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Mathematical and Computational Modeling in Geothermal Engineering

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A special issue of Energies (ISSN 1996-1073).

Deadline for manuscript submissions: closed (28 February 2018) | Viewed by 66892

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Prof. Dr. Mehrdad Massoudi

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1. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
2. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
Interests: multi-component flows; non-newtonian fluids; granular materials; heat transfer; mathematical modelling

Prof. Dr. Phuoc X. Tran

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Department of Mechanical Engineering and Material Science, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA 15261, USA
Interests: combustion studies; granular materials studies; laser ablation in liquid; laser-induced spark ignition; nanofluid studies; nanoparticles/nanomaterials
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Dear Colleagues,

Geothermal energy is the thermal energy generated and stored in the Earth's core, mantle and crust. At the center of the Earth, the temperatures may be in the range of 3500 to 4500°C. Geothermal technologies are used to generate electricity and to heat and cool buildings. They produce low level greenhouse gases and, therefore, are not only attractive sources of (renewable) energy, but, also, they produce less waste and pollutants. Major expenses in the operation and use of conventional geothermal systems are the cost associated with the drilling operation and the well maintenance, among other expenses. Combined heat and power generation where geothermal power plants and other sources of energy, such as solid biomass or fossil fuels, has also attracted much attention. In this Special Issue, all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction and convection in porous media, the drilling fluid, transport properties of the fluid, rock, etc., are considered. The emphasis here will be on mathematical and computational aspects of geothermal engineering, and contributions in all these areas are welcome.

Prof. Dr. Mehrdad Massoudi
Prof. Dr. Phuoc X. Tran
Guest Editors

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Keywords

Geothermal
Ground Heat Exchangers
Heat transfer
Transport Properties
Mathematical modeling
Computational Fluid Dynamics (CFD)
Drilling
Heat Pump
Porous media

Published Papers (14 papers)

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Research

18 pages, 14096 KiB

Open AccessArticle

Numerical Simulation of Nanofluid Suspensions in a Geothermal Heat Exchanger

by Xiao-Hui Sun, Hongbin Yan, Mehrdad Massoudi, Zhi-Hua Chen and Wei-Tao Wu

Energies 2018, 11(4), 919; https://doi.org/10.3390/en11040919 - 13 Apr 2018

Cited by 35 | Viewed by 5486

Abstract

It has been shown that using nanofluids as heat carrier fluids enhances the conductive and convective heat transfer of geothermal heat exchangers. In this paper, we study the stability of nanofluids in a geothermal exchanger by numerically simulating nanoparticle sedimentation during a shut-down process. The nanofluid suspension is modeled as a non-linear complex fluid; the nanoparticle migration is modeled by a particle flux model, which includes the effects of Brownian motion, gravity, turbulent eddy diffusivity, etc. The numerical results indicate that when the fluid is static, the nanoparticle accumulation appears to be near the bottom borehole after many hours of sedimentation. The accumulated particles can be removed by the fluid flow at a relatively high velocity. These observations indicate good suspension stability of the nanofluids, ensuring the operational reliability of the heat exchanger. The numerical results also indicate that a pulsed flow and optimized geometry of the bottom borehole can potentially improve the suspension stability of the nanofluids further. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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13 pages, 22938 KiB

Open AccessArticle

Influence of Fracture Heterogeneity Using Linear Congruential Generator (LCG) on the Thermal Front Propagation in a Single Geothermal Fracture-Rock Matrix System

by Nikhil Bagalkot, Alireza Zare and G Suresh Kumar

Energies 2018, 11(4), 916; https://doi.org/10.3390/en11040916 - 13 Apr 2018

Cited by 7 | Viewed by 3111

Abstract

An implicit finite difference numerical model has been developed to investigate the influence of fracture heterogeneity on the propagation of thermal front in a single horizontal fracture-matrix system. Instead of depending on a complex and data-demanding geostatistical method for a precise representation of fracture aperture, a statistical linear congruential generator (LCG) method was applied in the present study to replicate the unpredictable nature of fracture aperture morphology. The results have been compared with the parallel plate model and simple sinusoidal model. Finally, sensitivity analysis of fracture aperture size and fluid flow rate has been carried out to identify the conditions at which fracture heterogeneity is critical. The results indicate that LCG-aperture enhances the heat transfer between fracture and hot rock matrix compared to the parallel and sinusoidal fractures. Further, the temperature profiles in hot rock indicate that there was a greater loss of heat for the case of LCG-aperture (25% loss) compared to sinusoidal (16%) and parallel plate (8%) apertures. It was found that heterogeneity does not play a major role at small fracture aperture size (≤50 μm) and at low flow rates. However, as fracture aperture size increases, the heterogeneity plays a vital part even at low flow rates. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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21 pages, 4591 KiB

