Subsurface Reservoirs Research Articles

Numerical Simulation of Multiphase Flow in Subsurface Reservoirs: Existing Challenges and New Treatments

Numerical Simulation of Multiphase Flow in Subsurface Reservoirs: Existing Challenges and New Treatments

PHYSICS-INFORMED NEURAL NETWORKS BASED ON SEQUENTIAL TRAINING FOR CO2 UTILIZATION AND STORAGE IN SUBSURFACE RESERVOIR

CO<sub>2</sub> utilization and storage (CCUS) simulation in subsurface reservoirs with complex heterogeneous structures necessitates a model that can capture multiphase compositional flow and transport. The governing equations are highly nonlinear due to the complex thermodynamic behavior, which involves the appearance and disappearance of multiple phases. Accurate simulation of these processes necessitates the use of stable numerical methods. While machine learning (ML) approaches have been used to solve a variety of nonlinear computational problems, a new approach based on physics-informed neural networks (PINNs) has been proposed for solving partial differential equations (PDEs). Unlike typical ML algorithms that require a large dataset for training, PINNs can train the network with unlabeled data. The applicability of this method has been explored for multiphase flow and transport in porous media. However, for nonlinear hyperbolic transport equations, the solution degrades significantly. This work proposes sequential training PINNs to simulate two-phase transport in porous media. The main concept is to retrain the neural network to solve the PDE over successive time segments rather than train for the entire time domain simultaneously. We observe that sequential training can capture the solution more accurately concerning the standard training for conventional two-phase problems. Furthermore, we extend the sequential training approach for compositional problems in which nonlinearity is more significant due to the complex phase transition. Our approach was tested on miscible and immiscible test cases and showed higher accuracy than the standard training method.

Integrated thermo-poro-mechanical characterization for CO2 Sequestration at deep aquifer conditions

Modelling and forecasting of injected CO2 plume behaviour is an essential step in the baseline, monitoring, and verification [BMV] process in the CO2 sequestration lifecycle. The goal of reduction of uncertainty through forecasting models, can be better realized by accounting for the thermo-poro-mechanical nature of the deep subsurface reservoir systems. The current study focusses on developing and refining a laboratory workflow which will help in generating representative static and dynamic datasets at ambient and deep aquifer conditions. The workflow involves characterizing the poroelastic Biot coefficient and mechanical properties at ambient, high temperatures and at reservoir representative stress conditions. This information will be combined with the dataset from a CO2 flood experiment which replicates the displacement of brine by super critical CO2 at ambient and high temperatures and at reservoir representative stresses. Resistivity and acoustic signals will be monitored throughout the flood experiment. Existing analytical models for fluid substitution such as the Biot-Gassmann-Brie populated with representative data will be evaluated for finding the best description of the experimental observations. The integrated results of the workflow are meant to help develop better informed static and dynamic models improving the confidence in the BMV process of CCUS.

Corrosive Influence of Carbon Dioxide on Crack Initiation in Quartz: Comparison With Liquid Water and Vacuum Environments

AbstractThe stimulation of crack growth in quartz and siliceous materials by injecting carbon dioxide (CO2) represents a key technology in long‐term carbon storage and in the development of natural gas wells. While this technology is widely used, the molecular impact of CO2 interactions on the solid matrix is only incompletely understood. In this work, we employ reactive molecular dynamics simulations to study how the CO2 fluid environment affects the mechanical properties of pre‐cracked single‐crystal quartz. The thermodynamic conditions of interest are those relevant to subsurface reservoirs. We report how structural properties of quartz—bond length distribution and crack tip shape—evolve upon introduction of a fluid. These properties are directly related to macroscopic quantities of the global stress–strain curves, thus reaffirming the inherent coupling across multiple scales for fluid–solid interactions in the subsurface. We find that CO2 reduces the fracture toughness of quartz by 12.1% compared to that of quartz in vacuum, thereby promoting crack growth and enhancing fluid transport in the subsurface.

