Sustainability Commons^™

Mechanisms Underlying Lateral Force Applied To A Pdc Cutter On A Pdc Drill Bit During Rotary Rock Breaking, Wei Jiusen, Han Xin, Liu Wei, Gao Deli

Coal Geology & Exploration

Objective To improve the rock-breaking efficiency and durability of drill bits in the theoretical research on the optimal design of drill bits, the key is to systematically reveal both the rock-breaking mechanisms of polycrystalline diamond compact (PDC) cutters and the characteristics of forces applied to them. Methods Existing studies on rock breaking using a single PDC cutter generally adopt a linear or approximately linear cutting mode while neglecting the impacts of the radius of gyration. To address this issue, this study conducted experiments on cylindrical granite samples using a laboratory experimental setting for single-cutter rock breaking. With cutting depth and …

Strategic Layout And Optimization Paths Of The Standard System For The Exploration And Exploitation Of Deep Coalbed Methane, Chen Xinjun, Liu Zengqin, Shen Baojian, Zhao Shihu, Ye Jincheng, Zhang Jiaqi, Wang Tianyun

Coal Geology & Exploration

Objective In China, the deep coalbed methane (CBM) industry has emerged as a key sector for the reserve growth and production addition of natural gas. However, the current CBM technical standard system, which was developed based on shallow CBM practices, is incompatible with the demands for the exploration and development of deep CBM. To address this challenge, this study proposes the optimization paths of the current standard system, aiming to provide standardization support for large-scale exploitation of deep CBM.Methods Deep CBM reservoirs exhibit complex geological conditions of high temperature, pressure, and in-situ stress, as well as the CBM occurrence …

Parameter Optimization And Field Application Of Roof Volume Fracturing Using Horizontal Wells For Coalbed Methane Extraction From Broken-Soft Coal Seams, Zhang Qingli, Sun Siqing, Li Haozhe, Wu Xiaoxuan, Yang Fan, Zheng Yuqi, Li Wenbo

Coal Geology & Exploration

Objective and Method To achieve rapid coalbed methane (CBM) extraction from broken-soft coal seams using surface horizontal wells, this study proposed a volume fracturing technology for coal seam roof using horizontal wells. Focusing coal seam 4-1 in a mining area, this study established a numerical model using finite element analysis (FEA) software Abaqus Using this model, the impacts of in-situ stress on the cross-layer propagation characteristics of multiple fractures were investigated. Through true triaxial hydraulic fracturing experiments, the multi-fracture propagation patterns under varying injection rates of fracturing fluids, perforation cluster numbers, and cluster spacings were analyzed. Using 3D fracturing design …

Structural Design And Parameter Optimization Of A Vibration Absorber For Rescue Casing-While-Drilling Rigs, Liu Pu, Yao Ningping, Zou Zujie, Fan Dong, Wei Hongchao, He Binjie

Coal Geology & Exploration

Objective Rescue drilling rigs undergo intense vibration at borehole mouths when operating in a confined underground space of coal mines. To address this issue, this study designed a compact multi-directional, passive dynamic vibration absorber, aiming to improve the operational stability and safety of the rigs. Methods Based on the spring-mass-damping system theory, a stepwise optimization design method was proposed for the longitudinal and transverse dynamic models of the vibration absorber. For the longitudinal vibration model, the particle swarm optimization (PSO) algorithm was applied for multi-objective parameter optimization. In contrast, for the transverse vibration model, the fixed point theory was employed …

Exploring The Vertical Heterogeneity Of Extremely Thick Aquifers In Coal Mines Through Layered Fine-Scale Pumping Tests, Guo Xiaoming

Coal Geology & Exploration

Objective Extremely thick aquifers in mining areas typically exhibit strong heterogeneity and high water yield. Therefore, they are prone to cause severe water inflow in mines and induce water disasters, representing a major factor affecting the mining safety of numerous mines in China. However, the vertical heterogeneity of these aquifers remains poorly understood, emerging as a primary bottleneck in the prevention and control of such water hazards. Methods To scientifically reveal the vertical heterogeneity characteristics of extremely thick aquifers, this study investigated the extremely thick Luohe Formation aquifer in a coal seam roof of a representative coal mine in the …

