In Ref.[1],Eq.(8)has a typo,the following replacement should be done.γ_(bb)/2rδ/δr(rδ(r,t)/δr=2γ_(bb)/R_(bb)-Þ(t,t)-Ⅱ[h[r,t)](bubble=drop-bubble=drop)The publisher regrets an error in the original–article...In Ref.[1],Eq.(8)has a typo,the following replacement should be done.γ_(bb)/2rδ/δr(rδ(r,t)/δr=2γ_(bb)/R_(bb)-Þ(t,t)-Ⅱ[h[r,t)](bubble=drop-bubble=drop)The publisher regrets an error in the original–article,and the sentence that explained the equation“Eqs.(8)–(10)show the augmented Young–Laplace equation for the interactions of gas bubbles or liquid droplets in different configurations,where Rb is the bubble/drop radius,Rp is the particle radius,Rbp=(1/Rb+1/Rp)1.展开更多
The optimization of methods for the quantitative evaluation of risks in drilling engineering is an effective means to ensure safety in situations where high temperature and high pressure blocks are considered.In such ...The optimization of methods for the quantitative evaluation of risks in drilling engineering is an effective means to ensure safety in situations where high temperature and high pressure blocks are considered.In such a context,this study analyzes the complexity of the drilled wells in such blocks.It is shown that phenomena such as well kick,loss,circulation,and sticking,are related to the imbalance of wellbore pressure.A method for risk quantitative evaluation is proposed accordingly.The method is used to evaluate the risk for 9 drilled wells.By comparing the predictions of the method with actual historical data related to these wells,it is found that the coincidence rate is about 95%.展开更多
Accurate prediction of the rate of penetration(ROP)is significant for drilling optimization.While the intelligent ROP prediction model based on fully connected neural networks(FNN)outperforms traditional ROP equations...Accurate prediction of the rate of penetration(ROP)is significant for drilling optimization.While the intelligent ROP prediction model based on fully connected neural networks(FNN)outperforms traditional ROP equations and machine learning algorithms,its lack of interpretability undermines its credibility.This study proposes a novel interpretation and characterization method for the FNN ROP prediction model using the Rectified Linear Unit(ReLU)activation function.By leveraging the derivative of the ReLU function,the FNN function calculation process is transformed into vector operations.The FNN model is linearly characterized through further simplification,enabling its interpretation and analysis.The proposed method is applied in ROP prediction scenarios using drilling data from three vertical wells in the Tarim Oilfield.The results demonstrate that the FNN ROP prediction model with ReLU as the activation function performs exceptionally well.The relative activation frequency curve of hidden layer neurons aids in analyzing the overfitting of the FNN ROP model and determining drilling data similarity.In the well sections with similar drilling data,averaging the weight parameters enables linear characterization of the FNN ROP prediction model,leading to the establishment of a corresponding linear representation equation.Furthermore,the quantitative analysis of each feature's influence on ROP facilitates the proposal of drilling parameter optimization schemes for the current well section.The established linear characterization equation exhibits high precision,strong stability,and adaptability through the application and validation across multiple well sections.展开更多
The safe and efficient development of natural gas hydrate requires a deep understanding of the deformation behaviors of reservoirs.In this study,a series of triaxial shearing tests are carried out to investigate the d...The safe and efficient development of natural gas hydrate requires a deep understanding of the deformation behaviors of reservoirs.In this study,a series of triaxial shearing tests are carried out to investigate the deformation properties of hydrate-bearing sediments.Variations of volumetric and lateral strains versus hydrate saturation are analyzed comprehensively.Results indicate that the sediments with high hydrate saturation show dilative behaviors,which lead to strain-softening characteristics during shearing.The volumetric strain curves have a tendency to transform gradually from dilatation to compression with the increase in effective confining pressure.An easy prediction model is proposed to describe the relationship between volumetric and axial strains.The model coefficientβis the key dominating factor for the shape of volumetric strain curves and can be determined by the hydrate saturation and stress state.Moreover,a modified model is established for the calculation of lateral strain.The corresponding determination method is provided for the easy estimation of model coefficients for medium sand sediments containing hydrate.This study provides a theoretical and experimental reference for deformation estimation in natural gas hydrate development.展开更多
Based on the microfluidic technology,a microscopic visualization model was used to simulate the gas injection process in the initial construction stage and the bottom water invasion/gas injection process in the cyclic...Based on the microfluidic technology,a microscopic visualization model was used to simulate the gas injection process in the initial construction stage and the bottom water invasion/gas injection process in the cyclical injection-production stage of the underground gas storage(UGS)rebuilt from water-invaded gas reservoirs.Through analysis of the gas-liquid contact stabilization mechanism,flow and occurrence,the optimal control method for lifecycle efficient operation of UGS was explored.The results show that in the initial construction stage of UGS,the action of gravity should be fully utilized by regulating the gas injection rate,so as to ensure the macroscopically stable migration of the gas-liquid contact,and greatly improve the gas sweeping capacity,providing a large pore space for gas storage in the subsequent cyclical injection-production stage.In the cyclical injection-production stage of UGS,a constant gas storage and production rate leads to a low pore space utilization.Gradually increasing the gas storage and production rate,that is,transitioning from small volume to large volume,can continuously break the hydraulic equilibrium of the remaining fluid in the porous media,which then expands the pore space and flow channels.This is conducive to the expansion of UGS capacity and efficiency for purpose of peak shaving and supply guarantee.展开更多
Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsi...Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.展开更多
