Influence of pore structure heterogeneity on channeling channels during hot water flooding in heavy oil reservoir based on CT scanning

Hot water flooding is an effective way to develop heavy oil reservoirs.However,local channeling channels may form,possibly leading to a low thermal utilization efficiency and high water cut in the reservoir.The pore structure heterogeneity is an important factor in forming these channels.This study proposes a method that mixes quartz sand with different particle sizes to prepare weakly heterogeneous and strongly heterogeneous models through which hot water flooding experiments are conducted.During the experiments,computer tomography(CT)scanning identifies the pore structure and micro remaining oil saturation distribution to analyze the influence of the pore structure heterogeneity on the channeling channels.The oil saturation reduction and average pore size are divided into three levels to quantitatively describe the relationship between the channeling channel distribution and pore structure heterogeneity.The zone where oil saturation reduction exceeds 20%is defined as a channeling channel.The scanning area is divided into 180 equally sized zones based on the CT scanning images,and threedimensional(3D)distributions of the channeling channels are developed.Four micro remaining oil distribution patterns are proposed,and the morphology characteristics of micro remaining oil inside and outside the channeling channels are analyzed.The results show that hot water flooding is more balanced in the weakly heterogeneous model,and the oil saturation decreases by more than 20%in most zones without narrow channeling channels forming.In the strongly heterogeneous model,hot water flooding is unbalanced,and three narrow channeling channels of different lengths form.In the weakly heterogeneous model,the oil saturation reduction is greater in zones with larger pores.The distribution range of the average pore size is larger in the strongly heterogeneous model.The network remaining oil inside the channeling channels is less than outside the channeling channels,and the hot water converts the network remaining oil into cluster,film,and droplet remaining oil.

Experimental study of the effects of a multistage pore-throat structure on the seepage characteristics of sandstones in the Beibuwan Basin:Insights into the flooding mode

To investigate the relationship between grain sizes, seepage capacity, and oil-displacement efficiency in the Liushagang Formation of the Beibuwan Basin, this study identifies the multistage pore-throat structure as a crucial factor through a comparison of oil displacement in microscopic pore-throat experiments. The two-phase flow evaluation method based on the Li-Horne model is utilized to effectively characterize and quantify the seepage characteristics of different reservoirs, closely relating them to the distribution of microscopic pores and throats. It is observed that conglomerate sandstones at different stages exhibit significant heterogeneity and noticeable differences in seepage capacity, highlighting the crucial role played by certain large pore throats in determining seepage capacity and oil displacement efficiency. Furthermore, it was found that the displacement effects of conglomeratic sandstones with strong heterogeneity were inferior to those of conventional homogeneous sandstone, as evidenced by multiple displacement experiments conducted on core samples with varying granularities and flooding systems. Subsequently, core-based experiments on associated gas flooding after water flooding were conducted to address the challenge of achieving satisfactory results in a single displacement mode for reservoirs with significant heterogeneity. The results indicate that the oil recovery rates for associated gas flooding after water flooding increased by 7.3%-16.4% compared with water flooding alone at a gas-oil ratio of approximately 7000 m^(3)/m^(3). Therefore, considering the advantages of gas flooding in terms of seepage capacity, oil exchange ratio, and the potential for two-phase production, gas flooding is recommended as an energy supplement mode for homogeneous reservoirs in the presence of sufficient gas source and appropriate tectonic angle. On the other hand, associated gas flooding after water flooding is suggested to achieve a more favorable development effect compared to a single mode of energy supplementation for strongly heterogeneous sandstone reservoirs.