Optical Mechanisms Behind Vitrinite Reflectance Suppression Caused By Strong Anisotropy: A Case Study Of Contact Metamorphic Coals, An Yanfei, He Shuyang, Chen Kaixin, Gao Junhan

Coal Geology & Exploration

Objective For vitrinite with weak anisotropy, which proves uniaxial and optically negative, replacing random vitrinite reflectance (R_ran) with the maximum vitrinite reflectance (R_max) allows for the accurate correction of vitrinite reflectance suppression induced by anisotropy. However, as its anisotropy intensifies, vitrinite exhibits increasingly complex optical properties, rendering it challenging to reflect the thermal metamorphic temperature of vitrinite using R_max. Methods This study investigated the strongly anisotropic vitrinite in coals and natural coke subjected to magma intrusion in the Shitai coal mine, Huaibei City, Anhui Province. Using a reflected-polarized light microscope (R-PLM), an …

Mechanisms Behind Thermal Evolution Of The Structural Alignment Of Polycyclic Aromatic Hydrocarbons In Coals: Implications For Structural Transition Of Coal Macromolecules, Song Yu, Jiang Bo, Cheng Guoxi, Zheng Sijian, Li Ming, Ge Yao, Dai Yan, Wang Qian, Feng Guangjun

Coal Geology & Exploration

Objective Coals are highly sensitive to variations in temperature and pressure conditions. The structural evolution of coal macromolecules, driven by tectono-thermal processes, is the key to understanding coal rank transition and geological evolution. The structural alignment of polycyclic aromatic hydrocarbons (PAHs) in coals represents a critical indicator for characterizing coal rank transition and geological evolution. However, due to limited studies, there is a lack of systematic experimental demonstration and theoretical support for the structural alignment and microstructural characteristics of PAHs in coals, as well as their intrinsic relationships with the structural transition of coal macromolecules, during pyrolysis. Methods This study …

Sedimentary Characteristics And Coal Accumulation Patterns Of The Permian Shallow-Water Deltas In Shandong And Its Adjacent Regions, Feng Kai, Li Zengxue, Li Ying, Li Xuchao, Zhang Hui, Zhou Xiaojuan

Coal Geology & Exploration

Objective The Shanxi Formation, deposited during the critical transitional period from the sedimentary filling of epicontinental sea basins to the sedimentation of continental basins, exhibits well-developed shallow-water delta systems and significant coal-forming processes. This study aims to reveal the characteristics of sedimentary environment transformation during the late stage of sedimentary filling of epicontinental sea basins in North China. To this end, the Early Permian shallow-water delta systems in Shandong and its adjacent regions during that period was investigated, including their primary sedimentary characteristics, the predominant bases of sedimentary transformation, and the lithofacies paleogeographic characteristics of coal-forming processes.Methods Based on …

Geological Characteristics And Enrichment-Accumulation Patterns Of Coalbed Methane Within The Jurassic Strata In The Miquan Area Along The Southern Margin Of The Junggar Basin, Wu Luofei, Yang Kangjun, Zhang Jie, Shi Yongxia, Fu Haijiao, Yang Shuguang, Wang Gang, Liu Mengmeng, Li Yueguo, Wang Xiaoming

Coal Geology & Exploration

Objective The southern margin of the Junggar Basin (also referred to as the southern Junggar) possesses abundant medium- to low-rank coalbed methane (CBM) resources, with significant progress achieved in CBM exploration and production. However, there remains a lack of systematic understanding of the genetic mechanisms of CBM within the Middle-Lower Jurassic strata, along with its accumulation and evolution laws, in the Miquan area, southern Junggar. This absence restricts the commercial development of CBM in these strata.Method Focusing on CBM within the Middle-Lower Jurassic Xishanyao and Badaowan formations in the Miquan area, this study further identified the CBM origins and …

Exploring Water Migration Patterns In Reconstructed Soil Layers For Waste Dumps Of Open-Pit Coal Mines Based On Ct Scanning, Fan Tingyu, Zhang Xinghui, Lu Akang, Yang Changde, Wang Shun, Wang Xingming, Sun Xueliang, Ji Quancai

