lake Texoma and for where Tocoma Reservoir has been planned. Considering management and decision support purposes, the role of boundary and loading conditions also was tested. For Lake Texoma, controlling boundary conditions for chlorides is a determinant factor for water quality of the system. However, DO and TSS in the reservoir are governed by additional process besides the condition of the boundary. Estimated loadings for this system did not provided significant effects, even though the allocation of a load for chlorides resulted in significant changes in the trend for expected chloride concentrations at the Washita River Arm of Lake Texoma. For Tocoma Reservoir, the expected concentration of DO all over the reservoir is going to driven by boundary conditions, as well as by the management of autochthonous BOD loadings provided by vegetation decomposition. These two factors will be determinant for the resulting water quality of the future reservoir.
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Amorim, Elisa Portes dos Santos. "Ajuste automático de histórico em reservatórios de petróleo utilizando o método TSVD." Universidade Federal de Juiz de Fora (UFJF), 2009. https://repositorio.ufjf.br/jspui/handle/ufjf/4107.
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A simulação de reservatórios é uma ferramenta amplamente utilizada por engenheiros de reservatório. É principalmente utilizada com o objetivo de prever o comportamento de reservatórios sob diferentes condições, auxiliando os engenheiros a tomarem importantes decisões que podem envolver custos financeiros elevados. A fim de obter predições confiáveis, diferentes propriedades petrofísicas do reservatório, como a porosidade e a permeabilidade, devem ser conhecidas. Porém, medições diretas dessas propriedades são possíveis apenas nas proximidades dos poços. Uma forma de estimar essas propriedades é através do processo de ajuste de histórico. O processo de ajuste de histórico consiste no problema inverso de estimar as propriedades de um reservatório através do ajuste de dados simulados ao histórico do reservatório, o qual está disponível em reservatórios em operação já há algum tempo. Neste trabalho apresentamos um estudo para o ajuste de histórico automático baseado em um modelo de reservatório bifásico (óleo/água) e bidimensional. A taxa de produção de óleo e a pressão, medidas nos poços são tomadas como histórico do reservatório. Desejamos estimar a distribuição de permeabilidades do reservatório. O problema de ajuste de histórico consiste em minimizar uma função objetivo que quantifica o erro entre o histórico e os dados simulados, o que leva a um problema de mínimos quadrados não-linear. Para resolver este problema, utilizamos o método de Gauss-Newton combinado com o método de Decomposição em Valores Singulares Truncada (TSVD). O método TSVD reduz consideravelmente o número de parâmetros a serem estimados, reduzindo também o custo computacional envolvido na resolução do problema. A m de utilizarmos o método TSVD eficientemente é necessário dispor da derivada e adjunta do problema direto. O desenvolvimento dessas ferramentas consistiu de parte importante no desenvolvimento deste trabalho.
Reservoir simulation is an essential tool extensively used by reservoir engineers. It is mostly employed to predict reservoir behavior under different circumstances, thus supporting decisions that frequently involve large fnancial costs. In order to use this tool properly different petro-physical properties of the reservoir must be well known, such as permeability and porosity. Unfortunately, direct measures of these properties are viable only near the wells. A way of estimating these properties is through the so called History Matching process. History matching process consists on the inverse problem of estimating reservoir properties through matching simulated data to reservoir history, which are available in reservoirs that are operating for some time. In this work we present a study for the automatic history matching based in a two-phase (oil/water), two dimensional reservoir model. The rate of oil production and the pressure measured at the wells are taken as the history of the reservoir. In this work, we aim to estimate the permeability distribution of the reservoir. The history matching problem consists on minimizing an objective function that measures the mismatch between reservoir history and simulated data, which turns the problem into a nonlinear least square problem. In order to solve this problem the Gauss-Newton method was employed combined with the Truncated Singular Value Decomposition (TSVD) technique. The TSVD technique reduces considerably the number of parameters to estimate, reducing also the computational effort involved in solving the problem. In order to use the TSVD method in an effcient way it is necessary to have the derivative and the adjoint of the direct problem. The development of these tools was an important part of this work.
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Castro, Marcelo Mendes de. "Modelação matemática de lagos e reservatórios: caso do Reservatório Billings." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/3/3147/tde-18082010-165433/.
