Well test analysis in naturally fractured reservoirs using elliptical flow

This study has two main objectives: (1) Investigate the application of the elliptical flow model in well testing and (2) Quantify the permeability anisotropy of naturally fractured reservoirs using the elliptical flow model.; Permeability anisotropy and orientation is important to field development, most especially in improved recovery technique. Accurate knowledge of permeability anisotropy and orientation will help predicting the flow path during injection.; Prior to this study, the elliptical model has been used to quantify water influx and production decline in an elliptical shaped reservoir. Other areas of application include lateral composite systems and water injection in hydraulically fractured wells. Its application in well testing has been neglected. This is partly because there is no method of calculating the radius vector of the ellipse at the inner boundary. The method of calculating this parameter is presented for the first time in this study. This was made possible by making use of the intersection point of the characteristic lines of linear and radial flow regimes.; It has been suggested that a naturally fractured reservoir should be treated as an anisotropic system. This is based on the fact that such reservoirs can exhibit directional permeability due to the fracture pattern. Moreover, naturally fractured reservoirs are double permeability double porosity systems that consist of matrix and fractures. Matrix permeability is usually less than that of the fractures, most especially in types 1 and 2. All the existing flow models assumed matrix flow to be orthogonal to that of the fractures.; Experience has also shown that some naturally fractured reservoirs that are neither hydraulically fractured nor stimulated do show an early linear flow regime. The skin factors estimated from some well test data are negatively high, which is an indication of large scale fracture sizes around the well. Fracture orientation and sizes depend on the stress anisotropy of the formation, which may impart directional permeability to the system. Using the elliptical model, which combines both linear and radial flow together, to describe the flow behavior is most appropriate. The radial model can capture the late radial flow behavior but is not appropriate for the early linear flow if it does occur. In a system where elliptical flow occurs, a radial system will not capture the early linear flow behavior which is very essential to reservoir characterization. The anisotropy of any system only impacts the flow behavior during the early stage. This study therefore presented practical methods of using the elliptical flow model to quantify the permeability anisotropy, and several other reservoir parameters such as equivalent hydraulic length and fracture conductivity around a well in a naturally fracture reservoir. The solution obtained for the vertical well is easily adaptable to an infinite conductivity hydraulic fracture in a vertical well and horizontal well.; The interpretation procedure developed was applied to several field examples, and accurate results were obtained. The field examples prove the elliptical flow model to be the most appropriate method of analyzing pressure transient data in naturally fractured reservoirs. The information obtained from the radial flow model is limited and less descriptive for reservoir characterization. It can neither be used to quantify the anisotropy of the reservoir nor the flow pattern in the reservoir. The elliptical flow model made this possible with a single well test. Its application to the interpretation of an interference test is demonstrated with a field example.