Uncertainty in well test analysis results from errors in pressure and rate measurements, from uncertainties in basic well and reservoir parameters; from the quality of the match with the interpretation model; and from the non-uniqueness of the interpretation model.
These various uncertainties, except the non-uniqueness of the interpretation model, were examined in SPE 113888. It was concluded that the permeability-product kh is generally known within 15%; the permeability k, within 20% (because of the uncertainty on the thickness h); and the skin effect S, within 8% for high S values and within ±0.5 for low S values. Distances (half-fracture lengths, horizontal well lengths, and distances to reservoir boundaries) are usually known within 25%.
The issue of non-uniqueness of the interpretation model is more complex: not only may there be a multitude of possible models for any one derivative response (the usual inverse problem), but there may be also a multitude of derivative responses, due to the uncertainty inherent in the observed data.
This paper presents a methodology for assessing the derivative response uncertainty using deconvolution. It is shown that the uncertainty depends mainly on the error bounds for initial pressure and flow rates, which yield a range of possible shapes for the deconvolved pressure derivative and therefore different possible interpretation models. In some cases, the non-uniqueness of deconvolution can be reduced using knowledge of the expected model response, for instance from geology or seismic. In the absence of differentiating information, however, alternative interpretation models have to be considered, which may lead to completely different development options.
The methodology is illustrated with three field examples.