Steady-state Flow Model Research Articles

ASSESSMENT OF GAS PARAMETERS UNCERTAINTY IN A DAMAGED GAS PIPELINE BASED ON A STEADY-STATE GAS FLOW MODEL

Detecting gas leaks due to damage to gas pipelines and determining the volume of natural gas losses is important for reducing the imbalance in gas pipeline systems and increasing their reliability. The volume of lost gas can be determined based on the pressure and temperature of the gas at the location of the damage and the geometric characteristics of the damage. Since the gas parameters at the place of damage to the gas pipeline may differ significantly from the measured values ​​of the gas parameters at the nodal points, they should be determined based on mathematical models of gas movement. While determining the volume of lost gas, it is also essential to estimate the uncertainty of this volume, which requires also estimating the uncertainty of the pressure and temperature of the gas at the point of damage. This article is devoted to developing analytical equations for assessing the uncertainty of gas pressure and temperature at the damage point, obtained using a mathematical model of steady-state gas flow. The methodology for evaluating the uncertainty of gas pressure and temperature at the pipeline damage point is considered, taking into account various factors such as pressure, temperature, flow rate, gas composition, and the geometric characteristics of the pipeline. The research relies on standardized procedures and methods for uncertainty analysis presented in JCGM 100:2008 and ISO 5168:2013. As a result of the study, equations for the relative standard uncertainty of pressure and temperature of natural gas at the damage point were derived, and the influence coefficients of the uncertainty components were found, enabling the assessment of these parameters' uncertainty while considering the uncertainties of the pipeline's geometric characteristics and the flow gas-dynamic parameters. Examples of calculating the relative standard uncertainty of pressure and temperature of the gas at the damage point are provided for the case of a complete pipeline rupture. The obtained equations for the uncertainty of pressure and temperature of gas at the damage point will serve as the basis for the methodology for estimating the uncertainty of the volume of gas lost due to damage.

Numerical Simulation of Corrosive Flow in the Production End of Carbon Capture, Utilization, and Storage-Enhanced Oil Recovery Backflow Wastewater Pipeline

In a carbon capture, utilization, and storage-enhanced oil recovery (CCUS-EOR) system process, the high carbon dioxide content and high acid value of the fluid at the extraction end are treated at the wastewater treatment station and then flow through the transfer station of the gathering system. The reinjection system’s pipelines at the transfer station are prone to corrosion and leakage risks. A steady-state nonisothermal flow and corrosion model was established to examine this corrosive phenomenon by utilizing the principles of fluid dynamics and electrochemical corrosion. The study examined how flow velocity, temperature, pressure, and pH affected the pipeline’s corrosion. Simulation results showed flow velocity increased in specific places of both straight and curved pipeline sections. The velocity near the inner wall of curved portions was higher, making them more susceptible to cavitation damage. Faster flow rates, lower pH values, higher temperatures, and smaller pipeline diameters all contributed to increased corrosion on the inner walls of wastewater pipelines. The highest simulated corrosion rate was 8.3162 mm/a corresponding to the smallest pipeline diameter (100 mm), lowest pH (4), highest temperature (60°C), and highest flow rate (36.847 m/s). When designing the CCUS-EOR system, the nonmetallic pipeline should be given priority. If carbon steel metal pipelines are utilized, it is best to use larger-diameter materials in the engineering design. Additionally, procedures such as adding corrosion inhibitors to regulate pH values and lowering the temperature of wastewater conveyance might be explored to reduce corrosion on the pipeline’s inner walls.

Design optimization of floating offshore wind farms using a steady state movement and flow model

Abstract In this study, we demonstrate how to carry out the design optimization of floating offshore wind farms by considering the impacts brought by the movements of the floating wind turbines. A steady state movement and flow model is applied in the modelling process. This model is developed by building a turbine surrogate model for estimating the steady state movement and power production of floating wind turbines and incorporating it in an open-source static wind farm simulator, PyWake. Using this modelling methodology, layout optimization problems of floating offshore wind farms are solved by using algorithms like Random Search to maximize the energy yield while satisfying certain constraints. Case studies are carried out for two wind farms with met-ocean conditions from a real planned site in Scottland to show the potential of layout optimization for floating wind farms.