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Modelos numéricos são importantes ferramentas para avaliação do comportamento de corpos hídricos, notadamente com relação ao decaimento e mistura de constituintes ao longo do tempo. Neste trabalho apresenta-se o método empregado para adaptação e aplicação de um modelo matemático hidrodinâmico 2DH para simulação de variáveis de qualidade das águas a reservatórios rasos ou polimíticos. A descrição do desenvolvimento do modelo empregado (IPH-ECO), do processo de análise das condições do reservatório, seleção de dado intervenientes, discretização espacial e temporal, definição das condições de contorno hidrológicas e de aporto de cargas poluentes, bem como a definição espacial dos pontos de controle para aferição e validação são discutidos. São apresentados os resultados da resposta do modelo aplicado ao Reservatório Billings, em São Paulo.Numerical models are strong tools to evaluate the fate of pollutants in lakes and reservoirs under transient conditions. This article brings the steps employed for preparation and implementation of a hydrodynamic 2DH model to simulate water quality variables in shallow or polymitc lakes. Description of the adaptation and implementation of IPH-ECO model process, compiling and setting of the hydrological and constituent loadings, spatial and temporal discretization and selection of control points are demonstrated and discussed. Some results of model calibration for Billings Reservoir, Sao Paulo, Brazil, are also presented.
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Sancevero, Sergio Sacani. "Estudo de aplicação de metodos quantitativos em dados sismicos no processo de caracterização integrada de reservatorios." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/287444.
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Orientador: Armando Zaupa RemacreTese (doutorado) - Universidade Estadual de Campinas, Instituto de Geociencias
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Resumo: O processo de caracterização de reservatórios é atualmente uma das etapas mais importantes na exploração, desenvolvimento e produção de um campo. Porém, para que esse processo seja realizado da melhor forma possível é preciso se ter o conhecimento de determinados métodos, que integram as diferentes informações disponíveis. Desse modo, o objetivo principal dessa tese é estudar de forma criteriosa e quantitativa o processo de caracterização de reservatórios do ponto de vista dos dados sísmicos, avaliando antigos e novos métodos, e definindo novas metodologias que possam ser aplicadas de maneira decisiva neste processo. Para que esses métodos pudessem ser avaliados de maneira conclusiva foi utilizado nesta tese um modelo sintético que reproduzisse minimamente algumas características cruciais de determinados reservatórios como a complexa distribuição dos corpos de areia e a presença de corpos com espessura subsísmica que levassem ao limite as técnicas de modelagem tradicionais, proporcionando avaliar novos métodos. Assim, para caracterizar essas complexas feições, foram utilizados nesta tese dois meios principais de interpretação, primeiro a inversão sísmica dando um caráter preditivo ao dado sísmico e por fim a análise multiatributos, dando um caráter classificatório. No caso da inversão sísmica foram utilizados três métodos de obtenção da impedância acústica. Entre eles, foi a inversão geoestatística que demonstrou ser a mais eficiente das técnicas no que diz respeito à caracterização de reservatórios com espessura subsísmica e complexa distribuição dos corpos de areia. No caso dos atributos, pôde-se demonstrar que é necessário que sejam tratados com uma abordagem multivariada para que seja aproveitada a correlação entre eles e que por meio de técnicas de classificação e modelagem possa se decidir os mais relevantes para o processo. Neste caso 3 métodos de análise multivariada foram apresentados e testados, sendo que dois deles (ICA e MAF) de maneira inédita e que produziram resultados superiores àqueles alcançados quando a tradicional técnica de PCA é aplicada. Assim, com o que foi apresentado, pode-se concluir que o processo de caracterização é um estágio crucial para o desenvolvimento dos campos, mas não é fácil de ser realizado, a menos que os métodos e as técnicas envolvidas sejam conhecidas de maneira profunda. Só assim, é possível extrair o máximo de informações do dado sísmico, caracterizando o reservatório de forma quantitativa e integrada, otimizando sua produção e reduzindo os riscos e custos com a sua explotação