Open AccessArticle

Rate Decline Analysis for Modeling Volume Fractured Well Production in Naturally Fractured Reservoirs

by Mingxian Wang, Zifei Fan, Guoqiang Xing, Wenqi Zhao, Heng Song and Penghui Su

Energies 2018, 11(1), 43; https://doi.org/10.3390/en11010043 - 01 Jan 2018

Cited by 11 | Viewed by 3747

Abstract

Based on the property discontinuity in the radial direction, this paper develops a new composite model to simulate the productivity of volume fractured wells in naturally fractured reservoirs. The analytical solution of this model is derived in detail and its accuracy is verified by the same model’s numerical solution. Detailed analyses of the traditional transient and cumulative rate are provided for the composite model. Results show that volume fracturing mainly contributes to the early-flow period’s production rate. As interregional diffusivity ratio increases or interregional conductivity ratio decreases, the transient rate at the same wellbore pressure increases. Three characteristic decline stages may be observed on transient rate curves and the shape of traditional rate curves in the middle- and late-flow periods depends on naturally fractured medium and boundary condition. By introducing a new pseudo-steady constant, new Blasingame type curves are also established and their features are more salient than those of traditional rate curves. Five typical flow regimes can be observed on these new type curves. Sensitivity analysis indicates that new Blasingame type curves for varied interregional diffusivity ratio, interregional conductivity ratio, interporosity coefficient and dimensionless reservoir radius, except storativity ratio, will normalize in the late-flow period. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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7115 KiB

Open AccessArticle

Optimizing the Structure of the Straight Cone Nozzle and the Parameters of Borehole Hydraulic Mining for Huadian Oil Shale Based on Experimental Research

by Jiwei Wen and Chen Chen

Energies 2017, 10(12), 2021; https://doi.org/10.3390/en10122021 - 01 Dec 2017

Cited by 15 | Viewed by 4127

Abstract

Oil shale is a kind of potential alternative energy source for petroleum and has attracted the attention of energy researchers all over the world. Borehole hydraulic mining has more prominent advantages than both conventional open-pit mining and underground mining. It is very important to attempt to use the borehole hydraulic mining method to exploit underground oil shale. The nozzle is the key component of borehole hydraulic mining and reasonable mining parameters are also crucial in exploiting underground oil shale efficiently. The straight cone nozzle and the oil shale of Huadian area will be taken as the research objects. The self-developed, multifunctional, experimental device can test both the jet’s performance as well as the breaking of oil shale by the high-pressure water jet using the straight cone nozzle and varying structural parameters. Comprehensive analysis of the results of an orthogonal experimental design, including range analysis and variance analysis, demonstrate the optimal structural parameters of a straight cone nozzle as follows: the outlet diameter is 4 mm, the length to diameter ratio is 2.5, and the contraction angle is 60°. In addition, in order to maximize the efficiency of borehole hydraulic mining for Huadian oil shale, the non-submerged jet should be placed parallel to the oil shale bedding. These results can provide scientific and valuable references for borehole hydraulic mining of oil shale. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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6445 KiB

Open AccessArticle

A Cascade Disaster Caused by Geological and Coupled Hydro-Mechanical Factors—Water Inrush Mechanism from Karst Collapse Column under Confining Pressure

by Hao Li, Haibo Bai, Jianjun Wu, Zhanguo Ma, Kai Ma, Guangming Wu, Yabo Du and Shixin He

Energies 2017, 10(12), 1938; https://doi.org/10.3390/en10121938 - 23 Nov 2017

Cited by 18 | Viewed by 3936

Abstract

The water inrush from karst collapse column (KCC) is a cascading, vicious cycle disaster caused by geological and mining activities, that can cause serious casualties and property losses. The key to preventing this risk is to study the mechanism of water inrush under confining pressure. Aiming at the investigationg the characteristics of the KCC named X1 in Chensilou mine, a series of methods, including connectivity experiments, water pressure monitoring tests in two side-walls, and numerical simulations based on plastic damage-seepage (PD-S) theory have been developed. The methods are used to test the security of the 2519 mining area, the damage thickness, pore water pressure, and seepage vector in the X1. The results indicate that the X1 has a certain water blocking capacity. In addition, with the decrease of confining pressure and increase of shear stress, deviatoric stress could cause the increase of permeability, the reduction of strength, and the reduction of pore water pressure in KCC. Therefore the increased effective stress in the rock will force the rock to become more fractured. Conversely, the broken rock could cause the change of stress, and further initiate new plastic strains, damage and pore water pressure until a new equilibrium is reached. This cascading water inrush mechanism will contribute to the exploitation of deep coal resources in complex geological and hydrogeological conditions. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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5484 KiB