Unified, Integral Approach to Modeling and Design of High-Pressure Pipelines: Assessment of Various Flow and Temperature Models for Supercritical Fluids

Abstract A unified one-dimensional, steady-state flow and heat transfer model is presented for the pipeline transport of fluids at high pressures, including the supercritical conditions. The model includes a generalized temperature equation, presented here for the first time, and accounts for all of the important effects, including the property variation, viscous dissipation, Joule-Thomson (J-T) cooling, and heat exchange with the surrounding. With appropriate approximations, this model can yield all isothermal and non-isothermal pipe flow solutions reported thus far. A generalized multi-zone integral method is developed which solves the two resulting algebraic equations for pressure and temperature in conjunction with a property database, such as the National Institute of Standard and Technology (NIST) Reference Fluid Thermodynamic and Transport Properties (REFPROP). With appropriately selected number and size of the zones and using property values at the mean temperature and pressure within each zone, this integral method can accurately predict the complex effects of the governing parameters, such as the pipe diameter and length, inlet and exit pressures, mass flow rate, J-T cooling, and inlet and surrounding temperatures. Its accuracy for small-to-large diameter pipes has been ascertained by a comparison with the numerical solutions of the differential form of governing equations that requires a large number of small grids along the pipe and the values of mean properties within each grid. Indeed, this integral model can be used for the pipeline transport at both subcritical and supercritical pressures as long as the fluid does not encounter its anomalous states and the phase-change.

Constraints of geomorphic indices on the expansion mode of the southeastern margin of the Tibetan plateau

The growth and expansion of the southeastern Tibetan Plateau remain contentious. Positioned as one of the regions characterized by the most robust tectonic activities on the plateau, the southeastern edge provides a distinctive setting for investigating plateau uplift and landform evolution. This study focuses on the southeastern margin of the plateau in the Three Rivers Region, conducting comprehensive analyses of slope, relief, hypsometric integral (HI), and channel steepness index (ksn). We use this new dataset to highlight the more significant role of tectonic activities in shaping the landform compared to climate and lithology. By examining the spatiotemporal characteristics of long-term and short-term rock exhumation rates, derived from low-temperature thermochronology and cosmogenic nuclide 10Be analysis, we establish a correlation between erosion rates and ksn, slope, and terrain undulation. Integrating this information with geophysical evidence and GPS data, we support the model for the expansion of the southeastern edge—the steady-state terrain crustal flow model. According to this model, there is an equilibrium achieved between rock uplift and surface erosion on the southeastern edge of the Tibetan Plateau. Despite ongoing southeastward extrusion of plateau material, the overall plateau morphology remains unaltered due to intense erosion along the plateau’s edge. Consequently, the large-scale topographic expansion of the southeastern Tibetan Plateau has effectively halted.

Numerical simulation of aluminum-steel clad strip production using horizontal single belt casting process

A 3-D steady-state turbulent flow and solidification model was developed to simulate melt flow in a Horizontal Single Belt Caster for the production of an Al-Steel composite strip. The steel substrate is attached to the moving belt and moves at the same speed as the belt while the aluminum melt is introduced onto the substrate via an extended nozzle melt delivery system. A finite volume method was used to numerically solve the governing equations. In order to model the turbulent flow, a low Reynolds k − ε turbulent model was adopted. The developed numerical model was further employed to investigate the effect of such parameters as clad thickness, casting speed, molten aluminum superheat, and heat extraction rate from the belt surface on fluid flow and temperature fields in the system. It was found that for a certain clad thickness, casting speed and cooling rate should be adjusted properly and outlet strip temperature is independent of Inlet melt superheat.