Abstract: The reservoir characterization process can be considered curretly the most important stage in the exploration, development and production of the oil field. However, this process is only carried out in the best way if the geologists, geophisicist and engineering has the knowledge of some definitive methods and techniques that integrated all information available about the field. Thus, the aim of this thesis is to study in a criterious and quantitative way the reservoirscharacterization process, analyzing the seismic data,by the evaluation of classic and novel methods, to defining new methodlogies that can be applied in decisive way into this process. So, for these methods could be evaluated in a conclusive way, were used in this thesis asynthetic reference model that reproduced some critical features of determined reservoirs, as the complex distribution of sand bodies and the subseismic thickness. These characteristics pushing to the limit the traditional modelling techniques. In this thesis to characterizze the complex features present in the reference model we used two interpretation techniques, first we analyze the seismic inversion that give a preditive character to the seismic data and after we study the multiattribute analysis that give a classificatory caracter to the seismic interpretation. For the seismic inversion, the stochastic or geostatistical inversion, that demonstrated to be the most efficient technique to characterized the complex and the subseismic features present in the model. About the seismic attributes it could be demonstrated that even so in some cases they represent the features of the model, are necessary that they are dealt with a multivariate approach, to used the advantage of the correlation between them. For the seismic attribute analysis, 3 methods of multivariate statistics analysis were used, two of them (ICA and MAF) for the first time in the reservoir characterization processo With the results we can proved that these 2 new methods improved the process of multiattribute anlysis prducing superior results when compare with the results obtained by the application of traditional PCA technique. With it was presented, can be concluded that the reservoir characterization process is a crucial stage and have some difficults to be accomplishment, unless the methods and the involved techniques are known deeply. Thus it is possible to extract the maximum informations from the datasets, characterizing the reservoir in a quantitative and integrated environmental, optimizing its production and reducing the risks and the costs with its explotation
Doutorado
Administração e Politica de Recursos Minerais
Doutor em Ciências
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Costa, Samuel Barsanelli. "Modelo unidimensional preliminar de transporte de sedimentos para o reservatório Taiaçupeba." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/3/3147/tde-03052018-091135/.
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A modelagem unidimensional tem sido adotada desde os anos 1980, com sucesso nas práticas de engenharia, para a caracterização do regime de transporte de sedimentos de longo termo. É também uma importante ferramenta para o entendimento da dinâmica sedimentar de bacias e gestão de sedimentos em reservatórios. Esta pesquisa teve como objetivo aplicar a modelagem unidimensional de transporte de sedimentos na bacia do reservatório Taiaçupeba, São Paulo, Brasil, a partir do sistema computacional HEC-RAS, orientada à estimativa das descargas sólidas afluentes ao reservatório. O período de coleta de dados coincidiu com a estiagem de 2013-2015 na Região Sudeste, o que contribuiu com a análise crítica do método e dos resultados, cuja discussão ressalta o uso da modelagem unidimensional como instrumento eficaz de validação das curvas de sedimento para caracterização do regime de transporte. As funções de capacidade de transporte de Laursen-Copeland e Toffaleti mostraram-se aplicáveis a esse sistema fluvial, bem como os métodos de encouraçamento de fundo de Hirano e Thomas-Copeland. Os coeficientes de Manning ajustados foram considerados preliminares e dados de campo adicionais são encorajados para refinar seu ajuste e incorporar maior acurácia na estimativa do perfil da linha d\'água em trabalhos futuros. Além disso, são apresentadas recomendações metodológicas ao monitoramento fluvissedimentométrico que contribuem com a sistematização das técnicas e tecnologias disponíveis à pesquisa hidrossedimentológica.One-dimensional modeling has been successfully adopted since the 1980s in engineering practices to assess long-term sediment transport regimes. It is also an important tool for the understanding of sediment dynamics in watersheds and sediment management in reservoirs. The objective of this research was to apply the one-dimensional sediment transport modeling in the Taiacupeba reservoir basin, located in Sao Paulo, Brazil, implemented on HEC-RAS, aiming to estimate longterm loads into the reservoir. The data collection period coincided with the drought of 2013-2015 in Southeastern Brazil, which contributed to the critical analysis of the method and results, whose discussion highlights the use of one-dimensional modeling as an effective instrument for validating sediment curves. The transport capacity functions of Laursen-Copeland and Toffaleti have been shown to be applicable to this river system, as well as the bed sorting and armoring methods of Hirano and Thomas-Copeland. The Manning coefficients were considered preliminary and additional field data are encouraged to enhance its adjustment and incorporate greater accuracy in estimating the water surface profile in future work. Besides, methodological recommendations for sediment monitoring are presented, contributing to the systematization of available techniques and technologies applied to sediment research.
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Cruz, Rafael Oscar de Moraes. "Combustão In-Situ = considerações sobre projeto e simulações numéricas em escala de laboratório e de campo." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264311.
