Vertical Derivative Research Articles

Integration of magnetic and geological field data into geological mapping and rutile mineralization targets in the Minta locality (Haute-Sanaga, Cameroon)

This study combines the processing and interpretation of magnetic data with geological fieldwork. The purpose is to establish the geological map and rutile mineralization targets map of Minta area (Haute-Sanaga, Cameroon). To this, a strategic geological field survey was first conducted. It highlighted some geological structures, especially magnetite quartzites, which is considered as the potential sources of primary rutile mineralization. Several methods were applied to the magnetic data, including upward continuation (UC), vertical derivative (DZ), analytical signal (AS) and horizontal gradient magnitude (HGM). The regional-residual separation method based on the UC was used to develop the residual map which was very helpful to understand the distribution of magnetic anomalies related to rutile mineralization in this area. The structural model of the study area was established by combining the analysis of the AS and HGM maxima with the analysis of the topographic model. Since magnetic relief variation characterizes the lithological information changes according to the filtered map considered, a set of categorization processes based on the anomaly signals was applied to each of filtered maps according to the geological information sought. It is based on the interpretation of structural models, combined with previous works and the spatial distribution of geological data collected. This process produced a set of partial lithological models, which were then combined with the interpreted structural model to produce the geological map of the study area. This map also shows the spatial distribution of the various targets of potential rutile mineralization interpreted on the DZ model as rectilinear anomalies, with a signal range of 0.78–0.88 nT/m.

Interpreting the magnetic signatures and radiometric indicators within Kogi State, Nigeria for economic resources

The mineral and geothermal potentials of part of Kogi State was investigated through the interpretation of aeromagnetic and radiometric data of the study area. The analysis targeted bridging the gap of insufficient geophysical information of sub-crustal resources that could be of economic value within the area of study. Vertical derivatives, analytical signal and spectral depth analysis were used for the interpretation of the aeromagnetic data while the concentration and ternary images of the three radiogenic elements were used for the interpretation of the radiometric data. The result of first vertical derivative was helpful in delineating mineral potent lineaments labelled F1 to F8. The lineaments were seen trending E-W and NE-SW direction. A principal fault line F6 tends to separate the regions of sediments to the south-east and basement geologic formations to the south-western regions. Result of the analytical signal amplitude revealed regions with shallow intrusive magnetic rocks having high amplitudes ranging from 0.152 to 0.557 nT/m, while regions with magnetic rock intruding into sedimentary formations at greater depths, have medium to low amplitudes ranging from 0.014 to 0.136 nT/m. Regions delineated to be altered through hydrothermal process coincided with areas of major magnetic lineaments. The lineaments which could be fractures, faults or shear zones usually serve as conduits for mineral deposits during hydrothermal process. Result of potassium_thorium ratio map showed evidence of hydrothermal alteration in the NW and SW regions of study area. These regions of alterations also corresponds to regions where major lineaments were mapped and thus represent regions with significant potency for mineralisation. Result of spectral depth analysis on the aeromagnetic data showed that peak values of geothermal gradient and Heat flow were 27°C/km and 68 mW/m2 respectively, the values were recorded at the North-eastern part of study area, at the lower end of Koton-Karfe and part of Lokoja where the shallowest Curie point depth of 24 km also occurred. The estimated values of heat flow falls below the range of 80 to 100 mW/m2 recommended as threshold for a good source of geothermal energy, hence the region will not be prospectively good for a cost effective geothermal energy exploration. In order to assess the heat production within the study area due to activities of radioelements, a comparative analysis of the concentration of the three radiogenic elements was carried out. A relatively high radiogenic heat production (RHP) value of 3.4 μW/m3 was recorded at the North-western region indicating high occurrence of radioactivity within the granitic rocks. The (RHP) value of 3.4 μW/m3 is slightly below 4.0 μW/m3 which is a recommended value for a good source of geothermal energy.

