Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

In situ digital testing method for quality assessment of soft soil improvement with polyurethane

This study purposes an in situ testing method on quality assessment of soil improvement.Factual drilling data includes the spatial distribution and in situ strength of untreated and treated soil along three different drillholes measured by on-site drilling monitoring method.These factual drilling data can characterize the degree of soil improvement by penetration injection with permeable polyurethane.Result from on-site drilling monitoring shows that the linear zones represent constant drilling speeds shown in the plot of drill bit advancement vs.net drilling time,which indicates the spatial distributions of soil profile.The soil profile at the study site is composed of four layers,which includes fill,untreated silty clay,treated silty clay,and mucky soil.The results of soil profile are verified by the parallel site loggings.The constant drilling speeds profile the coring-resistant strength of drilled soils.By comparing with the untreated silty clay,the constant drilling speeds of the treated silty clay have been decreased by 13.0-62.8%.Two drilling-speed-based indices of 61.2%and 65.6%are proposed to assess the decreased average drilling speed and the increased in situ strength of treated silty clay.Laboratory tests,i.e.uniaxial compressive strength(UCS)test,have been performed with core sample to investigate and characterize in situ strength by comparing that with drilling speeds.Results show that the average predicted strengths of treated silty clay are 2.4-6.9 times higher than the average measured strength of untreated silty clay.The UCS-based indices of 374.5%and 344.2%verified the quality assessment(QA)results by this new in situ method.This method provides a cost-effective tool for quality assessment of soil improvement by utilizing the digital drilling data.

The Conversion of Non-Dispersed Polymers into Low-Potassium Anti-Collapse Drilling Fluids

Different drillingfluid systems are designed according to mineral composition,lithology and wellbore stability of different strata.In the present study,the conversion of a non-dispersed polymer drillingfluid into a low potas-sium anti-collapsing drillingfluid is investigated.Since the two drillingfluids belong to completely different types,the key to this conversion is represented by new inhibitors,dispersants and water-loss agents by which a non-dispersed drillingfluid can be turned into a dispersed drillingfluid while ensuring wellbore stability and reason-able rheology(carrying sand—inhibiting cuttings dispersion).In particular,the(QYZ-1)inhibitors and(FSJSS-2)dispersants are used.The former can inhibit the hydration expansion capacity of clay,reduce the dynamic shear force and weaken the viscosity;the latter can improve the sealing effect and reduce thefiltrate loss.The results have shown that after adding a reasonable proportion of these substances(QYZ-1:FSJSS-2)to the non-dispersed polymer drillingfluid,while the apparent viscosity,plastic viscosity,structural viscosity andfluidity index under-went almost negligible changes,the dynamic plastic ratio increased,and thefiltration loss decreased significantly,thereby indicating good compatibility.According to the tests(conducted in the Leijia area),the density was 1.293 g/cm3,and after standing for 24 h,the SF(static settlement factor)was 0.51.Moreover,thefiltration loss was reduced to 4.0 mL,the rolling recovery rate reached 96.92%,with excellent plugging and anti-collapse performances.

Digital monitoring of rotary-percussive drilling with down-the-hole hammer for profiling weathered granitic ground

Rock and geotechnical engineering investigations involve drilling holes in ground with or without retrieving soil and rock samples to construct the subsurface ground profile.On the basis of an actual soil nailing drilling for a slope stability project in Hong Kong,this paper further develops the drilling process monitoring(DPM)method for digitally profiling the subsurface geomaterials of weathered granitic rocks using a compressed airflow driven percussive-rotary drilling machine with down-the-hole(DTH)hammer.Seven transducers are installed on the drilling machine and record the chuck displacement,DTH rotational speed,and five pressures from five compressed airflows in real-time series.The mechanism and operations of the drilling machine are elaborated in detail,which is essential for understanding and evaluating the drilling data.A MATLAB program is developed to automatically filter the recorded drilling data in time series and classify them into different drilling processes in sub-time series.These processes include penetration,push-in with or without rod,pull-back with or without rod,rod-tightening and rod-untightening.The drilling data are further reconstructed to plot the curve of drill-bit depth versus the net drilling time along each of the six drillholes.Each curve is found to contain multiple linear segments with a constant penetration rate,which implies a zone of homogenous geomaterial with different weathering grades.The effect from fluctuation of the applied pressures is evaluated quantitatively.Detailed analyses are presented for accurately assess and verify the underground profiling and strength in weathered granitic rock,which provided the basis of using DPM method to confidently assess drilling measurements to interpret the subsurface profile in real time.

