An initial differential mathematical model of the process of catalytic reactions coupled in a membrane reactor is developed.The "donor" reaction refers to one that produces the key substance that may permeat...An initial differential mathematical model of the process of catalytic reactions coupled in a membrane reactor is developed.The "donor" reaction refers to one that produces the key substance that may permeate the membrane and be consumed by the "acceptor" reaction.According to the maximum principle in mathematics,the analysis indicates that,in order to obtain maximum yield of the "acceptor" reaction,there should exist our optimal profile of the packed-bed catalytic activity on the "acceptor" reaction side of the membrane reactor,which is a one-time open-close function at the optimum position,as followsξ *(z)=0 ? (0<z<z r ) ξ max (z r ≤z≤1)where ξ *(z) is optimal function of catalytic activity, ξ max its maximum value, z the position,and z r the optimum position.The function means physically that catalytic activity equals to zero near the inlet and that,at the optimum position,activity should be kept maximum constant value on the "acceptor" reaction side.Finally the effect of membrane permeability on the optimum catalytic activity is also investigated.It is found that,as the membrane permeability increases,the optimum open-close position of optimal catalytic activity profile function will move closer to the inlet of the membrane reactor.展开更多
文摘An initial differential mathematical model of the process of catalytic reactions coupled in a membrane reactor is developed.The "donor" reaction refers to one that produces the key substance that may permeate the membrane and be consumed by the "acceptor" reaction.According to the maximum principle in mathematics,the analysis indicates that,in order to obtain maximum yield of the "acceptor" reaction,there should exist our optimal profile of the packed-bed catalytic activity on the "acceptor" reaction side of the membrane reactor,which is a one-time open-close function at the optimum position,as followsξ *(z)=0 ? (0<z<z r ) ξ max (z r ≤z≤1)where ξ *(z) is optimal function of catalytic activity, ξ max its maximum value, z the position,and z r the optimum position.The function means physically that catalytic activity equals to zero near the inlet and that,at the optimum position,activity should be kept maximum constant value on the "acceptor" reaction side.Finally the effect of membrane permeability on the optimum catalytic activity is also investigated.It is found that,as the membrane permeability increases,the optimum open-close position of optimal catalytic activity profile function will move closer to the inlet of the membrane reactor.
