The fracturing of horizontal wells is a recently developed tool to help enable tight and shale formations to produce economically. Production data analysis of the wells in such formations is frequently performed using analytical and semi-analytical methods. However, in the presence of nonlinearities such as multi-phase flow and geomechanical effects, the numerical simulations are necessary for interpretations and history-matching techniques as they are required for model calibration.
Reservoir history-matching techniques are usually based on the frequentist approach and can provide a single solution that can maximize the Likelihood function. Production forecasts using a single calibrated model cannot honor the uncertainty in the model parameters. Therefore, a Bayesian approach is suggested where we can combine our prior knowledge about the model parameters together with the Likelihood to update our knowledge in light of the data. The Bayesian approach is enriched by applying a Markov chain Monte Carlo process to updated the prior knowledge and approximate the posterior distributions.
In this paper, a one-year production data of a real gas condensate well in a Canadian tight formation (lower Montney Formation) is considered. This is a horizontal well with eight fracture stages. A representative 2D model is constructed which is characterized by 17 parameters which include relative permeability curves, capillary pressure, geomechanical effects, fracture half-length, fracture conductivity, and permeability and water saturation in the stimulated region and the matrix. Careful analysis of available data provide acceptable prior ranges for the model parameters using non-informative uniform distributions. Markov chain Monte Carlo algorithm is implemented using a Gibbs sampler and the posterior distributions are found. The results provide an acceptable set of models that can represent the production history data. Using these distributions, a probabilistic forecast is performed and P10, P50 and P90 are estimated.
This paper highlights the limitations of the current history-matching approaches and provides a novel workflow on how to quantify the uncertainty for the shale and tight formations using numerical simulations to provide reliable probabilistic forecasts.