Reassessment of Geophysical Investigation of Zinc(Z), Cupper (Cu) and Lead (Pb) Potential Mineralization Deposits using Aeromagnetic Data in Wase Middle Benue Trough, Nigeria

Abstract: This effort aims to delineate structures responsible for exploring mineral resources in the Wase middle Benue trough area of Northcentral, Nigeria by evaluating the aeromagnetic data over that region. Oasis Montaj version 6.4 was used to qualitatively and quantitatively evaluate the aeromagnetic data. Techniques for Source Parameter Imaging (SPI) interpretation, including First Vertical Derivative, Analytical Signal, Upward Continuation, and Tilt Derivative, were used in the study. Analytic signal and tilt derivative maps showed different patterns of magnetic signatures independent of magnetization direction with amplitude ranging from 0.1 to 0.2nT/m and -1.3 to 1.4nT/m. They also showed qualitative interpretation applied aids enhance linear features at the expense of deep intrusive bodies like lineaments, fractures, and fault zones which trend Northeast Southwest (NE- SW) in the map of the study area. The boundaries of the geologically interesting anomalies were noticeably accentuated by the upward continuation done at 2 km. Nonetheless, this provides an approximation of the depth of the source of magnetic signatures in the area. The depth measured by SPI ranged from 103.9 to 1473.0 m. In the Eastern and Western regions of the region, respectively, shallow and deep-seated bodies are seen. The depth of the analysis was about 2000m, in conclusion, it was believed that the linear characteristics in the area that are trending northeast to southwest are possible structures for the prospecting of mineral deposits like zinc, copper, and lead

Delineation of source magnetization and subsurface discontinuity of Ririwai Ring Complex along Kano, North Western Nigeria

High Resolution Aeromagnetic (HRAM) data of Ririwai (sheet 126) which lies between latitude 10° 30' to 11° 00' N and longitude 8° 30' E to 9° 00' E, was used for this research. The study area, Ririwai is situated along Kano, in the Northwestern part of Nigeria, both qualitative and quantitative interpretation techniques were employed in this study. This procedure was carefully undertaken by employing enhancement filters; vertical derivative, upward continuation, analytical signal amplitude processing, and quantitative approaches such as Euler 3D deconvolution and an apparent susceptibility filter to help further give solutions for depth estimates and magnetization. The Euler deconvolution was able to show that the solution plotted clustered around the region where the geological structures are located with average depths range of <139.8 to >904.5 m, with very few solutions having depths less than 200 m, the most prominent structure particularly the Ririwai ring complex have a depth range of 182.9 to 301.5 m. The magnetic susceptibility reading obtained shows that the area is composed of rocks high in magnetic minerals such as magnetite along the western end of the area, it is also flanked by medium to high magnetic values around the central parts with only regions of low magnetic values predominantly along the Ririwai complex and its adjoining outcrops towards the eastern half of the area under study.

Boundaries Determination in Potential Field Anomaly Utilizing Analytical Signal Filtering and its Vertical Derivative in Qeshm Island SE Iran

The analytical signal method and its derivatives can be explicitly calculated and assessed for analyzing and estimating the boundary of geological structures, such as faults or dikes, from potential field anomalies. Gravity field of the east of Qeshm Island and its north coast from Sarkhun to Latidan in SE Iran has been measured in one-kilometer regular network. The regional anomaly effects are deducted from the Bouguer anomaly, where it can get the residual anomalies which is the considered dataset used in this study. The Bouguer range is -297 to -330 milligals (mGal) applying filters and modeling. It was revealed that there are five negative anomalies caused by salt penetration in the region. Regional anomalies expectedly have a low spatial frequency and long wavelengths, while the residual anomalies associated with shallow sub-surface potentials have high spatial frequencies and short-wave wavelengths.Two different fault trends were observed comparing the artificial model using MATLAB coding, the real one, and the filtered residual anomaly map of the Qeshm region. Also, another fault trend is suggested in the east height of Oman, which is a possible place of salt penetration. Due to the limited dimensions (120 * 100 km) and the information obtained from the existing drillings, the depth of the anomaly resources can be examined up to 8 km. Due to the gravitational condition between the two domes of Qeshm saline and the bridge located in the Hara saline area, it is suggested to be considered as an area for further oil exploration routines.

