Reservoir Characterization During Underbalanced Drilling: A New Model

Abstract

Abstract The downhole pressure and rate data acquired during underbalanced (UB) drilling is essentially a well test during drilling. However, these data are rarely used quantitatively. Usually, the data are used qualitatively during drilling to make changes in the drilling design. In most UB drilling designs, the reservoir is considered to be independent of the well, providing fluid at an assumed constant rate. A reservoir model interacting with the well in real-time is needed. Incorporating an appropriate reservoir model into the UB system results in a fully coupled system where changes in wellbore conditions are reflected in the flow rate from the reservoir. Data acquired from the UB process can then be analyzed to extract information about the reservoir, namely permeability versus depth, resulting in a more timely reservoir description. We present a new solution of the mathematical model representing reservoir response during UB drilling. The UB drilling model is a modification of the mathematical model that describes the standard pressure transient test (the diffusivity equation). This modification, which makes obtaining the analytical solution more difficult, involves the time dependence of the boundary condition at the wellbore. As drilling progresses, the length of the wellbore increases and the fluid flow rate from the reservoir changes in response to the well length and wellbore conditions. Several approximate solutions of this mathematical model exist in the literature. These solutions require simplifying assumptions such as no vertical permeability or the flow rate is a given function of time. In this study, a solution is obtained from the diffusivity equation with no further simplifying assumptions. Results obtained with the new analytical solution, with numerical simulations, and from the literature are shown to be comparable. An actual field case is presented demonstrating the practical use of the model in a real-time UB drilling application.