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1
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.
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Mateo-Lázaro, Jesús, Jorge Castillo-Mateo, José Sánchez-Navarro, Víctor Fuertes-Rodríguez, Alejandro García-Gil, and Vanesa Edo-Romero. "New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models." Water 10, no. 4 (April 11, 2018): 465. http://dx.doi.org/10.3390/w10040465.
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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.
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Sukhinov, Alexander, Valentina Sidoryakina, Elena Protsenko, and Sofya Protsenko. "Wind Currents Effects Numerical Simulation on the Coastal Zone of Large Reservoirs." Mathematical Physics and Computer Simulation, no. 3 (December 2022): 15–30. http://dx.doi.org/10.15688/mpcm.jvolsu.2022.3.2.
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Calculation and evaluation of wind currents hydrophysical characteristics of large reservoirs is the purpose of this work. Adequate dynamic mathematical models are necessary for conducting these studies and constructing appropriate algorithms implemented on supercomputers. The shallow water reservoirs hydrodynamic model is developed on the basis of three-dimensional mathematical model that includes the Navier — Stokes equations of motion in three coordinate directions, the equations of continuity of an incompressible fluid, the equations of heat transport and the equations of state or the density dependence of the aqueous medium on temperature. The discretization of the hydrodynamic equations is carried out by the pressure correction method. The developed numerical algorithms and the software package that implements them are used to study the pressure field and the aquatic medium velocity vector field the for a given section of the reservoir water area. The practical significance lies in the possibility of their application for studying the hydrophysical processes of these territories, assessing the hydrodynamic impact on the large reservoirs’ coastal zone.
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Guseynov, Sharif E., and Jekaterina V. Aleksejeva. "Mathematical Modelling of Aquatic Ecosystem." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 16, 2015): 92. http://dx.doi.org/10.17770/etr2015vol3.192.
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<p class="R-AbstractKeywords"><span lang="EN-US">In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used</span><span lang="EN-US">. </span></p>
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Asfaw, Tilahun Derib, and Ahmad Mustafa Hashim. "Development of Cascade Hydropower Reservoirs Operating System Rule Using Refill and Deplete Ranking Orders." Advanced Materials Research 433-440 (January 2012): 1735–39. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.1735.
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A new model is developed for a cascade of four hydropower reservoirs operation. The aim is to improve the total power generation from the system. Daily data of reservoir level, release and power generated which varies from 4-20 years are used for analysis. Long-term data of reservoir level and inflow are used to determine the critical period. The critical period is classified into four seasons; these are filling, depleting, upper and lower level operating season. Mathematical models are used to rank the refill and the deplete order of the reservoirs. A new rule models are presented using the results of refill and depletion ranks. Power generation using the developed model is compared to the long-term historical generated; and it is found that the new rule model boost the daily power production by 5.3% and the plant factor by 2%.
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Semerak, Mykhailo, and Hanna Lyantse. "Mathematical modeling and investigation of anomalies of the temperature field of the earth′s crust over oil and gas reservoirs." Physico-mathematical modelling and informational technologies, no. 28, 29 (December 27, 2019): 92–101. http://dx.doi.org/10.15407/fmmit2020.28.092.
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In geothermal studies of oil and gas fields, temperature anomalies were found in the surface layers of the crust. In the paper, mathematical models of temperature fields of the Earth's crust over the oil and gas reservoirs have been constructed. The anomalies of the temperature field in the neutral layer depending on the depth of deposits, the capacity of the reservoir have been investigated using experimental data. A mathematical model of the Earth's crust has been also constructed taking into account its lithological structure. The influence of lithological heterogeneity of the layer on the temperature fields in the neutral layer has been investigated.
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Bian, Huiyuan, Kewen Li, Binchi Hou, and Xiaorong Luo. "A New Model to Calculate Oil-Water Relative Permeability of Shaly Sandstone." Geofluids 2020 (September 24, 2020): 1–11. http://dx.doi.org/10.1155/2020/8842276.
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Oil-water relative permeability curves are the basis of oil field development. In recent years, the calculation of oil-water relative permeability in sandstone reservoirs by resistivity logging data has received much attention from researchers. This article first analyzed the existing mathematical models of the relationship between relative permeability and resistivity and found that most of them are based on Archie formula, which assumes the reservoir is clean sandstone. However, in view of the fact that sandstone reservoir is commonly mixed with shale contents, this research, based on the dual water conductivity model, Poiseuille’s equation, Darcy’s law, and capillary bundle model, derived a mathematical model (DW relative permeability model) for shaly sandstone reservoir, which calculates the oil-water relative permeability with resistivity. To test and verify the DW relative permeability model, we designed and assembled a multifunctional core displacement apparatus. The experiment of core oil-water relative permeability and resistivity was designed to prove the effectiveness of the DW relative permeability model in shaly sandstone reservoirs. The results show that the modified Li model can well express the transformational relation between resistivity and relative permeability in sandstone reservoir with low clay content. Compared with the modified Li model and the Pairoys model, the DW relative permeability model is more helpful to collect better results of relative permeability in shaly sand. These findings will play a significant role in the calculation of oil-water relative permeability in reservoirs based on resistivity logging data and will provide important data and theory support to the shaly sandstone reservoir characterized oil field development.
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Yarakhanova, D. G., and M. E. Hossain. "Algorithm for selecting systems horizontal wells and mathematical models for unconventional reservoirs." Russian Journal of Earth Sciences 20, no. 6 (October 29, 2020): 1–8. http://dx.doi.org/10.2205/2020es000727.
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Charles, D. D., H. H. Rieke, and R. Purushothaman. "Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs." SPE Reservoir Evaluation & Engineering 4, no. 03 (June 1, 2001): 221–30. http://dx.doi.org/10.2118/72098-pa.
