Introduction

1. Results Introduction It is well known that heterogeneities in a porous medium have an impact on the large scale transport. For single phase flow this effect can often be upscaled using the concept of effective dispersion. Here we use a similar concept for two phase displacement flow . Beyond spatial heterogeneities we also study the influence of a temporally fluctuating field as temporal fluctuations are known to enhance this effective dispersion. Mathematical Model Effective Dispersion Coefficient – Ensemble Average Enhanced Mixing in Heterogeneous Buckley Leverett Flow due to Temporal FluctuationsD Bolster, M Dentz & J CarreraContact Info: diogobolster@gmail.com Three Contributions Fig 2:Idealised Displacement Problem (Buckley Leverett) Heterogeneous Medium “Homogeneous” Equivalent • Each phase has constant density • Constant Porosity • Neglect Buoyancy Effects (Horizontal Plane) Assumptions: Temporally Enhanced ‘Mixing’ Spatial Heterogeneity ‘Mixing’ Temporal Mixing Term: Real /Uncertainty? Fractional Flow Model Temporal Term = Measure of Uncertainty of Location of Front Fig 1:Representing Transport by an Effective Homogeneous Medium Motivation Example 1 – CO2 Sequestration In the case of carbon sequestration CO2 is injected into a water /brine filled aquifer. The effective dispersion is particularly useful as it gives a measure of the ‘contact zone’, which plays a very important role regarding reactions between the fluids, dissolution and trapping. It may often desirable to enhance this ‘contact zone’ – or, enhance the effective dispersion coefficient. Example 2– Enhanced Oil Recovery As with sequestration the contact zone plays an important role. However, here it is typically desirable to minimise spreading. The study here presents physical insight into how this might be done. Fig 3:Uncertainty due to Temporal Heterogeneity & Temporal Fluctuations Total Flow Rate Fig 4:Fluid Number for vaious viscosity ratios Mean Spatial Temporal Spatio Temporal Ratio Variances Fluid Number (Depends only on ratio of viscsoties of fluids) Kuo Number (Ratio of Timescales) Effective Dispersion Captures fluctuations Upscaling • Conclusions • As in single phase contaminant transport spatial heterogeneity increases ‘mixing’ (spreading) • Similarly temporal fluctuations can enhance ‘mixing’ • Temporal fluctuations add an additional level of uncertainty, which can appear like false ‘mixing’ Perturbation Approach