Time-dependent model for two-phase flow in ultra-high water-cut reservoirs:Time-varying permeability and relative permeability

For the ultra-high water-cut reservoirs,after long-term water injection exploitation,the physical properties of the reservoir change and the heterogeneity of the reservoir becomes increasingly severe,which further aggravates the spatial difference of the flow field.In this study,the displacement experiments were employed to investigate the variations in core permeability,porosity,and relative permeability after a large amount of water injection.A relative permeability endpoint model was proposed by utilizing the alternating conditional expectation(ACE)transformation to describe the variation in relative permeability based on the experimental data.Based on the time dependent models for permeability and relative permeability,the traditional oil-water two-phase model was improved and discretized using the mimetic finite difference method(MFD).The two cases were launched to confirm the validation of the proposed model.The impact of time-varying physical features on reservoir production performance was studied in a real water flooding reservoir.The experimental results indicate that the overall relative permeability curve shifts to the right as water injection increases.This shift corresponds to a transition towards a more hydrophilic wettability and a decrease in residual oil saturation.The endpoint model demonstrates excellent accuracy and can be applied to time-varying simulations of reservoir physics.The impact of variations in permeability and relative permeability on the reservoir production performance yields two distinct outcomes.The time-varying permeability of the reservoir results in intensified water channeling and poor development effects.On the other hand,the time-varying relative permeability enhances the oil phase seepage capacity,facilitating oil displacement.The comprehensive time-varying behavior is the result of the combined influence of these two parameters,which closely resemble the actual conditions observed in oil field exploitation.The time-varying simulation technique of reservoir physical properties proposed in this paper can continuously and stably characterize the dynamic changes of reservoir physical properties during water drive development.This approach ensures the reliability of the simulation results regarding residual oil distribution.

Flow Dynamics during the Hydrocarbon Exploitation for Prevention and Management of Water Venues in Oil Field: A Study Case of Crystal Field in Badila/Chad

The southern part of the Lake Chad basin is under the gas and oil petroleum industry due to its hydrocarbon potential for about twenty years. This project stands out as the main challenges of the hydrocarbon production and the management of fluxes particularly the groundwater venues. A comprehensive study is thus conducted to develop a dynamic and analytic model for diagnosing the production performances with a particular view on the management of groundwater venues. The three main concerned reservoirs subdivided on subunits evidence their proper characteristics. The porous media, their densities, the internal flows and the water injection techniques such as water flooding were thus adopted. The oil viscosity variability within the reservoirs creates different levels of mobility between water and oil, highlighting the challenges of water management. The material balance model and the behavior of the well analysis were taken in consideration within the identified aquifer, emphasizing the importance of keeping the pressure through injection. The control of water productions, the management of the reservoir, the well strategical position and the specific completions lead to the model functioning. In addition, the CO log and the Pulsed Neutron indicate their limitations as a result of the water salinity and the porosity of the aquifer. The management of groundwater venues at Badila requires various approaches throughout the lifetime of the Crystal field such as the data acquisition and remediation actions and prevention, under a permanent monitoring of the dynamic fluxes in the reservoirs.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Theoretical exploration of water injection gravity flooding oil in ultra-deep fault-controlled fractured-cavity carbonate reservoirs

Based on the analysis of geological characteristics of ultra-deep fault-controlled fracture-cavity carbonate reservoirs and division of reservoir units, two physical models were made, and physical simulations of oil displacement by water injection were carried out to find out water flooding mechanism in the fault-controlled fracture-cavity carbonate reservoir under complex flow state. On this basis, a mathematical model of fault-controlled carbonate reservoir with coexisting seepage and free flow has been established. Pilot water injection tests have been carried out to evaluate the effects of enhancing oil recovery by water injection. The results show that: fault-controlled fracture-cavity carbonate reservoir units can be divided into three types:the strong natural energy connected type, the weak natural energy connected type and the weak natural energy isolated type;the fault-fracture activity index of the fault-controlled fractured-cavity body can effectively characterize the connectivity of the reservoir and predict the effective direction of water injection;the mathematical model of fault-controlled carbonate reservoir with coexisting seepage and free flows can quantitatively describe the fluid flow law in the fracture-cavity body;the water injected into the fault-controlled fracture-cavity body is weakly affected by the capillary force of the lithologic body, and the oil-water movement is mainly dominated by gravity. The development modes of single well water injection, unit water injection,and single well high pressure water injection proposed based on the connection structure of fracture-cavity space and well storage space configuration are confirmed effective by pilot tests, with obvious water injection gravity flooding effect.