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Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex. Introduction The interpretation of the effect of reservoir shape on pressure-transient well-test data needs improvement. It is economically imperative to be able to generate an accurate estimate of reserves and producing potential. This is especially critical for independent operators who wish to participate in deepwater opportunities in the Gulf of Mexico. Proper interpretation of data extracted from cost-effective well tests is an integral part of describing, evaluating, and managing such reservoirs. Well-test information such as average reservoir pressure, transmissivity, pore volume, storativity, formation damage, deliverability, distance to the boundary, and completion efficiency are some of the technical inputs into economic and operational decisions. Several key economic decisions that operators have to make are:Should the reservoir be exploited?How many wells are needed to develop the reservoir?Is artificial lift necessary (and if so, when)? The identification of morphological demarcation components such as impermeable barriers (faults, intersecting faults, facies changes, erosional unconformities, and structural generated depositional pinchouts) and constant-pressure boundaries (aquifer or gas-cap) from well testing help to establish the reservoir boundaries, shape, and volume. One must remember that the geological entrapment structure or sedimentological body does not always define the reservoir's limits. Our present study provides insight into wedge-shaped reservoirs in the Gulf of Mexico. Seismic exploration can define geological shapes in either two or three dimensions in the subsurface. These shapes are expressions of the preserved structural history and depositional environments and are verified by observations of such structures in outcrops and present-day depositional environments. From a sedimentological viewpoint, the following sedimentary deposits can exhibit wedge-shaped geometries. Preserved barchan sand dunes, reworked transgressive sands, barrier-island sands, offshore bars, alluvial fan deposits, delta-front sheet sands, and lenticular channel sands form the more plausible pinchout, wedge-shaped geological models recognized in the Gulf of Mexico sedimentary sequence. Wedge-Shaped Reservoirs Reviewing the petroleum engineering literature, we found very few technical papers addressing wedge-shaped reservoir geometries and their effects on reservoir performance. Their detailed analytical results are discussed and applied to the interpretations of our model results. An overview of the conceptual models is presented as a quick orientation to emphasize some model issues. Horne and Temeng1 were the first to address the problem of recognizing, discriminating, and locating reservoir pinchouts with the Green's functions method proposed by Gringarten and Ramey2 in pressure-transient analysis. The analytical solution considered a dimensionless penetration depth of the well. Their results showed that pinchout boundaries appear similar to constant-pressure boundaries with respect to pressure-drawdown behavior and not as a perpendicular sealing boundary. Yaxley3 presented a set of simple equations for calculating the stabilized inflow performance of a well in infinite rectangular and wedge-shaped drainage systems. The basis for Yaxley's mathematical model is the application of transient linear flow (as opposed to radial flow conditions assumed for the reservoir) and the mathematical difference between a plane source and a line source in linear-flow drainage systems for various rectangular drainage shapes. The equations were derived from transient linear-flow relationships for a well located between parallel no-flow boundaries. This concept was applied to intersecting no-flow boundaries and an outer circular, no-flow, constant-pressure boundary. His approach involved a constant ßr that is interpreted as an extra pressure drop relative to a well of radius ro (radial distance to the well location), which is a result of the distortion of the radial streamline pattern. Chen and Raghavan4 developed a solution to compute pressure distributions in wedge-shaped drainage systems using Laplace transforms. Their mathematical approach overcame existing limitations in some of the previous solutions, which were mentioned earlier. By applying the inversion theorem to the Laplace transformation, they verified that the slope of the pressure profile is inversely proportional to the wedge angle of the drainage system. An examination of their results is important to the interpretation of our own simulated pressure-response issues. Generally, their model solutions showed three radial-flow periods in the absence of wellbore-storage effects. The radial-flow periods showed that:During an initial radial-flow period, neither of the impermeable boundaries registered either singly or jointly.In the second phase, one or two boundaries became evident on the pressure signature.A third radial-flow period exhibited a semi logarithmic slope proportional to p/?o, where ?o=the angle of the wedge.
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Tang, Wen, Ying Gao, and Yi Ding. "Study on the Models of Water Shortage and its Simulation Analysis." Advanced Materials Research 807-809 (September 2013): 1653–57. http://dx.doi.org/10.4028/www.scientific.net/amr.807-809.1653.
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This paper introduces several mathematical models in order to analysis and solves the problem of the water shortage in China. Some economic strategies have been concluded for government. The strategies include adjusting water fee, constructing reservoirs and water transfer.
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Pérez Carrillo, Edgar Ricardo, José Francisco Zapata Arango, and Nicolás Santos Santos. "A NEW METHOD FOR THE EXPERIMENTAL DETERMINATION OF THREE-PHASE RELATIVE PERMEABILITIES." CT&F - Ciencia, Tecnología y Futuro 3, no. 4 (December 31, 2008): 23–43. http://dx.doi.org/10.29047/01225383.461.
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Petroleum reservoirs under primary, secondary or tertiary recovery processes usually experience simultaneous flow of three fluids phases (oil, water and gas). Reports on some mathematical models for calculating three-phase relative permeability are available in the Literature. Nevertheless, many of these models were designed based on certain experimental conditions and reservoir rocks and fluids. Therefore, special care has to be taken when applying them to specific reservoirs. At the laboratory level, three-phase relative permeability can be calculated using experimental unsteady-state or steady state methodologies. This paper proposes an unsteady-state methodology to evaluate three-phase relative permeability using the equipment available at the petrophysical analysis Laboratory of the Instituto Colombiano del Petróleo (ICP) of Ecopetrol S.A. Improvements to the equipment were effected in order to achieve accuracy in the unsteady-state measurement of three-phase relative permeability. The target of improvements was directed toward to the attainment of two objectives:1) the modification of the equipment to obtain more reliable experimental data and 2) the appropriate interpretation of the data obtained. Special attention was given to the differential pressure and uncertainty measurement in the determination of fluid saturation in the rock samples. Three experiments for three-phase relative permeability were conducted using a sample A and reservoir rock from the Colombian Foothills. Fluid tests included the utilization of synthetic brine, mineral oil, reservoir crude oil and nitrogen. Two runs were conducted at the laboratory conditions while one run was conducted at reservoir conditions. Experimental results of these tests were compared using 16 mathematical models of three-phase relative permeability. For the three-phase relative permeability to oil, the best correlations between experimental data and tests using Blunt, Hustad Hasen, and Baker's models were obtained at oil saturations between 40% and 70%.
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A. I., Sukhinov, Protsenko S.V., and Panasenko N. D. "MATHEMATICAL MODELING AND ECOLOGICAL DESIGN OF THE MARINE SYSTEMS TAKING INTO ACCOUNT MULTI-SCALE TURBULENCE USING REMOTE SENSING DATA." Computational Mathematics and Information Technologies 1, no. 3 (December 31, 2022): 104–13. http://dx.doi.org/10.23947/2587-8999-2022-1-3-104-113.
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The paper considers a mathematical model of biological kinetics and geochemical cycles based on a system of convection-diffusion equations with nonlinear coefficients, supplemented by a spatially inhomogeneous three-dimensional mathematical model of wave hydrodynamics of a shallow reservoir, with a refined coefficient of turbulent vertical exchange. The task of monitoring the water surface in order to detect phytoplankton spots involves the creation and verification of effective methods for clustering these objects on the surface of reservoirs, in particular, restoring their boundaries based on remote sensing data. The article uses multispectral satellite images as sounding data. Based on the obtained images of plankton populations, the initial conditions for mathematical models of biogeochemical cycles can be determined, on the basis of which prognostic calculations are performed.
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Cui, Jiangfeng, and Long Cheng. "Liquid Storage Characteristics of Nanoporous Particles in Shale: Rigorous Proof." Energies 12, no. 20 (October 19, 2019): 3985. http://dx.doi.org/10.3390/en12203985.
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Different from conventional reservoirs, a significant proportion of oil is in an adsorbed or even immobile state in shale and tight rocks. There are established comprehensive mathematical models quantifying the adsorbed, immobile, and free oil contents in shale rocks. However, the conclusions of the monotonicity of the complicated models from sensitivity analysis might not be universal, and rigorous mathematical derivation is needed to demonstrate their rationale. In this paper, the models for oil/water storage in the nanoporous grains in shale, i.e., kerogen and clay, are achieved based on the aforementioned storage models. Rigorous analytical derivations are employed to strictly prove the monotonicity of the immobile and adsorbed models, which is the main purpose of this work. This work expands the applicability of the storage models, is fundamental and important for mobility analysis in shale reservoirs, and can shed light on its efficient exploration and development.
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Prajapati, Srichand, and Eswaran Padmanabhan. "Application of Machine Learning for Shale Reservoir Permeability Prediction." IOP Conference Series: Earth and Environmental Science 1003, no. 1 (April 1, 2022): 012025. http://dx.doi.org/10.1088/1755-1315/1003/1/012025.