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Orientador: Osvair Vidal TrevisanDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências
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Resumo: A previsão de comportamento de reservatórios submetidos a combustão in-situ é trabalhosa e empírica já que além das complexidades geológicas, é necessário modelar a complexidade do hidrocarboneto de reservatório e das reações químicas que ocorrem no processo. As etapas de projeto de campo costumam envolver 1) seleção de reservatório; 2) experimentos termo-analíticos; 3) experimentos em tubo de combustão; 4) aplicação de métodos analíticos; 5) simulação numérica; 6) calibração dos modelos analíticos e numéricos através de dados de projeto piloto. O escopo de trabalho desta dissertação está concentrado nas Etapas 4 e 5 deste processo e o foco é a previsão de comportamento de projetos de campo. Propõe-se uma metodologia de mudança de escala para tratamento de dados advindos de laboratório para uso em previsão de comportamento. Adapta-se um equacionamento clássico de projeto de campo de Nelson e Mcneil (1961) para agregar o conceito de velocidade mínima de frente de chama. Para avaliar a extensão dos resultados obtidos com os experimentos em células de combustão 3D de Coates et al (1995) e de Greaves e Turta (2003), que foram realizados para testar as configurações de poço top-down e thai respectivamente, realiza-se simulações em escala de laboratório para reproduzir uma célula de combustão 3D, e avalia-se o impacto de diversos parâmetros de modelagem, como a composição dos fluidos e as reações químicas, além de parâmetros operacionais. Nestas simulações foi possível reproduzir maior complexidade do modelo de fluidos e das reações químicas, incluindo reações de adição de oxigênio e de quebra de cadeia. Foi possível ainda reproduzir a dependência entre estas reações, fazendo com que o combustível para as reações de quebra de cadeia fosse gerado nas reações de adição de oxigênio. Utilizou-se uma malha tão refinada quanto as dimensões da frente de chama, de forma que se controlou a evolução das reações pela temperatura. Para exemplificar a metodologia proposta de mudança de escala e de projeto de campo, utilizou-se os experimentos em tubo de combustão de Gonçalves (2010). Os parâmetros projetados foram aplicados em simulações em escala de campo, onde a evolução das reações químicas foi controlada pela velocidade. Definiu-se uma velocidade mínima para avanço da frente de chama através de tratamento dos dados advindos dos experimentos em tubo de combustão e aplicou-se no modelo de simulação, onde se investigou a capacidade de previsão da evolução da frente de chama em um cenário com propriedades geológicas heterogêneas
Abstract: Behavior forecast of reservoirs subjected to in-situ combustion is hard and empirical since besides geological complexities it is necessary to reproduce complex fluid models and several chemical reactions that are part of the process. The work flow for field project usually involves: 1) reservoir screening; 2) thermo-analytical experiments; 3) combustion tube experiments; 4) use of analytical models; 5) numerical simulation and 6) fitting of analytical and numerical models with field pilot data. The present work concerns the fourth and fifth stages of this process and the focus is behavior forecast of field projects. A methodology for upscaling laboratory results for application in behavior forecast is proposed. The classical Nelson and Mcneil (1961) field project equations are adapted to account for the minimum velocity of the combustion front. In order to evaluate the extension of the results obtained by Coates et al (1995) and Greaves and Turta (2003) with 3D combustion cells, wich were carried to test the thai and top-down well configuration respectively, laboratory scale numerical simulation that reproduces a 3D combustion cell is conducted and the influence of several modeling parameters, such as fluid composition and chemical reactions, is tested, along with operational parameters. In this simulations, a greater complexity in the fluid and reaction model is possible with both oxygen addition and bond scission reactions. It is also possible to model the dependency between reactions, making the reactant of high temperature reactions to be formed in low temperature reactions. A grid refinement in the same size of the combustion front is used and chemical reactions continuity is controlled through temperature. Data from the combustion tube experiments from Gonçalves (2010) are used to exemplify and apply the upscaling and field project methodology. The obtained project parameters are used as input for field scale numerical simulation, where the chemical reactions continuity is controlled through velocity. A minimum combustion front velocity is defined and applied in the simulation model, where the capacity of forecast of the combustion front migration in an heterogeneous geological context is evaluated
Mestrado
Reservatórios e Gestão
Mestre em Ciências e Engenharia de Petróleo
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Hnidei, Stephen D. "Selective withdrawal of a linearly stratified fluid in a triangular reservoir." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/28834.
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The water in most reservoirs is density stratified with depth. This stratification leads to the inhibition of vertical movement, consequently, when water is withdrawn from the reservoir it tends to move in a jet-like layer called a withdrawal layer, towards the sink. By placing the sink at a certain depth, one is able to selectively withdrawal water from a limited range of depths and thus obtain water of a desired quality.
