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A Fuzzy Logic Model of Deionised and Water for Injection Systems for Sizing and Capacity Assessment Under Uncertainty

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Abstract

The operating performance of deionized and water for injection (DI/WFI) distribution systems can be difficult to analyse due to the highly variable demand that is drawn from these systems, a situation compounded by schedule uncertainties. This paper presents a fuzzy logic (FL) model of a typical DI/WFI system simulating schedule uncertainties in the opening and closing events of the offtake valves based on operator behaviour, e.g. tiredness of the operators. The model utilises discrete-event simulation to calculate the demand profile of the distribution system and a continuous simulation to compute the variation of the level in the storage tank. It is shown that the FL model may be useful in the design of new DI/WFI systems if little historical data are available.

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Abbreviations

acti,k :

Opening/closing event of valve i, k

\( {\text act}_{{{\text{i}},{\text{k}}}}^{\text{Wait}} \) :

Opening/closing event of valve i, k waiting to be served

fDiv :

Diversity factor

i:

Integer parameter

k:

Integer parameter

n:

Integer parameter

nop :

Number of operators

nop, min :

Minimum number of operators

Pri, k :

Priority rules for each acti, k

t:

Time (h:m:s)

tapi :

Valve of offtake point (tap) i along the distribution system

\( {\text{t}}_{{2,{\text{ j}}}}^{\text{B}} \) :

Beginning of core break (h:m:s)

\( {\text{t}}_{{3, {\text{j}}}}^{\text{B}} \) :

End of core break (h:m:s)

\( {\text{t}}_{{{\text{i}}, {\text{k}}}}^{\text{close}} \) :

Scheduled closing time for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}},new}}^{\text{close}} \) :

New closing time for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{\text{D}} \) :

Time delay for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{{{\text{D}},De}} \) :

Defuzzified time delay for each acti, k (%)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{\text{Delay,1}} \) :

Time delay caused by operator for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{{Delay,2}} \) :

Time delay caused by operator for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{\text{Delay, No Op.}} \) :

Delay caused by no operator being available for acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}}}}^{\text{min,{\text{ D}}}} \) :

Minimum duration of each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{ k}}}}^{{open}} \) :

Scheduled opening time for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}},\text new}}^{\text{open}} \) :

New closing time for each acti, k (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}},\text new}}^{\text{open,R1}} \) :

New opening time due to influence of rule 1 (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}},\text new}}^{\text{open,R4}} \) :

New opening time due to influence of rule 4 (h:m:s)

\( {\text{t}}_{{{\text{i}},{\text{k}},\text new}}^{\text{open,R5}} \) :

New opening time due to influence of rule 5 (h:m:s)

tsim :

Simulated time (s)

tmax :

Maximum allowable time (see rule 1) (h:m:s)

tRule1 :

Sum defined as: tSim + tmax (h:m:s)

t0 :

Time at start of simulated time (h:m:s)

\( \Delta {\text{t}}_{{{\text{i}},{\text{ k}}}}^{\text{offtake}} \) :

Opening/closing interval for each acti, k (h:m:s)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{Design}}} \) :

Design flow rate (m3/h)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{Max}}} \) :

Maximum flow rate (m3/h)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI,Blow}}} \) :

WFI generation blowdown (%)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI,Gen}}} \) :

Volumetric flow rate WFI from WFI generation plant (m3/h)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI,Gen,max}}} \) :

Maximum volumetric flow rate from WFI generating plant (m3/h)

VWFI, L :

WFI volume in the WFI storage tank (m3)

VWFI, L, C :

Temperature compensated water volume in WFI storage tank (m3)

VWFI, L, max :

Maximum allowable water volume in WFI storage tank (m3)

VWFI, L, min :

Minimum allowable water volume in the WFI storage tank (m3)

VWFI, L, St :

Start volume in WFI storage tank at t0 (m3)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI, off}}} \) :

Volumetric offtake from the WFI system (m3/h)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI, off,{\text{ i}}}}} \) :

Volumetric offtake for each acti (m3/h)

\( {\mathop{\text{V}}\limits^{ \bullet }_{\text{WFI,Pump}}} \) :

WFI Distribution pump delivery volume (m3/h)

XD :

Defuzzified value

\( {{\mu }}\mathop{{_{\text{B}}}}\limits_{\sim } ({\text{t}}) \) :

Membership function “operator break pattern” (h:m:s)

\( {{\mu }}_{{\mathop{\text{D}}\limits_{\sim } }}^{{{\text{i}},{\text{k}}}}({\text{t}}) \) :

Membership function “duration of tasks” for each acti, k (h:m:s)

\( {{\mu }}\mathop{{_{\text{S}}}}\limits_{\sim } ({\text{t}}) \) :

Membership function operator “shift pattern” (h:m:s)

\( {{\mu }}\mathop{{_{\text{T}}}}\limits_{\sim } ({\text{t}}) \) :

Membership function “operator tiredness”

\( {{\mu }}_{{\mathop{{Out}}\limits_{\sim } }}^{{0\% }}({\text{r}}), \ldots, {{\mu }}_{{\mathop{{Out}}\limits_{\sim } }}^{{100\% }}({\text{r}}) \) :

Membership function “output”

ρ20 :

Water density at 20°C: ρ20 = 998.21 kg/m3 (kg/m3)

ρ80 :

Water density at 80°C: ρ80 = 971.79 kg/m3 (kg/m3)

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Authors and Affiliations

  1. Department of Process and Chemical Engineering, University College Cork, Cork, Ireland

    Frank Riedewald, Edmond Byrne & Kevin Cronin

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  1. Frank Riedewald
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Correspondence to Frank Riedewald.

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Riedewald, F., Byrne, E. & Cronin, K. A Fuzzy Logic Model of Deionised and Water for Injection Systems for Sizing and Capacity Assessment Under Uncertainty. J Pharm Innov 6, 125–141 (2011). https://doi.org/10.1007/s12247-011-9108-4

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