Identification of Geological Structure Based on Gravity Method in Tangkuban Parahu Volcano, Bandung, Indonesia

Tangkuban Parahu Volcano, located in Cikahuripan, Lembang, West Bandung Regency, West Java, Indonesia, has a geothermal potential. However, this potential is accompanied by geohazard risks, one of which is a volcanic eruption that can interfere with the development of geothermal potential. On February 12, 2022, there was a gust of volcanic gas from Ratu Crater, indicating an increase in volcanic activity after an eruption in 2019. Based on the geological map of Tangkuban Parahu/Sunda Volcano Complex, it is estimated that there is a fault structure in a northwest-southeast direction, where if a volcanic eruption occurs, it will cause greater deformation because it cuts through Ratu Crater. Further studies with geophysical methods are needed to estimate the fault structure. The study of the subsurface geological structure of Tangkuban Parahu Volcano was carried out using the gravity method by studying variations in the gravitational field on the earth’s surface to determine differences in rock density. The Complete Bouguer Anomaly (CBA) value from the gravity method at Tangkuban Parahu Volcano shows 68 – 73 mGal, and residual anomaly values ranged from -0.95 to 0.67 mGal. The negative residual anomaly value between -0.95 to 0 mGal shows the weak zone due to volcanism in the crater. On the other hand, high residual anomaly values ranging from 0 to 0.67 mGal are interpreted as the influence of Lava 1 Tangkuban Parahu (Tl1). Analysis using First Horizontal Derivative (FHD) and Second Vertical Derivative (SVD) shows a fault structure trending Northwest – Southeast, which can be a way out of the accumulation of high-pressure water vapor due to volcanic activity.

Монгол орны тектоник хагарлын системийг геосоронзон гажлын орноор үнэлсэн дүн

Magnetic anomaly map of Mongolia and its directional derivative maps were used to estimate the some fault parameters of different types of faults in the Mongolian territory. Direction and location of majority of faults, including deep-seated faults, were determined in good accordance with geomagnetic anomaly and its horizontal and vertical derivative maps. Also, some probable faults have been investigated according to the geomagnetic anomaly peculiarities.

Fast pre-stack multi-channel inversion constrained by seismic reflection features

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.

The Global Well-Posedness and Decay Estimates for the 3D Incompressible MHD Equations With Vertical Dissipation in a Strip

Abstract The three-dimensional incompressible magnetohydrodynamic (MHD) system with only vertical dissipation arises in the study of reconnecting plasmas. When the spatial domain is the whole space $\mathbb R^3$, the small data global well-posedness remains an extremely challenging open problem. The one-directional dissipation is simply not sufficient to control the nonlinearity in $\mathbb R^3$. This paper solves this open problem when the spatial domain is the strip $\Omega := \mathbb R^2\times [0,1]$ with Dirichlet boundary conditions. By invoking suitable Poincaré type inequalities and designing a multi-step scheme to separate the estimates of the horizontal and the vertical derivatives, we are able to establish the global well-posedness in the Sobolev setting $H^3$ as long as the initial horizontal derivatives are small. We impose no smallness condition on the vertical derivatives of the initial data. Furthermore, the $H^3$-norm of the solution is shown to decay exponentially in time. This exponential decay is surprising for a system with no horizontal dissipation. This large-time behavior reflects the smoothing and stabilizing phenomenon due to the interaction within the MHD system and with the boundary.

Using Airborne Geophysical and Geochemical Methods to Map Structures and Their Related Gold Mineralization

Egypt’s mineral resources are an effective means of raising the country’s income. Consequently, searching for deep subsurface ore deposits is essential. In this study, we map the subsurface structure and the occurrence of related gold-ore mineralization deposits in ophiolitic-assemblage rocks around the Wadi El-Saqia area in the Central Eastern Desert of Egypt. Our approach combines airborne geophysical data (aeromagnetic mapping) and geochemical analyses. We enhanced the aeromagnetic data and interpreted them using edge-detection methods, such as the first-order vertical derivative (FVD), the analytic signal (AS), the total horizontal derivative (THD), the tilt derivative (TD), the tilt angle (TA), the theta map, both grid and porphyry analyses from the Centre for Exploration Targeting (CET), and Euler deconvolution (ED) techniques. Utilizing these methods, we located the main structural lineaments/contacts that control the distribution of hydrothermal alteration zones. In addition, our geochemical analyses use the mineral chemistry of pyroxene and plagioclase to describe their tectonic and magmatic evolution. The airborne geophysical results revealed that NW–SE, NE–SW, N–S, and E–W structural orientations are prevalent in the studied area, with depths ranging from less than 50 m to about 600 m. To validate the findings, we carried out geochemical sampling, which indicates that pyrite, galena, pyrrhotite, and electrum contain good percentages of gold (ranging from 0.01–0.09 wt%, 0.03–0.1 wt%, 0.12–0.14 wt%, and 53.55–55.01 wt%, respectively). In this study, we were thus able to find preferred locations for gold mineralization, which highlights the value of combining aeromagnetic and geochemical data for mineral exploration.