Mathematical modelling for groundwater management for multilayers aquifers (Erbil basin)

This study addresses the pressing issues of groundwater depletion and drought problems in the Erbil basin, a vital resource region in the Middle East. Focused on an area of strategic importance due to its large size and critical water resources, the study employs the Groundwater Modeling System (GMS) software to create a detailed 3D hydrogeological model based on extensive borehole data. With over 240 boreholes analyzed, the study strategically selects 70 accurate wells drilled by the Groundwater Directorate. The construction of the 3D stratigraphic models for the Erbil basin relies on three main historical data including boreholes, geological formations and a comprehensive approach, incorporating deep well logging data and the definition of distinct geological layers. By discerning the presence of previous and impervious layers, the model effectively categorizes the aquifer types within the Erbil basin. The aquifer system is delineated based on stratigraphic units, designating materials with high conductivity (silt, sand, and gravel) as aquifers and clay (or claystone) as aquitards. A 3D steady-state groundwater flow model is successfully executed, employing PEST pilot point for automated parameter estimation. The model, validated with a coefficient of determination (R2) of 0.9998, reveals hydraulic conductivity values ranging from 0.000980705 to 100 m/day and a recharge value of 0.000976443 m/day. The study classifies Erbil's aquifer types as unconfined, confined, and semi-confined, providing a valuable foundation for groundwater management. The primary objective of this study is to construct a calibrated numerical groundwater model for the multi-aquifer system in the Erbil basin. The model aims to serve as a robust tool for analyzing the sustainability of diverse groundwater infrastructure development strategies within the region. The Erbil basin poses unique challenges for groundwater modeling, marked by a scarcity of critical data such as monitoring well information, pumping rates, recharge rates, and flow budgets. In response to these limitations, the study adopts an innovative approach by integrating in situ data with earth observation data. The integration of these datasets seeks to overcome data constraints and enhance the accuracy of the groundwater model. By achieving calibration and validation of the numerical model, this research strives to provide a valuable resource for decision-makers, planners, and stakeholders involved in groundwater management in the Erbil basin. Ultimately, the study aims to contribute to the development of sustainable and effective strategies for the utilization and preservation of groundwater resources in this vital region and also to enhance practical management strategies for the Erbil groundwater basin, ensuring sustainable utilization of the crucial sub-surface water resources, an objective successfully achieved through this research.

The effect of fracture aperture and matrix permeability on suitability of the equivalent porous medium model for steady-state flow in fractured porous media

The effect of fracture aperture and matrix permeability on suitability of the equivalent porous medium model for steady-state flow in fractured porous media

Gaussian process regression and conditional Karhunen-Loève models for data assimilation in inverse problems

We present a model inversion algorithm, CKLEMAP, for data assimilation and parameter estimation in partial differential equation models of physical systems with spatially heterogeneous parameter fields. These fields are approximated using low-dimensional conditional Karhunen-Loève expansions (CKLEs), which are constructed using Gaussian process regression (GPR) models of these fields trained on the parameters' measurements. We then assimilate measurements of the state of the system and compute the maximum a posteriori (MAP) estimate of the CKLE coefficients by solving a nonlinear least-squares problem. When solving this optimization problem, we efficiently compute the Jacobian of the vector objective by exploiting the sparsity structure of the linear system of equations associated with the forward solution of the physics problem.The CKLEMAP method provides better scalability compared to the standard MAP method. In the MAP method, the number of unknowns to be estimated is equal to the number of elements in the numerical forward model. On the other hand, in CKLEMAP, the number of unknowns (CKLE coefficients) is controlled by the smoothness of the parameter field and the number of measurements, and is generally much smaller than the number of discretization nodes, which leads to a significant reduction of computational cost with respect to the standard MAP method. To show this advantage in scalability, we apply CKLEMAP to estimate the transmissivity field in a two-dimensional steady-state subsurface flow model of the Hanford Site by assimilating synthetic measurements of transmissivity and hydraulic head. We find that the execution time of CKLEMAP scales nearly linearly as N1.33, where N is the number of discretization nodes, while the execution time of standard MAP scales as N2.91. The CKLEMAP method improved execution time without sacrificing accuracy when compared to the standard MAP method.

