Homogeneity and heterogeneity are two totally different concepts in nature.At the particle length scale,rocks exhibit strong heterogeneity in their constituents and porosities.When the heterogeneity of porosity obeys ...Homogeneity and heterogeneity are two totally different concepts in nature.At the particle length scale,rocks exhibit strong heterogeneity in their constituents and porosities.When the heterogeneity of porosity obeys the random uniform distribution,both the mean value and the variance of porosities in the heterogeneous porosity field can be used to reflect the overall heterogeneous characteristics of the porosity field.The main purpose of this work is to investigate the effects of porosity heterogeneity on chemical dissolution front instability in fluid-saturated rocks by the computational simulation method.The related computational simulation results have demonstrated that:1) since the propagation speed of a chemical dissolution front is inversely proportional to the difference between the final porosity and the mean value of porosities in the initial porosity field,an increase in the extent of the porosity heterogeneity can cause an increase in the mean value of porosities in the initial porosity field and an increase in the propagation speed of the chemical dissolution front.2) An increase in the variance of porosities in the initial porosity field can cause an increase in the instability probability of the chemical dissolution front in the fluid-saturated rock.3) The greater the mean value of porosities in the initial porosity field,the quicker the irregular morphology of the chemical dissolution front changes in the supercritical chemical dissolution systems.This means that the irregular morphology of a chemical dissolution front grows quicker in a porosity field of heterogeneity than it does in that of homogeneity when the chemical dissolution system is at a supercritical stage.展开更多
Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-fron...Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.展开更多
Chemical dissolution-front instability(CDFI)problems usually involve multiple temporal and spatial scales,as well as multiple processes.A key issue associated with solving a CDFI problem in a fluid-saturated rock is t...Chemical dissolution-front instability(CDFI)problems usually involve multiple temporal and spatial scales,as well as multiple processes.A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion,which can be used to judge the instability of a chemical dissolution-front(CDF)propagating in the fluidsaturated rock.This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner,rather than in a numerical simulation manner.The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme,a curved surface coordinate system is used,while in the second mathematical scheme,a planar surface coordinate system is employed.In particular,all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail.The main theoretical outcomes of this study have demonstrated that(1)two different mathematical schemes under consideration can produce exactly the same theoretical criterion;(2)the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically;(3)the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner.展开更多
In order to simulate the instability phenomenon of a nonaqueous phase liquid(NAPL) dissolution front in a computational model, the intrinsic characteristic length is commonly used to determine the length scale at whic...In order to simulate the instability phenomenon of a nonaqueous phase liquid(NAPL) dissolution front in a computational model, the intrinsic characteristic length is commonly used to determine the length scale at which the instability of the NAPL dissolution front can be initiated. This will require a huge number of finite elements if a whole NAPL dissolution system is simulated in the computational model. Even though modern supercomputers might be used to tackle this kind of NAPL dissolution problem, it can become prohibitive for commonly-used personal computers to do so. The main purpose of this work is to investigate whether or not the whole NAPL dissolution system of an annular domain can be replaced by a trapezoidal domain, so as to greatly reduce the requirements for computer efforts. The related simulation results have demonstrated that when the NAPL dissolution system under consideration is in a subcritical state, if the dissolution pattern around the entrance of an annulus domain is of interest, then a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.However, if the dissolution pattern away from the vicinity of the entrance of an annulus domain is of interest, then a trapezoidal domain can be used to replace an annular domain in the computational simulation of the NAPL dissolution system. When the NAPL dissolution system under consideration is in a supercritical state, a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.展开更多
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘Homogeneity and heterogeneity are two totally different concepts in nature.At the particle length scale,rocks exhibit strong heterogeneity in their constituents and porosities.When the heterogeneity of porosity obeys the random uniform distribution,both the mean value and the variance of porosities in the heterogeneous porosity field can be used to reflect the overall heterogeneous characteristics of the porosity field.The main purpose of this work is to investigate the effects of porosity heterogeneity on chemical dissolution front instability in fluid-saturated rocks by the computational simulation method.The related computational simulation results have demonstrated that:1) since the propagation speed of a chemical dissolution front is inversely proportional to the difference between the final porosity and the mean value of porosities in the initial porosity field,an increase in the extent of the porosity heterogeneity can cause an increase in the mean value of porosities in the initial porosity field and an increase in the propagation speed of the chemical dissolution front.2) An increase in the variance of porosities in the initial porosity field can cause an increase in the instability probability of the chemical dissolution front in the fluid-saturated rock.3) The greater the mean value of porosities in the initial porosity field,the quicker the irregular morphology of the chemical dissolution front changes in the supercritical chemical dissolution systems.This means that the irregular morphology of a chemical dissolution front grows quicker in a porosity field of heterogeneity than it does in that of homogeneity when the chemical dissolution system is at a supercritical stage.
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.42030809 and 72088101)。
文摘Chemical dissolution-front instability(CDFI)problems usually involve multiple temporal and spatial scales,as well as multiple processes.A key issue associated with solving a CDFI problem in a fluid-saturated rock is to mathematically establish a theoretical criterion,which can be used to judge the instability of a chemical dissolution-front(CDF)propagating in the fluidsaturated rock.This theoretical paper deals with how two different mathematical schemes can be used to precisely establish such a theoretical criterion in a purely mathematical manner,rather than in a numerical simulation manner.The main distinguishment between these two different mathematical schemes is that in the first mathematical scheme,a curved surface coordinate system is used,while in the second mathematical scheme,a planar surface coordinate system is employed.In particular,all the key mathematical deduction steps associated with using these two different mathematical schemes are described and discussed in great detail.The main theoretical outcomes of this study have demonstrated that(1)two different mathematical schemes under consideration can produce exactly the same theoretical criterion;(2)the main advantage of using the first mathematical scheme is that the interface conditions at the curved interface between the downstream and upstream regions can be easily described mathematically;(3)the main advantage of using the second mathematical scheme is that the first-order perturbation equations of the CDFI problem can be easily described in a purely mathematical manner.
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘In order to simulate the instability phenomenon of a nonaqueous phase liquid(NAPL) dissolution front in a computational model, the intrinsic characteristic length is commonly used to determine the length scale at which the instability of the NAPL dissolution front can be initiated. This will require a huge number of finite elements if a whole NAPL dissolution system is simulated in the computational model. Even though modern supercomputers might be used to tackle this kind of NAPL dissolution problem, it can become prohibitive for commonly-used personal computers to do so. The main purpose of this work is to investigate whether or not the whole NAPL dissolution system of an annular domain can be replaced by a trapezoidal domain, so as to greatly reduce the requirements for computer efforts. The related simulation results have demonstrated that when the NAPL dissolution system under consideration is in a subcritical state, if the dissolution pattern around the entrance of an annulus domain is of interest, then a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.However, if the dissolution pattern away from the vicinity of the entrance of an annulus domain is of interest, then a trapezoidal domain can be used to replace an annular domain in the computational simulation of the NAPL dissolution system. When the NAPL dissolution system under consideration is in a supercritical state, a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.