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Abstract Due to ultra-low permeability, the characterization of shale reservoir is always being a challenge. The traditional models are insufficient to estimate the ultra-low permeability of shale reservoirs. Based on Machine Learning, we proposed a simple mathematical approach to predict the permeability of shale reservoirs. Machine-learning techniques are good options for generating a rapid, robust, and cost-effective permeability prediction because of their strengths to deliver the variables. Additionally, used the Kozeny’s equation with power mean approach to constraint the estimated permeability for more reliable. To do this, we used a pure shale well-log downloaded from open source. The results show that the predicted permeability is well correlated with the neutron log and significantly match with the other well-logs.
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Araujo Guerrero, Edson Felipe, Cristhian Bernardo Morales–Monsalve, Guillermo Arturo Alzate Espinosa, and Alejandra Arbelaez Londoño. "Numerical model for predicting and evaluating sand production in weakly consolidated reservoirs." DYNA 89, no. 220 (March 24, 2022): 54–63. http://dx.doi.org/10.15446/dyna.v89n220.97093.
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Sand production is a common phenomenon in oil and gas reservoirs, which occurs when reservoir fluids exert a sufficient drag force on reservoir rocks to erode the matrix. Numerical models for sand production have been used to understand the sanding mechanisms and forecast sand-production potential of formations to design well completion, optimize production, and prevent setbacks in future operations. This paper presents a mathematical model for defining the conditions of sanding onset as well as to predict and quantify the sand rate. We also introduce fluid-flow coupling and a geomechanical and sand-production model. By using the proposed model and a set of experimental data, sanding-related variables are analyzed, and a matching process for the simulated results and forecast analysis are performed. The results show that elastoplastic constitutive models are indispensable, and a clear relationship exists between the sanding and plastic strains.
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Belozerov, Ivan, and Marsel Gubaydullin. "Concept of technology for determining the permeability and porosity properties of terrigenous reservoirs on a digital rock sample model." Journal of Mining Institute 244 (July 30, 2020): 402–7. http://dx.doi.org/10.31897/pmi.2020.4.2.
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The aim of the article is to form the concept of technology for determining the permeability and porosity properties of terrigenous reservoirs using mathematical modeling methods on a digital rock sample model.
Digital rock sample modeling is used to assess geological oil reserves. The article presents the concept of digital rock sample modeling technology, which allows carrying out qualitative investigations to determine the permeability and porosity characteristics of the formation, including modeling the pore space and filtration processes. The essence of the concept is that the simulation model of the microstructure for the digital model is formed on the basis of a large number of parameters obtained during lithological and petrographic investigations of thin sections, a study of the sludge and geophysical investigations of wells.
The acquired model can be used as a basis for subsequent modeling of filtration processes. Conductivity of single channels of the formed model can be calculated using molecular dynamics methods, models of Boltzmann's lattice equations, and other mathematical models and methods.
Based on the results of the study carried out, the application of stochastic packing methods for modeling the structure of the pore space in the digital rock sample model of terrigenous reservoirs is substantiated.
In connection with the development of computer and nanotechnologies and their use in the oil and gas industry, solutions that allow obtaining adequate results of digital rock sample models are of high importance and relevance for the production sector. It is especially important to use digital rock sample models in the study of reservoir rocks of shelf fields in the western part of the Russian Arctic, oil shales, rocks represented by loose weakly cemented reservoirs, and others, which are complex for physical experiments.
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Wu, Yu-Shu, Jianfang Li, Didier-Yu Ding, Cong Wang, and Yuan Di. "A Generalized Framework Model for the Simulation of Gas Production in Unconventional Gas Reservoirs." SPE Journal 19, no. 05 (April 4, 2014): 845–57. http://dx.doi.org/10.2118/163609-pa.
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Summary Unconventional gas resources from tight-sand and shale gas reservoirs have received great attention in the past decade around the world because of their large reserves and technical advances in developing these resources. As a result of improved horizontal-drilling and hydraulic-fracturing technologies, progress is being made toward commercial gas production from such reservoirs, as demonstrated in the US. However, understandings and technologies needed for the effective development of unconventional reservoirs are far behind the industry needs (e.g., gas-recovery rates from those unconventional resources remain very low). There are some efforts in the literature on how to model gas flow in shale gas reservoirs by use of various approaches—from modified commercial simulators to simplified analytical solutions—leading to limited success. Compared with conventional reservoirs, gas flow in ultralow-permeability unconventional reservoirs is subject to more nonlinear, coupled processes, including nonlinear adsorption/desorption, non-Darcy flow (at both high flow rate and low flow rate), strong rock/fluid interaction, and rock deformation within nanopores or microfractures, coexisting with complex flow geometry and multiscaled heterogeneity. Therefore, quantifying flow in unconventional gas reservoirs has been a significant challenge, and the traditional representative-elementary-volume- (REV) based Darcy's law, for example, may not be generally applicable. In this paper, we discuss a generalized mathematical framework model and numerical approach for unconventional-gas-reservoir simulation. We present a unified framework model able to incorporate known mechanisms and processes for two-phase gas flow and transport in shale gas or tight gas formations. The model and numerical scheme are based on generalized flow models with unstructured grids. We discuss the numerical implementation of the mathematical model and show results of our model-verification effort. Specifically, we discuss a multidomain, multicontinuum concept for handling multiscaled heterogeneity and fractures [i.e., the use of hybrid modeling approaches to describe different types and scales of fractures or heterogeneous pores—from the explicit modeling of hydraulic fractures and the fracture network in stimulated reservoir volume (SRV) to distributed natural fractures, microfractures, and tight matrix]. We demonstrate model application to quantify hydraulic fractures and transient flow behavior in shale gas reservoirs.
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Semerak, Mykhailo, Sergii Pozdeev, Roman Yakovchuk, Olga Nekora, and Oleksandr Sviatkevych. "Mathematical modeling of thermal fire effect on tanks with oil products." MATEC Web of Conferences 247 (2018): 00040. http://dx.doi.org/10.1051/matecconf/201824700040.
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The aim of the work is the development of mathematical models for research that allows to determine the ultimate indicators of the thermal effect on tanks with oil products in a fire. A calculation method was developed to implement the calculation for various scenarios for the development of a fire in a tank with oil. After the calculations, the results of mathematical modeling of the temperature on the walls of the reservoir in the conditions of a fire in neighboring reservoirs in the form of temperature distributions were obtained. Analysis of the temperature distributions showed that the most dangerous scenario is when the fire occurs according to scheme No. 3 in the case of burning an oil torch at a temperature of 1500 K. In each case, the maximum temperature of heating the tank wall is almost unaffected by the oil, which is confirmed by the curves of the maximum temperature curves heating of the reservoir wall, depending on the time of fire impact on adjacent tanks. The maximum temperature of the reservoir wall was determined at the place of its connection with the oil product, it is preserved.
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Panasenko, Natalia, Marina Ganzhur, Alexey Ganzhur, and Vladimir Fathi. "Multichannel satellite image application for water surface objects identification." E3S Web of Conferences 210 (2020): 07005. http://dx.doi.org/10.1051/e3sconf/202021007005.
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The paper is devoted to the analysis of methods of adoption of satellite observation data in order to identify the required information used in the development and verification of mathematical models of hydrodynamics and biological kinetics of shallow water reservoirs. For the information accumulation, we consider the use of remote sensing data. The aim of the paper is to identify the best implementation method for software tools in order to improve the quality of assimilation of date of satellite sensing of the Earth relating to hydrobiological processes in a shallow water reservoir.
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Al Rbeawi, Dr Salam. "The impact of closed perforation zones and damaged sections on flow dynamics and pressure behaviors of horizontal wells." Journal of Petroleum Research and Studies 7, no. 2 (May 6, 2021): 1–28. http://dx.doi.org/10.52716/jprs.v7i2.185.
