Bayesian Deconvolution of Rate Pressure Data Using Regularizing Priors
- Arjun Ravikumar (Texas A&M University) | John Lee (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Latin American and Caribbean Petroleum Engineering Conference, 27-31 July, Virtual
- Publication Date
- Document Type
- Conference Paper
- 2020. Society of Petroleum Engineers
- 7.2.3 Decision-making Processes, 5.6 Formation Evaluation & Management, 5.6.9 Production Forecasting, 5 Reservoir Desciption & Dynamics
- deconvolution, rate-pressure, bayesian, hierarchical
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- 55 since 2007
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The constant pressure production behavior of a reservoir system is a key component of reservoir diagnostics and production forecasting. Rate-pressure deconvolution is a technique that uses production data from variable rate-variable pressure production to calculate this constant pressure behavior. Regularization techniques are used to mitigate the instability inherent in the deconvolved result. In this work, we describe rate-pressure deconvolution in the time domain within the framework of Bayesian statistics, and obtain the deconvolved result by interpreting the posterior distribution.
We strategically parametrize the problem in terms of derivatives of the deconvolved solution to exploit the monotonic nature of the constant pressure behavior. We achieve regularization of the deconvolved solution using regularizing priors instead of conventional regularization methods. The regularizing prior is a probability distribution of the solution constructed using the prior knowledge of reservoir and fluid parameters from a variety of sources such as fluid samples, analogs, experience, and common sense. Finally, we obtain the deconvolved result using Markov chain Monte Carlo methods.
We show that conventional regularizing methods are a subset of the regularizing prior approach, by proving that, for specific choices of the prior, our method is equivalent to conventional regularization techniques. We establish the validity of our method using synthetic data with noise added. We analyze the sensitivity of the solution to the regularizing prior and discuss procedures for choosing an appropriate prior. We discuss methods to make the inference robust to outliers in the data. Finally, we demonstrate our deconvolution algorithm with field cases.
The constant pressure behavior of a reservoir is crucial to diagnostic and forecasting methods such as flow regime identification and decline curve analysis. Existing rate-pressure deconvolution techniques have no mechanism for including prior knowledge of the reservoir in the solution. Our framing of the problem incorporates this knowledge into the problem systematically. Our Bayesian approach also enables us to infer the uncertainty of the deconvolved solution directly from the posterior distribution.
|File Size||2 MB||Number of Pages||10|
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