A production prediction method of single well in water flooding oilfield based on integrated temporal convolutional network model

Since the oil production of single well in water flooding reservoir varies greatly and is hard to predict, an oil production prediction method of single well based on temporal convolutional network(TCN) is proposed and verified. This method is started from data processing, the correspondence between water injectors and oil producers is determined according to the influence radius of the water injectors, the influence degree of a water injector on an oil producer in the month concerned is added as a model feature, and a Random Forest(RF) model is built to fill the dynamic data of water flooding. The single well history is divided into 4 stages according to its water cut, that is, low water cut, middle water cut, high water cut and extra-high water cut stages. In each stage, a TCN based prediction model is established, hyperparameters of the model are optimized by the Sparrow Search Algorithm(SSA). Finally, the models of the 4 stages are integrated into one whole-life model of the well for production prediction. The application of this method in Daqing Oilfield, NE China shows that:(1) Compared with conventional data processing methods, the data obtained by this processing method are more close to the actual production, and the data set obtained is more authentic and complete.(2) The TCN model has higher prediction accuracy than other 11 models such as Long Short Term Memory(LSTM).(3) Compared with the conventional full-life-cycle models, the model of integrated stages can significantly reduce the error of production prediction.

Displacement behavior and mechanism of long-term water flooding in sandstone oil reservoirs

Sandstone oil reservoirs with huge bottom water and high permeability are generally developed with high flow rate.After long-term water flooding(LTWF),the water flooding characteristics are quite different from that of original reservoir.In this paper,the effects of the PV number,viscosity,and displacement rate during LTWF are studied through experiments.The mechanism is analyzed based on analysis of changes in oil composition,rock mineral composition and wettability.The oil-water relative permeability curves,oil recovery and wettability were obtained with new experiments methods,which avoids the oil metering error by measuring oil and water separately.The research indicates that when the viscosity increases,the water phase permeability decreases,the residual oil saturation increases,and the water content rate increases earlier.A higher water flooding rate results in a higher ultimate recovery.A higher asphaltene content results in a higher viscosity and more oil-wet reservoir conditions.After LTWF,the wettability tends to water-wet,which is more favorable for heavy oil recovery.Moreover,LTWF reduces the clay content,which creates a more water-wet surface and a larger reservoir pore throat environment.This research provides insightful characteristics of offshore sandstone oil reservoirs,which can be used to enhance oil recovery.

Application of New Water Flooding Characteristic Curve in the High Water-Cut Stage of an Oilfield

The oil production predicted by means of the conventional water-drive characteristic curve is typically affected by large deviations with respect to the actual value when the so-called high water-cut stage is entered.In order to solve this problem,a new characteristic relationship between the relative permeability ratio and the average water saturation is proposed.By comparing the outcomes of different matching methods,it is verified that it can well reflect the variation characteristics of the relative permeability ratio curve.Combining the new formula with a reservoir engineering method,two new formulas are derived for the water flooding characteristic curve in the high water-cut stage.Their practicability is verified by using the production data of Mawangmiao and Xijiakou blocks.The results show that the error between the predicted cumulative oil production and production data of the two new water drive characteristic curves is less than the error between the B-type water drive characteristic curve and the other two water drive characteristic curves.It is concluded that the two new characteristic curves can be used to estimate more accurately the recoverable reserves,the final recovery and to estimate the effects of water flooding.

Effects of salinity and ionic composition of smart water on mineral scaling in carbonate reservoirs during water flooding

This work was conducted to study the risk of formation damage as the result of mineral scales deposition during smart waterflooding into carbonate core sample,as well as the influence of injected water salinity and ionic composition on mineral scaling and precipitation.The reservoir flowing conditions were simulated by a new laboratory core-flooding procedure,which took into count of the effect of in-situ contact time(CT)of injected water and formation water on scaling.After the optimum CT was determined,extent of permeability decline was studied by the change in the salinity and ionic composition of injection seawater.The scaled core sample was analyzed visually by scanning electron microscopy(SEM)to study the crystal morphology of the scale.Under the experimental conditions,extent of permeability decline caused by CaSO_(4) and CaSO_(3) composite scales ranged from 61% to 79.1% of the initial permeability.The salinity and the ionic composition of injected smart water,and CT of the mixing waters had significant effects on the co-precipitation of CaSO_(4) and CaSO_(3) scales.The SEM images reveal that the loss of permeability is mainly caused by the accumulation and growth perpendicular to the pore wall of scale crystals.

