Quantifying Petrophysical Uncertainties

Abstract

Typical petrophysical deliverables for volumetric and modeling purposes are net reservoir, porosity, permeability, water saturation and contact locations. These data are usually provided without quantitative determination of their uncertainties. Current computing power renders it now feasible to use Monte-Carlo simulation to determine the uncertainty in petrophysical deliverables. Unfortunately, quantitative uncertainty definition is more than just using Monte-Carlo simulation to vary the inputs in your interpretation model. The largest source of uncertainty may be the interpretation model itself. This paper will use a variety of porosity interpretation models to illustrate how the impact of each input on the uncertainty varies with the combination of input values used in any given model. It will show that use of the incorrect model through oil and gas zones may give porosity estimates with Monte-Carlo derived uncertainty ranges that exclude the actual porosity. Core data provides the best means of quantifying actual uncertainty in the petrophysical deliverables. Methodologies for deriving uncertainties quantitatively by comparison with core data will be presented. In the absence of core data, interpretation models should have been tested against core data through the same or similar formations nearby. Monte-Carlo simulation can then be used as an effective means of quantifying petrophysical uncertainty. Comparisons between the core comparison and Monte-Carlo techniques will be made, showing that similar results are achieved with the appropriate interpretation models. The methodologies described in this paper are straightforward to implement and enable petrophysical deliverables to be treated appropriately in volumetric and modeling studies. In addition, quantification of petrophysical uncertainty assists in operational decision-making by letting users know how reliable the numbers produced actually are, and what range of properties is physically realistic. Such work also allows the key contributions to uncertainty to be defined and targeted if overall volumetric uncertainty must be reduced. Introduction Petrophysical evaluations are carried out for a number of different purposes, including operational decision-making, volume in place estimation and reservoir modeling. In all cases, the uncertainty in the deliverables of net reservoir, porosity, permeability, water saturation and contact locations are critical. However, these data are usually provided without quantitative determination of their uncertainties. This paper will highlight the ease with which uncertainties can be derived using Monte-Carlo simulation. It will also illustrate how flexible this technique is when it comes to working with different interpretation models, which is not commonly done. The largest source of uncertainty in petrophysical interpretation may be the interpretation model itself. Given the large number of possible interpretation models for all the different petrophysical deliverables, this paper will only use the most basic petrophysical deliverable, being porosity, to illustrate the relationship between uncertainty and the log interpretation model selected. It will also be shown that verification of log porosity using an independent measure such as core porosity can also provide quantitative uncertainties allowing comparison with the log derived uncertainties. The State of Uncertainty in Petrophysics The requirement for quantification of petrophysical uncertainty is not a recent development. Many papers are in the literature describing functions for uncertainty definition and how to use Monte-Carlo modeling for the same purposes. Although work such as that of Amaefule & Keelan (1989), Chen & Fang (1986) and Hook (1983) provides an excellent foundation on which to calculate uncertainties, the methodologies are both time consuming to program and inflexible with regard to interpretation model. With the computing power available on desktop machines today, engineers no longer have to use these analytical techniques to derive uncertainty. Monte-Carlo models are straightforward to build and no longer time consuming to run. The literature contains a number of examples of Monte-Carlo simulation being used to characterize petrophysical uncertainty, such as the work of Spalburg (2004).

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