GEOLOGICAL INTERPRETATION OF 2D GRAVITY MODELING IN TULUNG SELAPAN AREA AND SURROUNDINGS, SOUTH SUMATRA BASIN

The South Sumatra Basin is a prolific oil and gas basin. The Tulung Selapan area, which is to the east and part of the South Sumatra Basin, is considered to have hydrocarbon potential. Several sub-basins, including the South Palembang and the North Palembang sub-basins, exist in the region. One of the geophysical methods for determining the presence of sedimentary sub-basins, structural patterns, and bedrock is the gravity method. The purpose of this study is to determine the structural pattern and interpret the subsurface geological model of the Tulung Selapan area using 2D modeling. The complete Bouguer anomaly (CBA) reveals circular and relatively northwest-southeast trending patterns, ranging from +33 mGal to +62 mGal. 2D gravity forward modeling results in eight successive rock layers. From top to bottom, the uppermost layer is swamp sediment with a mass density of 2.1 g/cm3, followed successively by the sedimentary rocks of the Kasai Formation (2.28 g/cm3), the Muara Enim Formation (2.32 g/cm3), the Air Benakat Formation (2.39 g/cm3), the Gumai Formation (2.3 g/cm3), the Baturaja Formation (2.48 g/cm3), and lastly a layer with a density of 2.7 g/cm3, which represents the bedrock. Due to the limited depth of 2800 m in 2D forward modeling, it is unable to identify the source and reservoir rocks. The seal rock (caprock) is interpreted to be shale from the Gumai Formation at an average depth of 1.53 km. Based on Second Vertical Derivative (SVD) analysis, 2D modeling identifies the presence of geological structures with normal faults.

Geophysical characterization of a low sulfidation epithermal gold and silver deposit, Mendoza, Argentina

The combined analysis of aeromagnetic and gamma-ray spectrometry data, allowed us to determine and differentiate the responses of hydrothermal rocks units and low sulfidation epithermal gold systems, in the south area of the San Rafael Block, in the Mendoza province. The data processing approach was focused on mapping geological limits and structures, and their response over the gold mineralization area, linked to hydrothermal zones. To do this, filtering algorithms, such as vertical derivative, tilt derivative, logistic function, and analytic signal were applied to the aeromagnetic data. For the analysis of gamma-ray spectrometry data, images of K, eU, and eTh concentrations, K/eTh ratios, and an F-parameter were used. The analytic signal filtering of the data reveals relatively low magnetic intensity zones associated with hydrothermally altered rock areas. The radiometric data delineate local anomalies that reflect enrichment with high potassium values in the deteriorated zones. A broad K/eTh anomaly correlates with the extension of the magnetic low intensity zones, indicating a generalized potassium enrichment in the Don Sixto area. These results indicate that the main structural directions are arranged in NW-SE strikes and the secondary ones in N–S strikes. These lineaments are spatially correlated with the most significant structures in the study area, evidencing that the mineral deposits located in the study area respond to the main lineaments. In addition, the main geophysical characteristics allowed us to identify the zone of hydrothermal alteration related to the low sulfidation epithermal gold and silver deposit Don Sixto, which would be related to high levels of K/eTh ratios and low intensity magnetic zones.

GEOLOGICAL INTERPRETATION OF THE OFFSHORE SEDIMENTARY BASIN OF NORTH CENTRAL JAVA BASED ON SPECTRAL ANALYSIS AND 2D GRAVITY MODELING

The offshore sedimentary basin of North Central Java is a marine basin located in the northern part of North Serayu Basin. This basin was formed through the uplift of the southern part of Central Java (Bumiayu) caused by the movement of a pair of horizontal faults. Studies of sub-basin delineation and basement configuration are rarely carried out in this basin. Therefore, the gravity method referring to subsurface-density variations was carried out to obtain this information. This research aims to delineate sedimentary basins and interpret the geological subsurface based on gravity data using spectral analysis, highpass and lowpass filters, also 2D gravity modeling. An average estimation depth to the basement in the study area of about 2.22 km was determined using spectral analysis. Qualitative analysis shows the basement-high pattern, sub-basin, and structure lineament patterns. The 2D model shows three layers consisting of the upper sedimentary layer of Tertiary-Neogene and the middle layer of Tertiary-Paleogene sediment with a density value of 2.3 gr/cc and 2.5 gr/cc, respectively. The lower layer has the highest density of 2.67 gr/cc, assumed as a granitic basement. The results of the Second Vertical Derivative (SVD) analysis on the residual anomaly cross-sectional paths indicate the presence of thrust and normal faults which can be used to assist the interpretation of fault structures in subsurface geological models. Gravity analysis of the offshore North Central Java sedimentary basin indicates the occurrence of sub-basins and geological structure patterns that considered as a potential zone for the development of the petroleum system in this area.

