A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments

In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by $\pm 10 \%$ of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected

FLUID DISTRIBUTION IN TRANSITION ZONES (Using a New Initial-Residual Saturation Correlation)

ABSTRACT The fluid distribution as a function of height in transition zones is often very complex. This may be due to movement of water-oil contact, tilting of the reservoir at some point in time, leak of fluid out of the reservoir zone or complex inflow during secondary migration. The resultant fluid distribution seen in saturation logs may be difficult to model. In this paper we address the changes in fluid distribution versus height, inferred by changes of fluid distribution due to the movement of water-oil contact only. The experimental procedures for determining capillary pressure are based on fluid saturation monitoring by gamma absorption from centrifuge experiments. An analytical capillary pressure-saturation model was fit to the bounding imbibition capillary pressuresaturation data. The drainage-imbibition hysteresis curves were then constructed assuming that these curves have similar shape to that of the bounding imbibition curve. The imbibition hysteresis model proposed may be used to calculate fluid saturation in the reservoir due to the movement of water-oil contact. We also proposed necessary auxiliary equations to solve the new linear and four-parameter (sigmoidal type) initial-residual fluid saturation equations. Thus once the shape of the bounding-imbibition capillary pressuresaturation curve and maximum non-wetting fluid saturation are known one can easily construct any imbibition hysteresis curves that may be required

FLUID DISTRIBUTION IN TRANSITION ZONES (Using a New Initial-Residual Saturation Correlation)

ABSTRACT The fluid distribution as a function of height in transition zones is often very complex. This may be due to movement of water-oil contact, tilting of the reservoir at some point in time, leak of fluid out of the reservoir zone or complex inflow during secondary migration. The resultant fluid distribution seen in saturation logs may be difficult to model. In this paper we address the changes in fluid distribution versus height, inferred by changes of fluid distribution due to the movement of water-oil contact only. The experimental procedures for determining capillary pressure are based on fluid saturation monitoring by gamma absorption from centrifuge experiments. An analytical capillary pressure-saturation model was fit to the bounding imbibition capillary pressuresaturation data. The drainage-imbibition hysteresis curves were then constructed assuming that these curves have similar shape to that of the bounding imbibition curve. The imbibition hysteresis model proposed may be used to calculate fluid saturation in the reservoir due to the movement of water-oil contact. We also proposed necessary auxiliary equations to solve the new linear and four-parameter (sigmoidal type) initial-residual fluid saturation equations. Thus once the shape of the bounding-imbibition capillary pressuresaturation curve and maximum non-wetting fluid saturation are known one can easily construct any imbibition hysteresis curves that may be required

FLUID DISTRIBUTION IN TRANSITION ZONES (Using a New Initial-Residual Saturation Correlation)

ABSTRACT The fluid distribution as a function of height in transition zones is often very complex. This may be due to movement of water-oil contact, tilting of the reservoir at some point in time, leak of fluid out of the reservoir zone or complex inflow during secondary migration. The resultant fluid distribution seen in saturation logs may be difficult to model. In this paper we address the changes in fluid distribution versus height, inferred by changes of fluid distribution due to the movement of water-oil contact only. The experimental procedures for determining capillary pressure are based on fluid saturation monitoring by gamma absorption from centrifuge experiments. An analytical capillary pressure-saturation model was fit to the bounding imbibition capillary pressuresaturation data. The drainage-imbibition hysteresis curves were then constructed assuming that these curves have similar shape to that of the bounding imbibition curve. The imbibition hysteresis model proposed may be used to calculate fluid saturation in the reservoir due to the movement of water-oil contact. We also proposed necessary auxiliary equations to solve the new linear and four-parameter (sigmoidal type) initial-residual fluid saturation equations. Thus once the shape of the bounding-imbibition capillary pressuresaturation curve and maximum non-wetting fluid saturation are known one can easily construct any imbibition hysteresis curves that may be required