Minimum Shut-In Time Prediction Model for Pressure Build-Up Survey for a Niger Delta Onshore Field

Abstract

Abstract Allowing a well to stabilise is an important part of both pressure drawdown and build-up test. If stabilization is overlooked or is impossible, standard data analysis techniques may provide erroneous information about the formation. One of the principal objectives of pressure build-up analysis is to determine the static reservoir pressure without waiting weeks for the pressure in the entire reservoir to stabilize. The fact remains that no matter how we try to avoid long shut-in period, the shut-in time must exceed the transient and well bore storage period if a reliable result is sought. The bulk of the analysis is done at the middle transient period (MTP) which, sometimes, due to the complex nature of the reservoir, may be appreciable enough to invalidate the intention of shutting-in the well for just a short time. A minimum shut in time of six hours has been a common conventional practice in our land locations. This brings us to the question - "is this shut-in period enough or too small to provide a reliable analysis?" This shut-in period remains a paradox as long as complexities and uncertainties are present in the reservoir under study. Some reservoir with varying degree of complexities has varying shut in time. For example, the presence of faults and complex barriers may prolong the time of the reservoir to reach its middle or late transient state during build-up; hence, it becomes necessary to predict the minimum time of stabilization in the presence of these complexities so as to minimize cost. This was the focus of this paper. The general formulas used in analyzing pressure build-up data came from a solution of the diffusivity equation with homogenous, isotropic and slightly compressible single phase fluid conditions. This equation is in its simplest form and due to the assumptions made; it is obvious that the major uncertainties that may affect the shut in time is not captured; hence a need for a robust modelling. In this paper, a semi-analytical model for the Niger Delta onshore field was developed for optimum shut in time prediction for each well in the reservoir selected for study. A correction function which encapsulates the real reservoir complexities was introduced based on the well data under study. This correction function was modelled using Gompertz, 4 parameter Sigmoidal equation1 with the correlating constant determined by the method of least square for the specific well considered. A constrained nonlinear optimisation technique was applied to the newly developed model which serves as the objective function with the aim of minimizing the shut-in time as well as attaining an effective stabilization pressure. This procedure will, in no doubt, improve our optimism of accurate shut-in time prediction, a cost effective approach.