Target-oriented waveform inversion based on Marchenko redatumed data

Target-oriented inversion (TOI) can resolve subsurface reservoir parameters based on surface waveform data. Moreover, virtual data at the datum level and a precise local forward operator are required to accurately perform inversion in the target area. The Marchenko redatuming, a state-of-the-art seismic redatuming method, is used to obtain the virtual data of the target area. Local forward operators of crosscorrelation and cross-convolution forms are used to generate the local wavefields. A subsurface-domain interferometric objective function and the corresponding inversion algorithm are developed. A simple model is used to demonstrate the accuracy of this approach. This technique is applied to the Chevron 2014 benchmark data set to invert a specific area, indicating that the method can achieve accurate high-resolution inversion results with reduced computational costs. Finally, a time-lapse inversion is performed to exhibit the practicality of the new approach in 4D seismic exploration. These numerical results demonstrate great applications of the TOI based on the redatumed data and local forward operators of crosscorrelation or convolution forms.

A Deep Learning Method for Facies Recognition from Core Images and Its Application: A Case Study of Mackay River Oil Sands Reservoir

There is a large amount of drilling core data in the Mackay River oil sands block in Canada, and the accurate identification of facies from the cores is important and necessary for the understanding of the subsurface reservoir. The traditional recognition method of facies from cores is by human work and is very time consuming. Furthermore, the results are different according to different geologists because of the subjective judgment criterion. An efficient and objective method is important to solve the above problem. In this paper, the deep learning image-recognition algorithm is used to automatically and intelligently recognize the facies type from the core image. Through a series of high-reliability preprocessing operations, such as cropping, segmentation, rotation transformation, and noise removal of the original core image, that have been manually identified, the key feature information in the images is extracted based on the ResNet50 convolutional neural network. On the dataset of about 200 core images from 13 facies, an intelligent identification system of facies from core images is constructed, which realizes automatic facies identification from core images. Comparing this method with traditional convolutional neural networks and support vector machines (SVM), the results show that the recognition accuracy of this model is as high as 91.12%, which is higher than the other two models. It is also shown that for a relatively special dataset, such as core images, it is necessary to rely on their global features in order to classify them, and, with a large similarity between some of the categories, it is extremely difficult to classify them. The selection of a suitable neural network model can have a great impact on the accuracy of recognition results. Then, the recognized facies are input as hard data to construct the three-dimensional facies model, which reveals the complex heterogeneity and distribution of the subsurface reservoir for further exploration and development.

A novel hybrid model for hydraulic fracture simulation based on peridynamic theory and extended finite element method

The development of subsurface hydrocarbon reservoirs is highly dependent on hydraulic fracturing technology, and it is of great significance to use numerical simulation approaches to explore the propagation characteristics of hydraulic fractures. A novel hybrid model for investigating the hydraulic fracturing problem is proposed in this paper, wherein the crack segment is described using the extended finite element method (XFEM), and the region of the crack tip and potential fracture propagation is described using peridynamic (PD) theory. The fluid flow is governed by the continuity equation and the momentum equation, and the permeability in the fracture is calculated by the cubic law. The proposed model takes advantage of the small computational complexity of XFEM, and uses the stretch in the PD theory to determine whether the bond is broken, avoiding the need to obtain the stress intensity factor. The importance of the hybrid model is the coupling strategy for the transition region from XFEM to PD. Then the model is validated against two classic problems with available analytical solutions. The issue of hydraulic fractures intersecting natural fractures is also addressed. Meanwhile, the mesh size and the coupling region size is studied in this work. The model proposed in this paper is of benefit to provide a new perspective for numerical simulation of hydraulic fracture.

Geochemical modelling of hydrogen wettability on Quartz: Implications for underground hydrogen storage in sandstone reservoirs

Renewable energy particular hydrogen can be optimum solution to replace fossil fuels to achieve net-zero carbon emission targets and metigate global warming. One challenge of the hydrogen industry is to safely and economically store hydrogen. To meet this requirement, underground geological storage is a potentially suitable solution to store hydrogen in large-scale and long-term manner. Wettabillity is an important formation parameter that can affect flow behaviors of stored gas, cycling efficiency, structural and residual trap capacity. However, current research is still scarce in geochemical reactions associated hydrogen wettability alteraction in subsurface sandstone reservoirs under in-situ conditions. To fill this knowledge gap, in this study, we performed surface complexation modelling to understand the wettability of hydrogen-brine-organic acid-quartz system. The surface potential of pure quartz at various temperatures and pressure was calculated to characterize disjoining pressure isotherm. Besides, surface species concentrations of quartz and organic stearic acid were predicted to quantify the electrostatic attraction between quartz and organic acid molecues thus the hydrogen wettability on quartz surface.The modelling results show that for pure quartz, increasing temperature and pressure has a negligible effect on disjoining pressure and hydrogen wettability on the pure quartz surface, which is different from the results reported by Iglauer et al., but is in line with the results reported by Hashemi et al. When organic stearic acid is added into system, increasing organic molecules concentration and pressure strengthens the electrostatic attraction of quartz-organic acid and leads to less hydrophilicity and more hydrogen-wetting. This result is consistent with previous contact angle measurements that increasing organic acid concentration increases the brine contact angle, thus the hydrogen wettability. Our work provides a framework to characterize hydrogen wettability on mineral surface using geochemical tools to better assess the feasibility of UHS in depleted sandstone reservoirs.

