|dc.description.abstract||An analytical model for bacterial accumulation in a discrete fractllre has been developed.
The transport and accumlllation processes incorporate into the model include advection,
dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment,
detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical
solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the
code BIOFRAC vvhich is written in Fortran 99.
The model is derived for two phases, Phase I, where adsorption-desorption are dominant,
and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to
fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing
to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous
version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the
inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt
parameter vvhile all others were fixed and observing the impact on the shape of the clirve
describing bacterial concentration verSllS time.
Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich
diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be
covered. Increasing adsorption rate, was observed to increase the dllration of Phase I.
Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the
inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines,
sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of
Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration
than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of
detachment speeds up the transport. The grovvth and decay rates have no significant effect on
transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed.
Irreversible adsorption can stop accllillulation completely if the vallIes are high.||