Development of 3D surface reconstruction by the images triad based on the Lambertian reflection model

A method for reconstructing the surface of an object using on a series of images based on the Lambertian model of light reflection is proposed. The original images are obtained by the method of photography under natural lighting. The model parameters are determined by changing the position of the light source using additional shading and the stable position of the receiver. The series contains a triad of images obtained from different directions of illumination and a shaded image of the surface of the reconstruction object. In the first stage, the derived surfaces of the reconstruction object are reconstructed. The next step is the accumulation of derivatives and determination of the surface height of the reconstruction object. To simplify the complexity of the practical implementation of the 3D-reconstruction a pyramid layout is chosen. The photography of the triad of images of the pyramid is done before noon, at noon and in the afternoon. The information about the triad and the shadowed image of the pyramid surface enters the processing system, where the directions of the photograph lighting are first determined. The parameters of the lighting directions are determined based on data on the height of the Sun at its upper culmination on the day and the time of the photo shoot. The procedure for determining the elevation of the Sun on a particular day of the year has been implemented. Calculated lighting direction data and image information using the Lambertian model of light reflection are reconstructed into horizontal and vertical derivatives. As a result of the discrete accumulation of derivatives, the pyramid surface is reconstructed.

Fusion of overexposed and underexposed images using caputo differential operator for resolution and texture based enhancement

The visual quality of images captured under sub-optimal lighting conditions, such as over and underexposure may benefit from improvement using fusion-based techniques. This paper presents the Caputo Differential Operator-based image fusion technique for image enhancement. To effect this enhancement, the proposed algorithm first decomposes the overexposed and underexposed images into horizontal and vertical sub-bands using Discrete Wavelet Transform (DWT). The horizontal and vertical sub-bands are then enhanced using Caputo Differential Operator (CDO) and fused by taking the average of the transformed horizontal and vertical fractional derivatives. This work introduces a fractional derivative-based edge and feature enhancement to be used in conjuction with DWT and inverse DWT (IDWT) operations. The proposed algorithm combines the salient features of overexposed and underexposed images and enhances the fused image effectively. We use the fractional derivative-based method because it restores the edge and texture information more efficiently than existing method. In addition, we have introduced a resolution enhancement operator to correct and balance the overexposed and underexposed images, together with the Caputo enhanced fused image we obtain an image with significantly deepened resolution. Finally, we introduce a novel texture enhancing and smoothing operation to yield the final image. We apply subjective and objective evaluations of the proposed algorithm in direct comparison with other existing image fusion methods. Our approach results in aesthetically subjective image enhancement, and objectively measured improvement metrics.

A Stable Finite Difference Method Based on Upward Continuation to Evaluate Vertical Derivatives of Potential Field Data

A Stable Finite Difference Method Based on Upward Continuation to Evaluate Vertical Derivatives of Potential Field Data

The 2022 Mw 6.1 Pasaman Barat, Indonesia Earthquake, Confirmed the Existence of the Talamau Segment Fault Based on Teleseismic and Satellite Gravity Data

A Mw 6.1 earthquake on 25 February 2022, at around 8:39 a.m. local time, struck Pasaman Barat Regency, West Sumatra, Indonesia, and was felt in Singapore and Malaysia. The hypocenter of this earthquake was 12 km deep and preceded by an Mw 4.9 foreshock a few minutes earlier. The earthquakes originated on a blind fault and triggered a landslide at Mount Talamau. Herein, the slip distribution and asperities along the plane fault during the earthquake were examined by teleseismic inversion and the fault location was identified by Global Gravity Model plus (GGMPlus) satellite gravity data. The slip distribution was calculated from the source parameters (strike: 136°; dip: 70°; rake: 174°) by inversion techniques based on teleseismic data. Based on the slip distribution, the earthquake was generated by stress from the Sianok fault that spread to the north and reached the uncertain fault segment in the Talamau area. In addition, the results of the First Horizontal Derivative and Second Vertical Derivative from the GGMplus data revealed a straight Simple Bouguer Anomaly pattern, confirming the existence of the uncertain Talamau fault as part of the Great Sumatra Fault. This work shows the potential application of the combination of teleseismic and gravity observation for delineating the fault structure that caused the 2022 Mw 6.1 Pasaman earthquake, which can also be applied to other locations of similar geological backgrounds.