Review of electric vehicle (EV) charging using renewable solar photovoltaic (PV) nano grid

This review article gives a comprehensive review of existing research on renewable solar photovoltaic (PV) nanogrid, which is described from small-scale power system with a single domain for reliability, control, and power quality (PQ) for electric vehicle (EV) charging. A primary feeder on the Microgrid is connected to a nanogrid test bed that includes PV as power source, a battery energy storage system (BESS), smart-inverter multiple and EV charging stations (EVCS). The control algorithms are graded on four metrics: (1) voltage profiles, (2) renewable penetration, (3) PV curtailed and (4) net power flows. To investigate the local power quality, a steady-state power flow model of the nano-grid is created. The control algorithms successfully employ the battery to shift the nano-grid peak load while limiting the nano-grid demand to set level. Furthermore, an increasing emphasis is being placed on commonly used strategies for addressing the characteristics of each renewable system. This review paper characterizes the dynamic operation of 4 distinct BESS control algorithms for solar EV charging nanogrid: (1) peak load shifting, (2) reduce peak period impact, (3) cap demand, and (4) photovoltaic capture. These control modes are executed and analyzed on real-world nano-grid site, and optimal BESS control modes are assessed in terms of (1) solar electric vehicle charging, (2) power quality, (3) grid net demand, (4) photovoltaic curtailment, and (5) solar penetration. Finally, the problems highlight research gaps, and discussions on future trends are critical for enhancing the general technology of the renewable solar photovoltaic nano-grid for EV charging.

Groundwater Flow Modeling of A Microwatershed using Visual Modflow Flex

The present study attempts to make a simulation of groundwater flow modeling in Chikkodi micro-watershed Belagavi (District), Karnataka. A two-layer conceptualization and the three-dimensional groundwater flow model are primarily underlain by weathered basalt and fractured basalt. The first layer weathered zone is 30m from the ground surface and the second layer fractured zone is 80m below the ground surface spread over 20 rows and 20 columns. The cell height is 674m and the cell width is 440m. The work described here built a groundwater flow model in the micro-watershed using Visual MODFLOW Flex. The steady-state groundwater flow model was then numerically projected in April 2020 using seventeen observation wells using the present stress levels. The model aims to quantify input and output stresses and pinpoint the basin's overstressed regions. The water budget analysis estimates that evapotranspiration loss makes up 56.54% of the basin's total groundwater recharge while overall groundwater leaks from river systems are 28.72%. The findings indicated that the southern section of the basin is undergoing severe aquifer stress as a result of river overflow and evapotranspiration. To improve groundwater levels, it is suggested that artificial recharge structures should be developed in and near Chikkodi village at appropriate sites. The trial-and-error approach was used to assess the sensitivity of the calibrated model, and it was discovered that the model is extremely sensitive to changes in hydraulic conductivity and recharge levels. Model performance is excellent, with R2, RMSE, and NRMSE values of 0.97, 5.34, and 13.23% of the assessing criteria.

Numerical simulation of a managed aquifer recharge system designed to supply drinking water to the city of Amsterdam, The Netherlands

Managed aquifer recharge (MAR) is increasingly used to secure drinking water supply worldwide. The city of Amsterdam (The Netherlands) depends largely on the MAR in coastal dunes for water supply. A new MAR scheme is proposed for the production of 10 × 106 m3/year, as required in the next decade. The designed MAR system consists of 10 infiltration ponds in an artificially created sandbank, and 25 recovery wells placed beneath the ponds in a productive aquifer. Several criteria were met for the design, such as a minimum residence time of 60 days and maximum drawdown of 5 cm. Steady-state and transient flow models were calibrated. The flow model computed the infiltration capacity of the ponds and drawdowns caused by the MAR. A hypothetical tracer transport model was used to compute the travel times from the ponds to the wells and recovery efficiency of the wells. The results demonstrated that 98% of the infiltrated water was captured by the recovery wells which accounted for 65.3% of the total abstraction. Other sources include recharge from precipitation (6.7%), leakages from surface water (13.1%), and natural groundwater reserve (14.9%). Sensitivity analysis indicated that the pond conductance and hydraulic conductivity of the sand aquifer in between the ponds and wells are important for the infiltration capacity. The temperature simulation showed that the recovered water in the wells has a stable temperature of 9.8–12.5 °C which is beneficial for post-treatment processes. The numerical modelling approach is useful and helps to gain insights for implementation of the MAR.