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Horizontal wells with multiple completion parts have become a common completion technique in the oil and gas industry. Sand and asphalt production problems, damaged zones and water cresting or gas coning are the main reasons for using this technique to sustain or improve oil and gas recovery. However, using such completion technique introduces negative effects on pressure behavior of horizontal wells.This paper introduces new mathematical models for horizontal well containing several closed completed sections acting in finite and infinite reservoirs. These models can be used to evaluate the impact of the completion techniques on both pressure behaviors and flow regimes either in the vicinity of wellbore or at the outer boundary of reservoirs. They can be used also to investigate the change in productivity index that would result due to the usage of certain type of completion technique. In this research, the completed sections (cemented or isolated parts) and the places where packers are installed are considered as no-flow sections. These sections are expected to increase pressure drop required for flowing reservoir fluid toward wellbore. They are also expected to change flow regimes mainly in the vicinity of wellbore.Several models have been developed and solved in this study for different completion techniques, wellbore conditions and reservoir configuration. It has been found that the great impact of completion techniques is observed on flow regimes that commonly develop in the drainage area close to wellbore. This impact shows similar trends to the skin factor. Several new flow regimes have been observed, one of them has been developed due to the existence of closed completed sections which is intermediate or second radial flow regime. This flow regime can be found for some cases of long wellbore having multi-short perforated sections. The study will introduce the mathematical models for known and newly developed flow regimes for horizontal well including the completion technique.
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Ren, Long, Wendong Wang, Yuliang Su, Mingqiang Chen, Cheng Jing, Nan Zhang, Yanlong He, and Jian Sun. "Multiporosity and Multiscale Flow Characteristics of a Stimulated Reservoir Volume (SRV)-Fractured Horizontal Well in a Tight Oil Reservoir." Energies 11, no. 10 (October 11, 2018): 2724. http://dx.doi.org/10.3390/en11102724.
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There are multiporosity media in tight oil reservoirs after stimulated reservoir volume (SRV) fracturing. Moreover, multiscale flowing states exist throughout the development process. The fluid flowing characteristic is different from that of conventional reservoirs. In terms of those attributes of tight oil reservoirs, considering the flowing feature of the dual-porosity property and the fracture network system based on the discrete-fracture model (DFM), a mathematical flow model of an SRV-fractured horizontal well with multiporosity and multipermeability media was established. The numerical solution was solved by the finite element method and verified by a comparison with the analytical solution and field data. The differences of flow regimes between triple-porosity, dual-permeability (TPDP) and triple-porosity, triple-permeability (TPTP) models were identified. Moreover, the productivity contribution degree of multimedium was analyzed. The results showed that for the multiporosity flowing states, the well bottomhole pressure drop became slower, the linear flow no longer arose, and the pressure wave arrived quickly at the closed reservoir boundary. The contribution ratio of the matrix system, natural fracture system, and network fracture system during SRV-fractured horizontal well production were 7.85%, 43.67%, and 48.48%, respectively in the first year, 14.60%, 49.23%, and 36.17%, respectively in the fifth year, and 20.49%, 46.79%, and 32.72%, respectively in the 10th year. This study provides a theoretical contribution to a better understanding of multiscale flow mechanisms in unconventional reservoirs.
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Ning, Bo, Jiafeng Xu, Jing Jiang, and Minhua Cheng. "Transient pressure behavior of horizontal well in gas reservoirs with arbitrary boundary." Energy Exploration & Exploitation 38, no. 6 (August 26, 2020): 2370–88. http://dx.doi.org/10.1177/0144598720953255.
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Transient pressure analysis is a crucial tool to forecast the production performance during the exploration and production process in gas reservoirs. Usually, a regular shaped outer boundary is assumed in previous studies for well-testing analysis, which is just a simplification of practical cases and cannot reflect the actual boundaries of reservoirs. In this paper, a mathematical model is established to analyze the transient pressure behaviors of a horizontal well in an arbitrarily shaped gas reservoir. Dimensionless treatment, Laplace transformation, and boundary element method are applied in solving the model, which is verified by comparing with the results from the source function method. Based on the Stehfest numerical inversion method, the models of single-porosity media and dual-porosity media are solved respectively. Then, the time-domain curves of pseudo pressure and its derivative are obtained, and the flow regimes are identified. Finally, the impacts of some critical parameters on pressure transient behaviors are analyzed, including storativity ratio, interporosity coefficient, well length, and well orientation. This paper presents an effective way to handle complex external boundary problems in gas reservoirs.
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Uzun, Ilkay, Basak Kurtoglu, and Hossein Kazemi. "Multiphase Rate-Transient Analysis in Unconventional Reservoirs: Theory and Application." SPE Reservoir Evaluation & Engineering 19, no. 04 (May 18, 2016): 553–66. http://dx.doi.org/10.2118/171657-pa.
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Summary In unconventional reservoirs, production data are generally analyzed by use of rate-transient techniques derived from single-phase linear-flow models. Such linear-flow models use rate-normalized pressure, which is pressure drop divided by reservoir-flow rate vs. square root of time. In practice, the well-fluid production includes water, oil, and gas. The oil can be light oil, volatile oil, and gas/condensate as in the Bakken, Eagle Ford, and Barnett, respectively. Thus, single-phase analysis needs modification to account for production of fluid mixtures. In this paper, we present a multiphase-pressure-diffusivity equation to analyze multiphase flow in single- and dual-porosity models of unconventional reservoirs. Our approach is similar to the work presented by Perrine (1956); however, our approach has a theoretical foundation, whereas Perrine (1956) used pragmatic engineering analogy for constant flow rate in vertical wells only. In addition to oil, gas, and formation brine, our method accounts for gas/condensate production, and the flowback of the injected hydraulic-fracturing fluids. Overall, our proposed approach is more comprehensive than the single-phase models but maintains the simplicity of the conventional methods. Our paper includes diagnostic plots of rate-normalized well pressure for light oils and gas/condensates in unconventional reservoirs. Data from two Bakken and two Eagle Ford wells will be presented to demonstrate the usefulness of our approach. In addition to the mathematical analysis of flow-rate and pressure data, we will present the effect of well-stimulation and fluid-lift methods on the flow-rate characteristics of Bakken and Eagle Ford wells.
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Barros-Galvis, Nelson, Pedro Villaseñor, and Fernando Samaniego. "Analytical Modeling and Contradictions in Limestone Reservoirs: Breccias, Vugs, and Fractures." Journal of Petroleum Engineering 2015 (April 30, 2015): 1–28. http://dx.doi.org/10.1155/2015/895786.
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Modeling of limestone reservoirs is traditionally developed applying tectonic fractures concepts or planar discontinuities and has been simulated dynamically without considering nonplanar discontinuities as sedimentary breccias, vugs, fault breccias, and impact breccias, assuming that all these nonplanar discontinuities are tectonic fractures, causing confusion and contradictions in reservoirs characterization. The differences in geometry and connectivity in each discontinuity affect fluid flow, generating the challenge to develop specific analytical models that describe quantitatively hydrodynamic behavior in breccias, vugs, and fractures, focusing on oil flow in limestone reservoirs. This paper demonstrates the differences between types of discontinuities that affect limestone reservoirs and recommends that all discontinuities should be included in simulation and static-dynamic characterization, because they impact fluid flow. To demonstrate these differences, different analytic models are developed. Findings of this work are based on observations of cores, outcrops, and tomography and are validated with field data. The explanations and mathematical modeling developed here could be used as diagnostic tools to predict fluid velocity and fluid flow in limestone reservoirs, improving the complex reservoirs static-dynamic characterization.
