  Simulation of fluid flow in porous media has many applications, from the
micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater,
hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of flow
in porous media requires significant computational resources to solve within
reasonable timeframes. An integrated method combining predictions of fluid flow
(fast, limited accuracy) with direct flow simulation (slow, high accuracy) is
outlined. In the tortuous flow paths of porous media, Deep Learning techniques
based on Convolutional Neural Networks (CNNs) are shown to give an accurate
estimate of the steady state velocity fields (in all axes), and by extension,
the macro-scale permeability. This estimate can be used as-is, or as initial
conditions in direct simulation to reach a fully accurate result in a fraction
of the compute time. A Gated U-Net Convolutional Neural Network is trained on a
datasets of 2D and 3D porous media generated by correlated fields, with their
steady state velocity fields calculated from direct LBM simulation. Sensitivity
analysis indicates that network accuracy is dependent on (1) the tortuosity of
the domain, (2) the size of convolution filters, (3) the use of distance maps
as input, (4) the use of mass conservation loss functions. Permeability
estimation from these predicted fields reaches over 90\% accuracy for 80\% of
cases. It is further shown that these velocity fields are error prone when used
for solute transport simulation. Using the predicted velocity fields as initial
conditions is shown to accelerate direct flow simulation to physically true
steady state conditions an order of magnitude less compute time. Using Deep
Learning predictions (or potentially any other approximation method) to
accelerate flow simulation to steady state in complex pore structures shows
promise as a technique push the boundaries fluid flow modelling.