Cavitating jet is a promising drilling rate improvement technology in both the marine natural gas hydrate (NGH) fluidization exploitation method and the integrated radial jet drilling and completion method. In present...Cavitating jet is a promising drilling rate improvement technology in both the marine natural gas hydrate (NGH) fluidization exploitation method and the integrated radial jet drilling and completion method. In present study, we aim to improve the efficiency of jet erosion and extracting NGH. With a computational fluid dynamics (CFD) method, the pressure, velocity and cavitation field characteristics of organ-pipe cavitating jet (OPCJ) are analysed. The divergent angle, throat length, and divergent length of OPCJ nozzle are preferred to obtain stronger jet cavitation erosion effect. Laboratory experiments of gas hydrate-bearing sediments (GHBS) erosion by OPCJ and conical jet (CJ) are conducted to compare and validate the jet erosion performance. The impinging models of OPCJ and CJ are constructed to study the impact characteristics. Results show that the preferred values of divergent angle, throat length, and divergent length are 15°, 1d, and 3d, respectively, in present simulation conditions. For GHBS, the OPCJ possesses the advantages of high efficiency and low energy consumption. Moreover, the OPCJ has higher penetration efficiency, while showing equivalent penetration ability compared to CJ. During the impinging process, the OPCJ can induce stronger impact pressure and turbulence effect, and also shows stronger chambering effect and bottom cleaning ability compared to CJ. This study presents the erosion performance of OPCJ and CJ on GHBS, and provides preliminary insights on the potential field applications in NGH exploitation.展开更多
An essential technology of carbon capture, utilization and storage-enhanced oil recovery (CCUS-EOR) for tight oil reservoirs is CO_(2) huff-puff followed by associated produced gas reinjection. In this paper, the effe...An essential technology of carbon capture, utilization and storage-enhanced oil recovery (CCUS-EOR) for tight oil reservoirs is CO_(2) huff-puff followed by associated produced gas reinjection. In this paper, the effects of multi-component gas on the properties and components of tight oil are studied. First, the core displacement experiments using the CH_(4)/CO_(2) multi-component gas are conducted to determine the oil displacement efficiency under different CO_(2) and CH_(4) ratios. Then, a viscometer and a liquid density balance are used to investigate the change characteristics of oil viscosity and density after multi-component gas displacement with different CO_(2) and CH_(4) ratios. In addition, a laboratory scale numerical model is established to validate the experimental results. Finally, a composition model of multi-stage fractured horizontal well in tight oil reservoir considering nano-confinement effects is established to investigate the effects of multi-component gas on the components of produced dead oil and formation crude oil. The experimental results show that the oil displacement efficiency of multi-component gas displacement is greater than that of single-component gas displacement. The CH_(4) decreases the viscosity and density of light oil, while CO_(2) decreases the viscosity but increases the density. And the numerical simulation results show that CO_(2) extracts more heavy components from the liquid phase into the vapor phase, while CH_(4) extracts more light components from the liquid phase into the vapor phase during cyclic gas injection. The multi-component gas can extract both the light components and the heavy components from oil, and the balanced production of each component can be achieved by using multi-component gas huff-puff.展开更多
he cement sheath is the heart of any oil or gas well for providing zonal isolation and well integrity during the life of a well.Loads induced by well construction operations and borehole pressure and temperature chang...he cement sheath is the heart of any oil or gas well for providing zonal isolation and well integrity during the life of a well.Loads induced by well construction operations and borehole pressure and temperature changes may lead to the ultimate failure of cement sheath.This paper quantifies the potential of cement failure under mechanically and thermally induced stress during the life-of-well using a coupled thermalehydrologicalemechanical(THM)modeling approach.A staged finite-element procedure is presented considering sequential stress and displacement development during each stage of the well life,including drilling,casing,cementing,completion,production,and injection.The staged model quantifies the stress states and state variables,e.g.,plastic strain,damage,and debonding at cement/rock or cement/casing interface,in each well stage from simultaneous action of in-situ stress,pore pressure,temperature,casing pressure,and cement hardening/shrinkage.Thus,it eliminates the need to guess the initial stress and strain state before modeling a specific stage.Moreover,coupled THM capabilities of the model ensure the full consideration of the interaction between these influential factors.展开更多
The well-known“lost circulation”problem refers to the uncontrolled flow of whole mud into a formation.In order to address the problem related to the paucity of available data,in the present study,a model is introduc...The well-known“lost circulation”problem refers to the uncontrolled flow of whole mud into a formation.In order to address the problem related to the paucity of available data,in the present study,a model is introduced for the lost-circulation risk sample profile of a drilled well.The model is built taking into account effective data(the Block L).Then,using a three-dimensional geological modeling software,relying on the variation function and sequential Gaussian simulation method,a three-dimensional block lost-circulation risk model is introduced able to provide relevant information for regional analyses.展开更多