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Ombaki, Richard, and Joash Kerongo. "Formulated Mathematical Model for Delayed Particle Flow in Cascaded Subsurface Water Reservoirs with Validation on River Flow." Journal of Applied Mathematics 2022 (November 10, 2022): 1–11. http://dx.doi.org/10.1155/2022/3438200.
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Migration of pollutant particles into subsurface water reservoirs through point sources is largely involved mixing processes within the system of water flow. Possible potential sources of pollution to these point sources include municipal wastes, septic loads, landfills, uncontrolled hazardous wastes, and sewage storage tanks. The mixing processes of pollutant significantly alter their predictive rate of flow in the water reservoirs, and therefore the time inherent in mixing processes need to be accounted for. In this study, pollution of subsurface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied through a conceptual perspective of mixing problem processes in water tanks. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of water reservoir pollution that involve single species contaminants such as nitrates, phosphorous, and detergents injecting from a point source. The concentration x t of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. The major assumption made in modeling of mixing problems using tanks is that mixing is instantaneous. Practical realities dictate that mixing cannot occur instantaneously throughout the tank. So as to accommodate these realities, the study refined the systems of ordinary differential equations (ODEs) generated from principles of mixing problems in cascading tanks, into a system of delayed differential equations (DDEs) so that the concentration of pollutant leaving the reservoir at time t would be equal to the average concentration at some earlier instant, t − τ for the delay τ > 0 . The formulated model is a mathematical discrete time delay model which can be used to describe the dynamics of subsurface water reservoir pollution through a point source. The model was simulated on municipal River Nyakomisaro in Kisii County, Kenya. Physical and kinematic parameters of the river (cross-sectional lengths, depths, flow velocities) at three river sectional reservoirs were measured and the obtained parameter values were then used to evaluate coefficients of the formulated model equation. The system of DDEs from this simulation was solved numerically on MATLAB using dde23 software. From the graphical views generated for concentration of pollutant x t versus time t , it was established that the developed DDEs cover longer time series solutions (characteristic curves) than that from the corresponding ODEs in the same reservoir indicating that time necessary for particle flow through water reservoirs is underestimated if ODEs are used to describe particle flow. Also, the graphical views indicated similar tendencies (characteristics) in particle flow with time elapse even though initial values of concentration x t were different for every potentially recognized single species pollutant considered in each river reservoir. Hence, longer values of time t will imply more pollution in the water reservoir and vice versa. By introducing time delays due to constituent mixing processes in water quality simulation models that make use of advection-diffusion equation such as Qual2kw, the findings of this study can help for better understanding of the contaminant’s accumulation levels and their rate of transport in water resource. These will assist, for example, water-quality protection agencies such as Environmental Protection Agency (EPA), World Health Organization (WHO), and National Environmental Management Authority (NEMA) for the need to generate efficient and effective remedial strategies to control or mitigate hazardous or risks arising from water pollution.
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Paterson, Lincoln. "A REVIEW OF COMPUTER MODELS TO CHARACTERISE HETEROGENEITY IN PETROLEUM BASINS." APPEA Journal 33, no. 1 (1993): 322. http://dx.doi.org/10.1071/aj92023.
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Heterogeneity is a major problem in the evaluation of petroleum reservoirs. Yet the search for oil requires increasingly complex reservoirs to be evaluated. It is often necessary to interpolate sparse data, which may be performed inaccurately.One approach to this problem has resulted in the development of a number of computer models that produce statistically correct interpolation of data. Two types of models exist, namely process and response. Process models attempt to build sedimentary formations from the physical processes involved in deposition, such as aggradation, avulsion, compaction and tectonism. Response models are founded on existing data, and use purely mathematical techniques to interpolate values, such as kriging and fractal methods.It is the aim of this paper to review these computer models for description of stratal geometries in petroleum basins, pointing out their strengths and weaknesses. Most of the process models have historically focussed on marine clastics and carbonate deposits, and are limited to two dimensions, or treat the third dimension simplistically. Response models on the other hand do not consider depositional processes, and have tended to smooth the data. Fractal statistics have attempted to overcome the smoothing problem, but many formations do not appear to be described by simple fractals.Compared to other topics in numerical simulation, modelling of sedimentary deposition is in its infancy. However, great opportunities exist to make significant developmental advances. Adequate description of reservoir geometry should improve success rates in exploration and assist in development strategies.
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Gu, Shaohua, Yunqing Shi, and Zhangxin Chen. "Numerical Simulation of Fracture Permeability Change in Production of Pressure-sensitive Reservoirs with In-situ Stress Field." Open Petroleum Engineering Journal 8, no. 1 (October 22, 2015): 440–50. http://dx.doi.org/10.2174/1874834101508010440.
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In pressure sensitive reservoirs, interaction effects among the porous media flow field, the fracture field and the stress field can cause some specific flow characteristics entirely different from those in conventional reservoirs. Dynamic fracture behavior is one of them, which generates a change in the value of fracture aperture and even a variation in the anisotropy of permeability. In this paper, we focus on the dynamic behavior of fractures and some affecting factors, including driving pressure and in-situ stress. Numerical discrete fracture network (DFN) models are built and solved by the finite element method to investigate what the range-ability the fracture presents and what impact these affecting factors have. In these mathematical models, both dynamic fractures and the fluid-solid coupling are taken into account, and a stress-strain model, a flow field model and a fluid-solid coupling model are included. Based on the models, the variation of fracture aperture in pressure sensitive reservoirs is studied and the results show that a different direction and connectivity of fractures lead fracture dilation to varying degrees as pressure changes so that the idea of anisotropic fracture porosity is proposed for reservoir scale simulation. The study also indicates that the drop of formation pressure determines the conductivity of fractures and anisotropy of permeability but just has a slight impact on the direction of principal permeability. Finally, the study shows the interaction of the in-situ stress pressure and the fracture field.
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Otchere, Daniel Asante, Mohammed Abdalla Ayoub Mohammed, Tarek Omar Arbi Ganat, Raoof Gholami, and Zulkifli Merican Aljunid Merican. "A Novel Empirical and Deep Ensemble Super Learning Approach in Predicting Reservoir Wettability via Well Logs." Applied Sciences 12, no. 6 (March 14, 2022): 2942. http://dx.doi.org/10.3390/app12062942.
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Accurately measuring wettability is of the utmost importance because it influences several reservoir parameters while also impacting reservoir potential, recovery, development, and management plan. As such, this study proposes a new formulated mathematical model based on the correlation between the Amott-USBM wettability measurement and field NMR T2LM log. The exponential relationship based on the existence of immiscible fluids in the pore space had a correlation coefficient of 0.95. Earlier studies on laboratory core wettability measurements using T2 distribution as a function of increasing water saturation were modified to include T2LM field data. Based on the trends observed, water-wet and oil-wet conditions were qualitatively identified. Using the mean T2LM for the intervals of interest and the formulated mathematical formula, the various wetting conditions in existence were quantitatively measured. Results of this agreed with the various core wettability measurements used to develop the mathematical equation. The results expressed the validity of the mathematical equation to characterise wettability at the field scale. With the cost of running NMR logs not favourable, and hence not always run, a deep ensemble super learner was employed to establish a relationship between NMR T2LM and wireline logs. This model is based on the architecture of a deep learning model and the theoretical background of ensemble models due to their reported superiority. The super learner was developed using nine ensemble models as base learners. The performance of nine ensemble models was compared to the deep ensemble super learner. Based on the RMSE, R2, MAE, MAPD and MPD the deep ensemble super learner greatly outperformed the base learners. This indicates that the deep ensemble super learner can be used to predict NMR T2LM in the field. By applying the methodology and mathematical formula proposed in this study, the wettability of reservoirs can be accurately characterised as illustrated in the field deployment.