Much work has been done in this field by considering a simplified boundary geometry, usually rectangular. However little attention has been given to the effects of accurate boundary geometry. For this thesis, five numerical experiments were conducted for the problem of a two-dimensional, viscous, incompressible, slightly-stratified flow towards a sink in a triangular reservoir.Science, Faculty of
Mathematics, Department of
Graduate
Books on the topic "Reservoirs – Mathematical models"
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Archibald, T. W. Controlling multi-reservoirsystems. Edinburgh: University of Edinburgh Management School, 1996.
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Optimizing reservoir resources: Including a new model for reservoir reliability. New York: Wiley, 1999.
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Nekotorye voprosy upravlenii͡a vodokhranilishchami. Moskva: Vychislitelʹnyĭ t͡sentr AN SSSR, 1986.
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N, Chaban A., ed. Dispetcherskie pravila upravlenii͡a︡ vodokhranilishchem mnogoletnego regulirovanii͡a︡. Moskva: Vychislitelʹnyĭ t͡s︡entr AN SSSR, 1985.
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Kl̓účovská, Jelica. Dvojrozmerné matematické modelovanie prúdenia v nádržiach. Bratisłava: Výskumný ústav vodného hospodárstva, 1992.
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Integrated flow modeling. Amsterdam: Elsevier Science B.V., 2000.
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Ślusarczyk, Zbigniew. Numeryczne modele transformacji fal powodziowych przez zbiorniki retencyjne. Kraków: Politechnika Krakowska, 1992.
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Wolski, Piotr. Application of reservoir modelling to hydrotopes identified by remote sensing. Enschede, the Netherlands: International Institute for Aerospace Survey and Earth Sciences (ITC), 1999.
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Chang, Ming. Model simulation of the Manasquan water-supply system in Monmouth County, New Jersey. West Trenton, N.J: U.S. Dept. of the Interior, U.S. Geological Survey, 2001.
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Effler, Steven W. Origins, behavior, and modeling of THM precursors in lakes and reservoirs. Denver, Colo: Awwa Research Foundation, 2005.
Find full textBook chapters on the topic "Reservoirs – Mathematical models"
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Bedrikovetsky, Pavel, and Gren Rowan. "Analytical Models of Water-Flooding of Stratified Reservoirs." In Mathematical Theory of Oil and Gas Recovery, 40–59. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-2205-6_3.
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Ali, Iftikhar, Bilal Chanane, and Nadeem A. Malik. "Compressibility Coefficients in Nonlinear Transport Models in Unconventional Gas Reservoirs." In Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 3–13. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30379-6_1.
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Henderson-Sellers, B. "A hierarchy of mathematical models: towards understanding the physical processes in reservoirs." In Comparative Reservoir Limnology and Water Quality Management, 93–97. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1096-1_5.
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Fourmigué, Patrick, and Patrick Arnaud. "Reservoir Models in Hydrology." In Mathematical Models, 397–407. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118557853.ch12.
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Thiéry, Dominique. "Reservoir Models in Hydrogeology." In Mathematical Models, 409–18. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118557853.ch13.
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Lie, Knut-Andreas, and Bradley T. Mallison. "Mathematical Models for Oil Reservoir Simulation." In Encyclopedia of Applied and Computational Mathematics, 850–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_277.
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Atangana, Abdon, and Seda İgret Araz. "A Mathematical Model with Covid-19 Reservoir." In Fractional Stochastic Differential Equations, 423–80. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6_11.
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Augustin, Matthias Albert. "Physical and Mathematical Foundation." In A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs, 39–63. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17079-4_3.
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de Paula, Renato, Patrícia Gonçalves, and Adriana Neumann. "Porous Medium Model in Contact with Slow Reservoirs." In Springer Proceedings in Mathematics & Statistics, 123–47. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99689-9_7.
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Ran, Qiquan. "Mathematical Model of Multiphase Flow in Multiple Media at Different Scales." In Unconventional Tight Reservoir Simulation: Theory, Technology and Practice, 71–95. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-32-9848-4_3.
Full textConference papers on the topic "Reservoirs – Mathematical models"
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Stiles, D. A., and J. F. Baret. "Sedimentation and Free Water of Cement Slurries: Mathematical Models and Practical Solutions." In Low Permeability Reservoirs Symposium. Society of Petroleum Engineers, 1993. http://dx.doi.org/10.2118/25866-ms.
