Abstract
In this paper, we investigate the cause of the time-shift that occurs between the derivatives of the observed and simulated pressure transient data and present a methodology to perform full-field transient modeling without the need for single well fine grid sector models.
Pressure transient modeling is the process of simulating an observed well test sequence with the goal of comparing the derivative of field measured pressure transient to the derivative of numerically simulated pressure transient. Beginning from first principles, we investigated and showed in the current paper that simulation grid-block size introduces an undesireable shift in the derivative of simulated data which disappears as we approach fine grid simulation. We have termed this shift as grid-block storage phenomenon. As a result of this undesireable shift that occurs when coarse gid blocks are used, transient modeling is currently done using local grid refinement on sector models. The limitations of the current practice include; (i) large simulation run times due to use of fine grid simulation (ii) error related to boundary conditions when using sector models.
In this paper, we develop the equations governing pressure buildup behavior during grid-block storage dominated period as a function of simulation grid-size and simulation grid permeability. The insight from the derived equations reveals that the infinite acting radial flow stabilization (IARF) of the derivative of simulated pressure transient is always the same regardless of simulation grid-size. However, the onset of this stabilization is delayed as simulation grid-size increases and as simulation grid permeability decreases. Based on this insight, we then present the basis for an approach to history match the derivative of observed pressure transient without using local grid refinement on sector models. This approach is based on the use of derivative time-shift. Instead of using a fine grid sector model, we simply use the coarse full-field model to simulate pressure transient until the onset of IARF stabilization. We then shift the derivative of observed pressure transient right-wards to overlay corresponding features of the derivative of simulated data in a manner similar to type-curve matching.
This new approach called Time-Shift Methodology (TSM), presents a practical and efficient way of performing transient modeling on a full-field multi-well model without resorting to the time consuming conventional approach of using several single-well fine grid sector models.
