Sequential Simulation under local non-linear constraints: Application to history matching

Sequential simulation has emerged as a robust and fast method for generating stochastic realizations. The recent development of a sequential simulation method by drawing structures from training images allows generating a wide variety of geological styles in a controlled fashion. Various methods for conditioning realizations to secondary information from geophysical or remote sensing techniques have been developed and applied. However, the current state-of-the-art in sequential simulation lacks the ability to include data that has a strongly non-linear and multiple-point relationship with the unknown. A classical example of such data is a subsurface flow response measured in a well, over time, and may consist of pressure, fractional flow or tracer data. Incorporating such data is of crucial importance in building models with fields such as petroleum engineering and hydrology.