Development of a probabilistic model to estimate productivity improvement due to underbalanced drilling
Authors: Suryanarayana P. V. , Rahman S. , Natarajan R. , Reiley R. 
Published: December 2007

Abstract
Improvement in productivity from wells drilled and completed underbalanced can be substantial. This is especially true in formations susceptible to damage induced during overbalanced drilling. Substantial improvement in productivity can be the driver for the selection of ubderbalanced drilling (UBD) candidates. However, the problem of quantitatively estimating such improvements to assist in candidate selection remains. This paper presents a unique probabilistic approach to the estimation of productivity improvement that can be expected from application of UBD for a given well candidate. The unique feature of this work is the use of analog data to influence the predictions of the base probabilistic model. The approach described uses a reservoir flow model that incorporates linear and nonlinear inflow relationships. The model can be applied to horizontal or vertical completion in either gas or oil wells. Both compositional and Black Oil PVT methods are used to estimate reservoir fluid properties. Damage is modeled as a skin effect, a relative or absolute permeability reduction, or uneven flow across the producing section. Statistical uncertainty in the reservoir parameters is characterized using different applicable probability distribution functions, depending upon the natural behavior of the parameter. Standard Monte Carlo simulations are then used to estimate the expected productivity improvement. However, review of analog data from 40 different UBD wells indicates that theoretical estimates alone are not sufficient to estimate the expected productivity improvement. Therefore, the predictions of the theoretical reservoir flow model are statistically updated using available analog data. The key concept employed is one of making a prediction using standard reservoir models, incorporating the raw uncertainties of reservoir parameters, and then modifying the prediction based on a statistically legitimate combination of analog data (results from previous UBD wells) and parameter uncertainties. The resulting updated distribution is more reflective of expectation from UBD in a given field. Two statistical updating methods are discussed- a Bayesian updating approach, and a weighted mixture sampling approach. Both methods are legitimate for productivity predictions. Results are given in terms of a productivity improvement factor (PIF) distribution, the ratio of the productivity index using UBD to that of the reference productivity without UBD. The resulting PIF distribution can then be used in full-field reservoir simulators to evaluate the economic impact of UBD for a given campaign. The predictive model runs on an Excel-based program with the statistical package @Risk, and is easy to use. Two examples are provided to illustrate the use of this method and the impact of updating on the PIF distribution. The authors suggest improvements to the model, including gathering and statistical treatment of additional analog data, better reservoir models, and improvements in the statistical updating methods.