Mathematical Modeling of Cake Filtration Using Filter Number and Experimental Verification

Abstract

최근에 탈수공법은 고체-액체 분리가 중요한 역할을 하는 입자분리, 하수 슬러지 처리, 제약 산업, 양조장과 음식 폐기물 관리 등 여러 분야에서 많은 관심을 이끌었다. 슬러지 탈수 공법 중에도 케이크 여과는 광범하게 사용되고 있다. 케이크 여과에는 양 압력이 적용되어 슬러지 내의 수분이 제거된다. 수분 제거는 슬러지와 필터에 의해 저항으로 한다. 현재까지 케이크 여과의 거동모형은 케이크 저항이나 필터 차단으로 개발되었다. 본 논문은 1-차원 케이크 여과 과정의 여과 거동과 단계를 평가하는 해석적 모형을 제시하였다. 제시된 모형은 에너지법칙을 이용하여 여과 매체의 저항 영향을 고려하고 새로운 매개 변수인 필터계수 (FN)가 적용된다. 하수 슬러지에 대해 여과 실험으로 제시된 모형을 검토했다. 실험 과 모형을 비교한 결과, 압력 300 kPa에는 평균상대오차가 21%이고 500 kPa에는 평균상대오차가 31%이다. 결론으로 본 논문에서 제시된 모형은 여과시간과 케이크 여과 과정의 단계를 예측할 수 있다. 압력 및 시간은 실제 운영에는 에너지 및 비용과 밀접한 관계가 있다. 슬러지의 종류와 상태에 따라 어떤 경우에는 압력이 제한 조건으로 되고 어떤 경우에는 시간이 제한 조건으로 된다. 요구되는 탈수 정도와 제한 조건을 고려해서 탈수 운영 그래프를 플롯팅할 수 있다. 그래프 플롯팅은 예측 모형에 의해 이뤄졌고 이 그래프를 통하여 가장 경제적 방법을 선택할 수 있다.

Recently, dewatering has received great attention in many fields, including

particle separation, wastewater sludge treatment, pharmaceutical industries, wineries and food waste management in which solid and liquid separation is important. Among the several types of sludge dewatering techniques, the most widely used is cake filtration. In cake filtration a positive pressure is applied to force liquid through the cake and filter medium. The cake filtration can be divided into two phases

filtration phase and expression phase. In filtration phase liquid pass through the cake and filter medium while a free suspension is still left on top of the cake. However the expression phase focuses in the removal of the water by squeezing the cake. In expression phase the sludge and filter resistances are stabilized. For decades, the performance of cake filtration has been modeled based on the cake resistance and/or filter blockage. However further study and development of less complicated model is required to appropriately assess the relationship between the cake and the filter resistance, especially filter clogging, as well as the conditions of both the filtration and expression phases. In this study, a new model for evaluating the filtration and expression phases of a one-dimensional cake filtration process is proposed. The effect of the filtering medium resistance was considered applying energy law and using a new concept of filter number (FN). The effects of the governing parameters on the model predications for both the filtration and expression phases were also investigated. Based on sensitivity analysis of the model on the governing parameters, during the filtration phase the effect of the cake hydraulic conductivity was found to be negligible whereas the compacted sludge layer and filter medium plays the primary role. On the other hand, the hydraulic conductivity of the filtration cake is the dominant factor during the expression phase. Moreover the findings of the model sensitivity analysis are also used to make some cake filtration suggestions. Four filtration experiments with two types of filter at two pressures (300 kPa and 500 kPa) were performed for wastewater sludge from Gawchon wastewater plant and repeated (totally 8 tests). The Experimental data obtained in this study were used to verify the proposed model. The experimental data and model prediction were compared and regression analysis was made to find the agreement and disagreements part of the model with data. Based on observations form laboratory tests, we found that the new model provides a mean relative error (MRE) of 21%, 31%, 28% and 29% between predicted and observed values of the filter types I and II at 300 and 500 kPa respectively. The model can be used to predict the time for achieving the certain percent of sludge dewatering which can be very useful in many industrial applications. Pressure and time in the real operational field means energy and money. In some cases, pressure is the limiting factor and sometimes time is the limiting factor, depending on the type of sludge and condition. Based on the demand to achieve the certain degree of dewatering and also by considering the limiting factors of the company, it is possible to plot dewatering operational graph based on model prediction into the most economical way that the company can have.