Fuzzy-ball working fluids(FBWFs)have been successfully applied in different development phases of tight reservoirs.Field reports revealed that FBWFs satisfactorily met all the operational and reservoir damage control ...Fuzzy-ball working fluids(FBWFs)have been successfully applied in different development phases of tight reservoirs.Field reports revealed that FBWFs satisfactorily met all the operational and reservoir damage control requirements during their application.However,the damage-control mechanisms and degree of formation damage caused by fuzzy-ball fluids have not been investigated in lab-scale studies so far.In this study,the degree of fuzzy-ball-induced damage in single-and double-layer reservoirs was evaluated through core flooding experiments that were based on permeability and flow rate indexes.Additionally,its damage mechanisms were observed via scanning electron microscope and energy-dispersive spectroscopy tests.The results show that:(1)For single-layer reservoirs,the FBWF induced weak damage on coals and medium-to-weak damage on sandstones,and the difference of the damage in permeability or flow rate index on coals and sandstones is below 1%.Moreover,the minimum permeability recovery rate was above 66%.(2)For double-layer commingled reservoirs,the flow rate index revealed weak damage and the overall damage in double-layer was lower than the single-layer reservoirs.(3)There is no significant alteration in the microscopic structure of fuzzy-ball saturated cores with no evidence of fines migration.The dissolution of lead and sulfur occurred in coal samples,while tellurium in sandstone,aluminum,and magnesium in carbonate.However,the precipitation of aluminum,magnesium,and sodium occurred in sandstone but no precipitates found in coal and carbonate.The temporal plugging and dispersion characteristics of the FBWFs enable the generation of reservoir protection layers that will minimize formation damage due to solid and fluid invasion.展开更多
Steam flooding is a widely used technique to enhance oil recovery of heavy oil.Thermal viscosity reduction and distillation effect are considered as two main displacement mechanisms in steam flooding process.However,t...Steam flooding is a widely used technique to enhance oil recovery of heavy oil.Thermal viscosity reduction and distillation effect are considered as two main displacement mechanisms in steam flooding process.However,the molecular composition understanding and contribution for oil production are still unclear.In this study,the composition analysis of the heavy oil was investigated in the core scale steam flooding process with the temperature from 120 to 280℃.The crude oil,produced oils and residual oils were characterized comprehensively by gas chromatography and high-resolution mass spectrometry.It is found that steam flooding preferentially extracts aromatics and remains more resins in the residual oil.Viscosity reduction is the dominant mechanism when steam is injected at a low temperature.Large molecular heteroatoms with high carbon number and high double bond equivalent(DBE)are eluted into the produced oil,while compounds with low carbon number and low DBE are remained in the residual oil.As the steam temperature rises,the increased distillation effect results in the extraction of light hydrocarbons from the residual oil to the produced oil.More small heteroatoms with low carbon number and low DBE enter into the produced oil,especially in the none water cut stage.The compositional difference of produced oils is characterized in DBE versus carbon number distribution of the N and O containing compound classes.This work uses a variety of composition analysis methods to clarify the steam flooding mechanism and provides a novel understanding of steam flooding mechanisms with various temperatures and production stages from the molecular perspective.展开更多
Air channeling in the annulus between the casing and the cement sheath and/or between the cement sheath and formation is the main factor affecting the safe operation of natural gas wells at high temperatures and press...Air channeling in the annulus between the casing and the cement sheath and/or between the cement sheath and formation is the main factor affecting the safe operation of natural gas wells at high temperatures and pressures.Prevention of this problem requires,in general,excellent anti-channeling performances of the cement sheath.Three methods to predict such anti-channeling performances are proposed here,which use the weightless pressure of cement slurry,the permeability of cement stone and the volume expansion rate of cement sheath as input parameters.Guided by this approach,the anti-channeling performances of the cement slurry are evaluated by means of indoor experiments,and the cement slurry is optimized accordingly.The results show that the dangerous transition time of the cement slurry with optimized dosage of admixture is only 76 min,the permeability of cement stone is 0.005 md,the volume shrinkage at final setting is only 0.72%,and the anti-channeling performances are therefore maximized.The effective utilization of the optimized cement slurry in some representative wells(LD10–1-A1 and LD10–1-A2 in LD10–1 gas field)is also discussed.展开更多
Multiple fractured horizontal wells (MFHWs) currently are the only possible means of commercial production from the low and ultra-low permeability unconventional gas reservoirs. In early production time, flowback flui...Multiple fractured horizontal wells (MFHWs) currently are the only possible means of commercial production from the low and ultra-low permeability unconventional gas reservoirs. In early production time, flowback fluid, which constitutes of hydraulic water and gas flow within fractures, is collected and analyzed. Flowback analysis has been shown to be a useful tool to estimate key properties of the hydraulic fracture such as conductivity and pore volume. Until date, most tools of flowback analysis rely on empirical and approximate methods. This study presents an improved Green-function-based semi-analytical solution for performance analysis of horizontal gas wells during flowback and early production periods. The proposed solution is derived based on coupling the solutions of two domains: a rigorously derived Green’s function-based integral solution for single-phase gas flow in matrix, and a finite-difference, multiphase solution for gas–water two-phase flow in the fracture. The validity of proposed semi-analytical solution is verified by finely gridded numerical models built in a commercial simulator for a series of synthetic cases considering a variety of fluid and reservoir property combinations, as well as various different production constraints. Comparisons against available empirical and approximate methods are also provided for these cases.展开更多
Due to its long lifespan and high sand-removal efficiency,gravel packing is one of the most applied sand control methods during the recovery of reservoirs with sanding problems.The blockage and retention of injected s...Due to its long lifespan and high sand-removal efficiency,gravel packing is one of the most applied sand control methods during the recovery of reservoirs with sanding problems.The blockage and retention of injected sand in a gravel pack is a complex process affected by multiple mechanisms.The majority of existing studies based on the phenomenological deep bed filtration(DBF)theory focused on the gravel pack’s overall permeability damage and failed to obtain the inner-pore particle distribution pattern.In this work,experiments and simulations were carried out to reveal the particle distribution in a gravel pack during flooding.In particular,through real-time monitoring of particle migration,the penetration depth and distribution pattern of invaded particles with different gravel-sand particle ratios,fluid viscosities and injection rates could be determined.By simplifying each unit bed element(UBE)into a pore-throat structure with four tunnels(two horizontals for discharge and two verticals for sedimentation),a new network simulation method,which combines deep bed filtration with a particle trajectory model,was implemented.Cross comparison of experimental and numerical results demonstrates the validity and accuracy of the model.展开更多