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Jiang, Ruizhong, Jianchun Xu, Zhaobo Sun, Chaohua Guo, and Yulong Zhao. "Rate Transient Analysis for Multistage Fractured Horizontal Well in Tight Oil Reservoirs considering Stimulated Reservoir Volume." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/489015.
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A mathematical model of multistage fractured horizontal well (MsFHW) considering stimulated reservoir volume (SRV) was presented for tight oil reservoirs. Both inner and outer regions were assumed as single porosity media but had different formation parameters. Laplace transformation method, point source function integration method, superposition principle, Stehfest numerical algorithm, and Duhamel’s theorem were used comprehensively to obtain the semianalytical solution. Different flow regimes were divided based on pressure transient analysis (PTA) curves. According to rate transient analysis (RTA), the effects of related parameters such as SRV radius, storativity ratio, mobility ratio, fracture number, fracture half-length, and fracture spacing were analyzed. The presented model and obtained results in this paper enrich the performance analysis models of MsFHW considering SRV.
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Martyushev, Dmitriy A., Inna N. Ponomareva, and Vladislav I. Galkin. "Conditions for Effective Application of the Decline Curve Analysis Method." Energies 14, no. 20 (October 9, 2021): 6461. http://dx.doi.org/10.3390/en14206461.
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Determining the reliable values of the filtration parameters of productive reservoirs is the most important task in monitoring the processes of reserve production. Hydrodynamic studies of wells by the pressure build-up method, as well as a modern method based on production curve analysis (Decline Curve Analysis (DCA)), are some of the effective methods for solving this problem. This paper is devoted to assessing the reliability of these two methods in determining the filtration parameters of terrigenous and carbonaceous productive deposits of oil fields in the Perm Krai. The materials of 150 conditioned and highly informative (obtained using high-precision depth instruments) studies of wells were used to solve this problem, including 100 studies conducted in terrigenous reservoirs (C1v) and 50 carried out in carbonate reservoirs (C2b). To solve the problem, an effective tool was used—multivariate regression analysis. This approach is new and has not been previously used to assess the reliability of determining the filtration parameters of reservoir systems by different research methods. With its use, a series of statistical models with varying degrees of detail was built. A series of multivariate mathematical models of well flow rates using the filtration parameters determined for each of the methods is constructed. The inclusion or non-inclusion of these filtration parameters in the resulting flow rate models allows us to give a reasonable assessment of the possibility of using the pressure build-up method and the DCA method. All the constructed models are characterized by high statistical estimates: in all cases, a high value of the determination coefficient was obtained, and the probability of an error in all cases was significantly less than 5%. As applied to the fields under consideration, it was found that both methods demonstrate stable results in terrigenous reservoirs. The permeability determined by the DCA method and the pressure build-up curve does not control the flow of the fluid in carbonate reservoirs, which proves the complexity of the filtration processes occurring in them. The DCA method is recommended for use to determine the permeability and skin factor in the conditions of terrigenous reservoirs.
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Katanov, Yu E. "A probabilistic and statistical model of rock deformation." E3S Web of Conferences 266 (2021): 03011. http://dx.doi.org/10.1051/e3sconf/202126603011.
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A new approach to the study of strength characteristics of the rocks on the basis of probabilistic and statistical models of the deformation processes (models of dilatancy initiation processes) under conditions of uncertainty is presented. The main purpose of the study is to create geological and mathematical tools, which could be used to study the development of volumetric deformation (dilatancy, disintegration) of reservoirs at a constant tension, acting on the array. The information and analytical basis of the performed study consists of methods of mathematical statistics and probability theory and the sedimentary rocks research methods. The probabilistic-statistical approach is formed in the study of deformation processes of the productive stratum structure, taking into account the degree of heterogeneity of the reservoirs. The obtained analytical expressions allow us to determine the moment of the beginning of the volumetric deformation process (dilatancy, disintegration) in the rock, similar to the identification of the bifurcation point in the development of geological and dynamic systems
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Bouaanani, Najib, Patrick Paultre, and Jean Proulx. "Dynamic response of a concrete dam impounding an ice-covered reservoir: Part I. Mathematical modelling." Canadian Journal of Civil Engineering 31, no. 6 (December 1, 2004): 956–64. http://dx.doi.org/10.1139/l04-075.
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This paper examines the dynamic response of a concrete dam impounding an ice-covered reservoir and subjected to forced-vibration testing. The analytical research presented is a follow-up to an extensive dynamic testing program carried out on a 84-m high concrete gravity dam located in northeastern Quebec, Canada, under harsh winter conditions, including a 1.0- to 1.5-m-thick ice sheet covering the reservoir. One of the major challenges encountered when analyzing ice-dam-reservoir-foundation interaction is modelling the complex nature of the ice and the boundary conditions governing reservoir motion. The problem is further complicated because there are little or no appropriate experimental data and observational evidence relevant to ice-dam interaction processes. Some of these challenges are addressed herein using a two-dimensional analytical approach, which investigates the effects due to ice cover, water compressibility, and reservoir bottom absorption. A frequency-domain substructure method technique is used and a new boundary condition along the ice-cover-reservoir interface is proposed. The technique developed is implemented in a finite element code specialized in the seismic analysis of concrete dams. Numerical results are discussed in the companion paper in this issue. Key words: gravity dams, concrete dams, ice, reservoirs, mathematical models, ice-structure interaction, fluid-structure interaction, forced-vibration testing, finite elements modelling.
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Wang, Yuhan, Zhengdong Lei, Zhenhua Xu, Jie Liu, Xiaokun Zhang, Erhui Luo, Yuqi Liu, and Pengcheng Liu. "A Novel Mathematical Model for Fracturing Effect Evaluation Based on Early Flowback Data in Shale Oil Reservoirs." Geofluids 2021 (December 16, 2021): 1–14. http://dx.doi.org/10.1155/2021/1780937.
Full textAbstract:
For shale oil reservoirs, the horizontal well multistage fracturing technique is mostly used to reform the reservoir in order to achieve economic and effective development. The size of the reservoir reconstruction volume and the quantitative characterization of the fracture system are of great significance to accurately predict the productivity of shale oil wells. There are few flowback models for shale oil reservoirs. To solve this problem, first, a physical model of the simultaneous production of oil, gas, and water in the early flowback stage of shale oil development is established using the material balance equation for a fracture system. Second, the physical model of the underground fracture system is simplified, which is approximately regarded as a thin cylindrical body with a circular section. The flow of the fluid in the fracture system is approximately regarded as radial flow. In this model, the expansion of the fluid and the closure of the fracture are defined as integrated storage coefficients to characterize the storage capacity of the fracture system. Then, the curves illustrating the relationships between the oil-water ratio and the cumulative oil production and between the gas-water ratio and the cumulative gas production are drawn, and the curves are used to divide the flowback stage into an early stage and a late stage because the flowback process of shale oil wells exhibits obvious stage characteristics. Finally, the reservoir reconstruction volume and the related hydraulic fracture parameters are estimated based on the material balance method, and the rationality of the model is verified via numerical simulation. The interpretation results of this novel model are more accurate, making it an effective way to evaluate the hydraulic fracture parameters and transformation effect, and it has guiding significance for the evaluation of the hydraulic fracturing effect in the field.