Dynamics of Coastal Aquifers: Conceptualization and Steady-State Calibration of Multilayer Aquifer System—Southern Coast of Emilia Romagna

Worldwide, coastal aquifers have been heavily exploited by socio economic activities for several decades, and climate change and sea level rise have also been threatening coastal aquifers. The authorities and policymakers have been advised to find the solutions in order to achieve sustainable water resources management. The southern part of Po delta, Italy is a low-lying coastal area also experiencing tectonic activity. Along with low-lying topography, unstable shore line and sea level, the groundwater is heavily exploited by this deltaic multilayered system of aquifers. Hence, a multilayer three-dimensional model of this aquifer system has allowed for the investigation of the response of aquifer to natural and anthropogenic exploitation. The present work regards the conceptualization of the multilayer aquifer system using lithological cross-sections, surface water features, and appropriate boundary conditions and the steady-state flow modelling. The spatially distributed elevations of the groundwater table and piezometric head from the different aquifers have been calibrated. The values of model error statistics at a satisfactory range, such as R-squared, mean error, root-mean-squared error and model efficiency, confirm that the developed model is reliable, and calibration is obtained with good match between observed and simulated data. The developed model can be used as a decision-making tool for the authorities and policymakers in order to plan for sustainable water management.

Assessing Vulnerability of Regional-Scale Aquifer-Aquitard Systems in East Gulf Coastal Plain of Alabama by Developing Groundwater Flow and Transport Models

Groundwater vulnerability assessment helps subsurface water resources management by providing scientific information for decision-makers. Rigorous, quantitative assessment of groundwater vulnerability usually requires process-based approaches such as groundwater flow and transport modeling, which have seldom been used for large aquifer-aquitard systems due to limited data and high model uncertainty. To quantify the vulnerability of regional-scale aquifer-aquitard systems in the East Gulf Coastal Plain of Alabama, a three-dimensional (3D) steady-state groundwater flow model was developed using MODFLOW, after applying detailed hydrogeologic information to characterize seven main aquifers bounded by aquitards. The velocity field calibrated by observed groundwater heads was then applied to calculate groundwater age and residence time for this 3D aquifer-aquitard system via backward/forward particle tracking. Radioactive isotope data (14C and 36Cl) were used to calibrate the backward particle tracking model. Results showed that shallow groundwater (<300 ft below the groundwater table) in southern Alabama is mainly the Anthropocene age (25–75 years) and hence susceptible to surface contamination, while the deep aquifer-aquitard systems (700 ft or deeper below the groundwater table) contain “fossil” waters and may be safe from modern contamination if there is no artificial recharge/discharge. Variable horizontal and vertical vulnerability maps for southern Alabama aquifer-aquitard systems reflect hydrologic conditions and intermediate-scale aquifer-aquitard architectures in the regional-scale models. These large-scale flow/transport models with coarse resolutions reasonably characterize the broad distribution and vertical fluctuation of groundwater ages, probably due to aquifer-aquitard structures being captured reliably in the geology model. Parameter sensitivity analysis, vadose zone percolation time, wavelet analysis, and a preliminary extension to transient flow were also discussed to support the aquifer vulnerability assessment indexed by groundwater ages for southern Alabama.

Tunnel Face Stability Considering the Influence of Excess Slurry Pressure

With excess slurry pressures exerted on the tunnel face, slurry particles tend to infiltrate into the soil in front of the tunnel. There will be excess pore pressure ahead of the tunnel in the case of infiltration, leading to an impairment in the supporting effect contributed by the excess slurry pressure. Corresponding to three slurry infiltration scenarios distinguished by the forms of the filter cake, different pressure transfer models are employed to describe the pore pressure distribution. Using the kinematic approach of limit analysis and the numerically simulated seepage field, the study of tunnel face stability under different slurry infiltration cases is extended by employing a 3D discretization-based failure mechanism. In addition, two simple empirical formulas describing the pore pressure distributions above the tunnel and in advance of the tunnel are established and verified. Combined with the dichotomy method and strength reduction method, the safety factors yielding rigorous upper-bound solutions are obtained by optimization. The proposed method is validated by a comparative analysis. The developed framework allows considering the influence of excess pore pressure on the whole failure mechanism and the three-dimensional characteristics of seepage. A parameter analysis is performed to study the effect of the excess slurry pressure, hydraulic conditions, soil strength properties, and pressure drop coefficient. The results show that the steady-state flow model leads to much more conservative results than the full-membrane model. The safety factor increases with the increasing excess slurry pressure and the decreasing pressure drop coefficient. The present work provides an effective framework to quickly assess the face stability of tunnels under excess slurry pressure considering different filter cake scenarios.