Dynamic evolution of shale permeability under coupled temperature and effective stress conditions

The permeability of shale in unconventional subsurface reservoirs under high-temperature and high effective stress conditions is of great significance for evaluating the extraction efficiency of shale gas and determining reservoir development programs. In this study, a series of permeability experiments using nitrogen gas were conducted on a sample from the lower Longmaxi Formation over a range of temperature (25–100 °C), effective stress (22.5–52.5 MPa), and pore pressure (0.5–8 MPa) conditions. The dynamic relationships between permeability and temperature, effective stress, and pore pressure are analyzed in detail. The results show that the apparent permeability decreases approximately linearly with increasing pore pressure, temperature, and effective stress. The absolute permeability also decreases with increasing temperature or effective stress. Upon increasing the reservoir depth by 1000 m, the permeability decreases by an average of approximately 25%. Approximately two-thirds of this decline is caused by changes in the effective stress and approximately one-third by changes in temperature. The Klinkenberg parameter is also found to be positively correlated with temperature and effective stress. The results herein provide important guidance for evaluating permeability changes and the extraction efficiency for deep shale gas development.

Impact of uncertainties associated with the choice of the yield stress on the prediction of subsurface reservoir compaction: A field study

The compaction of subsurface chalk during hydrocarbon production leads to technical and societal issues related to well trajectory design, wellbore collapse, seafloor subsidence, and seismic events. Predicting reservoir deformation over time requires well-calibrated constitutive equations to capture the viscoplastic response of chalk according to several parameters including porosity, age, water saturation, and rate of applied stress or strain. The experimental data used to extrapolate trends between e.g., porosity and yield stress, show a non-negligible data scattering, thereby raising questions about the reliability of the predicted compaction. The present study aims at assessing how the uncertainty associated with the determination of the yield stress manifests itself at the field scale. To this purpose, one-dimensional simulations are performed on four producing hydrocarbon reservoirs from the Danish North Sea and quality-checked against seafloor subsidence measurements. Two simulations are run per case study by considering in the constitutive equations the initial (conservative approach) and final (optimistic approach) yield stress values, which delimit the transition between the elastic and plastic regime of chalk. The results indicate that the accumulated strain and the seafloor subsidence vary by a factor of up to 73% and 50%, respectively between the conservative and optimistic approaches. These differences in the compaction behaviour are influenced by three parameters, the initial porosity, the virgin stress condition, and the stress history of the reservoir. This study demonstrates that the uncertainty analysis of compaction simulation studies is essential for estimation of compaction drive of hydrocarbon fields and to identify the locations potentially subject to failure in the context of hydrocarbon production and field abandonment as well as CO2 and thermal storage projects.

Dynamic development of geochemical reaction fronts during hydraulic stimulation of shale

Injection of acidic hydraulic fracture fluid (HFF) into shale formations for unconventional oil/gas production results in chemical reactions in the shale matrix that can alter fluid transport. Here, we report the results of set of experiments designed to evaluate the impact of calcite dissolution as a function of carbonate mineral content on matrix chemical reactivity and pore-space modification concomitant with imbibition. We tracked acidic HFF transport in four samples of Wolfcamp shale with calcite contents varying from 4% to 59% by monitoring the rate and spatial extent of bromide tracer transport using synchrotron-based X-ray fluorescence microprobe (XFM) imaging. Concurrently, we also carried out XFM imaging of the spatial distribution of Ca in the Wolfcamp shale cores (as a proxy of calcite distribution). Our approach thus yields a direct record of time-resolved selective ion transport resulting from the penetration of acidic HFF and the associated mineral transformations in the shale cores.We show that the variability in calcite content of Wolfcamp shale samples can directly affect the rate and spatial extent of imbibition. Although reaction of the acidic HFF with carbonates in shales enhances calcite dissolution and increases porosity, the spatial extent of calcite dissolution in the shale matrix is limited due to a rapid neutralization of pH. The relative abundance and spatial distribution of calcite control the chemical saturation state of the HFF progressing into the matrix. As a result, calcite has a major impact on the spatial extent and rate of matrix alteration and thus on HFF transport during subsurface reservoir stimulation. Consequently, increased calcite content in the shale matrix inhibits the spatial extent of the pore-volume increase and, by extension, the spatial extent and rate of imbibition.Our results thus show that the overall rates of calcite dissolution approach the rates of acidic HFF transport (i.e., Damköhler number ∼1), which could contribute to the efficiency of subsurface reservoir stimulation. A better understanding of HFF-calcite reaction rates is crucial for improving the prediction and optimization of fluid transport across HFF-shale interfaces during hydraulic fracturing.