Chemical modification of barite for improving the performance of weighting materials for water-based drilling fluids

With increasing drilling depth and large dosage of weighting materials,drilling fluids with high solid content are characterized by poor stability,high viscosity,large water loss,and thick mud cake,easier leading to reservoir damage and wellbore instability.In this paper,micronized barite(MB)was modified(mMB)by grafting with hydrophilic polymer onto the surface through the free radical polymerization to displace conventional API barite partly.The suspension stability of water-based drilling fluids(WBDFs)weighted with API barite:mMB=2:1 in 600 g was significantly enhanced compared with that with API barite/WBDFs,exhibiting the static sag factor within 0.54 and the whole stability index of 2.The viscosity and yield point reached the minimum,with a reduction of more than 40%compared with API barite only at the same density.Through multi-stage filling and dense accumulation of weighting materials and clays,filtration loss was decreased,mud cake quality was improved,and simultaneously it had great reservoir protection performance,and the permeability recovery rate reached 87%.In addition,it also effectively improved the lubricity of WBDFs.The sticking coefficient of mud cake was reduced by 53.4%,and the friction coefficient was 0.2603.Therefore,mMB can serve as a versatile additive to control the density,rheology,filtration,and stability of WBDFs weighted with API barite,thus regulating comprehensive performance and achieving reservoir protection capacity.This work opened up a new path for the productive drilling of extremely deep and intricate wells by providing an efficient method for managing the performance of high-density WBDFs.

Synthetic polymers:A review of applications in drilling fluids

With the growth of deep drilling and the complexity of the well profile,the requirements for a more complete and efficient exploitation of productive formations increase,which increases the risk of various complications.Currently,reagents based on modified natural polymers(which are naturally occurring compounds)and synthetic polymers(SPs)which are polymeric compounds created industrially,are widely used to prevent emerging complications in the drilling process.However,compared to modified natural polymers,SPs form a family of high-molecular-weight compounds that are fully synthesized by undergoing chemical polymerization reactions.SPs provide substantial flexibility in their design.Moreover,their size and chemical composition can be adjusted to provide properties for nearly all the functional objectives of drilling fluids.They can be classified based on chemical ingredients,type of reaction,and their responses to heating.However,some of SPs,due to their structural characteristics,have a high cost,a poor temperature and salt resistance in drilling fluids,and degradation begins when the temperature reaches 130℃.These drawbacks prevent SP use in some medium and deep wells.Thus,this review addresses the historical development,the characteristics,manufacturing methods,classification,and the applications of SPs in drilling fluids.The contributions of SPs as additives to drilling fluids to enhance rheology,filtrate generation,carrying of cuttings,fluid lubricity,and clay/shale stability are explained in detail.The mechanisms,impacts,and advances achieved when SPs are added to drilling fluids are also described.The typical challenges encountered by SPs when deployed in drilling fluids and their advantages and drawbacks are also discussed.Economic issues also impact the applications of SPs in drilling fluids.Consequently,the cost of the most relevant SPs,and the monomers used in their synthesis,are assessed.Environmental impacts of SPs when deployed in drilling fluids,and their manufacturing processes are identified,together with advances in SP-treatment methods aimed at reducing those impacts.Recommendations for required future research addressing SP property and performance gaps are provided.