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Dale, Stein Inge, Magne Sjaastad, Hakon Hogstol, and Alf Birger Rustad. "Improving Visualization of Large Scale Reservoir Models." In Mathematical Methods in Fluid Dynamics and Simulation of Giant Oil and Gas Reservoirs. Society of Petroleum Engineers, 2012. http://dx.doi.org/10.2118/163088-ms.
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Osuala, Justice Chidera, Daniel Ikechukwu Egu, Anthony John Ilozobhie, and Blessing Ogechi Nwojiji. "Enhancing Reservoir Stimulation through Mathematical Remodeling of Pre-Flush Acidizing Volume Algorithm for Different Reservoir Flow Geometries." In SPE Nigeria Annual International Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/211916-ms.
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Abstract Studies show that an average of 35% of reservoir acid stimulation operations executed every year fails because of limited knowledge of downhole acid placement. Existing models designed for acid pre-flush volumes are limited to Linear, Radial and Ellipsoidal reservoir geometries, therefore, do not account for geological drifts of a typical heterogenic reservoir. This can be erroneous while estimating acid placement volumes as reservoirs can deviate from defined flow geometries due to their dynamic and heterogeneous nature, thereby challenging to estimate acid volumes precisely for stimulations. This study aims to foster sustainability in reservoir flow engineering by deriving a mathematical model that evaluates volumes for reservoirs with flow geometries that deviate from linear and radial. This was established to help introduce a new geometry contributing to the accountability of complex and heterogeneous reservoirs. Sensitivity analysis and investigation using reservoir core data from SPDC Petroleum Chemistry Laboratory were carried out to understand the relationship between Linear, Radial and Modified flow geometries. Analytical results for linear, radial and the fied were generated. These results proved the precision of the modified equation for calculating pre-flush acid volume for reservoir acid stimulation operation.
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Khachay, Andrey. "Mathematical models of active acoustic impact on diffusion in reservoirs with oil hierarchic inclusions." In 29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0060442.
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Karim, Md Mostafijul, M. Enamul Hossain, Mahamudul Hashan, and Syed Imtiaz. "A Comparative Study of Mathematical Models for Fractured Reservoirs: Anomalous Diffusion and Continuum Approach." In SPE Trinidad and Tobago Section Energy Resources Conference. Society of Petroleum Engineers, 2018. http://dx.doi.org/10.2118/191203-ms.
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Al-Marhoun, Muhammad. "A Single Artificial Neural Network Model Predicts Bubble Point Physical Properties of Crude Oils." In SPE Middle East Oil & Gas Show and Conference. SPE, 2021. http://dx.doi.org/10.2118/204648-ms.
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Abstract Reservoir fluid properties at bubble points play a vital role in reservoir and production engineering computations. Ideally, the bubble point physical properties of crude oils are obtained experimentally. On some occasions, these properties are neither available nor reliable; then, empirically derived correlations or artificial neural network models are used to predict the properties. This study presents a new single multi-input multi-output artificial neural network model for predicting the six bubble point physical properties of crude oils, namely, oil pressure, oil formation volume factor, isobaric thermal expansion of oil, isothermal compressibility of oil, oil density, and oil viscosity. A large database comprising conventional PVT laboratory reports was collected from major producing reservoirs in the Middle East. The model input is constrained mathematically to be consistent with the limiting values of the physical properties. The new model is represented in mathematical format to be easily used as empirical correlations. The new neural network model is compared with popular fluid property correlations. The results show that the developed model outperforms the fluid property correlations in terms of the average absolute percent relative error.
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Kayode, B., F. Al-Tarrah, and G. Hursan. "Methodology for Static and Dynamic Modeling of Hydrocarbon Systems Having Sharp Viscosity Gradient." In International Petroleum Technology Conference. IPTC, 2021. http://dx.doi.org/10.2523/iptc-21184-ms.