Water Management for Conservation and Ecosystem Function: Modeling the Prioritization of Source Water in a Working Landscape

Conservation in working landscapes is an important aspect of stream restoration. Landowners with agricultural water rights are increasingly adding instream flow as a beneficial use of their allocated water. However, stream restoration projects commonly focus on the quantity of water dedicated to the environment and overlook water quality. For cold-water ecosystems, the preservation of natural thermal regimes is a key to conservation efforts in the face of a changing climate. This study explored the effects of increasing stream flow using alternative water sources (e.g., instream runoff versus offchannel springs) to enhance cold-water stream habitat on a working cattle ranch. Using empirical data to create a steady-state stream flow and water temperature model, we evaluated temperature benefits and management trade-offs for ecological and agricultural water use. The modeled results showed that the source of water and the method used to deliver water to the channel affected the quality and extent of cold-water habitat. Offchannel spring water cooled 7-day average maximum temperatures and 7-day average mean temperatures by as much as 3.7°C and 2.9°C, respectively, but only when potential offchannel aquatic habitat was sacrificed for mainstem habitat. When offchannel, spring-fed habitat was provided, the value of spring water to the main channel decreased. Our findings suggest that source water thermal quality is of paramount importance for enhancing ecosystem function and improving cold-water habitat in working landscapes. In addition, the restoration of a historic spring channel may provide added ecosystem benefits by enhancing aquatic habitat for cold-water species.

Hydrogeological modeling of the Roussillon coastal aquifer (France): stochastic inversion and analysis of future stresses

Global climate change-induced stresses on coastal water resources include water use restrictions, saline intrusions, and permanently modifying or damaging regional resources. Groundwater in coastal regions is often the only freshwater resource available, so an in-depth understanding of the aquifer, and the aquifer’s response to climate change, is essential for decision-makers. In this study, we focus on the coastal aquifer of Roussillon (southern France) by developing and investigating a steady-state groundwater flow model (MODFLOW 6) and calibrated with PEST++ on a Python interface (FloPy and PyEmu). Model input and boundary conditions are constrained by various scenarios of climate projections by 2080, with model results predicting the aquifer’s response (and associated uncertainty) to these external forcings. Using simple assumptions of intrusion estimates, model results highlight both strong climatic and anthropogenic impacts on the water table. These include aquifer drawdowns reaching several meters locally, and the seawater interface advancing locally several hundred meters inland and rising by several meters. Intrusions of this magnitude risk endangering exploited water wells and their sustainability. Our results demonstrate the critical importance of properly characterizing the geology and its heterogeneity for understanding aquifers at risk because poor predictions may lead to inappropriate decisions, putting critical resources at risk, particularly in coastal environments.