We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NL...We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.展开更多
To investigate the influence of diagenetic water media on the hydrogen isotopes of individual sedimentary aromatic compounds,a series of hydrous pyrolyses were conducted on herbaceous peat.Polycyclic aromatic hydrocar...To investigate the influence of diagenetic water media on the hydrogen isotopes of individual sedimentary aromatic compounds,a series of hydrous pyrolyses were conducted on herbaceous peat.Polycyclic aromatic hydrocarbons(PAHs)in hydrous pyrolysed samples and their hydrogen isotopic composition characteristics were studied.The aqueous medium demonstrated a significant influence on the hydrogen isotopic composition of the individual PAHs generated during pyrolysis.The results showed that the PAHs formed after pyrolysis in the presence of a saltwater medium with high δD value from a salt lake had a heavy hydrogen isotopic composition.The PAHs formed after pyrolysis in the presence of a fresh water medium with low δD value from a swamp had a light hydrogen isotopic composition.The difference in the average PAHδD value between the two hydrous experiments varied from -174‰ to -109‰,suggesting that the hydrogen isotopic composition of individual sedimentary PAHs can reflect the source of the diagenetic water medium.In addition,a comparative study found that the hydrogen isotopes of PAHs were superior to those of n-alkanes in the same sample for diagenetic water indications.The results indicated that the exchange of water-derived inorganic hydrogen and organic hydrogen was more intensive in freshwater experiments than in saltwater experiments.With an increase in the simulation temperature,the average δD value of PAHs generated in the hydrous simulation experiments showed an increasing trend,reflecting that the δD value of sedimentary PAHs formed with the participation of diagenetic water media was still closely related to the thermal maturity of organic matter.Comparative studies showed that theδD values of different types of organic compounds produced by hydrous pyrolysis of peat were in the order,PAHs>n-alkanes>methane.展开更多
To obtain high yields of monocyclic aromatic hydrocarbons with methyl side chains,such as toluene and xylene,methane(CH_(4))can be introduced into the hydrocracking of polycyclic aromatic hydrocarbons.CH_(4)can partic...To obtain high yields of monocyclic aromatic hydrocarbons with methyl side chains,such as toluene and xylene,methane(CH_(4))can be introduced into the hydrocracking of polycyclic aromatic hydrocarbons.CH_(4)can participate in the reaction,supply methyl side chains to the product,and improve product distribution.In this study,the hydrogenation reaction of polycyclic aromatic hydrocarbons over a carbonized NiMo/Hβcatalyst in a CH_(4)and hydrogen(H_(2))environment was investigated to study the promotional effect of CH_(4)on the hydrocracking of polycyclic aromatics.Under conditions of 3.5 MPa,380℃,volume air velocity of 4 h^(-1),gas-oil volume ratio of 800,and H_(2):CH_(4)molar ratio of 1:1,the conversion rate of naphthalene was 99.97%,the liquid phase yield was 93.62%,and the selectivity of BTX were 17.76%,25.17%,and 20.47%,respectively.In comparison to the use of a H_(2)atmosphere,the selectivity of benzene was significantly decreased,whereas the selectivity of toluene and xylene were increased.It was shown that CH_(4)can participate in the hydrocracking of naphthalene and improve the selectivity of toluene and xylene in the liquid product.The carbonized NiMo/Hβcatalyst was characterized by a range of analytical methods(such as X-ray diffraction(XRD),ammonia-temperature-programmed desorption(NH3-TPD),hydrogen-temperature-programmed reduction(H_(2)-TPR),and X-ray photoelectron spectroscopy(XPS)).The results indicated that Ni and Mo carbides were the major species in the carbonized NiMo/Hβcatalyst and were considered to be active sites for the activation of CH_(4)and H_(2).After loading the metal components,the catalyst displayed prominent weak acidic sites,which may be suitable locations for cracking,alkylation,and other related reactions.Therefore,the carbonized NiMo/Hβcatalyst displayed multiple functions during the hydrocracking of polycyclic aromatic hydrocarbons in a CH_(4)and H_(2)environment.These results could be used to develop a new way to efficiently utilize polycyclic aromatic hydrocarbons and natural gas resources.展开更多
Current methods for the analysis of channeling-path phenomena in reservoirs cannot account for the influence of time and space on the actual seepage behavior.In the present study,this problem is addressed considering ...Current methods for the analysis of channeling-path phenomena in reservoirs cannot account for the influence of time and space on the actual seepage behavior.In the present study,this problem is addressed considering actual production data and dynamic characteristic parameters quantitatively determined in the near wellbore area by fitting the water-cut curve of the well.Starting from the dynamic relationship between injection and production data,the average permeability is determined and used to obtain a real-time quantitative characterization of the seepage behavior of the channeling-path in the far wellbore area.For the considered case study(Jidong oilfield),it is found that the seepage capacity of the channeling-path in the far wellbore area is far less(10 times smaller)than that of the channeling-path in the near wellbore area.The present study and the proposed model(combining near wellbore area and far wellbore area real-time data)have been implemented to support the definition of relevant adjustment measures to ultimately improve oil recovery.展开更多
Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity ...Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.展开更多
文摘In Ref.[1],Eq.(8)has a typo,the following replacement should be done.γ_(bb)/2rδ/δr(rδ(r,t)/δr=2γ_(bb)/R_(bb)-Þ(t,t)-Ⅱ[h[r,t)](bubble=drop-bubble=drop)The publisher regrets an error in the original–article,and the sentence that explained the equation“Eqs.(8)–(10)show the augmented Young–Laplace equation for the interactions of gas bubbles or liquid droplets in different configurations,where Rb is the bubble/drop radius,Rp is the particle radius,Rbp=(1/Rb+1/Rp)1.
