Evaluators use a lognormal probability distribution of estimated ultimate recovery (EUR) to predict the EUR that may be expected when drilling more wells. The EURs used in the distribution are determined by extrapolating the rate-time profiles of analogous wells; existing wells that are expected to behave like the planned wells. The range of expected values is captured by the difference or ratio of P10 and P90 EUR. Even with many analog wells, the analog distribution may differ from the population distribution, creating meaningful uncertainty usually absent when the only uncertainty is assumed to come from non-uniform sampling. This paper presents a statistical method to quantify the possible deviation between analog and population distributions and to construct type wells that incorporate this uncertainty.
The process uses Monte Carlo simulation to select EURs from known population distributions and create a sample distribution for each trial. The "known" population P50 EURs and the P10/P90 ratios are random. The number of analog wells is equal to the number of wells (samples) selected for the trial.
We record trials with near equal sample and analog distributions of both P50 EURs and P10/P90 ratios. A scatter plot of P50 versus P10/P90 ratio for this recorded subset of trials shows the range and frequency of possible population distributions. The EUR distribution of random samples taken from each population distribution in the subset will include the combined uncertainty of non-uniform sampling and an unknown true population. This distribution would be considered the most likely representation of the population.
Analog samples are properly positioned on the most likely population distribution to determine the probability for each analog sample. Reserves and type well construction follow from this distribution.
We test our observation that uncertainty is understated using recommendations in SPEE Monograph 3. With 60 wells having P10/P90 = 4, the Monograph predicts a reliable value for the mean where reliable is stated as an "acceptable confidence interval" with a "target of greater than mean less 10 percent and a confidence interval of 90 percent". At 80 percent confidence, our analysis obtains a variance range of −9 to +11 percent for the mean and + /- 20﹪ for P50 and P10/P90. We think variances this large are not reliable.
Probability distributions are used for building aggregation type wells (SPE 175967). As the number of planned wells increases (the number of wells in the aggregation), the P10/P90 ratio becomes smaller (less uncertainty). When the number of planned wells is in the hundreds, the P10/P90 ratio approaches one, there is limited uncertainty and that is not observed in practice. Employing the methods described in this paper, other uncertainty is captured and persists, even when the number of wells is large.
We find that analog distributions are unlikely to represent the population due to non-uniform sampling. The method proposed in this paper works to identify the uncertainty caused by non-uniform sampling, and to correct distributions to align with the risked population and obtain better evaluations.
Our objective is to obtain more certain probability distributions and to construct type wells that reflect the presence of uncertainty for drilling many wells in the future. Because the process is Monte Carlo based, errors in calculating EUR are also incorporated in the analysis, providing those errors are not systemic.
When statisticians construct probability or frequency distributions there is only one uncertain variable. The methods we describe in this paper identify the equivalent of a frequency distribution for two non-correlated variables that are not easily analyzed using conventional multivariate analysis.