Coal Geology & Exploration

Objective In the arid regions of western China, the ecological restoration of waste dumps within open-pit coal mines plays a key role in green mine construction, while creating a suitable soil profile structure serves as a prerequisite for the ecological restoration.Methods This study investigated the reconstructed soils with a three-layer sponge-like structure consisting of the topsoil, sandy-soil, and mudstone layers for the waste dump of the Hongshaquan open-pit coal mine in Xinjiang. Using computed tomography (CT) scanning, a three-dimensional (3D) pore network model (PNM), and water migration simulation, this study systematically analyzed the pore structures and water migration characteristics …

Technologies For Controlling Water Inrushes From Coal Seam Floors Under Flowing Water And Their Water Plugging Performance, Yang Zhibin

Coal Geology & Exploration

Objective Limestone water hazards in coal seam floors represent one of the two primary categories of mine water hazards in China. Limestone aquifers are generally characterized by abundant static water reserves and considerable dynamic water recharge. To reduce economic losses and casualties caused by water inrushes from limestone aquifers, post-disaster emergency rescue through grouting for water plugging is frequently carried out under flowing water.Methods Based on numerous cases of water inrush control under flowing water in China and the fundamental requirements for control scheme design, this study presents a systematic review of existing technologies for water inrush control under …

Joint Inversion For Heat Transfer Parameters Of Porous Media With Geothermal-Seepage Coupling Based On A Physics-Informed Neural Network, Zhang Xiao, Yang Duoxing, Cong Lin, Cheng Yimei, Zhang Lianzhong

Coal Geology & Exploration

Background The thermal diffusivity and vertical seepage velocity of porous media are critical to characterizing the mechanisms underlying subsurface heat transfer. These two parameters are typically determined through inversion using temperature data since they are difficult to measure directly. Fiber-optic distributed temperature sensing (FO-DTS) can yield high-resolution, continuous temperature profiles, providing data for parameter identification. However, conventional numerical inversion suffers from limitations such as mesh dependency and sensitivity to initial values when used to process continuous monitoring data. Methods This study proposed a joint geothermal parameter inversion method that integrates FO-DTS data with a physics-informed neural network (PINN). Specifically, the …

Joint Inversion Of Borehole-Surface Direct-Current Resistivity Data, Xu Kaijun, Jin Heran, Cao Danping, Mou Bin, Hu Zuzhi

Coal Geology & Exploration

Objective The conventional inversion of surface direct-current (DC) resistivity data faces challenges such as limited exploration accuracy and depth. This study aims to enhance the accuracy and reliability of exploration in complex engineering and geological settings through the joint inversion of borehole-surface DC resistivity data. Methods First, different geoelectric models were constructed through three-dimensional (3D) forward modeling of full-space DC resistivity. Then, the potential response characteristics under surface and borehole observation methods were systematically analyzed to determine the differences in detection sensitivity between surface and borehole observations. Accordingly, a joint 3D inversion technique for borehole-surface DC resistivity data was developed …

Oil-Based Mud Electrical Imaging Logging Responses Of Carbonate Strata, Wu Yuyu, Lai Qiang, Pan Feng, Zhao Zuo’An, Wang Xiaoxing, Wang Yue, Cheng Lu, Wang Zeyu, Yin Rong

Coal Geology & Exploration

Objectives This study aims to characterize the oil-based mud (OBM) electrical imaging logging responses of carbonate strata, highlighting the response characteristics of dissolution vugs, fractures, stratigraphical structures, and special minerals. Methods Tests were conducted on logging data acquisition of a drilled well within the Dengying Formation in the Sichuan Basin before and after OBM was replaced with water-based mud (WBM). Based on the fine-scale core-to-log (CTL) calibration, this study compared the WBM and OBM electrical imaging logging responses of different geological and pore structures. Furthermore, the characteristics of OBM electrical imaging logging responses were further discussed from the measurement principles …

A Cutting Trajectory Planning Technology Driven By Coal Seam Data In A Comprehensive Mining Face, Guo Yifeng, Xue Xusheng, Ma Hongwei, Zhang Guangming, Su Hao, Qi Ailing, Nie Zhen, Ma Kexiang, Wu Xuefei

Coal Geology & Exploration

Objective Currently, the insufficient full-element digitization and the prevalence of “data silos” in fully mechanized mining faces (FMMF) result in poor cutting precision and operational instability of shearers under complex undulating and abrupt geological conditions. These factors pose significant challenges to high-precision proactive trajectory planning. Methods Guided by the academic philosophy that “mining is data acquisition”, this paper proposes a coal seam data-driven cutting trajectory planning method for FMMFs. It elaborates on three core technologies: high-precision digital coal seam modeling, generative model updating and digital twin construction, and data-driven trajectory planning.To address low modeling precision, an intelligent interpolation-based digital coal …

