Abstract In the modelling process, inversion techniques are generally used to estimate unknown parameters. However, we need to determine the model structure and other conditions before solving inverse problems, and there are many alternatives, such as the inversion method, the number of parameters, and the weightings in objective functions. The aim of this study is to discuss the process so that the alternatives can be assessed by evaluating their reliability. Multi-well transient flow tests, such as hydropulse testing, had been proposed for the treatment of heterogeneous media in subsurface flow modelling using data obtained through laboratory air injection tests for a dried heterogeneous sandstone plate. The numerical inversion method includes a quasi-Newton method and an adjoint-state method for pressure change rate matching that can deal with various types of objective functions. Porosity at the injection and observation points can be treated as different unknown parameters. Data quality and quantity are also important factors for the inverse problem. Several injection patterns were carried out to assess the observation pattern. The bootstrap re-sampling method was used to evaluate the reliability of the inversion results. We prefer this method because it is not necessary to assume a probability density function and because the method can estimate prediction errors. Using the estimated reliability indices, we can assess the best model, i.e. the adequate combination of injection pattern and model structure and objective function, etc.

Keywords air injection test; heterogeneous; inverse modelling; reliability index; sandstone