Fracture sealing performance of granular lost circulation materials at elevated temperature:A theoretical and coupled CFD-DEM simulation study

Lost circulation is a common downhole problem of drilling in geothermal and high-temperature,high-pressure(HTHP)formations.Lost circulation material(LCM)is a regular preventive and remedial measure for lost circulation.However,conventional LCMs seem ineffective in high-temperature formations.This may be due to the changes in the mechanical properties of LCMs and their sealing performance under high-temperature conditions.To understand how high temperature affects the fracture sealing performance of LCMs,we developed a coupled computational fluid dynamics-discrete element method(CFD-DEM)model to simulate the behavior of granular LCMs in fractures.We summarized the literature on the effects of high temperature on the mechanical properties of LCMs and the rheological properties of drilling fluid.We conducted sensitivity analyses to investigate how changing LCM slurry properties affected the fracture sealing efficiency at increasing temperatures.The results show that high temperature reduces the size,strength,and friction coefficient of LCMs as well as the drilling fluid viscosity.Smaller,softer,and less frictional LCM particles have lower bridging probability and slower bridging initiation.Smaller particles tend to form dual-particle bridges rather than single-particle bridges.These result in a deeper,tighter,but unstable sealing zone.Reduced drilling fluid viscosity leads to faster and shallower sealing zones.

Dynamic Analysis of A Deepwater Drilling Riser with A New Hang-off System

The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to a challenging problem:coupling the dynamics of risers with a new hang-off system combined with multiple structures and complex constraints.To accurately analyze the dynamic responses of the coupled system,a coupled dynamic model is established based on the Euler-Bernoulli beam-column theory and penalty function method.A comprehensive analysis method is proposed for coupled dynamic analysis by combining the finite element method and the Newmarkβmethod.An analysis program is also developed in MATLAB for dynamic simulation.The simulation results show that the dynamic performances of the risers at the top part are significantly improved by the new hang-off system,especially the novel design,which includes the centralizer and articulation joint.The bending moment and lateral deformation of the risers at the top part decrease,while the hang-off joint experiences a great bending moment at the bottom of the lateral restraint area which requires particular attention in design and application.The platform navigation speed range under the safety limits of risers expands with the new hang-off system in use.

A Gel-Based Solidification Technology for Large Fracture Plugging

Fault fractures usually have large openings and considerable extension. Accordingly, cross-linked gel materials aregenerally considered more suitable plugging agents than water-based gels because the latter often undergo contaminationvia formation water, which prevents them from being effective over long times. Hence, in this study, aset of oil-based composite gels based on waste grease and epoxy resin has been developed. These materials havebeen observed to possess high compressive strength and resistance to the aforementioned contamination, therebyleading to notable increase in plugging success rate. The compressive strength, thickening time, and resistance toformation water pollution of these gels have been evaluated indoors. The results show that the compressivestrength of the gel can reach 11 MPa;additionally, the related gelation time can be controlled to be more than3 h, thereby providing a safe construction time;Invasion of formation water has a small effect on the gel strengthand does not shorten the thickening time. All considered performance indicators of the oil-based gel confirm itssuitability as a plugging agent for fault fractures.

Research on the Method of Heat Preservation and Heating for the Drilling System of Polar Offshore Drilling Platform

This study investigates the heat dissipation mechanism of the insulation layer and other plane insulation layers in the polar drilling rig system.Combining the basic theory of heat transfer with the environmental requirements of polar drilling operations and the characteristics of polar drilling processes,we analyze the factors that affect the insulation effect of the drilling rig system.These factors include the thermal conductivity of the insulation material,the thickness of the insulation layer,ambient temperature,and wind speed.We optimize the thermal insulation material of the polar drilling rig system using a steady-state method to measure solid thermal conductivity.By analyzing the distribution of temperature in space after heating,we optimize the distribution and air outlet angle of the heater using Fluent hydrodynamics software.The results demonstrate that under polar conditions,polyisocyanurate with stable thermodynamic properties is selected as the thermal insulation material.The selection of thermal insulation material and thickness significantly affects the thermal insulation effect of the system but has little effect on its heating effect.Moreover,when the air outlet angle of the heater is set to 32.5°,the heating efficiency of the system can be effectively improved.According to heat transfer equations and heat balance theory,we determine that the heating power required for the system to reach 5°C is close to numerical simulation.

A New Heat Transfer Model for Multi-Gradient Drilling with Hollow Sphere Injection

Multi-gradient drilling is a new offshore drilling method.The accurate calculation of the related wellbore temperature is of great significance for the prediction of the gas hydrate formation area and the precise control of the wellbore pressure.In this study,a new heat transfer model is proposed by which the variable mass flow is properly taken into account.Using this model,the effects of the main factors influencing the wellbore temperature are analyzed.The results indicate that at the position where the separation injection device is installed,the temperature increase of the fluid in the drill pipe is mitigated due to the inflow/outflow of hollow spheres,and the temperature drop of the fluid in the annulus also decreases.In addition,a lower separation efficiency of the device,a shallower installation depth and a smaller circulating displacement tend to increase the temperature near the bottom of the annulus,thereby helping to reduce the hydrate generation area and playing a positive role in the prevention and control of hydrates in deepwater drilling.