Image Processing Technique To Find The Burden Rock Velocity And Its Interdependency On Bench Blasting Parameters – A Case Study, Channabassamma N, Akhil Avchar, Sahas V Swamy, Vedala Rama Sastry, Hemant Agrawale

Journal of Sustainable Mining

In any rock engineering or excavation project, optimizing blast design is essential for controlling post-blast phenomena such as flyrock, burden throw, and burden rock velocity (BRV). This study investigates the dynamic response of BRV in bench blasting operations by employing a high-speed camera and ProAnalyst software to quantify rock displacement. The relationships between BRV and key blast parameters, number of holes (NH), explosive charge per hole (EPH), total explosive charge (TEC), stiffness ratio (K), and stemming ratio (STR), were analyzed to identify linear or non-linear trends. Non-linear trends, …

Using Geoscience To Empower A Community And Provide Access To Potable Groundwater, Hendratta Ali Dr

SACAD: Scholarly Activities

Access to potable water remains challenging around the world and remains one of the UN Sustainable Development Goals for 2030. Barriers to clean water access are exacerbated by the lack of technical expertise, limited funding for education and training, and the absence of reliable infrastructure that provides access to clean water. The Geoscientists Without Borders program, supported FHSU with funding to test, explore and provide access to clean potable groundwater to a rural community in Cameroon. We conducted water quality analyses, identified, mapped and located deep aquifers in fractured metamorphic rocks. Water quality analyses showed acidic pH and elevated amounts …

A Method To Accelerate Rock Breakage With Soundless Chemical Demolition Agents, Patrick A. Darko, Hani S. Mitri

Journal of Sustainable Mining

Soundless chemical demolition agents (SCDA) are recognized as a safe and sustainable alternative for rock breakage, with the potential to reduce reliance on explosives in mining. However, their mechanical performance is considerably hampered in the extreme cold climate, with slow or no rock fracturing observed. To overcome this deficiency, two methods were developed in recent studies by 1) electric heating the SCDA borehole with high-temperature wire, and 2) increasing the SCDA mixing water temperature. Good results were obtained with both methods. This paper explores the merits of a hybrid approach combining the two methods to further enhance the SCDA efficiency …

Research Status And Development Trend Of Acidification And Permeability Improvement Technology For Low-Permeability Coal Seam, Shaochuan Chen, Yun Lei, Fuchao Tian, Jie Kang

Journal of Sustainable Mining

Low-permeability coal seams in China are often characterized by mineral-clogged pore-fracture systems, severely limiting coalbed methane (CBM) extraction efficiency. Acidification technology, which involves injecting acidic solutions into coal seams to dissolve minerals and enhance permeability, has emerged as a promising approach. This paper systematically reviews the mechanisms, laboratory findings, and field applications of acidification technology for permeability enhancement in low-permeability coal seams. Key findings include significant improvements in pore connectivity, reductions in gas adsorption capacity, and enhanced gas extraction rates post-acidification. Field tests demonstrate that acid fracturing can increase gas extraction volume by 4-7 times. The study also identifies current …

Improving Energy Reliability In Mining Areas Through Modelling And Control Of Resonance Phenomena In Solar-Integrated Power Systems, Yurii Papaika, Gennadiy Pivnyak, Maksim Malyshko, Yuliya Pazynich, Natalia Howaniec, Adam Smolinski

Journal of Sustainable Mining

This study addresses the emergency and operational transient processes that arise when integrating large-scale solar power plants (SPPs) into electrical load nodes, particularly under conditions of limited power system capacity. With the increasing penetration of distributed generation in Ukraine's energy landscape, challenges related to electromagnetic compatibility and harmonic resonance are becoming more prominent. The research builds upon the foundational work of leading Ukrainian scientific schools and focuses on the specific resonance phenomena observed during the operation of solar inverters in medium-voltage networks, especially in regions with high industrial and mining Energy demand. A novel algorithm is proposed for determining the …

Feasibility Study Of Barite Sourcing From Sediments Emerging Due To Treatment Of Waste Water From Coal Mining, Hubert Makuła, Zbigniew Bzowski, Bogusław Michalik

Journal of Sustainable Mining

The accumulation of mine water in settling ponds, which is discharged due to coal mining, allows them to be cleaned out of suspension, and it is the reason for the accumulation of hundreds of thousands of tons of sediments. One interesting mineral enclosed in these sediments is barite, which is considered in the EU as a critical raw material, but it also contains radium originating from formation water.