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Abstract This paper describes a methodology for delineating tar surface, incorporating it into a geological model, and the process for numerical modeling of oil viscosity variation with depth above the tar surface. The methodology integrates well log data and compositional fluid analysis to develop a mathematical model that mimics the oil's property variation with depth. While there are a good number of reservoirs that fit this description globally, there is a knowledge gap in literature regarding best practices for dealing with the peculiar challenges of such reservoirs. These challenges include; (i) how to delineate the top-of-tar across the field, (ii) modeling of Saturation Height Function (SHF) in a system where density and wettability is changing with depth, and (iii) the methodology for representing the depth-dependent oil properties (especially viscosity) in reservoir simulation. Nuclear magnetic resonance (NMR) logs were used to predict fluid viscosity using a technique discussed by Hursan et al. (2016). Viscosity regions are identified at every well that has an NMR log, and these regions are mapped from well to well across the reservoir. Within each viscosity region, the analysis results of fluid samples collected from wells are used to develop mathematical models of fluid composition variation with depth. A reliable SHF model was achieved by incorporating depth-varying oil density and depth varying wettability into the calculation of J-Function. A compositional reservoir simulation was set-up, using the viscosity regions and the mathematical models describing composition variation with depth, for the respective regions. Using information obtained from literature as a starting point, residual oil saturation was modeled as a function of oil viscosity. Original reservoir understanding places the top of non-movable oil (tar) at a constant fieldwide subsurface depth, which corresponds to the shallowest historical no-flow drillstem test (DST) depth. Mapping of the NMR viscosity regions across the field resulted in a sloping tar-oil contact (TOC), which resulted in an increase of movable hydrocarbon pore volume. The viscosity versus depth profile from the simulation model matched the observed data, and allow the simulation model better predict well performance. In addition, the simulation model results also matched the depth-variation of observed formation volume factor (FVF) and reservoir fluid density. Some wells that have measured viscosity data but no NMR logs were used as blind-test wells. The simulation model results also matched the measured viscosity at those blind-test wells. These good matches of the oil property variation with depth gave confidence, that the simulation model could be used as an efficient planning tool for ensuring that injectors are placed just-above the tar mat. The use of the simulation model for well planning could reduce the need for geosteering while drilling flank wells, leading to savings in financial costs. This paper contains a generalized approach that can be used in static and dynamic modeling of reservoirs, where oil changes from light to medium to heavy oil, underlain by tar. It contains recommendations and guidelines to construct a reliable simulation model of such systems.
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Hedzyk, Nazarii, and Oleksandr Kondrat. "Low-Permeable Reservoirs as High Potential Assets for EGR." In SPE Eastern Europe Subsurface Conference. SPE, 2021. http://dx.doi.org/10.2118/208555-ms.
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Abstract Natural gas fields that are being developed in Ukraine, mainly relate to the high and medium permeability reservoirs, most of which are at the final stage of field life. In this situation one of the main sources of additional gas production is unconventional fields. This paper presents the analysis of challenges concerning development of low-permeable reservoirs and experimental results of conducted research, which provide the opportunity to establish technologies for enhance gas recovery factor. For this purpose, a series of laboratory experiments were carried out on the sand packed models of gas field with different permeability (from 9.7 to 93 mD) using natural gas. The pressure in the experiments varied from 1 to 10 MPa, temperature – 22-60 °C. According to the features of low-permeable gas fields development the research of displacement desorption with carbon dioxide and inert gas stripping by nitrogen was conducted. These studies also revealed the influence of pressure, temperature, reservoir permeability and non-hydrocarbon gases injection rate on the course of adsorption-desorption processes and their impact on the gas recovery factor. According to the experimental results of relative adsorption capacity determination it can be concluded that the carbon dioxide usage as the displacement agent can lead to producing adsorbed gas by more than 30% than by using nitrogen. To remove the adsorbed gas just reservoir pressure lowering is not enough due to the nature of adsorption isotherms. Particularly at pressure decreasing by 8-10 times compared to initial reservoir pressure only about 30-40% of the total amount of initially adsorbed gas is desorbed. And at considerable reservoir pressure reduction the further deposit development is not economically profitable. According to the results it was found that in the case of nitrogen usage the most effective method is full voidage replacement at injection pressure of 0.8 of the initial reservoir pressure, and in case of carbon dioxide usage - full voidage replacement method at pressure of 0.6 of the initial reservoir pressure. Taking into account availability of N2 and CO2, N2injection is recommended for further implementation. The influence of displacement agent injection pressure on gas recovery was experimentally proved. The physical sense of the processes taking place during natural gas desorption stimulation by non-hydrocarbon gases was justified. The effect of temperature, pressure and reservoir permeability on methane adsorption capacity were determined. The mathematical model for estimating adsorbed gas amount depending on the reservoir parameters was developed. Obtained results were summarized and recommendations for practical implementation of elaborated technological solutions were suggested.
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Alruwayi, Sarah Abdullatif, Ozan Uzun, and Hossein Kazemi. "Matrix Refinement in Mass Transport Across Fracture-Matrix Interface: Application to Improved Oil Recovery in Fractured Reservoirs." In Abu Dhabi International Petroleum Exhibition & Conference. SPE, 2021. http://dx.doi.org/10.2118/208038-ms.