An Efficient Approach for Automatic Complex Fractured Networks Parameter Inversion Based on Surrogate Model and Deep Reinforcement Learning

AbstractComplex fracture networks are commonly generated in subsurface reservoirs, and the first and primary task is to understand their transport characteristics and properties. Like pumping test interpretation, the well‐testing interpretation is an effective means for transport characteristics analysis and parameter estimations, this work attempts to propose a parameter inversion approach for complex fracture networks based on well‐testing interpretation. Given that non‐unique solutions and computational inefficiencies are obstacles to practical interpretation, especially when complex fractures are existing, a new deep reinforcement learning (DRL) based approach is proposed for automatic curve matching on complex fractured networks well‐testing interpretation. Based on twin delayed deep deterministic policy gradient (TD3) algorithm, the proposed DRL approach is successfully applied to automatic matching of complex fractured networks' well test curves. In addition, to improve the training efficiency, a surrogate model of the well test model based on bidirectional GRU (Bi‐GRU) neural network was established. After episodic training, the agent finally converged to an optimal curve matching policy through interaction with the surrogate model. The results show that the average relative error of the curve's parameter interpretation is 4.34%. Additionally, the results from the case studies show that the proposed DRL approach has a high calculation speed.

Scale dependence of petrophysical measurements in reservoirs with Thalassinoides: Insights from CT scans

Subsurface reservoirs with Thalassinoides are well known. Using a CT scan of an 18.5 cm-diameter core (top cross section, 267.21 cm2; length, 26.5 cm) with Thalassinoides, this study demonstrates the scale dependence of sampling, and variables important in selecting representative sample dimensions for modeling these reservoirs. In the CT scan, 40 vertical square prism subsamples were extracted with cross sectional area ranging from 1.44 cm2 to 92.16 cm2. The results illustrate the scale dependence and sampling biases on Thalassinoides morphology, burrow percentage (BP), and connectivity of burrows from the top to bottom of subsamples (a proxy for permeability). Analysis of the entire scan shows a BP of ∼38%. The 40 subsamples vary in BP from 7% to 44% with the smallest cross sections showing the expected highest variance, but also showing the lowest mean BP. This illustrates that small-diameter vertical subsamples are likely to under sample Thalassinoides networks. In the full core, Thalassinoides connects across the top and bottom. Subsample cross sections >51.84 cm2 have 100% probability of showing this, whereas subsample cross sections <12.96 cm2 have 0% probability of showing this. To find the dimensions of representative samples to model Thalassinoides-bearing reservoirs, burrow diameter, BP, vertical length of sample, and core diameter must all be considered.

The effect of weak Mohr–Coulomb layers on the onset of caldera collapse - A limit analysis modelling approach

Calderas are subcircular volcanic depressions that can occur due to drainage of a subsurface magma reservoir. Numerous models simulating the initiation and growth of caldera collapse consider homogeneous overburden of the magma reservoir. This study describes plastic models implementing limit analysis to investigate the effects of weak layers (low cohesion and low friction) on caldera formation and structure. Our models show that the presence of weak layers within the crust favours the onset of caldera collapse, as it reduces the critical magma underpressure within the magma chamber to initiate roof failure. This effect is more pronounced with greater cumulated thickness of weak layers. In homogeneous models, the onset of caldera collapse is accommodated by a simple, localized outward dipping reverse damage band (caldera fault), whereas in layered models caldera collapse is accommodated by more complex damage structures. Weak layers confine damage underneath the layers, limiting the growth of the caldera fault toward the surface. Calculated stress trajectories are rotated across weak layers, showing that weak layers act as stress barriers. The effect of weak layers is stronger when the layer is closer to the magma reservoir, where layer-parallel damage form underneath the layer, interpreted as a potential detachment level. Multiple layers trigger more distribution of the damage and several layer-parallel damage bands. The subsurface distribution of damage due to weak layers may lead to more distributed surface subsidence, enhancing sagging before a caldera fault reaches the surface. Finally, internal detachments due to weak layers are likely important for observed episodic transient subsurface collapse episodes before collapse occurs at surface. All in all, our models that implement plastic deformation predict significant stress perturbations as a result of varying Mohr–Coulomb properties only. Our study thus shows that widely used static elastic models are not sufficient for physically relevant stress analyses of geological systems. In addition, our study shows that plastic (or elasto-plastic) models are necessary to predict the location and extent of inelastic damage accommodating volcano deformation and failure.

