David Steven (2020-05). Use of Bayesian Probabilistic Graphical Models for Simultaneous Variable Rate / Variable Pressure-Drop Deconvolution of Single Well and Multi-Well Cases. Master's Thesis. Fulford - Texas A&M University (TAMU) Scholar

Fulford, David Steven (2020-05). Use of Bayesian Probabilistic Graphical Models for Simultaneous Variable Rate / Variable Pressure-Drop Deconvolution of Single Well and Multi-Well Cases. Master's Thesis.
Thesis

Deconvolution is a useful tool for removing of the effects of non-constant production rate on the observed flowing pressures, or the effects of non-constant flowing pressure on the observed producing rates. The caveat of deconvolution is that it is non-unique and numerically unstable. To maximize the chance of success, an operator can run a controlled experiment in order to minimize these properties of the deconvolution. Examples of such experiments are a stepped production rate test (constant rate steps) or stepped flowing pressure test (constant flowing pressure steps) where the value of a step is constant over a specified time interval. These experiments are costly and therefore frequently not performed, thereby limiting the use of deconvolution as a practical tool for reservoir performance analysis. In this work we deconvolve both cases simultaneously--constant rate and constant flowing pressure--by correlation of the deconvolved responses. A probabilistic graphic model (PGM) captures the relationships of influence (or probability) between the observed time, rate, and pressure values, and the unobserved latent constant-rate pressure function and constant-pressure rate function. A stochastic algorithm using Hamiltonian Monte Carlo simulation iteratively solves and directly samples the solution space to illustrate the inherent non-uniqueness of the solution. Acceptance or rejection of a specific iteration's proposed solution after evaluation of all functions ensures that acceptance only occurs if all variables and functions are probabilistically likely given the posterior joint distribution of the entire PGM. Numerical stability is achieved by solving the forward convolution problem-as opposed to the inverse deconvolution problem-as well as utilization of cost functions that are less biased by noise than the squared error cost function. The structure of the PGM is not altered no matter whether we choose to evaluate just the variable rate case or the variable pressure-drop case, both independently, both together (enforcing correlation), whether we impute missing data, correct data in error, or whether we are analyzing a single well or a multi-well case. We verify our new method with analytical solutions and application to field cases.