Membranous filtration prediction method, prediction apparatus, and membranous filtration prediction program

In a membranous filtration method wherein a liquid to-be-filtrated is filtrated by a separation membrane with a driving force being a pressure difference (hereinbelow, termed “transmembrane pressure”) between a liquid to-be-filtrated side and a penetration liquid side of the separation membrane;

• a membranous filtration prediction method in which, in case of continuing the membranous filtration while controlling the transmembrane pressure to a set value, a variation of a membranous filtration resistance with time and/or a variation of a membranous filtration flowrate (flux) with time are/is predicted, characterized in that at least the set value of the transmembrane pressure, an initial value of the membranous filtration resistance, and a constituent component quantity value of the liquid to-be-filtrated are used as numerical values for a membranous filtration prediction computation, and that at least the following computation step 1a, computation step 1b and/or computation step 1c, and computation step 2 and/or computation step 4 are executed, thereby to find a membranous filtration resistance value and/or a membranous filtration flowrate (flux) value at any desired time:
• (computation step 1a) at which the constituent component quantity value of the liquid to-be-filtrated attaching on a surface of the separation membrane at a time t+Δt (here, Δt denotes any plus number) is calculated on the basis of the membranous filtration flowrate (flux) value or a transmembrane pressure value and the constituent component quantity value of the liquid to-be-filtrated at a time t (here, t denotes any number of at least zero).
• (computation step 1b) at which the constituent component quantity value of the liquid to-be-filtrated existing in pores of the separation membrane at the time t+Δt is calculated on the basis of the transmembrane pressure value and/or the membranous filtration flowrate (flux) value at the time t.
• (computation step 1c) at which a consolidation degree of a constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt is calculated on the basis of the transmembrane pressure value at the time t.
• (computation step 2) at which the membranous filtration resistance value at the time t+Δt is calculated on the basis of the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface as has been found at the computation step 1a, the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores as has been found at the computation step 1b, and/or the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface as has been found at the computation step 1c.
• (computation step 4) at which the membranous filtration flowrate (flux) value at the time t+Δt is calculated on the basis of the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface as has been found at the computation step 1a, the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores as has been found at the computation step 1b, and/or the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface as has been found at the computation step 1c, or on the basis of the membranous filtration resistance value found at the computation step 2.
• and further, in that the computation steps are repeatedly executed while updating the time, thereby to obtain the variation of the membranous filtration resistance with the time, and/or the variation of the membranous filtration flowrate (flux) with the time.

In a computer program product for predicting a temporal variation of a membranous filtration resistance value and/or a temporal variation of a transmembrane pressure value as vary with time, in a case where a filtration of a liquid to-be-filtrated with a separation membrane is continued while controlling a membranous filtration flowrate (flux) to a set value, a membranous filtration prediction program product comprising a computer readable medium storing software instructions for enabling a computer to perform functions of the following data input means, data record means, surface-attaching component-quantity calculation means, surface-attaching component-quantity calculation-value record means, pore inner-component-quantity calculation means, and/or pore inner-component-quantity calculation-value record means, and/or consolidation-degree calculation means, and/or consolidation-degree calculation-value record means, membranous-filtration-resistance calculation means, transmembrane-pressure calculation means, membranous-filtration prediction-value record means, time-series-value record means, and output means:

• (data input means) data input means for inputting time series values of the membranous-filtration-flowrate (flux), time series values of a constituent component quantity of the liquid to-be-filtrated, an initial value of the constituent component quantity of the liquid to-be-filtrated attaching on a surface of the separation membrane, an initial value of the constituent component quantity of the liquid to-be-filtrated existing in pores of the separation membrane, and an initial value of the membranous filtration resistance;
• (data record means) data record means for recording therein the time series values of the membranous filtration flowrate (flux), the time series values of the constituent component quantity of the liquid to-be-filtrated, the initial value of the constituent component quantity of the liquid to-be-filtrated attaching on the separation membrane surface, the initial value of the constituent component quantity of the liquid to-be-filtrated existing in the separation membrane pores, and the initial value of the membranous filtration resistance as have been inputted by the data input means;
• (surface-attaching component-quantity calculation means) surface-attaching component-quantity calculation means for reading out the membranous-filtration-flowrate (flux) value, or the transmembrane pressure value and the constituent component quantity value of the liquid to-be-filtrated at any desired time t (where t denotes any number of at least zero), from the data record means, for reading out the initial value of the constituent component quantity of the liquid to-be-filtrated attaching on the separation membrane surface, in case of the time t=0, and further, the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t as has been recorded in the data record means by surface-attaching component-quantity calculation value record means to-be-stated-below, in case of the time t=non-zero, and for calculating the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at a time t+Δt (where Δt denotes any plus number), in conformity with a surface-attaching component-quantity calculation formula recorded beforehand.
• (surface-attaching component-quantity calculation value record means) surface-attaching component-quantity calculation value record means for recording the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the surface-attaching component-quantity calculation means.
• (pore inner-component-quantity calculation means) pore inner-component-quantity calculation means for reading out the transmembrane pressure value at any desired time t from the data record means, for reading out the initial value of the constituent component quantity of the liquid to-be-filtrated existing in the separation membrane pores, in the case of the time t=0, and further, the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t as has been recorded in the data record means by pore inner-component-quantity calculation value record means to-be-stated-below, in the case of the time t=non-zero, and for calculating the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt, in conformity with a pore inner-component-quantity calculation formula recorded beforehand.
• (pore inner-component-quantity calculation value record means) pore inner-component-quantity calculation value record means for recording the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt as has been calculated by the pore inner-component-quantity calculation means.
• (consolidation-degree calculation means) consolidation-degree calculation means for reading out the transmembrane pressure value at any desired time t, from the data record means, for reading out the initial value of the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface, in the case of the time t=0, and further, the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t as has been recorded in the data record means by consolidation-degree calculation value record means to-be-stated-below, in the case of the time t=non-zero, and for calculating the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt, in conformity with a consolidation-degree calculation formula recorded beforehand.
• (consolidation-degree calculation value record means) consolidation-degree calculation value record means for recording the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the consolidation-degree calculation means.
• (membranous-filtration-resistance calculation means) membranous-filtration-resistance calculation means for reading out the membranous-filtration-resistance initial value from the data record means, and for calculating the prediction value of the membranous filtration resistance at the time t+Δt, on the basis of the membranous-filtration-resistance initial value read out, the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the surface-attaching component-quantity calculation means, and the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt as has been calculated by the pore inner-component-quantity calculation means, and in conformity with a membranous-filtration-resistance prediction value calculation formula recorded beforehand. (transmembrane-pressure calculation means) transmembrane-pressure calculation means for reading out the membranous filtration flowrate (flux) value at the time t+Δt, from the data record means, and for calculating the prediction value of the transmembrane pressure at the time t+Δt, on the basis of the membranous filtration flowrate (flux) value at the time t+Δt as has been read out, and the membranous-filtration-resistance prediction value at the time t+Δt as has been calculated by the membranous-filtration-resistance calculation means, and in conformity with a transmembrane-pressure prediction value calculation formula recorded beforehand.
• (membranous-filtration prediction-value record means) membranous-filtration prediction-value record means for recording the prediction value of the membranous filtration resistance at the time t+Δt as has been calculated by the membranous-filtration-resistance calculation means, and/or the prediction value of the transmembrane pressure at the time t+Δt as has been calculated by the transmembrane-pressure calculation means.
• (time-series-value record means) time-series-value record means for recording as time series values the prediction value of the membranous filtration resistance and/or the prediction value of the transmembrane pressure at the time t as have/has been recorded by the membranous-filtration prediction-value record means, and.
• (output means) output means for outputting the time series value of the membranous-filtration-resistance prediction value and/or the time series value of the transmembrane-pressure prediction value as have/has been recorded by the time-series-value record means.

In a computer program product for predicting a temporal variation of a membranous filtration resistance value and/or a temporal variation of a membranous filtration flowrate (flux) value as vary with time, in a case where a filtration of a liquid to-be-filtrated with a separation membrane is continued while controlling a transmembrane pressure to a set value, a membranous filtration prediction program product comprising a computer readable medium storing software instructions for enabling a computer to perform functions of the following data input means, data record means, surface-attaching component-quantity calculation means, surface-attaching component-quantity calculation-value record means, pore inner-component-quantity calculation means, and/or pore inner-component-quantity calculation-value record means, and/or consolidation-degree calculation means, and/or consolidation-degree calculation-value record means, membranous-filtration-resistance calculation means, membranous-filtration-flowrate (flux) calculation means, membranous-filtration prediction-value record means, time-series-value record means, and output means:

• (data input means) data input means for inputting time series values of the transmembrane pressure, time series values of a constituent component quantity of the liquid to-be-filtrated, an initial value of the constituent component quantity of the liquid to-be-filtrated attaching on a surface of the separation membrane, an initial value of the constituent component quantity of the liquid to-be-filtrated existing in pores of the separation membrane, and an initial value of the membranous filtration resistance;
• (data record means) data record means for recording therein the time series values of the transmembrane pressure, the time series values of the constituent component quantity of the liquid to-be-filtrated, the initial value of the constituent component quantity of the liquid to-be-filtrated attaching on the separation membrane surface, the initial value of the constituent component quantity of the liquid to-be-filtrated existing in the separation membrane pores, and the initial value of the membranous filtration resistance as have been inputted by the data input means;
• (surface-attaching component-quantity calculation means) surface-attaching component-quantity calculation means for reading out the membranous-filtration-flowrate (flux) value, or the transmembrane pressure value and the constituent component quantity value of the liquid to-be-filtrated at any desired time t (where t denotes any number of at least zero), from the data record means, for reading out the initial value of the constituent component quantity of the liquid to-be-filtrated attaching on the separation membrane surface, in case of the time t=0, and further, the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t as has been recorded in the data record means by surface-attaching component-quantity calculation value record means to-be-stated-below, in case of the time t=non-zero, and for calculating the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at a time t+Δt, in conformity with a surface-attaching component-quantity calculation formula recorded beforehand.
• (surface-attaching component-quantity calculation value record means) surface-attaching component-quantity calculation value record means for recording the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the surface-attaching component-quantity calculation means.
• (pore inner-component-quantity calculation means) pore inner-component-quantity calculation means for reading out the transmembrane pressure value at any desired time t from the data record means, for reading out the initial value of the constituent component quantity of the liquid to-be-filtrated existing in the separation membrane pores, in the case of the time t=0, and further, the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t as has been recorded in the data record means by pore inner-component-quantity calculation value record means to-be-stated-below, in the case of the time t=non-zero, and for calculating the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt, in conformity with a pore inner-component-quantity calculation formula recorded beforehand.
• (pore inner-component-quantity calculation value record means) pore inner-component-quantity calculation value record means for recording the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt as has been calculated by the pore inner-component-quantity calculation means.
• (consolidation-degree calculation means) consolidation-degree calculation means for reading out the transmembrane pressure value at any desired time t, from the data record means, for reading out the initial value of the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface, in the case of the time t=0, and further, the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t as has been recorded in the data record means by consolidation-degree calculation value record means to-be-stated-below, in the case of the time t=non-zero, and for calculating the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt, in conformity with a consolidation-degree calculation formula recorded beforehand.
• (consolidation-degree calculation value record means) consolidation-degree calculation value record means for recording the consolidation degree of the constituent component of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the consolidation-degree calculation means.
• (membranous-filtration-resistance calculation means) membranous-filtration-resistance calculation means for reading out the membranous-filtration-resistance initial value from the data record means, and for calculating the prediction value of the membranous filtration resistance at the time t+Δt, on the basis of the membranous-filtration-resistance initial value read out, the constituent component quantity value of the liquid to-be-filtrated attaching on the separation membrane surface at the time t+Δt as has been calculated by the surface-attaching component-quantity calculation means, and the constituent component quantity value of the liquid to-be-filtrated existing in the separation membrane pores at the time t+Δt as has been calculated by the pore inner-component-quantity calculation means, and in conformity with a membranous-filtration-resistance prediction value calculation formula recorded beforehand.
• (membranous-filtration-flowrate (flux) calculation means) membranous-filtration-flowrate (flux) calculation means for reading out the transmembrane pressure value at the time t+Δt, from the data record means, and for calculating the prediction value of the membranous filtration flowrate (flux) at the time t+Δt, on the basis of the transmembrane pressure value at the time t+Δt as has been read out, and the membranous-filtration-resistance prediction value at the time t+Δt as has been calculated by the membranous-filtration-resistance calculation means, and in conformity with a membranous-filtration-flowrate (flux) prediction value calculation formula recorded beforehand.
• (membranous-filtration prediction-value record means) membranous-filtration prediction-value record means for recording the prediction value of the membranous filtration resistance at the time t+Δt as has been calculated by the membranous-filtration-resistance calculation means, and/or the prediction value of the membranous filtration flowrate (flux) at the time t+Δt as has been calculated by the membranous-filtration-flowrate (flux) calculation means.
• (time-series-value record means) time-series-value record means for recording as time series values the prediction value of the membranous filtration resistance and/or the prediction value of the membranous filtration flowrate (flux) at the time t as have/has been recorded by the membranous-filtration prediction-value record means, and.
• (output means) output means for outputting the time series value of the membranous-filtration-resistance prediction value and/or the time series value of the membranous-filtration-flowrate (flux) prediction value as have/has been recorded by the time-series-value record means.