Using legacy core material to assess subsurface carbon storage reservoir potentiality

Abstract The growing importance of subsurface carbon storage for tackling carbon emissions requires an accurate characterization of potential reservoirs to understand their capabilities. In this context, the use of legacy data originally acquired in the last fifty years for scientific projects and petroleum exploration and production activities would represent a suitable cost-effective solution and help to maximize the value of this extended national asset. Core material represents the only direct observation of subsurface deposits and must be preserved from the current disposal process related to the decommissioning of hydrocarbon fields. In this contribution, a suite of samples from core material stored at national (i.e. British Geological Survey) and local (i.e. Department of Earth Sciences, Royal Holloway, University of London) core repositories, previously characterized at the micro scale using X-ray micro-computed tomographic (μCT) imaging are discussed. Using this technique, it has been possible to investigate how pore and grain geometries control crucial features of a suitable reservoir such as porosity and permeability. The aim of this contribution is to describe the methodology behind digital image analysis (DIA) following μCT imaging applied to core material. We show how DIA can be used to provide significant measures of reservoir suitability when making initial assessments of storage reservoirs, without the need for expensive and time-consuming analyses.

Structural diagenesis and dolomitization of Cenozoic post-rift carbonates in the Red Sea rift basin: A multiproxy approach

Middle Miocene post-rift sediments are considered prolific subsurface reservoirs, representing one of the thickest sequences in the Red Sea rift basin. In the Umm Luj Basin of the eastern Red Sea, post-rift sediments are well exposed and represented by a carbonate-dominated system of the Raghama Formation. This formation was intensely fractured, following the rifting trend of the Red Sea. Such fractures and their associated diagenetic products could provide a significant archive of past tectonic fluid evolution. However, little is known about the origin and timing of the different fluid flows and diagenetic processes in the area. This study aims to resolve this issue by integrating fracture and multiproxy geochemical analyses of calcite precipitated in veins, fault breccia, and dolomitized host rock. The δ18O and δ13C isotopic compositions of calcite veins show tight clustering, varying between −10.6 and −9.5‰ and between −7.9 and −7.2‰, respectively. Meanwhile, the precipitated calcite along the fault breccia exhibited a closer to host rock isotopic composition (δ18O = −6.8‰; δ13C = −4.8‰). The δ18OVPDBof the dolomitized host rock shows a heavier average value, closer to the expected range of Miocene seawater. X-ray diffraction analysis shows that the veins have a high magnesium calcite content (up to 79.5%). In contrast, all the host rock samples, except samples 1-1BH, have dolomite contents of up to 94.3%, as well as breccia fragments. Thus, we argue that the structural diagenesis history of the study area comprises two distinct fluid members and tectonic events. The first member is the deposition of heavier isotopic composition related to dolomitization at slightly higher temperatures of up to 42.2°C. The second fluid flow member corresponded to a depleted isotopic calcite member with a temperature of 33°C. Compared with the Midyan Peninsula, the study area shares the same regional tectonic events, but the local tectonic and depositional settings could act as the determining factors of the dolomitization mechanism and meteoric alteration in each location. Hence, our results provide a new understanding of paleo-fluid circulation related to the evolution of tectonic events and highlights the value of integrating fracture and multiproxy geochemical analysis for structural diagenetic studies.

