MATLAB scripts for solving partial differential equations of tracer transport and history matching of tracers' breakthrough curves

SolvePDE.m solves the mutti-tracer transport in subsurface formations, involving convection, diffusion and first-order reaction. Multiple operation steps are considered including two steps of injection, well shut-in, and production. After solving equations for each stage, the solution is used as the initial condition of the next stage. We use this function to generate synthetic breakthrough curves for testing effects of formation porosity/thickness and tracer's partition coefficients on interpreting single-well partitioning tracer test data.

History_matching.m performs iterative, constraining multi-variate optimization to curve fit the synthetic breakthrough curves, yielding estimation of residual saturation, longitudinal dispersion coefficient and hydrolysis reaction constant.

target_funciton.m defines the difference between simulated and synthetic breakthrough curves, and the objective is to minimize the value of this function. 

The optimization algorithm is based on the function minConf that is developed by Mark Schmidt and the manual for the code can be found at https://www.cs.ubc.ca/~schmidtm/Software/minConf.html.