文摘The optimization of methods for the quantitative evaluation of risks in drilling engineering is an effective means to ensure safety in situations where high temperature and high pressure blocks are considered.In such a context,this study analyzes the complexity of the drilled wells in such blocks.It is shown that phenomena such as well kick,loss,circulation,and sticking,are related to the imbalance of wellbore pressure.A method for risk quantitative evaluation is proposed accordingly.The method is used to evaluate the risk for 9 drilled wells.By comparing the predictions of the method with actual historical data related to these wells,it is found that the coincidence rate is about 95%.
基金The authors greatly thanked the financial support from the National Key Research and Development Program of China(funded by National Natural Science Foundation of China,No.2019YFA0708300)the Strategic Cooperation Technology Projects of CNPC and CUPB(funded by China National Petroleum Corporation,No.ZLZX2020-03)+1 种基金the National Science Fund for Distinguished Young Scholars(funded by National Natural Science Foundation of China,No.52125401)Science Foundation of China University of Petroleum,Beijing(funded by China University of petroleum,Beijing,No.2462022SZBH002).
文摘Accurate prediction of the rate of penetration(ROP)is significant for drilling optimization.While the intelligent ROP prediction model based on fully connected neural networks(FNN)outperforms traditional ROP equations and machine learning algorithms,its lack of interpretability undermines its credibility.This study proposes a novel interpretation and characterization method for the FNN ROP prediction model using the Rectified Linear Unit(ReLU)activation function.By leveraging the derivative of the ReLU function,the FNN function calculation process is transformed into vector operations.The FNN model is linearly characterized through further simplification,enabling its interpretation and analysis.The proposed method is applied in ROP prediction scenarios using drilling data from three vertical wells in the Tarim Oilfield.The results demonstrate that the FNN ROP prediction model with ReLU as the activation function performs exceptionally well.The relative activation frequency curve of hidden layer neurons aids in analyzing the overfitting of the FNN ROP model and determining drilling data similarity.In the well sections with similar drilling data,averaging the weight parameters enables linear characterization of the FNN ROP prediction model,leading to the establishment of a corresponding linear representation equation.Furthermore,the quantitative analysis of each feature's influence on ROP facilitates the proposal of drilling parameter optimization schemes for the current well section.The established linear characterization equation exhibits high precision,strong stability,and adaptability through the application and validation across multiple well sections.
基金supported by the Qingdao Natural Science Foundation(No.23-2-1-54-zyyd-jch)the National Natural Science Foundation of China(Nos.42076217,41976074)+1 种基金the Laoshan Laboratory(No.LSKJ202203506)the Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education,Tongji University(No.KLE-TJGE-G2202).
文摘The safe and efficient development of natural gas hydrate requires a deep understanding of the deformation behaviors of reservoirs.In this study,a series of triaxial shearing tests are carried out to investigate the deformation properties of hydrate-bearing sediments.Variations of volumetric and lateral strains versus hydrate saturation are analyzed comprehensively.Results indicate that the sediments with high hydrate saturation show dilative behaviors,which lead to strain-softening characteristics during shearing.The volumetric strain curves have a tendency to transform gradually from dilatation to compression with the increase in effective confining pressure.An easy prediction model is proposed to describe the relationship between volumetric and axial strains.The model coefficientβis the key dominating factor for the shape of volumetric strain curves and can be determined by the hydrate saturation and stress state.Moreover,a modified model is established for the calculation of lateral strain.The corresponding determination method is provided for the easy estimation of model coefficients for medium sand sediments containing hydrate.This study provides a theoretical and experimental reference for deformation estimation in natural gas hydrate development.
文摘Based on the microfluidic technology,a microscopic visualization model was used to simulate the gas injection process in the initial construction stage and the bottom water invasion/gas injection process in the cyclical injection-production stage of the underground gas storage(UGS)rebuilt from water-invaded gas reservoirs.Through analysis of the gas-liquid contact stabilization mechanism,flow and occurrence,the optimal control method for lifecycle efficient operation of UGS was explored.The results show that in the initial construction stage of UGS,the action of gravity should be fully utilized by regulating the gas injection rate,so as to ensure the macroscopically stable migration of the gas-liquid contact,and greatly improve the gas sweeping capacity,providing a large pore space for gas storage in the subsequent cyclical injection-production stage.In the cyclical injection-production stage of UGS,a constant gas storage and production rate leads to a low pore space utilization.Gradually increasing the gas storage and production rate,that is,transitioning from small volume to large volume,can continuously break the hydraulic equilibrium of the remaining fluid in the porous media,which then expands the pore space and flow channels.This is conducive to the expansion of UGS capacity and efficiency for purpose of peak shaving and supply guarantee.
基金the National Natural Science Foundation of China(No.52274048)Beijing Natural Science Foundation(No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(No.2021DJ2104)the Science Foundation of China University of Petroleum,Beijing(No.2462021YXZZ010).
文摘Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.
基金financially supported by National Natural Science Foundation of China(No.52174009 and No.51827804)Marine Economy Development Foundation of Guangdong Province(GDNRC[2022]44)“Technical Support for Stimulation and Testing of Gas Hydrate Reservoirs”.