Inter-well interferences and their influencing factors during water flooding in fractured-vuggy carbonate reservoirs

Based on the characteristics of injection-production units in fractured-vuggy carbonate reservoirs,nine groups of experiments were designed and performed to analyze the interference characteristics and their influencing factors during water flooding.Based on percolation theory,an inversion model for simulating waterflooding interferences was proposed to study the influence laws of different factors on interference characteristics.The results show that well spacing,permeability ratio,cave size,and cave location all affect the interference characteristics of water flooding.When the cave is located in high permeability fractures,or in the small well spacing direction,or close to the producer in an injection-production unit,the effects of water flooding are much better.When the large cave is located in the high-permeability or small well spacing direction,the well in the direction with lower permeability or smaller well spacing will see water breakthrough earlier.When the cave is in the higher permeability direction and the reserves between the water injector and producer differ greatly,the conductivity differences in different injection-production directions are favorable for water flooding.When the injection-production well pattern is constructed or recombined,it’s better to make the reserves of caves in different injection-production directions proportional to permeability,and inversely proportional to the well spacing.The well close to the cave should be a producer,and the well far from the cave should be an injector.Different ratios of cave reserves to fracture reserves correspond to different optimal well spacings and optimal permeability ratios.Moreover,both optimal well spacing and optimal permeability ratio increase as the ratio of cave reserves to fracture reserves increases.

Mechanisms of remaining oil formation by water flooding and enhanced oil recovery by reversing water injection in fractured-vuggy reservoirs

To get a deeper understanding on the formation mechanisms and distribution laws of remaining oil during water flooding, and enhanced oil recovery(EOR) mechanisms by reversing water injection after water flooding, 3D visualization models of fractured-vuggy reservoir were constructed based on the elements and configuration of fractures and vugs, and typical fracture-vug structures by using advanced CT scanning and 3D printing technologies. Then, water flooding and reversing water injection experiments were conducted. The formation mechanisms of remaining oil during water flooding include inadequate injection-production well control, gravity difference between oil and water, interference between different flow channels, isolation by low connectivity channel, weak hydrodynamic force at the far end. Under the above effects, 7 kinds of remaining oil may come about, imperfect well-control oil, blind side oil, attic oil at the reservoir top, by-pass residual oil under gravity, by-pass residual oil in secondary channel, isolated oil in low connectivity channel, and remaining oil at far and weakly connected end. Some remaining oil can be recovered by reversing water injection after water flooding, but its EOR is related to the remaining oil type, fracture-cavity structure and reversing injection-production structure. Five of the above seven kinds of remaining oil can be produced by six EOR mechanisms of reversing water injection: gravity displacement, opening new flow channel, rising the outflow point, hydrodynamic force enhancement, vertically equilibrium displacement, and synergistic effect of hydrodynamic force and gravity.

Geochemical characteristics of reservoir after water and polymer flooding in Xingshugang oilfield of Daqing

Collecting 44 oil-sand specimens of Pu-I Member in two inspection wells before and after polymer flooding in the thirteenth district of Xingshugang oilfield,with experimental analysis,the author obtained the data about oil viscosity,flow,oil saturation and oil displacement efficiency.The result shows that viscous oil predominates in the main remaining oil in Xingshugang oilfield after water flooding with a certain amount of low viscosity oil,high viscosity oil and heavy oil;after polymer flooding,the viscous oil is main ingredient.Compared with water flooding,the low mobility and poor oil can be spread by polymer flooding,expanding the affected area and improving sweep efficiency and oil recovery.The geochemical affecting factors of water flooding and oil displacement efficiency refer to reservoir flow,permeability and the viscosity of residual oil.In the reservoir with permeability from low to high,the polymer flooding efficiency is better than water flooding.It provides the basis for improving the water and polymer flooding efficiency of the Xingshugang oilfield.