Evaluation of proppant injection based on a data-driven approach integrating numerical and ensemble learning models

Injecting proppant to prop open fluid-driven fractures in subsurface reservoirs is one of the key missions of hydraulic fracturing. However, quantitative evaluation of the distribution of successfully propped fractures is limited due to the infeasibility of direct measurement. This work defines an indexing parameter for field practice to estimate the proportion of proppant-filled fractures in the reservoir – the proppant filling index (PFI). A new data-driven workflow, combining numerical models and an ensemble learning algorithm, is proposed and trained on field records of both screen-out and near screen-out cases and is then applied to predict PFIs for regular cases. The algorithm performance is promoted via variable importance measure (VIM) analyses and a backward elimination strategy. Four screen-out and twelve regular cases are presented to demonstrate the predicted PFI and highlight its potential utilizations. The new PFI and workflow evaluate the proppant injection quantitatively and reveal any mismatch between proppant injection and underground fractures, which may be essential for post-fracturing analyses and reservoir characterization to improve both oil & gas recovery, the sequestration of CO2, storage then recovery of H2 and the recovery of deep geothermal fluids as important components in enabling the energy transition.

Infill well placement optimization for secondary development of waterflooding oilfields with SPSA algorithm

A significant amount of bypassed oil resources often remain in a mature waterflooding reservoir because of non-uniform sweep caused by natural complexities of a subsurface reservoir and improper management of the reservoir. Infill drilling is one of the most attractive options for increasing oil recovery in consequence of its operational simplicity, low risk and promising results. Determining optimal infill well placements in heterogeneous mature reservoirs is a critical and challenging task that has a significant impact on the recovery performance and economic revenue of subsurface remaining oil resources. An integrated framework is constructed to attain best-obtained optimal location and completion of infill wells in multi-layer mature oil reservoirs. The placement of an infill vertical well is parameterized in terms of two sets of variables that define the location and completion respectively. A variant of SPSA algorithm is used to solve the defined optimization problem. The performance of the proposed algorithm is first tested for the joint optimization of well location and completion of an injection well using a synthetic model. The results show that the algorithm with average SPSA gradients outperforms the single SPSA gradient method both in solution and convergence rate. Besides, there are two plateaus on the performance curve of all algorithms: on the first plateau, each algorithm is approaching to its optimal well location with relatively little change on the completion parameters, while on the second plateau, each algorithm obtains the corresponding optimal completions. A complex heterogeneous reservoir model is then constructed by using the data of a mature oil reservoir in Shengli Oilfield in China to design an optimal 10 years’ infill drilling program. Four vertical production wells are placed in the oil-rich regions and both simultaneous and sequential algorithms are tried to obtain their optimal locations and completions. The performances of simultaneous joint optimization and sequential joint optimization are compared and as a result it is recommended to use sequential joint optimization as the optimization algorithm in the integrated framework.

Element variation in a clam shell and its implications for cold seep irregular eruptions: Calyptogena sp. in the Haima cold seep

Cold seep is characterized by methane-rich fluids released from subsurface reservoirs, and it sustains the chemosynthetic ecosystems on the seafloor. Previous studies suggest that the activity of cold seep could affect the seawater chemistry and ambient temperature. However, the short-term seep activity was hardly reconstructed due to the focus of studies on carbonate or sediment. Vent macrofauna provide such an opportunity by recording in shells the immediate environment in which they grow. The carbonate skeleton of organisms could theoretically preserve environmental variation. Therefore, high-resolution archives are urgently required to understand the influence of cold seep activity on biogeochemistry. In this study, SEM, EDS mapping, EBSD mapping, and LA-ICP-MS analyses were conducted on a clam (Calyptogena sp.) shell collected alive in 2018 from the Haima cold seep in South China Sea. The CaCO3, Na, Mg, Sr, and Ba contents and the Sr/Ca, Ba/Ca, and Na/Ca ratios in the hinge plate were measured on LA-ICP-MS by spot analysis and line scanning. The element contents in the hinge are as follows: Mg (38.5–109 μg/g), Na (3117–5246 μg/g), Sr (970–5371 μg/g), and Ba (2.9–11.5 μg/g). The results show that Sr, Re, and Ba content vary synchronously along the direction of growth, but Na has an opposite trend. The element analyses indicate that the eruption of the Haima cold seep was irregular, causing temperature, redox state, and pH changes in the cold seep ecosystem. These findings show that the irregular cold seep activities exert vital influences on the biogeochemistry of the cold seep ecosystem, which shed a light on cold seep biomonitoring.

Formulated Mathematical Model for Delayed Particle Flow in Cascaded Subsurface Water Reservoirs with Validation on River Flow

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 &gt; 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.