Modelling Subsurface Uncertainties with Experimental Design: Some Arguments of Non-Conformists

Abstract

As a consequence of limited capability for the acquisition, analysis and interpretation of subsurface data, uncertainties pervade the Exploration and Production (E&P) business. To minimise investment risks, robust development plans, premised on adequate understanding of uncertainties, are critical. Experimental Design (ED), complemented with Response Surface Method (RSM), which uses a statistical proxy equation to model the response (dependent variable) as a function of independent variables (uncertainties), is a common method for studying subsurface uncertainties. In this paper, current applications of ED to subsurface modelling are evaluated from fundamental principles- mathematical and physical consistencies of the proxy equations, as well as robustness in modelling uncertainties. Within the context of modelling and mitigating subsurface uncertainties, major shortcomings of the ED and their implications for decision-making are highlighted. These include inconsistency and non-uniqueness of proxy models, violation of basic theoretical physics, non-preservation of the correlation between variables that are known to be inherently related, non-controllability of input variables, under-estimation of the impact of uncertainties, and the challenge of constructing (interpolating) realistic simulation models from an ED output. Although ED is consistent with statistical principles, its description of reservoir physics is not satisfactory. In its present form, reservoir complexities are apparently too overwhelming for reliable modelling or optimisation by the proxy models. Consequently, it is recommended that the application of ED be limited to situations where a simple understanding of the effect of a controllable variable on a dependent variable is required, or where the range of uncertainties is well known within a narrow interval. These include production/injection management, ‘model-based’ control algorithms for ‘intelligent’ completions, business planning and similar areas of the E&P business characterised by continuous data, and where the independent variables could be engineered for the desired objectives.

Application of Design of Experiments for Well Pattern Optimization in Umiat Oil Field: A Natural Petroleum Reserve of Alaska Case Study

“…The well spacing determines the well count and thus it is important to study effect of number of wells in a field on recovery. discrepancy with basic physics principles, inability to provide a correlation between variables that are known to be related, and the challenges faced in application of DoE output in simulation models (Lawal, 2009).…”

Integration of Response Surface and Decision Support to optimize a Well Sidetrack under Uncertainty II. Secondary Recovery Mechanism

“…In effectively having a time-based dynamic proxy-model, non-conformity of derivatives of models in solving rate-based analytical equations will be rendered possible (Lawal, 2009). Thereby, enhancing the use of proxy models.…”

“…This non-linearity can be caused by the introduction of a secondary recovery mechanism or just production discontinuity from the already producing horizon in primary recovery. Lawal (2009), suggested that the non-linearity can be solved by proxy models chosen for designated time intervals to match the prevailing physical flow mechanism underplay. There is the study of the risk in sidetrack operations as found in probability of success (POS) which was examined for primary and secondary recovery mechanism by Lerche & Mudford (2001) and respectively.…”