Hybrid low salinity water and surfactant process for enhancing heavy oil recovery

Combining low salinity water (LSW) with surfactants has an enormous potential for enhancing oil recovery processes. However, there is no consensus about the mechanisms involved, in addition to the fact that several studies have been conducted in model systems, while experiments with rocks and reservoir fluids are scarce. This study presents a core-flooding experiment of LSW injection, with and without surfactant, using the core and heavy oil samples obtained from a sandstone reservoir in southeastern Mexico. The effluents and the crude oil obtained at each stage were analyzed. The study was complemented by tomographic analysis. The results revealed that LSW injection and hybrid process with surfactants obtained an increase of 11.4 percentage points in recovery factor. Various phenomena were caused by LSW flooding, such as changes in wettability and pH, ion exchange, mineral dissolution, detachment of fines and modification of the hydrocarbon profile. In the surfactant flooding, the reduction of interfacial tension and alteration of wettability were the main mechanisms involved. The findings of this work also showed that the conditions believed to be necessary for enhanced oil recovery with LSW, such as the presence of kaolinite or high acid number oil, are not relevant.

Research progress and potential of new enhanced oil recovery methods in oilfield development

This paper reviews the basic research means for oilfield development and also the researches and tests of enhanced oil recovery(EOR)methods for mature oilfields and continental shale oil development,analyzes the problems of EOR methods,and proposes the relevant research prospects.The basic research means for oilfield development include in-situ acquisition of formation rock/fluid samples and non-destructive testing.The EOR methods for conventional and shale oil development are classified as improved water flooding(e.g.nano-water flooding),chemical flooding(e.g.low-concentration middle-phase micro-emulsion flooding),gas flooding(e.g.micro/nano bubble flooding),thermal recovery(e.g.air injection thermal-aided miscible flooding),and multi-cluster uniform fracturing/water-free fracturing,which are discussed in this paper for their mechanisms,approaches,and key technique researches and field tests.These methods have been studied with remarkable progress,and some achieved ideal results in field tests.Nonetheless,some problems still exist,such as inadequate research on mechanisms,imperfect matching technologies,and incomplete industrial chains.It is proposed to further strengthen the basic researches and expand the field tests,thereby driving the formation,promotion and application of new technologies.

Two-phase flow thermo-hydro-mechanical modeling for a water flooding field case

Simulation of subsurface energy system involves multi-physical processes such as thermal,hydraulical,and mechanical(THM)processes,and requires a so-called THM coupled modeling approach.THM coupled modeling is commonly performed in geothermal energy production.However,for hydrocarbon extraction,we need to consider multiphase flow additionally.In this paper,we describe a three-dimensional numerical model of non-isothermal two-phase flow in the deformable porous medium by integrating governing equations of two-phase mixture in the porous media flow in the reservoir.To account for inter-woven impacts in subsurface condi-tions,we introduced a temperature-dependent fluid viscosity and a fluid density along with a strain-dependent reservoir permeability.Subsequently,we performed numerical experiments of a ten-year water flooding pro-cess employing the open-source parallelized code,OpenGeoSys.We considered different well patterns with colder water injection in realistic scenarios.Our results demonstrate that our model can simulate complex interactions of temperature,pore pressure,subsurface stress and water saturation simultaneously to evaluate the recovery per-formance.High temperature can promote fluid flow while cold water injection under non-isothermal conditions causes the normal stress reduction by significant thermal stress.Under different well patterns the displacement efficiency will be changed by the relative location between injection and production wells.This finding has provided the important reference for fluid flow and induced stress evolution during hydrocarbon exploitation under the environment of large reservoir depth and high temperature.

On the Development of an Effective Pressure Driving System for Ultra-Low Permeability Reservoirs

Given its relevance to the exploitation of ultra-low permeability reservoirs,which account for a substantial proportion of the world’s exploited and still unexploited reserves,in the present study the development of an adequate water injection system is considered.Due to the poor properties and weak seepage capacity of these reservoirs,the water injection pressure typically increases continuously during water flooding.In this research,the impact on such a process of factors as permeability,row spacing,and pressure gradient is evaluated experimentally using a high-pressure large-scale outcrop model.On this basis,a comprehensive evaluation coefficient is introduced able to account for the effective driving pressure.

