Several empirical or analytical/semi-analytical simulation models have been developed to assess the Estimated Ultimate Recovery (EUR) of an oil or gas formation for a short or long term of production. Furthermore, providing the EUR of a set of regional wells, it often becomes essential to perform a spatial analysis to develop the overall perception of possible depletion rate across the play. However, the lack of knowledge regarding the likely statistical structure of simulation models' parameters coupled with the unknown influence of correlation amidst wells' locations, makes it pertinent to apply a mechanism to quantify the uncertainty associated with the analysis. Therefore, in this study, researchers initially exerted the principles of the Bayesian paradigm together with the Markov Chain Monte Carlo (MCMC) theory to capture the posterior of the simulation model random field. Also, a vector of randomly drawn samples from the retrieved posterior allows delineation of the expected model realizations for a course of progressive time. Despite the fact that MCMC incorporating the acceptance-rejection criterion of the Metropolis-Hastings (MH) algorithm eventually converges to the true mean of the random process, it appears that the general trend of sampling often suffers from being computationally inefficient. Accordingly, to address the aforementioned issue, a novel sophisticated framework which is called "Parallel Scaled Adaptive Metropolis-Hastings" is developed. PSAMH constructs several synchronous chains to adapt the step size of MH proposal distribution and hence optimize the acceptance rate. Moreover, in this study, three major EUR evaluation techniques are employed. The Power Law Exponential Decline (PLED) and Modified Hyperbolic Decline (MHD) functions, along with a semi-analytical method, serve to project the well production performance over the varying time. Additionally, the depletion logs given from the Eagle Ford Shale and Barnett Shale deliver the required observation data. Besides, the Ordinary Kriging and Inverse Distance Weight are two key techniques that are applied to approximate the spatial behavior of the formation. In addition, researchers elaborated a sequential Bayesian updating mechanism to take the updating evidence into the prior's computation for various time intervals. Also, a Bayesian-spatial algorithm is used to feature the spatial characteristics of unexplored locations hypothesizing the fact that the only given information comprises the production observed data and corresponding coordinate for each individual well. It is implied that exerting the Bayesian approach permits quantifying the inherent uncertainty in the model analysis. Furthermore, it is concluded that the sequential Bayesian updating mechanism is able to noticeably increase the performance and efficiency of the process by precisely constructing an appropriate prior distribution. Also, it is connoted that, given merely the observation data, associated coordinates and EUR evaluation models, it becomes possible to estimate the statistics of model variables and the production behavior for different courses of time at desired locations. Last but not least, attaining the Bayesian-spatial production forecasting for varying depletion times, it becomes plausible to generate the daily basis and cumulative production dynamic maps.
