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Second-order cone optimization of the gradostat
Computers & Chemical Engineering ( IF 4.3 ) Pub Date : 2021-05-01 , DOI: 10.1016/j.compchemeng.2021.107347
Josh A. Taylor , Alain Rapaport

The gradostat consists of multiple chemostats interconnected by mass flows and diffusion. It has been used to model biochemical systems such as wastewater treatment networks and microbial activity in soil. In this paper we maximize the production of biogas in a gradostat at steady state. The physical decision variables are the water, substrate, and biomass entering each tank and the flows through the interconnecting pipes. Our main technical focus is the nonconvex constraint describing microbial growth. We formulate a relaxation and prove that it is exact when the gradostat is outflow connected, its system matrix is irreducible, and the growth rate satisfies a simple condition. The relaxation has second-order cone representations for the Monod and Contois growth rates. We extend the steady state models to the case of multiple time periods by replacing the derivatives with numerical approximations instead of setting them to zero. The resulting optimizations are second-order cone programs, which can be solved at large scales using standard industrial software.



中文翻译:

Gradostat的二阶锥优化

格拉多司他由通过质量流和扩散相互连接的多个恒化器组成。它已被用来模拟生化系统,例如废水处理网络和土壤中的微生物活性。在本文中,我们在稳定状态下在格拉多斯达型控制器中最大化了沼气的产量。物理决策变量是进入每个水箱的水,底物和生物质以及通过互连管的流量。我们的主要技术重点是描述微生物生长的非凸约束。我们拟定了一个松弛,证明当格拉多司他流出连接时是正确的,它的系统矩阵是不可约的,并且增长率满足一个简单的条件。弛豫具有Monod和Contois增长率的二阶圆锥表示。通过将导数替换为数值逼近,而不是将其设置为零,我们将稳态模型扩展到多个时间段的情况。产生的优化结果是二阶锥程序,可以使用标准工业软件进行大规模求解。

更新日期:2021-05-15
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