Compaction of confined porous sub-surface reservoirs

COMPACTION OF CONFINED POROUS SUB-SURFACE RESERVOIRS Tom Aage Jelmert 1, Tommy Toverud 2 1 Dep. of Geoscience and Petroleum, N-7491 Trondheim, Norway 2 Dep. of Geoscience and Petroleum, N-7491 Trondheim, Norway ABSTRACT Fluid extraction has led to compaction, subsidence and even earthquakes many places around the world. Although rare, the environmental cost could be overwhelming. Once compaction has been identified, possible future consequences should be investigated. If deemed adverse, preventive actions should be started as soon as possible to prevent further damage. The purpose of this study is to enable prediction of possible compaction by a simplified analytical model. Studies by numerical models are time consuming and expensive. A fluid extraction period may also be necessary to match the model to observed behaviour. Due to simplicity, we believe our methodology will be useful as an initial screening tool. Our model, which is a generalization of a classical one (Pedrosa, 1986), has been extended to account for boundary dominated flow and for the effect of wellbore storage and skin. During the last decades, many studies have expanded and improved the Pedrosa theory. According to our knowledge, the inclusion of compaction is original with us. Our model will simplify to the model of Pedrosa and many others by simple changes in the input data. In addition, the traditional model without stress-sensitivity is included as limiting behaviour. Results are presented by way of type curves, both for the pressure and pressure-derivative. The model depends on the assumption of exponential behaviour of all pressure-dependent variables. Then, a logarithmic substitution transforms the non-linear governing equation into a diffusivity equation of linear appearance. Hence, most commercial well test simulators already include the majority of coding to take advantage of the technique. We derive an equation for the dynamic behaviour of the thickness and present plots of the normalized thickness as a function of time. Conclusions: Theories for flow in stress-sensitive formations, with exponential behaviour, have been generalized to account for compaction. The pressure and pressure-derivative type curves fall above the ones without stress-sensitivity. The non-linear correction shows up as the vertical displacement between the non-linear (stress-sensitive) and the linear (traditional) type curves. Failure to recognize stress-sensitivity will lead to erroneous well test interpretation. The method ca easily be adapted in commercial well test simulators. Corresponding Author: Jelmert