Deep-large faults controlling on the distribution of the venting gas hydrate system in the middle of the Qiongdongnan Basin, South China Sea

Many locations with concentrated hydrates at vents have confirmed the presence of abundant thermogenic gas in the middle of the Qiongdongnan Basin(QDNB).However,the impact of deep structures on gasbearing fluids migration and gas hydrates distribution in tectonically inactive regions is still unclear.In this study,the authors apply high-resolution 3D seismic and logging while drilling(LWD)data from the middle of the QDNB to investigate the influence of deep-large faults on gas chimneys and preferred gasescape pipes.The findings reveal the following:(1)Two significant deep-large faults,F1 and F2,developed on the edge of the Songnan Low Uplift,control the dominant migration of thermogenic hydrocarbons and determine the initial locations of gas chimneys.(2)The formation of gas chimneys is likely related to fault activation and reactivation.Gas chimney 1 is primarily arises from convergent fluid migration resulting from the intersection of the two faults,while the gas chimney 2 benefits from a steeper fault plane and shorter migration distance of fault F2.(3)Most gas-escape pipes are situated near the apex of the two faults.Their reactivations facilitate free gas flow into the GHSZ and contribute to the formation of fracture‐filling hydrates.

Spatial structural characteristics of the Deda ancient landslide in the eastern Tibetan Plateau:Insights from Audio-frequency Magnetotellurics and the Microtremor Survey Method

It is of crucial importance to investigate the spatial structures of ancient landslides in the eastern Tibetan Plateau’s alpine canyons as they could provide valuable insights into the evolutionary history of the landslides and indicate the potential for future reactivation.This study examines the Deda ancient landslide,situated in the Chalong-ranbu fault zone,where creep deformation suggests a complex underground structure.By integrating remote sensing,field surveys,Audio-frequency Magnetotellurics(AMT),and Microtremor Survey Method(MSM)techniques,along with engineering geological drilling for validation,to uncover the landslide’s spatial feature s.The research indicates that a fault is developed in the upper part of the Deda ancient landslide,and the gully divides it into Deda landslide accumulation zoneⅠand Deda landslide accumulation zoneⅡin space.The distinctive geological characteristics detectable by MSM in the shallow subsurface and by AMT in deeper layers.The findings include the identification of two sliding zones in the Deda I landslide,the shallow sliding zone(DD-I-S1)depth is approximately 20 m,and the deep sliding zone(DD-I-S2)depth is 36.2-49.9 m.The sliding zone(DD-Ⅱ-S1)depth of the DedaⅡlandslide is 37.6-43.1 m.A novel MSM-based method for sliding zone identification is proposed,achieving less than 5%discrepancy in depth determination when compared with drilling data.These results provide a valuable reference for the spatial structural analysis of large-deepseated landslides in geologically complex regions like the eastern Tibetan Plateau.

Conventional Geothermal Systems and Unconventional Geothermal Developments: An Overview

This paper provides an overview of conventional geothermal systems and unconventional geothermal developments as a common reference is needed for discussions between energy professionals. Conventional geothermal systems have the heat, permeability and fluid, requiring only drilling down to °C, normal heat flow or decaying radiogenic granite as heat sources, and used in district heating. Medium-temperature (MT) 100°C - 190°C, and high-temperature (HT) 190°C - 374°C resources are mostly at plate boundaries, with volcanic intrusive heat source, used mostly for electricity generation. Single well capacities are °C - 500°C) and a range of depths (1 m to 20 Km), but lack permeability or fluid, thus requiring stimulations for heat extraction by conduction. HVAC is 1 - 2 m deep and shallow geothermal down to 500 m in wells, both capturing °C, with °C are either advanced by geothermal developers at <7 Km depth (Enhanced Geothermal Systems (EGS), drilling below brittle-ductile transition zones and under geothermal fields), or by the Oil & Gas industry (Advanced Geothermal Systems, heat recovery from hydrocarbon wells or reservoirs, Superhot Rock Geothermal, and millimeter-wave drilling down to 20 Km). Their primary aim is electricity generation, relying on closed-loops, but EGS uses fractures for heat exchange with earthquake risks during fracking. Unconventional approaches could be everywhere, with shallow geothermal already functional. The deeper and hotter unconventional alternatives are still experimental, overcoming costs and technological challenges to become fully commercial. Meanwhile, the conventional geothermal resources remain the most proven opportunities for investments and development.

