The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant ...The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.展开更多
The mathematical model for the thermokinetics of irreversible consecutive first order reactions has been suggested,which was used for the calculation of rate constants and molar enthalpies of the two consecutive steps...The mathematical model for the thermokinetics of irreversible consecutive first order reactions has been suggested,which was used for the calculation of rate constants and molar enthalpies of the two consecutive steps.And its validity has been verified by the ex- perimental results.展开更多
The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylen...The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylene blue adsorption on activated carbon was used for this research.Both the correlation coefficient(R2)and the normalized standard deviationΔq(%)were employed as error analysis methods to determine the best-fitting equations.The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data.The experimental kinetics may have been distorted by linearization of the linear kinetic equations,and thus,the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters.In addition,theΔq(%)method for error analysis may be better to determine the best-fitting model in this case.展开更多
Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper...Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.展开更多
基金financially supported by the National Natural Science Foundation of China(Project No.51874336)the National Key Technologies Research and Development Program of China during the 13th Five-Year Plan Period(Project No.2017ZX005030005)。
文摘The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.
文摘The mathematical model for the thermokinetics of irreversible consecutive first order reactions has been suggested,which was used for the calculation of rate constants and molar enthalpies of the two consecutive steps.And its validity has been verified by the ex- perimental results.
基金the Research Scheme of Education Department of Zhejiang Province,China(No.Y200806037).
文摘The best-fit equations of linear and non-linear forms of the two widely used kinetic models,namely pseudo-first-order and pseudo-second-order equations,were compared in this study.The experimental kinetics of methylene blue adsorption on activated carbon was used for this research.Both the correlation coefficient(R2)and the normalized standard deviationΔq(%)were employed as error analysis methods to determine the best-fitting equations.The results show that the non-linear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data.The experimental kinetics may have been distorted by linearization of the linear kinetic equations,and thus,the non-linear forms of kinetic equations should be primarily used to obtain the adsorption parameters.In addition,theΔq(%)method for error analysis may be better to determine the best-fitting model in this case.
文摘Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.