The effective barite separation and its beneficiation could constitute a win-win solution because then it would be possible to obtain the valuable radium concentrate for further processing, e.g., in nuclear medicine, and …

Wettability Evaluation Via Contact Angle And Data Mining For Enhanced Oil Recovery, Syasya Wadihah Md. Ja’Afar, Bashir Busahmin

Journal of Sustainable Mining

The oil industry has used many enhanced oil recovery (EOR) strategies to increase crude oil production from reservoirs, particularly as production begins to fall. With a significant quantity of hydrocarbon reserves still existing in the reservoirs, improved oil recovery techniques have the potential to increase oil production, with wettability alteration playing a significant role. To date, there has been no comprehensive investigation of wettability in Brunei's sandstone reservoir. The goal of this research is to determine wettability by contact angle measurement and data mining approaches based on the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm. …

Discovery Of Quasi-Carbon Nanotube Structures In Tectonically Deformed Coals And Their Formation Mechanisms, Li Yunbo, Wang Rongqi, Song Dangyu, Wang Chengtao, Li Qiang, Yi Ke, Wang Yuanyuan, Pan Jienan

Coal Geology & Exploration

Objective Carbon nanotubes (CNTs) have attracted wide attention due to their unique structures and performance. However, their artificial synthesis requires stringent conditions, including high temperatures (700 ℃ to 2 300 ℃), stable carbon sources, and catalysts. Furthermore, these structures are rarely discovered in nature. As a carbon-rich medium, coals can form a variety of ordered carbon structures during their metamorphic and deformational processes, serving as an ideal carrier for exploring the formation mechanisms of natural CNTs.Methods Typical tectonically deformed coals from the Pingdingshan and Huaibei mining areas were investigated in this study. After demineralization and chloroform extraction, coal samples …

Dynamic Evolution Of Rock Mechanical Properties Of Coal Seam Roofs Under Thermal Loading: A Case Study Of The Baikouquan Area, Xinjiang, China, Sun Fangfang, Li Xin, Sang Shuxun, Qu Huailin, Yang Shuguang, Wei Bo, Wang Ziqiang, Zhang Bin, Chen Yanpeng, Tian Wenling

Coal Geology & Exploration

Objective Underground coal gasification (UCG) represents a key technology for the clean utilization of coal resources. However, during the UCG process, thermal damage to surrounding rocks under thermal effects directly affects the stability and engineering safety of gasification channels.Methods To address the thermal damage to surrounding rocks during UCG, this study investigated the silty mudstones and coarse-grained sandstones in the coal seam roof of the Xishanyao Formation, Baikouquan area, Xinjiang. Through high-temperature uniaxial compression experiments, combined with characterization methods like X-ray diffraction (XRD) and scanning electron microscopy (SEM), this study delved into the dynamic evolutionary patterns of rock mechanical …

Coupling Mechanisms Of Fracture Propagation And Proppant Transport Indeep Coalbed Methane Reservoirs, Guo Xiaodong, Zhang Shicheng, Zhang Jingchen, Zhou Changjing, Zhang Chengsheng, Qiu Shixin, Xi Xiangrui

Coal Geology & Exploration

Objectives and Methods Deep coalbed methane (CBM) reservoirs commonly exhibit well-developed beddings, strong mechanical heterogeneity, and high in-situ stress gradients. These characteristics result in pronounced nonlinear fracture propagation and strong multi-field coupling effects during hydraulic fracturing. Consequently, it is challenging to accurately describe the mechanisms governing fracture complexity in deep coal reservoirs using conventional mechanical models for fractures. Using a super-large true triaxial system with dimensions of 2.0 m × 2.0 m × 1.0 m, this study conducted physical simulation experiments on hydraulic fracturing under varying injection rates and viscosities of fracturing fluids. In combination with fracture mechanics and energy …