Open AccessArticle

Application of Confined Blasting in Water-Filled Deep Holes to Control Strong Rock Pressure in Hard Rock Mines

by Jingxuan Yang, Changyou Liu and Bin Yu

Energies 2017, 10(11), 1874; https://doi.org/10.3390/en10111874 - 15 Nov 2017

Cited by 33 | Viewed by 5139

Abstract

In extra-thick coal seams, mining operations can lead to large-scale disturbances, complex overburden structures, and frequent and strong strata behavior in the stope, which are serious threats to mine safety. This study analyzed the overburden structure and strata behavior and proposed the technique of confined blasting in water-filled deep holes as a measure to prevent strong rock pressure. It found that there are two primary reasons for the high effectiveness of the proposed technique in presplitting hard coal and rock. First, the fracture water enables much more efficient transfer of dynamic load due to its incompressibility. Second, the subsequent expansion of water can further split the rock by compression. A mechanical model was used to reveal how the process of confined blasting in water-filled deep holes presplit roof. Moreover, practical implementation of this technique was found to improve the structure of hard, thick roof and prevent strong rock pressure, demonstrating its effectiveness in roof control. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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10307 KiB

Open AccessArticle

Heat Transfer Characteristics and Prediction Model of Supercritical Carbon Dioxide (SC-CO₂) in a Vertical Tube

by Can Cai, Xiaochuan Wang, Shaohua Mao, Yong Kang, Yiyuan Lu, Xiangdong Han and Wenchuan Liu

Energies 2017, 10(11), 1870; https://doi.org/10.3390/en10111870 - 15 Nov 2017

Cited by 14 | Viewed by 4511

Abstract

Due to its distinct capability to improve the efficiency of shale gas production, supercritical carbon dioxide (SC-CO₂) fracturing has attracted increased attention in recent years. Heat transfer occurs in the transportation and fracture processes. To better predict and understand the heat transfer of SC-CO₂ near the critical region, numerical simulations focusing on a vertical flow pipe were performed. Various turbulence models and turbulent Prandtl numbers (Pr_t) were evaluated to capture the heat transfer deterioration (HTD). The simulations show that the turbulent Prandtl number model (TWL model) combined with the Shear Stress Transport (SST) k-ω turbulence model accurately predicts the HTD in the critical region. It was found that Pr_t has a strong effect on the heat transfer prediction. The HTD occurred under larger heat flux density conditions, and an acceleration process was observed. Gravity also affects the HTD through the linkage of buoyancy, and HTD did not occur under zero-gravity conditions. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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9824 KiB

Open AccessArticle

An Innovative Approach for Gob-Side Entry Retaining in Thick Coal Seam Longwall Mining

by Manchao He, Yubing Gao, Jun Yang and Weili Gong

Energies 2017, 10(11), 1785; https://doi.org/10.3390/en10111785 - 06 Nov 2017

Cited by 121 | Viewed by 6435

Abstract

Gob-side entry retaining (GER) is a popular non-pillar mining technique regarding how to reserve a gateroad for the use of next panel mining. When used in thick coal seams, the conventional entry retaining method requires a huge amount of filling materials and may cause entry (gateroad) accidents. Thus, an innovative non-pillar longwall mining approach is introduced. First, structural and mechanical models were built to explore the mechanism of the new approach. The modeling results indicate that effective bulking of the gob roof and reasonable support of the entry roof were key governing factors in improving entry stabilities and reducing roof deformations. Accordingly, a directional roof fracturing technique was proposed to contribute to gob roof caving, and a constant resistance and large deformation anchor (CRLDA) cable was used to stabilize the entry roof. Subsequently, the evolutionary laws of the roof structure and stresses were explored using numerical simulation. It was found that the structure of the surrounding rocks around the retained entry changed significantly after roof fracturing. The stress-bearing center was transferred to the gob area, and the entry roof was in a low stress environment after adopting the approach. Finally, the approach was tested on a thick coal seam longwall mining panel. Field monitoring indicates that the retained entry was in a stable state and the index of the retained entry met the requirement of the next mining panel. This work provides an effective and economical approach to non-pillar longwall mining in thick coal seams. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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2128 KiB

