Probabilistic Production Forecasts Using Decline Envelopes

摘要

One of the most frequently method used for production forecasting is the decline curves analysis, which can be harmonic, exponential or hyperbolic; being the most commonly used the exponential decline curve. However there are wells that exhibit complex production behaviors, where the exponential decline curve does not fit the entire production history. One of the solutions that have been used is to divide the production history into several segments and then apply different decline factors for each segment. This complex behavior results from a long transient period observed in formations with very low permeability that have been stimulated with hydraulic fractures. In this paper, we propose an approach that considers a table of time-dependent factors; each factor results from dividing the production rate at time t, q (t), by the initial production rate, q (0), so the production history becomes a profile of factors with values between 0 and 1, which represents more accurately the behavior of the well decline. When this method is used to analyze a reservoir or a field, each well produces a decline profile, and using the information from all wells generates an area in which a profile for each well can be found. This area is defined by two envelopes, an upper bound, representing the most favorable performance, with lower production decline, and a lower bound which represents the worst performance with higher production decline. The upper bound is generated using the maximum function, and then a smooth curve is found with a hyperbolic fit; for the lower bound a similar process is used but using the minimum function. Additionally an average curve is determined. In order to perform a probabilistic production forecast using these envelopes, a profile is generated within the envelopes using a probabilistic distribution of the ubication. A random value between 0 and 1 is generated and added to the respectives values for each month of the lower envelope, to get a new profile. Using this profile a production forecast can be made and multiple simulations can be performed to obtain a probability distribution curve of all the possible outcomes.