Osteotomy Protocol for Implant Insertion of One Day Biotech: One Drill, One Implant

Background: Four factors determine the quality of an implantology kit: 1) Heat generated by the drills;2) Morphology of the osteotomy according to the diameter of the implant;3) Efficiency of collecting autologous bone;and 4) Osteotomy execution time. Materials and Methods: This article examines the heat produced by drills during osteotomy, focusing on the effect of the following factors: drilling technique;volume of autologous bone harvested;drilling time;implant primary stability;and the percentage of osseointegrated implants after primary healing. Discussion: The four factors mentioned above are analyzed based on the data obtained for sequential, biological, and One Drill milling techniques. Conclusions: 1) One Drill is the fastest technique for performing the osteotomy;2) All techniques stay within the biological temperature range of living bone, with the lowest increase in temperature achieved using One Drill with irrigation;3) The bone harvested showed no statistically significant differences between biological milling and the One Drill technique, both far superior to the sequential technique;and 4) There is no statistically significant difference in the number of osseointegrated implants among the three techniques analyzed.

Phaco drill与小切口非超声乳化白内障摘除术治疗硬核白内障患者的效果

目的:探讨Phaco drill与小切口非超声乳化白内障摘除术治疗硬核白内障患者的效果。方法:回顾性选取2020年10月—2022年4月麻城市中医医院收治的60例硬核白内障患者。根据不同手术治疗方法将其分为Phaco组(n=25)和小切口组(n=35)。小切口组给予小切口非超声乳化白内障摘除术,Phaco组给予Phaco drill。比较两组术前、术后1个月眼睛恢复情况,术前,术后3 d、术后1个月及术后3个月角膜散光度,并发症。结果:术后1个月,Phaco组最佳矫正视力(best corrected visual acuity,BCVA)、眼压(intraocular pressure,IOP)、角膜内皮细胞(corneal endothelial cell,CEC)密度均高于小切口组,差异有统计学意义(P<0.05),两组中央角膜厚度(central corneal thickness,CCT)比较,差异无统计学意义(P>0.05)。重复测量方差分析显示,角膜散光度组间、时间、交互比较,差异有统计学意义(P<0.001)。术后3 d、术后1个月,Phaco组角膜散光度均低于小切口组,差异有统计学意义(P<0.05)。Phaco组术后并发症发生率低于小切口组,差异有统计学意义(P<0.05)。结论:Phaco drill治疗硬核白内障可促进患者恢复,近期对角膜散光度的影响较小,对角膜内皮损伤较小,且术后并发症发生率低。

Surgical Treatment of Osteonecrosis of the Femoral Head Using Minimally Invasive Surgical Drilling and Cancellous Grafting at Brazzaville University Hospital

Introduction: Osteonecrosis of the femoral head (ONTF) is a debilitating condition. Several treatments have been proposed with controversial results. The aim of our study was to evaluate treatment by surgical drilling coupled with in situ cancellous grafting. Materials and methods: Our study was a case-control study conducted at Brazzaville University Hospital from 1st January 2018 to 31 December 2023. It compared two groups of patients with ONTF: non-operated (13 patients, 20 hips) and operated (22 patients, 35 hips). We used the visual digital scale (VDS) for pain assessment, the Merle D’Aubigne-Postel (MDP) scoring system for clinical and functional assessment, and the evolution of necrosis. Results: The group of non-operated patients had a mean age of 35.69 ± 3.4 years, no improvement in pain with an EVN above seven at the last recoil and a mean global MDP score falling from 12.7 before offloading to 10.13 at one year. The group of patients operated on had a mean age of 37.86 ± 7.02 years, a significant reduction in pain (p = 0.00004) and a significantly increased MDP score (p = 0.0034). A comparison of the two groups of patients showed significant stabilization of the necrotic lesions in the operated patients (p = 0.00067), with better satisfaction in the same group. Conclusion: Surgical drilling combined with grafting in the treatment of early-stage ONTF has improved progress in our series. The technique is reproducible and less invasive. It has made it possible to delay unfavorable progression and, consequently, hip replacement surgery.