Open AccessArticle

Long-Term Stability Evaluation and Pillar Design Criterion for Room-and-Pillar Mines

by Yang Yu, Shen-en Chen, Ka-zhong Deng and Hong-dong Fan

Energies 2017, 10(10), 1644; https://doi.org/10.3390/en10101644 - 18 Oct 2017

Cited by 29 | Viewed by 5469

Abstract

The collapse of abandoned room-and-pillar mines is often violent and unpredictable. Safety concerns often resulted in mine closures with no post-mining stability evaluations. As a result, large amounts of land resources over room-and-pillar mines are wasted. This paper attempts to establish an understanding of the long-term stability issues of goafs (abandoned mines). Considering progressive pillar failures and the effect of single pillar failure on surrounding pillars, this paper proposes a pillar peeling model to evaluate the long-term stability of coal mines and the associated criteria for evaluating the long-term stability of room-and-pillar mines. The validity of the peeling model was verified by numerical simulation, and field data from 500 pillar cases from China, South Africa, and India. It is found that the damage level of pillar peeling is affected by the peel angle and pillar height and is controlled by the pillar width–height ratio. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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2295 KiB

Open AccessArticle

Numerical Simulation of Density-Driven Flow and Heat Transport Processes in Porous Media Using the Network Method

by Manuel Cánovas, Iván Alhama, Gonzalo García, Emilio Trigueros and Francisco Alhama

Energies 2017, 10(9), 1359; https://doi.org/10.3390/en10091359 - 08 Sep 2017

Cited by 12 | Viewed by 3661

Abstract

Density-driven flow and heat transport processes in 2-D porous media scenarios are governed by coupled, non-linear, partial differential equations that normally have to be solved numerically. In the present work, a model based on the network method simulation is designed and applied to simulate these processes, providing steady state patterns that demonstrate its computational power and reliability. The design is relatively simple and needs very few rules. Two applications in which heat is transported by natural convection in confined and saturated media are studied: slender boxes heated from below (a kind of Bénard problem) and partially heated horizontal plates in rectangular domains (the Elder problem). The streamfunction and temperature patterns show that the results are coherent with those of other authors: steady state patterns and heat transfer depend both on the Rayleigh number and on the characteristic Darcy velocity derived from the values of the hydrological, thermal and geometrical parameters of the problems. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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5466 KiB

Open AccessArticle

Heat Transfer in a Drilling Fluid with Geothermal Applications

by Wei-Tao Wu, Nadine Aubry, James F. Antaki, Mark L. McKoy and Mehrdad Massoudi

Energies 2017, 10(9), 1349; https://doi.org/10.3390/en10091349 - 06 Sep 2017

Cited by 8 | Viewed by 4678

Abstract

The effects of various conditions on the fluid flow, particle migration and heat transfer in non-linear fluids encountered in drilling and geothermal applications are studied. We assume that the drilling fluid is a suspension composed of various substances, behaving as a non-linear complex fluid, where the effects of particle volume fraction, shear rate, and temperature on the viscosity and thermal diffusivity are considered. The motion of the particles is described using a concentration flux equation. Two problems are studied: flow in a vertical pipe and flow between two (eccentric) cylinders where the inner cylinder is rotating. We consider effects of earth temperature, the rotational speed of the inner cylinder, and the bulk volume fraction on the flow and heat transfer. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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5636 KiB

Open AccessArticle

Investigation of Hydraulic-Mechanical Properties of Paste Backfill Containing Coal Gangue-Fly Ash and Its Application in an Underground Coal Mine

by Xinguo Zhang, Jia Lin, Jinxiao Liu, Fei Li and Zhenzhong Pang

Energies 2017, 10(9), 1309; https://doi.org/10.3390/en10091309 - 01 Sep 2017

Cited by 87 | Viewed by 5566

Abstract

Backfilling is widely used to control surface subsidence and stope stability to improve pillar recovery. Furthermore, it is also an effective way to process and dispose of mining waste such as coal gangue and tailings. In this study, the hydraulic-mechanical properties of cemented paste backfill materials (CPB) were investigated. Twenty-eight cemented coal gangue-fly ash backfill mixtures were prepared with different water, cement, fly ash and coal gangue content and the slump, segregation and water bleeding ratio tests were conducted. Increasing fly ash content increased the slump value and decreased the segregation value of the slurry. The uniaxial compressive strength (UCS) of the cemented coal gangue-fly ash backfill samples were tested at different curing times. Based on the test results, an optimized recipe was used for the field trial. Longwall cut and backfilling mining method was used in the 2300 mining district to recycle the coal pillar between longwall 2301 and 2302. Both stress and displacement meters were installed in the goaf and their performance was monitored continuously. An increase in stress and displacement values were observed to occur with the working face advanced (up to 325 m and 375 m, respectively); thereafter, a trend of stabilization was observed. The monitoring results suggest that the backfills can efficiently control the roof movement and surface subsidence as well as improve pillar recovery. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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8611 KiB