文摘Cavitating jet is a promising drilling rate improvement technology in both the marine natural gas hydrate (NGH) fluidization exploitation method and the integrated radial jet drilling and completion method. In present study, we aim to improve the efficiency of jet erosion and extracting NGH. With a computational fluid dynamics (CFD) method, the pressure, velocity and cavitation field characteristics of organ-pipe cavitating jet (OPCJ) are analysed. The divergent angle, throat length, and divergent length of OPCJ nozzle are preferred to obtain stronger jet cavitation erosion effect. Laboratory experiments of gas hydrate-bearing sediments (GHBS) erosion by OPCJ and conical jet (CJ) are conducted to compare and validate the jet erosion performance. The impinging models of OPCJ and CJ are constructed to study the impact characteristics. Results show that the preferred values of divergent angle, throat length, and divergent length are 15°, 1d, and 3d, respectively, in present simulation conditions. For GHBS, the OPCJ possesses the advantages of high efficiency and low energy consumption. Moreover, the OPCJ has higher penetration efficiency, while showing equivalent penetration ability compared to CJ. During the impinging process, the OPCJ can induce stronger impact pressure and turbulence effect, and also shows stronger chambering effect and bottom cleaning ability compared to CJ. This study presents the erosion performance of OPCJ and CJ on GHBS, and provides preliminary insights on the potential field applications in NGH exploitation.
基金supported by the National Natural Science Foundation of China(No.52174038 and No.52004307)China Petroleum Science and Technology Project-major project-Research on tight oil-shale oil reservoir engineering methods and key technologies in Ordos Basin(ZLZX2020-02-04)Science Foundation of China University of Petroleum,Beijing(No.2462018YJRC015).
文摘An essential technology of carbon capture, utilization and storage-enhanced oil recovery (CCUS-EOR) for tight oil reservoirs is CO_(2) huff-puff followed by associated produced gas reinjection. In this paper, the effects of multi-component gas on the properties and components of tight oil are studied. First, the core displacement experiments using the CH_(4)/CO_(2) multi-component gas are conducted to determine the oil displacement efficiency under different CO_(2) and CH_(4) ratios. Then, a viscometer and a liquid density balance are used to investigate the change characteristics of oil viscosity and density after multi-component gas displacement with different CO_(2) and CH_(4) ratios. In addition, a laboratory scale numerical model is established to validate the experimental results. Finally, a composition model of multi-stage fractured horizontal well in tight oil reservoir considering nano-confinement effects is established to investigate the effects of multi-component gas on the components of produced dead oil and formation crude oil. The experimental results show that the oil displacement efficiency of multi-component gas displacement is greater than that of single-component gas displacement. The CH_(4) decreases the viscosity and density of light oil, while CO_(2) decreases the viscosity but increases the density. And the numerical simulation results show that CO_(2) extracts more heavy components from the liquid phase into the vapor phase, while CH_(4) extracts more light components from the liquid phase into the vapor phase during cyclic gas injection. The multi-component gas can extract both the light components and the heavy components from oil, and the balanced production of each component can be achieved by using multi-component gas huff-puff.
基金This work was financially supported by Science Foundation of China University of Petroleum,Beijing(No.2462019BJRC011 and No.2462020YXZZ051)National Natural Science Foundation of China(No.52004298).
文摘he cement sheath is the heart of any oil or gas well for providing zonal isolation and well integrity during the life of a well.Loads induced by well construction operations and borehole pressure and temperature changes may lead to the ultimate failure of cement sheath.This paper quantifies the potential of cement failure under mechanically and thermally induced stress during the life-of-well using a coupled thermalehydrologicalemechanical(THM)modeling approach.A staged finite-element procedure is presented considering sequential stress and displacement development during each stage of the well life,including drilling,casing,cementing,completion,production,and injection.The staged model quantifies the stress states and state variables,e.g.,plastic strain,damage,and debonding at cement/rock or cement/casing interface,in each well stage from simultaneous action of in-situ stress,pore pressure,temperature,casing pressure,and cement hardening/shrinkage.Thus,it eliminates the need to guess the initial stress and strain state before modeling a specific stage.Moreover,coupled THM capabilities of the model ensure the full consideration of the interaction between these influential factors.
文摘The well-known“lost circulation”problem refers to the uncontrolled flow of whole mud into a formation.In order to address the problem related to the paucity of available data,in the present study,a model is introduced for the lost-circulation risk sample profile of a drilled well.The model is built taking into account effective data(the Block L).Then,using a three-dimensional geological modeling software,relying on the variation function and sequential Gaussian simulation method,a three-dimensional block lost-circulation risk model is introduced able to provide relevant information for regional analyses.
基金The authors wish to thank the Ministry of Science and Technology of the People's Republic of China(2016ZX05066).
文摘Fuzzy-ball working fluids(FBWFs)have been successfully applied in different development phases of tight reservoirs.Field reports revealed that FBWFs satisfactorily met all the operational and reservoir damage control requirements during their application.However,the damage-control mechanisms and degree of formation damage caused by fuzzy-ball fluids have not been investigated in lab-scale studies so far.In this study,the degree of fuzzy-ball-induced damage in single-and double-layer reservoirs was evaluated through core flooding experiments that were based on permeability and flow rate indexes.Additionally,its damage mechanisms were observed via scanning electron microscope and energy-dispersive spectroscopy tests.The results show that:(1)For single-layer reservoirs,the FBWF induced weak damage on coals and medium-to-weak damage on sandstones,and the difference of the damage in permeability or flow rate index on coals and sandstones is below 1%.Moreover,the minimum permeability recovery rate was above 66%.(2)For double-layer commingled reservoirs,the flow rate index revealed weak damage and the overall damage in double-layer was lower than the single-layer reservoirs.(3)There is no significant alteration in the microscopic structure of fuzzy-ball saturated cores with no evidence of fines migration.The dissolution of lead and sulfur occurred in coal samples,while tellurium in sandstone,aluminum,and magnesium in carbonate.However,the precipitation of aluminum,magnesium,and sodium occurred in sandstone but no precipitates found in coal and carbonate.The temporal plugging and dispersion characteristics of the FBWFs enable the generation of reservoir protection layers that will minimize formation damage due to solid and fluid invasion.