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Gilmanov, Alexander Ya, Tatyana N. Kovalchuk, and Alexander P. Shevelev. "Physical and mathematical modeling of cyclic steam stimulation for oil reservoirs." Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy 6, no. 1 (2020): 176–91. http://dx.doi.org/10.21684/2411-7978-2020-6-1-176-191.
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This article discusses the construction of a physical and mathematical model of the steam cycle effect on oil reservoirs. Existing models require calculations in hydrodynamic simulators or significantly simplify the description of the motion of the heat front. Within the framework of the proposed model, a number of assumptions are introduced regarding the movement of the thermal interface between the heated oil located in the bottomhole zone and the oil whose temperature is equal to the initial one. It is assumed that this boundary has the form of a straight line in a rectangular coordinate system. Moreover, at the initial moment of time, the straight line is determined by two points: the value of the maximum power taken on the vertical axis, directed downward, and the maximum radius of heating on the horizontal axis. In the future, these parameters are reduced. It is assumed that over time, the interface between the “cold” and heated oil shifts parallel to its initial position with a decrease in the parameters that determine it. This approach to describing the displacement over time of this boundary is proposed for the first time. The purpose of the article is to determine the flow rate of the well in the case of steam-thermal treatment of the formation, taking into account the size of the heated zone. In particular, the coolant injection cycle time and the characteristic time of the steam and thermal impregnation for the proposed model are determined. The physical processes considered during the construction of this model are described by conservation laws. The calculation of the area in which the heated oil will be located takes into account parameters such as flow rate and heat content of the coolant, reservoir thickness and thermal properties of the surrounding rocks. The article discusses the issues related to the relevance of the application of the methodology of vapor-cyclical effects on oil reservoirs. The result of the developed model is the dependence of the oil production rate on time for the cyclic treatment of bottom-hole zones of wells. The proposed method allows us to analyze the development efficiency depending on the main technological parameters. Such calculations allow you to choose the most optimal development strategy, and therefore, increase oil recovery.
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Pourpak, Hamid, Bernard J. Bourbiaux, Frédéric Roggero, and Frederick Delay. "An Integrated Methodology for Calibrating a Heterogeneous/Fractured Reservoir Model From Wellbore Flow Measurements: Case Study." SPE Reservoir Evaluation & Engineering 12, no. 03 (May 31, 2009): 433–45. http://dx.doi.org/10.2118/113528-pa.
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Summary Reliable flow modeling of highly heterogeneous/fractured reservoirs necessarily goes through the calibration of poorly determined geological and/or petrophysical parameters to field flow measurements. To that end, optimization procedures based on gradient methods or on gradual-deformation techniques have been developed in recent years. This paper proposes a sequential method combining those two approaches. The case under consideration is a water-bearing reservoir constituted of heterogeneous, karstic and fractured limestones located near Poitiers, France. In a preliminary step, drilling, core, and log data acquired in approximately 30 wells were integrated into a geostatistical facies model used as the support for flow simulation. First the facies petrophysical properties of this model were calibrated to well pumping and interference responses within a gradient-based inversion loop. Flow responses could be reproduced, with the exception of a few "problematic" observation wells. Second the gradual-deformation method was applied, globally then locally, to improve the distribution of facies while keeping the previously optimized petrophysical properties. The problematic wells' responses could be reproduced better without altering the other wells' match. Furthermore, that good match of calibration wells was obtained on a simplified geostatistical model involving fewer facies than in the initial model. The gradual-deformation method then appears as a robust and effective approach to find a model best matching a set of flow data among equiprobable geostatistical models. To conclude, the sequential-modeling method demonstrated herein is an effective way to actually integrate geological and flow data and to link geosciences and reservoir-engineering skills, for setting up consistent models of hardly tractable highly heterogeneous reservoirs. Introduction During the past 20 years, the technique of mathematical modeling has been used extensively in the study of groundwater-resources management and aquifer remediation (Sun 1994). Concern was especially focused on fluid transfer in heterogeneous and/or fractured reservoirs. That resulted in conclusive advances in the characterization and modeling of fractured reservoirs (Cacas et al. 2001). Actually, wellbore information on underground reservoir heterogeneities and fractures (e.g., core descriptions, image logs, and production profiles) is now used to condition the geostatistical pixel-based models or the object-based stochastic models of these reservoirs and to calibrate the hydraulic properties of major flow heterogeneities such as fractures (Sarda et al. 2002). However, the problem of reservoir-model construction remains highly undetermined. The purpose of this paper is to design and validate an inversion method for calibrating the poorly defined flow models of highly heterogeneous reservoirs to wellbore dynamic data. The design and the application of that method are performed on an experimental hydrogeological site (EHS) settled on a karstic and fractured limestone aquifer located near Poitiers, France. The flow model is based on a geostatistical distribution of facies. The method involves two successive steps:the inversion of facies petrophysical properties andthe gradual deformation of the facies distribution. The resulting model is shown to predict well responses effectively. Finally, the possibility of further calibration improvement is investigated by means of alternative flow-modeling approaches, such as the use of a dual-porosity model or a more accurate modeling of conductive bodies.
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Katanov, Yu E. "Neural network model of the wells' drilling speed and modes predicting in complex reservoirs." Oil and Gas Studies, no. 1 (March 19, 2021): 55–76. http://dx.doi.org/10.31660/0445-0108-2021-1-55-76.
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The article considers the problem connected with the study of well drilling rates in complex reservoirs. Its solution is presented in the form of a neural network model that takes into account the structural, geomechanical and technological features of the «rock mass — well» system.The possibility of predicting the well drilling method with different strength and structural-lithological characteristics of the massif, based on neural network modeling, is presented.The purpose of this study is to obtain mathematical models for analysis of the probabilistic and statistical patterns of well drilling processes in conditions of uncertainty.The scientific novelty of the work performed is the qualitative and quantitative assessment of the mutual influence of geological and technological factors on the well drilling rate; search for optimal well drilling modes in complex reservoirs on the basis of mathematical modeling.
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Li, Quan Hou, Chun Yu Zhang, and Yuan Feng Zhang. "Applications of Research and Development of Logging in Oil-Field Visualization." Applied Mechanics and Materials 340 (July 2013): 867–70. http://dx.doi.org/10.4028/www.scientific.net/amm.340.867.
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The research of visualization will be carried out in the aspects of parameters distribution, dynamic history matching and geological models and numerical simulation of reservoirs respectively. In terms of the research on reservoir parameters, we can improve the accuracy of the prediction through comparing, analyzing and modeling the data of old wells and the secondary explained data. As to dynamic history matching and numerical simulation, by combination of dynamic and statistic methods, we can modify the deficiency of the traditional method. As for geological modeling, we can utilize the characters of logging responses and current mathematical theory to establish modeling. Only by combination of the dynamic and static methods, we can achieve actual visualization of oil-field development.
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Paolino, Donatella, Andra Tudose, Christian Celia, Luisa Di Marzio, Felisa Cilurzo, and Constantin Mircioiu. "Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals." Materials 12, no. 5 (February 26, 2019): 693. http://dx.doi.org/10.3390/ma12050693.
