1) What is the regularization algorithm?

We use several ways of regularization, some are known - like the weight on curvity, some are our know-hows basing on physics - we restrict the area of search so our unit rate responses would have the shape typical for pressure diffusion equation solution.

2) How do you deal with multiphases?

In a multiphase case we use total downhole rate. There's a natural limitation on the use of MRT - we need to assume that during the tested period the saturation at any point in reservoir was constant. Again - not the same saturation everywhere, but constant saturation in time at any point.

3) ​considering that deconvolution is an analytical approach then the deconvolution for the entire field with 20 wells should not cost a lot of computing, ​right?

As the number of unit rate responses grows quadratically with the number of wells - 20 wells could take a lot of time on a cluster, depending on how long is the history and how frequent is the data sampling. It also depends on the data quality. The more time we spend on pre-processing the data (removing outliers, synchronizing flowrates and pressures, filtering and waveleting etc) - the less time it will take to perform the deconvolution.