Efficiency of enhanced oil recovery by injection of low-salinity water in barium-containing carbonate reservoirs

When low-salinity water containing sulfate ions is injected into carbonate reservoirs, rock dissolution and in situ precipitation occur, altering rock permeability and wettability. Particularly, when barium ions are present in formation water,they react chemically with SO;, and BaSO;is precipitated. These reactions can cause a serious impact on the efficiency of enhanced oil recovery（EOR）. Therefore, the main purpose of this study was to identify EOR efficiency induced by lowsalinity waterflooding（LSWF） when Ba;is present in carbonate reservoirs. From the experimental results, it was confirmed that the permeability calculated by the measured pressure difference was improved because of rock dissolution predominating over in situ precipitation for the case of low Ba;concentrations. In the analysis of wettability alteration through the measurements of relative permeabilities before and after LSWF, the higher Ba;concentration case consumed more SO;in precipitating the BaSO;, resulting in weaker wettability alteration due to the reduction of sulfate activity.These phenomena ultimately influenced EOR efficiency, i.e., the oil recovery was greater for the lower Ba;concentration.

Factors influencing oil recovery by surfactant-polymer flooding in conglomerate reservoirs and its quantitative calculation method

This study aims to clarify the factors influencing oil recovery of surfactant-polymer(SP)flooding and to establish a quantitative calculation model of oil recovery during different displacement stages from water flooding to SP flooding.The conglomerate reservoir of the Badaowan Formation in the seventh block of the Karamay Oilfield is selected as the research object to reveal the start-up mechanism of residual oil and determine the controlling factors of oil recovery through SP flooding experiments of natural cores and microetching models.The experimental results are used to identify four types of residual oil after water flooding in this conglomerate reservoir with a complex pore structure:oil droplets retained in pore throats by capillary forces,oil cluster trapped at the junction of pores and throats,oil film on the rock surface,isolated oil in dead-ends of flow channel.For the four types of residual oil identified,the SP solution can enhance oil recovery by enlarging the sweep volume and improving the oil displacement efficiency.First,the viscosity-increasing effect of the polymer can effectively reduce the permeability of the displacement liquid phase,change the oil-water mobility ratio,and increase the water absorption.Furthermore,the stronger the shear drag force of the SP solution,the more the crude oil in a porous medium is displaced.Second,the surfactant can change the rock wettability and reduce the absorption capacity of residual oil by lowering interfacial tension.At the same time,the emulsification further increases the viscosity of the SP solution,and the residual oil is recovered effectively under the combined effect of the above two factors.For the four start-up mechanisms of residual oil identified after water flooding,enlarging the sweep volume and improving the oil displacement efficiency are interdependent,but their contribution to enhanced oil recovery are different.The SP flooding system primarily enlarges the sweep volume by increasing viscosity of solution to start two kinds of residual oil such as oil droplet retained in pore throats and isolated oil in dead-ends of flow channel,and primarily improves the oil displacement efficiency by lowing interfacial tension of oil phase to start two kinds of residual oil such as oil cluster trapped at the junction of pores and oil film on the rock surface.On this basis,the experimental results of the oil displacement from seven natural cores show that the pore structure of the reservoir is the main factor influencing water flooding recovery,while the physical properties and original oil saturation have relatively little influence.The main factor influencing SP flooding recovery is the physical and chemical properties of the solution itself,which primarily control the interfacial tension and solution viscosity in the reservoir.The residual oil saturation after water flooding is the material basis of SP flooding,and it is the second-most dominant factor controlling oil recovery.Combined with the analysis results of the influencing factors and reservoir parameters,the water flooding recovery index and SP flooding recovery index are defined to further establish quantitative calculation models of oil recovery under different displacement modes.The average relative errors of the two models are 4.4%and 2.5%,respectively;thus,they can accurately predict the oil recovery of different displacement stages and the ultimate reservoir oil recovery.

Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

Fines migration induced by injection of low-salinity water(LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deepbed filtration(DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model,the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.