Effective Rheology of Immiscible Two-Phase Flow in Porous Media

We demonstrate through numerical simulations and a mean field calculation that immiscible two-phase flow in a porous medium behaves effectively as a Bingham viscoplastic fluid. This leads to a generalized Darcy equation where the volumetric flow rate depends quadratically on an excess pressure difference in the range of flow rates where the capillary forces compete with the viscous forces. At higher rates, the flow is Newtonian

Dynamic wettability alteration in immiscible two-phase flow in porous media: Effect on transport properties and critical slowing down

The change in contact angles due to the injection of low salinity water or any other wettability altering agent in an oil-rich porous medium is modeled by a network model of disordered pores transporting two immiscible fluids. We introduce a dynamic wettability altering mechanism, where the time dependent wetting property of each pore is determined by the cumulative flow of water through it. Simulations are performed to reach steady-state for different possible alterations in the wetting angle ($\theta$). We find that deviation from oil-wet conditions re-mobilizes the stuck clusters and increases the oil fractional flow. However, the rate of increase in the fractional flow depends strongly on $\theta$ and as $\theta\to 90^\circ$, a critical angle, the system shows critical slowing down which is characterized by two dynamic critical exponents.Comment: 8 pages, 9 figure

Isolation of a cdc28 mutation that abrogates the dependence of S phase on completion of M phase of the budding yeast cell cycle

We have isolated a mutation in the budding yeast Saccharomyces cerevisisae CDC28 gene that allows cdc13 cells, carrying damaged DNA, to continue with the cell division cycle. While cdc13 mutant cells are arrested as largebudded cells at the nonpermissive temperature 37°C, the cdc13 cdc28 double mutant culture showed cells with one or more buds, most of which showed apical growth. The additional buds emerged without the intervening steps of nuclear division and cell separation. We suggest that the cdc28 mutation abrogates a checkpoint function and allows cells with damaged or incompletely replicated DNA an entry to another round of cell cycle and bypasses the mitotic phase of the cell cycle

Phase transitions and correlations in fracture processes where disorder and stress compete

We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.Comment: 8 pages, 5 figure

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

It is becoming increasingly clear that there is a regime in immiscible two-phase flow in porous media where the flow rate depends of the pressure drop as a power law with exponent different than one. This occurs when the capillary forces and viscous forces both influence the flow. At higher flow rates, where the viscous forces dominate, the flow rate depends linearly on the pressure drop. The question we pose here is what happens to the linear regime when the system size is increased. Based on analytical calculations using the capillary fiber bundle model and on numerical simulations using a dynamical network model, we find that the non-linear regime moves towards smaller and smaller pressure gradients as the system size grows.Comment: 10 pages, 6 figure

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.Comment: 12 pages, 5 figure