Open AccessArticle

Study on the Propagation Laws of Hydrofractures Meeting a Faulted Structure in the Coal Seam

by Haiyang Wang, Binwei Xia, Yiyu Lu, Tao Gong and Rui Zhang

Energies 2017, 10(5), 654; https://doi.org/10.3390/en10050654 - 10 May 2017

Cited by 12 | Viewed by 4440

Abstract

Hydraulic fracturing is an important technique for increasing coal seam permeability and productivity of CBM (coalbed methane). As a common type of faulted structure in the coal seam, the fault has a direct impact on the direction and scope of hydrofracture propagation, weakening fracturing effects. To study the propagation laws of a hydrofracture meeting a fault in the coal seam, based on a two-dimensional model of a hydrofracture meeting a fault, the combined elastic mechanics and fracture mechanics, the propagation mode, critical internal water pressure, and influencing factors were analyzed. A numerical simulation on the propagation laws of hydrofracture meeting a fault was conducted by using the coupling system of flow and solid in the rock failure process analysis (RFPA2D-Flow). The results show that the horizontal crustal stress difference, the intersection angle between hydrofracture and fault plane, and the physical mechanics characteristics of coal-rock bed are the main factors influencing fracture propagation. With a decrease of horizontal crustal stress differences, intersection angle and an increase of roof elasticity modulus, it is easier for the footwall hydrofracture to enter the hanging wall along the bedding plane, forming an effective fracture. When the stress difference is large and the dip angle of fault plane surpasses 45°, the hydrofracture is easy to propagate towards the coal roof and floor by going through the fault plane. At this time, the coal seams of the footwall and the hanging wall should be fractured respectively to ensure fracturing effects, and the support of the roof and floor should be strengthened. The field experiment, theoretical analysis and numerical simulation were consistent in their results, which will contribute to the optimization of hydraulic fracturing and the prediction of hydrofracture in the coal seams containing faults. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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9124 KiB

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Grain Size Distribution Effect on the Hydraulic Properties of Disintegrated Coal Mixtures

by Dan Ma, Zilong Zhou, Jiangyu Wu, Qiang Li and Haibo Bai

Energies 2017, 10(5), 612; https://doi.org/10.3390/en10050612 - 29 Apr 2017

Cited by 32 | Viewed by 5517

Abstract

In order to better understand groundwater influx and protection in coal mining extraction works, an in-house water flow apparatus coupled with an industrial rock testing system, known as MTS 815.02, were used to study the effects of grain size mixtures on the compaction and flow properties of disintegrated, or non-cemented, coal samples. From the Reynolds number evaluation of the samples with different grain mixtures, and the relationship between the water flow velocity and pore pressure gradient differences, it was found that seepage through the mixtures are of non-Darcy flow type. The porosity of coal specimens was found to be highly affected by compaction, and the variations of the porosity were also influenced by the samples’ grain size distribution. It was found that the sample porosity decreases with increasing compaction and decreasing grain sizes. Grain crushing during compaction was observed to be the main cause of the appearance of fine grains, and the washing away of fine grains was consequently the main contributing factor for the weight loss due to water seepage. It was observed that during the tests and with the progression of compaction, permeability k decreases and non-Darcy factor β increases with decreasing porosity φ. The k-φ and β-φ plots show that as the sizes of disintegrated coal samples are getting smaller, there are more fluctuations between the porosity values with their corresponding values of k and β. The permeability value of the sample with smallest grains was observed to be considerably lower than that of the sample with largest grains. Non-Darcy behavior could reduce the hydraulic conductivity. It was found that the porosity, grain breakage and hydraulic properties of coal samples are related to grain sizes and compaction levels, as well as to the arrangement of the grains. At high compaction levels, the porosity of disintegrated coal samples decreased strongly, resulting in a significant decrease of the permeability at its full compression state; Non-Darcy flow behavior has the slightest effect in uniform samples, therefore, indicating that disintegrated coal in uniform grain size mixtures could be treated as an aquicluding (water-resisting) stratum. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling in Geothermal Engineering)

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