渤海油田超高温深井钻井液配套技术

随着钻井深度的增加,地层温度成为制约钻井液体系选择的主要因素。高温条件下对钻井液性能稳定、井壁完整性和润滑剂配伍性要求相对严苛,低生物毒性、易降解的抗高温聚合物、抗盐聚合物PF-DFL180、PF-DFL200可以满足条件,配合抗高温润滑剂PF-LUBE220可有效降低钻进扭矩。通过对抗高温钻井液THERM DRILL、无固相HTFLOW钻井液体系的现场应用总结,结合室内评价进行钻井液体系优化升级,形成渤海油田配套超高温深井钻井液技术。

Effects of Drilling in Mastoid Cavity over Hearing in the Contralateral Ear

In advanced otological surgeries, powered instruments form an indispensable part. The risk of deterioration to hearing in the operated ear is a commonly discussed issue, however, there remains a possibility of affecting the hearing in the contralateral ear due to transcranial vibration. So in this study we aimed to assess the possibility of the non-operated ear being affected by the noise generated during ear surgeries and whether it is temporary or permanent in nature. Methodology: This study included 63 patients diagnosed with unilateral disease who underwent mastoid surgery. Preoperatively all the patients were subjected to Pure tone audiometry (PTA), Transient evoked otoacoustic emission (TEOAE) and Distortion product otoacoustic emission (DPOAE). Patients were operated using both cutting and diamond burrs of ranging from sizes 1 - 6 mm. Total drilling time was recorded. Results: Post-operative hearing evaluation was done at 1 week, 4 weeks and 12 weeks. The sound emitted by various burrs was recorded by Sound Level Meter. Out of the total 58 patients that followed up, 46 showed change in at least one of the hearing parameters. Patients showing changes had a higher drilling time as compared to those with no changes. Of these, the changes associated with the total drilling time and with cutting burr time were found to be significant. The hearing changes seen on PTA, TEOAE and DPOAE were transient in nature with only one patient having a persistent decreased high frequency threshold at the end of 12 weeks. It was also found that cutting burrs produce more sound as compared to diamond burrs and a larger size burr of a type produces more sound than a smaller one of its type. Conclusion: The drilling of mastoid bone during ear surgeries can transiently impair the hearing in the contralateral ear which is of great significance in patients with only one hearing ear.

Effects of QD2R Numeracy Enhancement Strategy on the Mathematics Performance of Grade 10 Students

Learning mathematics requires an effective and strategic teaching approach.This study aimed to assess the mathematics performance of the learners with the implementation of the numeracy enhancement strategy QD2R(Questions,Drills,Repetition,and Recitation)and to propose a strategy implementation plan to elevate their performances.This study employed the use of a quasi-experimental research design,purposive sampling with 70 Grade 10 students of Lian National High School who were distributed equally to control and treatment groups.The pre-test and post-test results were statistically analyzed using independent and paired sample t-tests,and a survey questionnaire was examined by getting the mean and standard deviation.The results indicated that better performance was achieved by the students from the treatment group compared to the students from the control group,as revealed by the Mean Percentage Score(MPS)results,mean scores,and P values of their pre-test and post-test scores.The learners’perception of the implementation of this strategy was to a great extent,wherein it was perceived to be more helpful in concepts related to understanding the lesson compared to concepts related to developing their attitude and skills.Moreover,the proposed implementation plan of numeracy enhancement strategy QD2R had three expected outcomes:elevated understanding and performance in mathematics lessons;modified strategy to focus on the development of attitude and skills towards mathematics;and refined and well-implemented QD2R strategy in teaching mathematics.Relative to these expected outcomes,appropriate measures,timeframe,and resources of each were comprehensively formulated.