Dynamics of gas-driven eruption on Ceres as a probe to its interior

The mineralogy of localized bright deposits on Ceres observed by the DAWN mission suggests their brine-enriched cryovolcanic origin. Based on the morphological observations of these deposits, explosive and effusive styles have been proposed for their eruption. Because volcanic eruption style and velocity are controlled by the extent of gas expansion inside the conduit, constraints on the internal aqueous environment, such as gas concentration and temperature, could be placed based on the observations of localized deposits on Ceres. However, the way these properties control the eruption style and velocity is complex. Cryomagma ascending from a subsurface reservoir gains buoyancy due to both boiling of water and exsolution of dissolved gas, owing to decompression to the extremely low pressure near the Ceres surface. Gas–melt segregation should also affect the dynamics. Thus, it is not yet fully understood how the internal environment of Ceres affects the ascent dynamics of cryovolcanism and subsequently controls the styles (explosive versus effusive) and velocities of eruptions. To address this problem, we developed a one-dimensional steady-state two-phase flow model for the ascent dynamics of gas-driven cryomagma under the conditions of Ceres taking both water boiling and gas exsolution into account. We found that the velocity and explosivity of an eruption are strongly controlled by the following three parameters, which characterize the cryomagmatic environment of Ceres's interior: (a) conduit conductivity (CC; rc2/μ, where rc is the conduit radius and μ is the magma viscosity), (b) dissolved gas concentration c0, and (c) magma reservoir temperature T0. Our model results reveal that low CC always leads to effusive or low-explosivity eruptions. Higher CC allows explosive eruption when either c0 or T0 is sufficiently high. These dependences can be summarized as four modes of eruption under the following CC-c0-T0 conditions. (1) Exsolution-driven explosive eruptions (X1 type) occur with volatile-rich magma (CC ≳ 10−3 m2/(Pa·s) and c0 ≳ 0.1 wt% of CO2). (2) Boiling-driven explosive eruptions (X2 type) occur with warm magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and high T0). (3) Viscosity-induced effusive eruptions (F1 type) occur with a narrow conduit and/or high-viscosity magma (CC ≲ 10−3 m2/(Pa·s)). (4) Low-gas-production-induced effusive eruptions (F2 type) occur with low-temperature and low-volatile magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and low T0). Our model predicts that either c0 ≳ 0.5 wt% of CO2 or T0 ≳−5°C is required for explosive eruptions to achieve eruption velocities ≳30 m/s, which has been proposed based on the size of some large faculae on Ceres. Such gas-rich or warm magma condition is unlikely to be achieved by equilibrium within the shallow crust. Thus, our results suggest that magma needs to be supplied from a deeper subsurface. In contrast, low-velocity effusion of brines has also been proposed based on morphometric analyses of evaporites on Ceres. Our results show that magma of such brine effusions is viscous and transported to the surface through a narrow conduit or they are sourced from reservoirs equilibrated to the ambient material within the shallow crust. Because the effusive eruption origin of faculae in the Occator crater is consistent with small conduits, the effusive nature may not necessarily rule out relatively high-volatile or warm magma inside Ceres in the recent past. These results show that the morphometric properties of facula deposits can place important constraints on the internal conditions of Ceres when the relevant eruption style/velocity is known. Our modeling results indicate that detailed observations (e.g., vesicularity, cooling history, and inclusion of eroded conduit material) of deposits and the possible vent structure in faculae by landing missions allow us to further probe the interior conditions of Ceres (e.g., magma temperature, gas concentration, viscosity, and conduit size).

Is thixotropy important in small-scale, steady-state flow modeling?

Is thixotropy important in small-scale, steady-state flow modeling?

Integrated flow model for evaluating maximum fracture spacing in horizontal wells

Multi-stage fractured horizontal wells are extensively used in unconventional reservoir; hence, optimizing the spacing between these hydraulic fractures is essential. Fracture spacing is an important factor that influences the production efficiency and costs. In this study, maximum fracture spacing in low-permeability liquid reservoirs is studied by building an integrated flow model incorporating key petrophysical characteristics. First, a kinematic equation for non-Darcy seepage flow is constructed using the fractal theory to consider the non-homogeneous characteristics of the stimulated rock volume area (StRV) and its stress sensitivity. Then, the kinematic equation is used to build an integrated mathematical model of one-dimensional steady-state flow within the StRV to analytically determine the pressure distribution in StRV. The resultant pressure distribution is utilized to propose an optimal value for the maximum fracture spacing. Finally, the effects of fractal index, initial matrix permeability, depletion, and stress sensitivity coefficient on the limit disturbed distance and pressure distribution are studied. This study not only enriches the fundamental theory of nonlinear seepage flow mechanics but also provides some technical guidance for choosing appropriate fracture spacing in horizontal wells.