文摘Steam flooding is a widely used technique to enhance oil recovery of heavy oil.Thermal viscosity reduction and distillation effect are considered as two main displacement mechanisms in steam flooding process.However,the molecular composition understanding and contribution for oil production are still unclear.In this study,the composition analysis of the heavy oil was investigated in the core scale steam flooding process with the temperature from 120 to 280℃.The crude oil,produced oils and residual oils were characterized comprehensively by gas chromatography and high-resolution mass spectrometry.It is found that steam flooding preferentially extracts aromatics and remains more resins in the residual oil.Viscosity reduction is the dominant mechanism when steam is injected at a low temperature.Large molecular heteroatoms with high carbon number and high double bond equivalent(DBE)are eluted into the produced oil,while compounds with low carbon number and low DBE are remained in the residual oil.As the steam temperature rises,the increased distillation effect results in the extraction of light hydrocarbons from the residual oil to the produced oil.More small heteroatoms with low carbon number and low DBE enter into the produced oil,especially in the none water cut stage.The compositional difference of produced oils is characterized in DBE versus carbon number distribution of the N and O containing compound classes.This work uses a variety of composition analysis methods to clarify the steam flooding mechanism and provides a novel understanding of steam flooding mechanisms with various temperatures and production stages from the molecular perspective.
基金funded by the CNOOC Scientific Research Project“Study of cementing key properties and its matching technology of LD-10 gas field”(Grant No.CCL2019ZJFN1227).
文摘Air channeling in the annulus between the casing and the cement sheath and/or between the cement sheath and formation is the main factor affecting the safe operation of natural gas wells at high temperatures and pressures.Prevention of this problem requires,in general,excellent anti-channeling performances of the cement sheath.Three methods to predict such anti-channeling performances are proposed here,which use the weightless pressure of cement slurry,the permeability of cement stone and the volume expansion rate of cement sheath as input parameters.Guided by this approach,the anti-channeling performances of the cement slurry are evaluated by means of indoor experiments,and the cement slurry is optimized accordingly.The results show that the dangerous transition time of the cement slurry with optimized dosage of admixture is only 76 min,the permeability of cement stone is 0.005 md,the volume shrinkage at final setting is only 0.72%,and the anti-channeling performances are therefore maximized.The effective utilization of the optimized cement slurry in some representative wells(LD10–1-A1 and LD10–1-A2 in LD10–1 gas field)is also discussed.
基金support from National Natural Science Foundation of China(No.52174042)China University of Petroleum Beijing(No.2462021YXZZ011,No.PRP/indep-4-2113)for the completion of this study.
文摘Multiple fractured horizontal wells (MFHWs) currently are the only possible means of commercial production from the low and ultra-low permeability unconventional gas reservoirs. In early production time, flowback fluid, which constitutes of hydraulic water and gas flow within fractures, is collected and analyzed. Flowback analysis has been shown to be a useful tool to estimate key properties of the hydraulic fracture such as conductivity and pore volume. Until date, most tools of flowback analysis rely on empirical and approximate methods. This study presents an improved Green-function-based semi-analytical solution for performance analysis of horizontal gas wells during flowback and early production periods. The proposed solution is derived based on coupling the solutions of two domains: a rigorously derived Green’s function-based integral solution for single-phase gas flow in matrix, and a finite-difference, multiphase solution for gas–water two-phase flow in the fracture. The validity of proposed semi-analytical solution is verified by finely gridded numerical models built in a commercial simulator for a series of synthetic cases considering a variety of fluid and reservoir property combinations, as well as various different production constraints. Comparisons against available empirical and approximate methods are also provided for these cases.
基金supported by Outstanding Youth Fund of Shandong Province(ZR2020YQ36).
文摘Due to its long lifespan and high sand-removal efficiency,gravel packing is one of the most applied sand control methods during the recovery of reservoirs with sanding problems.The blockage and retention of injected sand in a gravel pack is a complex process affected by multiple mechanisms.The majority of existing studies based on the phenomenological deep bed filtration(DBF)theory focused on the gravel pack’s overall permeability damage and failed to obtain the inner-pore particle distribution pattern.In this work,experiments and simulations were carried out to reveal the particle distribution in a gravel pack during flooding.In particular,through real-time monitoring of particle migration,the penetration depth and distribution pattern of invaded particles with different gravel-sand particle ratios,fluid viscosities and injection rates could be determined.By simplifying each unit bed element(UBE)into a pore-throat structure with four tunnels(two horizontals for discharge and two verticals for sedimentation),a new network simulation method,which combines deep bed filtration with a particle trajectory model,was implemented.Cross comparison of experimental and numerical results demonstrates the validity and accuracy of the model.
基金Project supported by the Natural Science Foundation of Beijing Municipality (Grant No.1212007)the National Natural Science Foundation of China (Grant No.11705284)the Open Project Program of State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum (Grant No.PRP/DX-2211)。
文摘We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.