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Abstract In this paper, we will show that it is highly beneficial to model dual-porosity reservoirs using matrix refinement (similar to the multiple interacting continua, MINC, of Preuss, 1985) for water displacing oil. Two practical situations are considered. The first is the effect of matrix refinement on the unsteady-state pressure solution, and the second situation is modeling water-oil, Buckley-Leverett (BL) displacement in waterflooding a fracture-dominated flow domain. The usefulness of matrix refinement will be illustrated using a three-node refinement of individual matrix blocks. Furthermore, this model was modified to account for matrix block size variability within each grid cell (in other words, statistical distribution of matrix size within each grid cell) using a discrete matrix-block-size distribution function. The paper will include two mathematical models, one unsteady-state pressure solution of the pressure diffusivity equation for use in rate transient analysis, and a second model, the Buckley-Leverett model to track saturation changes both in the reservoir fractures and within individual matrix blocks. To illustrate the effect of matrix heterogeneity on modeling results, we used three matrix bock sizes within each computation grid and one level of grid refinement for the individual matrix blocks. A critical issue in dual-porosity modeling is that much of the fluid interactions occur at the fracture-matrix interface. Therefore, refining the matrix block helps capture a more accurate transport of the fluid in-and-out of the matrix blocks. Our numerical results indicate that the none-refined matrix models provide only a poor approximation to saturation distribution within individual matrices. In other words, the saturation distribution is numerically dispersed; that is, no matrix refinement causes unwarranted large numerical dispersion in saturation distribution. Furthermore, matrix block size-distribution is more representative of fractured reservoirs.
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Chen, Songhua, Wei Shao, Huiwen Sheng, and Hyung Kwak. "Use of Symbolic Regression for Developing Petrophysical Interpretation Models." In 2022 SPWLA 63rd Annual Symposium. Society of Petrophysicists and Well Log Analysts, 2022. http://dx.doi.org/10.30632/spwla-2022-0113.
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A new physics-guided AI machine learning method for petrophysical interpretation model development is described. The workflow consists of the following five constituents: (1) statistical tools such as correlation heatmaps are employed to select the best candidate input variables for the target petrophysical equations; (2) genetic programming based symbolic regression approach is used to fuse multiphysics measurements data for training the petrophysical prediction equations; (3) an optional ensemble modeling procedure is applied for maximally utilizing all available training data by integrating multiple instances of prediction equations objectively, which is especially useful for a small training dataset; (4) a means of obtaining conditional branching in prediction equations is enabled in symbolic regression to handle certain formation heterogeneity; and (5)a model discrimination framework is introduced to finalize the model selection based on mathematical complexity, physics complexity, and model performance. The efficacy of the five-constituents petrophysical interpretation development process is demonstrated on a dataset collected from six wells for a goal of obtaining formation resistivity factor (F) and permeability (k) equations for heterogenous carbonate reservoirs. This study demonstrates that this new petrophysical model development process has many advantages over traditional empirical methods or other commonly used AI methods.
Reports on the topic "Reservoirs – Mathematical models"
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Lohne, Arild, Arne Stavland, Siv Marie Åsen, Olav Aursjø, and Aksel Hiorth. Recommended polymer workflow: Interpretation and parameter identification. University of Stavanger, November 2021. http://dx.doi.org/10.31265/usps.202.
Full textAbstract:
Injecting a polymer solution into a porous medium significantly increases the modeling complexity, compared to model a polymer bulk solution. Even if the polymer solution is injected at a constant rate into the porous medium, the polymers experience different flow regimes in each pore and pore throat. The main challenge is to assign a macroscopic porous media “viscosity” to the fluid which can be used in Darcy law to get the correct relationship between the injection rate and pressure drop. One can achieve this by simply tabulating experimental results (e.g., injection rate vs pressure drop). The challenge with the tabulated approach is that it requires a huge experimental database to tabulate all kind of possible situations that might occur in a reservoir (e.g., changing temperature, salinity, flooding history, permeability, porosity, wettability etc.). The approach presented in this report is to model the mechanisms and describe them in terms of mathematical models. The mathematical model contains a limited number of parameters that needs to be determined experimentally. Once these parameters are determined, there is in principle no need to perform additional experiments.
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Schneider, Michael L., and Richard E. Price. Temperature Analysis: Howard A. Hanson Reservoir, Washington. Mathematical Model Investigation. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada200228.
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