线性规划法确定用水网络最小用水量

Linear programming method for determining minimum water flowrate in water-using network

水污染和水资源短缺是人类面临的重大问题。因此,改善用水过程以节约新鲜水,减少废水排放是值得认真研究的课题。本文提出了确定用水过程最小用水量的新方法—线性规划法。分别研究了单组分再利用、再生再利用、再生循环最小用水量问题,把它们归结为线性规划来求解,其中对于再生再利用和再生循环分别提出了两步线性规划法。对于再生再利用过程,第一步建立线性规划1,以确定整个过程的最小新鲜水和相应的最小再生水用量,第二步将第一步所获得的整个过程的最小用水量和相应的最小再生量以及最低再生浓度区间作为已知量,采用与线性规划1同样的约束建立线性规划2,再次求解即可得最低再生浓度C_b。此外,本文发现再生再利用过程的最小用水量和再生浓度之间存在两种关系,这两种关系表明获得最小新鲜水用量和再生量的最低再生浓度存在两种可能:夹点处和夹点之上,从而得出了与文献“夹点处再生能获得最小新鲜水用量”不同的结论,即夹点处再生未必总能获得最小新鲜水用量。给出了一个实例,计算结果表明本文方法是有效和简便易行的。

Water pollution and scarcity of water is a life-and-death problem that human being is facing, it is worthy of investigation evolving water-using networks to reduce both fresh water consumption and wastewater production. A new method is addressed for determining minimum flowrate of fresh and regenerated water in water-using processes. This paper approaches reuse, regeneration reuse, regeneration recycling process for single contaminant respectively, the mathematical formulation of these synthesis problems lead to a linear programming. Which of the two-step linear programming are presented respectively for regeneration reuse and regeneration recycling. For regeneration reuse, in step 1, the linear programming 1 ( LP1 ) is established, which targets the minimum flowrate of fresh water and corresponding regenerated water. In step 2, based on the minimum flowrate of fresh water and corresponding regenerated water along with the interval in which Cb exists, the linear programming (LP2) with the same constraints with LP1 is established, which can be easily solved to yield the value of the Cb. In addition, two different relationships between the fresh water flowrate required and inlet concentration to regeneration are found out, which indicate two possibilities with Cb: at pinch or above pinch, therefore a new conclusion is drawn, which differs from 'Regeneration of water at pinch minimizes fresh water flowrate' derived by some papers and points out that in some cases, regeneration at pinch point can't always minimizes fresh water flowrate. One example is solved to demonstrate the advantage and validity of the new method.