Advances In Research On Mechanisms And Prevention And Control Technologies For Solid-Phase Production In Hydraulically Fractured Coalbed Methane Wells, Zhang Fengsan, Wu Jinqiao, Lin Jin, Li Yu, Zhang Ying, Li Bing, Zhang Guobiao, Sun Ying, Gan Yuke

Coal Geology & Exploration

Background The effective coalbed methane (CBM) exploitation using hydraulic fracturing wells is severely constrained by two major solid-phase production issues: coal fines blockage and proppant flowback. The mechanisms behind both issues are associated with complex interplays between geological conditions and engineering disturbances. This study presents a systematic review of the current status of domestic and international research on the mechanisms of the solid-phase production, as well as relevant prevention and control methods. Furthermore, future research directions are proposed.Advances The solid-phase production in hydraulically fractured CBM wells essentially arises from flow-solid-chemical multi-field coupling processes under interplays between geological conditions and …

Characteristics And Mechanisms Of The Adsorption Of Shales For Ba2+ In Fracturing Fluids, Xie Chenyang, Liu Bo, Zhang Yuting, Zhu Fang

Coal Geology & Exploration

Objectives and Methods Large-scale hydraulic fracturing represents a key technology for shale gas exploitation. However, engineering practices indicate that the flowback rates of fracturing fluids are low and vary significantly across different blocks. Furthermore, some components in fracturing fluids may cause groundwater contamination. To explore the adsorption characteristics and mechanisms of Ba²⁺ within fracturing fluids in shale reservoirs, this study investigated four typical types of samples, including shale and three shale samples with different compositions, from the Longmaxi Formation in the Changning Block, southern Sichuan Basin. Systematic experiments were conducted on the adsorption of shales with different mineral …

Predicting The Risk Of Water-Sand Inrushes From Coal Seam Roofs Based On A Small-Size Sample Dataset, Zhang Wenquan, Li Zixu, Zhu Xianxiang, Qiu Wei, Zhang Chengjie

Coal Geology & Exploration

Objective The eastern and northern regions of China exhibit thick unconsolidated layers and thin bedrocks, with water-sand inrush disasters occurring frequently. Therefore, accurately predicting the risk of water-sand inrushes from coal seam roofs holds great significance for safe coal mining. However, the water-sand inrushes in these regions exhibit complex disaster-causing mechanisms, which involve the coupling effects of multiple factors. Accordingly, the real-time prediction of the water-sand inrush risk in the field poses challenges including high risk and cost. These issues lead to difficult data acquisition and severely insufficient samples, limiting the accuracy and performance of traditional prediction models. Therefore, there …

An Experimental Study On The Mechanical Property Evolution Of Granites Post-High-Temperature Treatment Under Loading And Unloading Conditions, Hao Wencai, Qiao Wei, Liu Huichen, Zhu Zhennan, Wang Hao, Liu Richeng, Guo Jie, Xie Jingyu, Cheng Xianggang, Lyu Ruijie

Coal Geology & Exploration

Objective The surrounding rocks of wellbores remain in a state of stress release during the drilling and heat extraction of deep geothermal reservoirs. Therefore, investigating the characteristic stresses of heat-treated granites under loading and unloading conditions is critical to understanding the crack evolution in deep hot dry rock (HDR) reservoirs during their stimulation. Methods Targeting the granite specimens after heat treatment at varying high temperatures (e.g., 200 ℃, 300 ℃, 400 ℃, 500 ℃, and 600 ℃), this study conducted triaxial loading and unloading tests under a confining pressure of 60 MPa, aiming to investigate the impacts of high temperature …

A Model For Predicting Coal Mining-Induced Surface Subsidence During Theinitial, Active, And Decline Stages, Zhang Liangliang, Liu Xiya, Cheng Hua, Du Shaoneng

Coal Geology & Exploration

Objectives and Methods Presently, there remains a lack of theoretical models for predicting the coal mining-induced surface subsidence during the initial, active, and decline stages. Given this, this study derived the time-varying exponential function of the ratio of maximum to dynamic surface subsidence first using measured data from seven coal mines. Accordingly, an improved Knothe time function model was established. Then, the impacts of the model parameters on dynamic surface subsidence W(t), subsidence velocity v(t), and subsidence acceleration a(t) were analyzed. Subsequently, based on the improved Knothe model and the critical …