Characteristics of Palu-Koro Fault based on Derivative Analysis and Euler Deconvolution Model of Gravity Data

Indonesia is located at the confluence of three plates, namely the Eurasian, Indo-Australian, and Pacific plates which causes the formation of an active fault line. One of these active faults is the Palu-Koro fault, Sulawesi, with a shift rate of 30-44 mm/year. A geophysical method such as gravity determines the fault’s characteristics. Gravity data is processed by a derivative analysis process in the form of First Horizontal Derivative (FHD) and Second Vertical Derivative (SVD), which is carried out to represent the type of fault, and the Euler Deconvolution method is used to determine the location and depth of the fault anomaly source. The results show that the Palu-Koro fault has a high anomaly value in the west of 0.00557-0.01087 mGal in the north-south direction on the FHD map and an anomaly value of 0 in the north-south direction on the SVD map. The source of the anomaly can be seen more clearly in the results of the Euler Deconvolution modelling at a depth of 50-400 m from the topography of the study area. The Palu-Koro fault is proven to have many structures at shallow depths with very active movements that can trigger earthquakes.

New Targets of Potential Mining Interest Using Gravimetric and Satellite Data: Case Study of Hercynian Rehamna Massif, Morocco

The known mineralization in the Rehamna Massif is essentially vein type and linked to the presence of granitic bodies and pneumatolytic - hydrothermal fluid circulations. This part of western Moroccan Meseta, belongs to the Hercynian belt, was the seat of enormous mining productions mainly base metals during the 20th century. Subsequently, exploitations are ended with artisanal extractions, in relation to exploration decline. The present work aims to search for new favourable mining targets, using gravimetric and remote sensing data. Gravimetric data allowed us to delineate leucogranitic apexes of shallow depth. Data filtering and processing consist of separation between Regional and Residual fields from Bouguer anomaly, then, calculation of horizontal, vertical and tilt derivatives to get different gravity anomalies. A Satellite image is used to obtain structural lineaments of the study region through directional filters (N0°, N45°, N90°, N135°). These treatments, supported by field investigations, enabled us to discriminate potential areas, suitable for tactical mining exploration.

Development and validation of Nusselt number correlations for a helical coil based energy storage integrated with solar water heating system

Storage tanks based on helical coil heat exchangers are an integral part of solar water heating systems and require optimal design configuration to achieve maximum heat transfer and a longer storage period. This study is focused on thermal analysis of a vertical helical coil-based water storage tank and derivation of inner and outer Nusselt number correlations by considering the storage tank as well as helical coil and catering to both forced and natural convection effects. A fluid-fluid conjugate heat transfer transient state model is validated with experiments performed with 50/50 % water-glycol mixture as heat transfer fluid at flow rates of 2 and 3 L/min in a solar water heating system, while water remains at static flow condition inside the tank. To reduce the computational cost, a symmetrical downsized (50 % of the real storage tank size) model is also designed and validated, which showed a mean absolute percentage error of 3.25 %. In order to derive the mathematical correlations, alterations were made to the validated model by using coils with curvature ratios ranging from 0.09 to 0.184 with HTF flow rates in laminar flow regimes, ranging from 30 to 100 L h−1 at temperatures from 40 °C to 80 °C. Furthermore, inner Nusselt number mathematical correlations based on M number, curvature ratio, and Prandtl number showed good agreement with correlations derived by past investigators. Similarly, the outer Nusselt number of the coil was related to Rayleigh's number and the derived relations showed good agreement with the past studies, while Nuo = 0.1996 (Rado0.326) showed the least error of 2.06 %. Finally, thermal stratification analysis helped to understand that coil position and aspect ratio determine the thermocline developed inside the storage tank. Results show that extension of coil inside the tank up to 83.7 % of the tank height, ensured greater thermocline range, and tank with aspect ratio 3 turned to be better for thermal energy storage for longer period.