The management of a hydrocarbon reservoir is based on measurements made in and around the well. The available information is used as input into models of the reservoir, so as to operate the well in the most optimal way. A reservoir managers success thus depends on the quality and type of information available. The objective of the work presented in this report was to develop a method for providing high quality mobile measurements from the inside of oil wells. It is shown that electrical capacitance tomography is a suitable method for the purpose. The conventional methods are only partially applicable, since the demands on the sensor results in a new ’inside-out’ sensor geometry, where the permittivity on an annulus is reconstructed and the electrodes are placed on the inner boundary. In specific, it is found that the normalization normally applied to obtain a pseudo-inverse for the sensitivity matrices, causes artifacts to appear in the reconstructed images for the inside-out geometry. A reconstruction method which can handle these problems is developed. Sensitivity matrices for the inside-out geometry are calculated. To assist in investigating the sensitivity matrices, an analytical expression for the electric field inside the sensor is derived and subsequently an analytical expression for the sensitivity matrix is found. The analytical solution is for a slightly idealized geometry, so numerical methods are applied to obtain the sensitivity matrix for the exact sensor geometry. The numerical methods used were a finite difference method and a finite element method. A few different reconstruction methods are employed to investigate which one to use. The recorded capacitance data are transmitted over the wireline, which is a cable used in the oil-industry to lower tools into a well and to supply the tool with power, and the data can be used to perform live tomography with linear backprojection. A customized version of Landweber was developed and is demonstrated to work very well for the inside-out geometry. Several test setups were constructed. It is found that a resolution of 5fF is achieved and that the system is able to operate in temperatures of 120C. The image quality of the customized Landweber algorithm is superior to other reconstruction methods for the inside-out geometry. The system was tested in a well under surface conditions. Live tomography could be provided over the wireline and the sections with water could be clearly identified. It was concluded that the system is ready for field-test. Three sensors were shipped for offshore field test, but unfortunately the test was canceled because of problems with the well.