Assessing the Non-Uniqueness of a Well Test Interpretation Model Using a Bayesian Approach

Objectives/Scope: A stable, single-well deconvolution algorithm has been introduced for well test analysis in the early 2000’s, that allows to obtain information about the reservoir system not always available from individual flow periods, for example the presence of heterogeneities and boundaries. One issue, recognised but largely ignored, is that of uncertainty in well test analysis results and non-uniqueness of the interpretation model. In a previous paper (SPE 164870), we assessed these with a Monte Carlo approach, where multiple deconvolutions were performed over the ranges of expected uncertainties affecting the data (Monte Carlo deconvolution). Methods, Procedures, Process: In this paper, we use a non-linear Bayesian regression model based on models of reservoir behaviour in order to make inferences about the interpretation model. This allows us to include uncertainty for the measurements which are usually contaminated with large observational errors. We combine the likelihood with flexible probability distributions for the inputs (priors), and we use Markov Chain Monte Carlo algorithms in order to approximate the probability distribution of the result (posterior). Results, Observations, Conclusions: We validate and illustrate the use of the algorithm by applying it to the same synthetic and field data sets as in SPE 164870, using a variety of tools to summarise and visualise the posterior distribution, and to carry out model selection. Novel/Additive Information: The approach used in this paper has several advantages over Monte Carlo deconvolution: (1) it gives access to meaningful system parameters associated with the flow behaviour in the reservoir; (2) it makes it possible to incorporate prior knowledge in order to exclude non-physical results; and (3) it allows to quantify parameter uncertainty in a principled way by exploiting the advantages of the Bayesian approach

Constrained Least-Squares Multiwell Deconvolution

In this paper, we reduce non-uniqueness and ensure physically feasible results in multiwell deconvolution by incorporating constraints and knowledge to the methodology of Cumming et al. (2014). The constraints discourage non-physical shapes for the deconvolved derivatives and improve solution quality. We also encode knowledge on the reservoir, for instance, if it is a closed system, we impose that all deconvolved derivatives should tend towards a common unit slope at some future time. Methods, Procedures, Process Single-well deconvolution (von Schroeter, Hollaender and Gringarten, 2001, 2004) transforms variable-rate pressure data from a well test, into a single constant-rate drawdown with the same duration as the pressure history. The resulting deconvolved derivative shows features not visible within the durations of any of the test build up or drawdown periods and therefore enhance analysis and interpretation. Single-well deconvolution, however, is applicable only to individual isolated wells. Multiwell deconvolution - introduced by Levitan (2006) and developed by Cumming et al. (2013) - generalises the solution methodology to the problem of multiple wells within the same connected system. Results, Observations, Conclusions Multiwell deconvolution yields not only the constant-rate deconvolved derivatives for every well in the system, but also the interference effects from any one well to any other. These interference effects provide valuable information concerning storativity and connectivity within the reservoir, which is not accessible otherwise. Multiwell deconvolution is, however, an overdetermined problem and may therefore yield non-unique solutions that can reproduce pressure histories to a similar degree of precision, but correspond to different, potentially conflicting, and possibly non-physical responses and interpretations. This non-uniqueness and the possibility of non-physical solutions need to be reduced for practical multiwell deconvolution of field data. Novel/Additive Information We demonstrate how a combination of constraints on the shapes of the deconvolved derivatives and knowledge of the reservoir results in an improved level of quality and consistency in multiwell deconvolution solutions. We illustrate this new constrained least-squares multiwell deconvolution approach with synthetic examples with known solutions involving up to nine wells

Multiwell Deconvolution for Shale Gas

In the last decade, single well deconvolution (von Schroeter et al., 2001) has become recognised as a powerful tool for reservoir characterization. Deconvolution transforms well test pressure data measured at varying rates into an equivalent unit rate single drawdown which has the same duration as the pressure history and can be analysed using conventional techniques to identify boundaries and assess connectivity between different compartments and layers. As its name suggests, single well convolution is only applicable when there is no interference from other wells. i.e. to exploration, appraisal and isolated production wells. In 2013, a multiwell deconvolution algorithm was presented (Cumming et al., 2013) which enables deconvolution to be applied to groups of interfering wells. The algorithm yields a unit rate deconvolved derivative for every well, representing the well signature with interferences removed; and the interference derivatives between well pairs. An example of use with eight interfering North Sea oil wells was presented by Thornton et al. (2015). This paper describes the application of the Cumming et al. multiwell deconvolution algorithm to eight wells in a multilayer shale gas reservoir. The main objective of the study was to verify the capability of the multiwell deconvolution algorithm to remove the effects of interference between horizontal wells and to assess the efficiency of the actual well spacing, which had been intended to avoid interferences. This study can have an impact on upcoming LNG projects in Canada and other countries which are evaluating LNG prospects. An additional objective was to identify an optimal testing procedure to minimise uncertainties on the deconvolved derivatives. This was done by numerically simulating the behaviours of a number of interfering, multiply-fractured, horizontal wells (from 2 to 8) for various rate sequences. The impact of including non-interfering wells in the multiwell deconvolution was also investigated. It was found that the accuracy of the multiwell deconvolution process was very much dependent on the rate sequence: producing and shutting in wells sequentially provides better results that having the same rate sequence on all the wells. In addition, to minimize errors on the derivatives, the start of interference effects should be evaluated correctly and non-interfering wells should be excluded from deconvolution. Both require a good understanding of the reservoir