基金supported by the National Natural Science Foundation of China(Grant Nos.41972110 and 41772108)。
文摘To investigate the influence of diagenetic water media on the hydrogen isotopes of individual sedimentary aromatic compounds,a series of hydrous pyrolyses were conducted on herbaceous peat.Polycyclic aromatic hydrocarbons(PAHs)in hydrous pyrolysed samples and their hydrogen isotopic composition characteristics were studied.The aqueous medium demonstrated a significant influence on the hydrogen isotopic composition of the individual PAHs generated during pyrolysis.The results showed that the PAHs formed after pyrolysis in the presence of a saltwater medium with high δD value from a salt lake had a heavy hydrogen isotopic composition.The PAHs formed after pyrolysis in the presence of a fresh water medium with low δD value from a swamp had a light hydrogen isotopic composition.The difference in the average PAHδD value between the two hydrous experiments varied from -174‰ to -109‰,suggesting that the hydrogen isotopic composition of individual sedimentary PAHs can reflect the source of the diagenetic water medium.In addition,a comparative study found that the hydrogen isotopes of PAHs were superior to those of n-alkanes in the same sample for diagenetic water indications.The results indicated that the exchange of water-derived inorganic hydrogen and organic hydrogen was more intensive in freshwater experiments than in saltwater experiments.With an increase in the simulation temperature,the average δD value of PAHs generated in the hydrous simulation experiments showed an increasing trend,reflecting that the δD value of sedimentary PAHs formed with the participation of diagenetic water media was still closely related to the thermal maturity of organic matter.Comparative studies showed that theδD values of different types of organic compounds produced by hydrous pyrolysis of peat were in the order,PAHs>n-alkanes>methane.
基金the financial support from the Graduate Student Innovation and Practical Ability Training Program of Xi’an Shiyou University (No. YCS21212111)Open Fund Project of the State Key Laboratory of Heavy Oil, China (SKLHOP201703)+3 种基金National Natural Science Foundation of China (No. 52274039)Natural Science Foundation of Shaanxi Provincial Department of Education (Grant 2023-JC-YB-414)Natural Science Foundation of Shaanxi Province in China (No. 2022JZ-28)the Open Fund Project of the National Oil Shale Exploitation Research and Development Center, China (No. 33550022-ZC0613-0255)
文摘To obtain high yields of monocyclic aromatic hydrocarbons with methyl side chains,such as toluene and xylene,methane(CH_(4))can be introduced into the hydrocracking of polycyclic aromatic hydrocarbons.CH_(4)can participate in the reaction,supply methyl side chains to the product,and improve product distribution.In this study,the hydrogenation reaction of polycyclic aromatic hydrocarbons over a carbonized NiMo/Hβcatalyst in a CH_(4)and hydrogen(H_(2))environment was investigated to study the promotional effect of CH_(4)on the hydrocracking of polycyclic aromatics.Under conditions of 3.5 MPa,380℃,volume air velocity of 4 h^(-1),gas-oil volume ratio of 800,and H_(2):CH_(4)molar ratio of 1:1,the conversion rate of naphthalene was 99.97%,the liquid phase yield was 93.62%,and the selectivity of BTX were 17.76%,25.17%,and 20.47%,respectively.In comparison to the use of a H_(2)atmosphere,the selectivity of benzene was significantly decreased,whereas the selectivity of toluene and xylene were increased.It was shown that CH_(4)can participate in the hydrocracking of naphthalene and improve the selectivity of toluene and xylene in the liquid product.The carbonized NiMo/Hβcatalyst was characterized by a range of analytical methods(such as X-ray diffraction(XRD),ammonia-temperature-programmed desorption(NH3-TPD),hydrogen-temperature-programmed reduction(H_(2)-TPR),and X-ray photoelectron spectroscopy(XPS)).The results indicated that Ni and Mo carbides were the major species in the carbonized NiMo/Hβcatalyst and were considered to be active sites for the activation of CH_(4)and H_(2).After loading the metal components,the catalyst displayed prominent weak acidic sites,which may be suitable locations for cracking,alkylation,and other related reactions.Therefore,the carbonized NiMo/Hβcatalyst displayed multiple functions during the hydrocracking of polycyclic aromatic hydrocarbons in a CH_(4)and H_(2)environment.These results could be used to develop a new way to efficiently utilize polycyclic aromatic hydrocarbons and natural gas resources.
基金supported by Bohai Oilfield Efficient Development Demonstration Project(2016ZX05058-003-011).
文摘Current methods for the analysis of channeling-path phenomena in reservoirs cannot account for the influence of time and space on the actual seepage behavior.In the present study,this problem is addressed considering actual production data and dynamic characteristic parameters quantitatively determined in the near wellbore area by fitting the water-cut curve of the well.Starting from the dynamic relationship between injection and production data,the average permeability is determined and used to obtain a real-time quantitative characterization of the seepage behavior of the channeling-path in the far wellbore area.For the considered case study(Jidong oilfield),it is found that the seepage capacity of the channeling-path in the far wellbore area is far less(10 times smaller)than that of the channeling-path in the near wellbore area.The present study and the proposed model(combining near wellbore area and far wellbore area real-time data)have been implemented to support the definition of relevant adjustment measures to ultimately improve oil recovery.
基金funded by the National Natural Science Foundation of China(Grant No.52274048)Beijing Natural Science Foundation(Grant No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(Grant No.2021DJ2104)the Science Foundation of China University of Petroleum-Beijing(No.2462021YXZZ010).
文摘Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.