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In this study, we investigated the release kinetic of fluorescein from colloidal liquid crystals made from monoglyceride and different non-ionic surfactants. The crystals were physicochemically characterized and the release experiments were carried out under the sink conditions, while mathematical models were described as extrapolations from solutions of the diffusion equation, in different initial and boundary conditions imposed by pharmaceutical formulations. The diffusion equation was solved using Laplace and Fourier transformed functions for release kinetics from infinite reservoirs in a semi-infinite medium. Solutions represents a general square root law and can be applied for the release kinetic of fluorescein from lyotropic colloidal liquid crystals. Akaike, Schwartz, and Imbimbo criteria were used to establish the appropriate mathematical model and the hierarchy of the performances of different models applied to the release experiments. The Fisher statistic test was applied to obtain the significance of differences among mathematical models. Differences of mathematical criteria demonstrated that small or no significant statistic differences were carried out between the various applied models and colloidal formulations. Phenomenological models were preferred over the empirical and semi-empirical ones. The general square root model shows that the diffusion-controlled release of fluorescein is the mathematical models extrapolated for lyotropic colloidal liquid crystals.
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Ho, Thong Chi, Ngo Van Dau, Giang Song Le, and Oanh Thi Phi Tran. "Mathematical model in assesment of saltwater intrusion in Saigon – Dong Nai river system (Southern Vietnam) due to sea level rise." Science and Technology Development Journal 17, no. 3 (September 30, 2014): 94–102. http://dx.doi.org/10.32508/stdj.v17i3.1486.
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SaiGon –DongNai (SG-DN) river system plays a vital role in developing the southern key economic triangle including Ho Chi Minh City, DongNai and BinhDuong provinces. Saltwater intrusion results from many factors and complex movements in SG–DN river system, in the midst of which are sea level rise and water regulation of upstream reservoirs. Theses causes have gradually changed the hydraulic regimes of the river system. As a result, saltwater intrusion has become seriously. In this article, the authors used mathematical models to investigate the change of saltwater boundary of the river system before and after the impact of sea level rise and the regulatory regime of the reservoirs. The findings contributed to the predicted scenarios where sea level rise and salinity boundary could be controlled through the regulation of upstream reservoirs.
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Han, Lili, Yanyan Li, Wei Hu, Siyu Wei, Wei Wang, Fengyan Zhang, and Ye Wang. "Numerical Study on Hydraulic Fracture Propagation in a Layered Continental Shale Reservoir." Energies 15, no. 23 (November 23, 2022): 8840. http://dx.doi.org/10.3390/en15238840.
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The distribution of beddings varies greatly in shale reservoirs. The influence of beddings on hydraulic fracture propagation has often been studied using simplified geological models, i.e., uniformly distributed bedding models. However, the propagation processes of hydraulic fractures in shale reservoirs with complicated distributed beddings remains unclear. In this research, an outcrop-data-based bedding model of a continental shale formation in the Ordos Basin, China, is built. A mathematical model for fracture propagation is built using the discrete element method and is then verified by a hydraulic fracturing experiment. Reservoir-scale simulations are employed to investigate the influence of geological factors and engineering factors on fracture geometry. The study finds that beddings have significant inhibitory effects on fracture height growth; hydraulic fractures have difficulty in breaking through zones with densely distributed beddings. If a hydraulic fracture encounters a bedding plane with a larger aperture, it is more likely to be captured and expand along the weak interface. High vertical stress difference and a high fluid injection rate can promote the vertical penetration of hydraulic fractures through beddings and activate the bedding system to yield a complex fracture network. Increments in fluid viscosity can increase the resistance of fracture propagation, thereby reducing fracture complexity.
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Wood, Derek J., Larry W. Lake, Russell T. Johns, and Vanessa Nunez. "A Screening Model for CO2 Flooding and Storage in Gulf Coast Reservoirs Based on Dimensionless Groups." SPE Reservoir Evaluation & Engineering 11, no. 03 (June 1, 2008): 513–20. http://dx.doi.org/10.2118/100021-pa.
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Summary Concerns over global warming have led to interest in removing greenhouse gases, specifically CO2, from the atmosphere. Sequestration of CO2 in oil reservoirs as part of enhanced oil recovery (EOR) projects is one method that is being considered. This paper first presents the scaling groups necessary to describe CO2 flooding for a typical line-drive pattern and then uses these groups in a Box-Behnken experimental design to create a screening model most applicable to candidate Gulf Coast reservoirs (Box and Behnken 1960). By generating oil recovery and CO2 storage curves, the model estimates the cumulative oil recovery and CO2 storage potential for a given reservoir. Past screening models—Rivas et al. (1992) and Diaz et al. (1996)—focused only on oil recovery and simply assigned qualitative rankings to reservoirs. Models that did include quantitative results, including CO2 Prophet (Dobitz and Prieditis 1994) and the CO2 Predictive Model (Paul et al. 1984), did not include the effects of dip. This model focuses on both oil recovery and CO2 storage potential, produces quantitative results for each, and includes the effects of dip. This model quickly estimates the oil recovery and CO2 storage potential for a reservoir. Operators can quickly screen large databases of reservoirs to identify the best candidates for CO2 flooding and storage. The scaling groups also provide the basis for future models that may be more specific to other regions. The results show that continuous CO2 flooding can be fully described using 10 dimensionless groups: aspect ratio, dip angle group, water and CO2 mobility ratios, buoyancy number, dimensionless injection and producing pressures, residual oil saturation to water and gas, and initial oil saturation. The effects of capillary forces and dispersion were secondary effects in this model and were not included in the scaling. Dimensionless oil recovery was effectively modeled with the dimensionless oil breakthrough time and the dimensionless recovery at three different dimensionless times, while CO2 storage potential was calculated only at the final dimensionless time. The reservoir-specific parameters discussed above were calculated from response surface fits. The scaling does not work as well at small buoyancy numbers; however, it is effective in the range of values typical of Gulf Coast reservoirs. Introduction CO2 flooding is a popular EOR technique; however, it has not heretofore been scaled for dipping reservoirs. Scaling is done using a process called inspectional analysis. In this process, the equations governing fluid flow in a reservoir are described and then converted into dimensionless equations. For example, the variable z (distance in the vertical direction) can be transformed into a dimensionless variable by dividing by a scalar parameter z1*, which can be set equal to H, the height of the reservoir. This new group z/z1* is dimensionless. These transformations are made until the equations are entirely in dimensionless form. Then, through various assumptions and mathematical manipulations of the equations, dimensionless terms are canceled out and removed until a final group of independent dimensionless groups is extracted from the equations. Using inspectional analysis, Shook et al. (1992) scaled waterfloods for a homogeneous, 2D, cartesian, dipping reservoir with two phases (oleic and aqueous) present and found five necessary dimensionless groups. They are:RL = [Equation] effective aspect ratioMow = [Equation] mobility ratio (water)Na = [Equation] dip angle groupNog = [Equation] buoyancy numberNPc = [Equation] capillary number These groups served as the initial basis for the scaling of CO2 flooding; however, they proved insufficient. This paper presents the additional groups necessary to scale CO2 flooding. The desire to undertake CO2 flooding begets the need to identify economically attractive candidate reservoirs. Comprehensive simulations may be too costly and time-consuming when large databases of reservoirs must be evaluated. This paper presents a model based on the aforementioned dimensionless groups that quickly estimates the oil recovery and CO2 storage potential for candidate reservoirs.