Mutual Inductance Inversion Algorithm for Radial Magnetic Permeability Imaging Downhole

R. Adams, J.M. Felix Servin, W. Wang, M. Deffenbaugh
Aramco Americas: Aramco Research Center – Houston,
United States

Keywords: imaging, inversion, mutual inductance, permeability, reservoir, magnetite


Oilfield reservoir models simulate movement of oil, gas and brine downhole. These simulations determine where to locate wells in the reservoir, how quickly to produce from wells throughout the reservoir, and where to inject other fluids to help sweep out hydrocarbons from the reservoir. The accuracy of these models depends primarily on how accurately the geologic permeability throughout the reservoir is known, and where high geologic permeability barriers are located. Despite their importance for optimizing oil and gas production, accurate measurements of geologic permeability are difficult to obtain. Typical measurements are performed ex-situ with samples taken from the subsurface and measured in laboratory tests. This process is time-consuming, costly, and may not be representative of the behavior of the reservoir in a downhole environment. A system is in development, which images geologic permeability of the reservoir in situ downhole. Colloidal magnetite fluid with high magnetic permeability is injected from the surface into the subsurface formation. A sensor is deployed downhole, which measures the radial distribution of magnetic permeability surrounding the tool. By comparing the magnetic permeability radial distribution surrounding the sensor before/during/after fluid injection, the system is able to directly measure geologic permeability of the surrounding formation in situ. It is important to note that changes to the distribution of magnetic permeability can only be caused by the movement of the magnetic permeability doped fluid, as naturally occurring downhole fluids are non-magnetic and thus do not alter the distribution of magnetic permeability of their own accord. The sensor determines the surrounding magnetic permeability of the formation by measuring the mutual inductance between solenoid coils axially distributed along a downhole tool. As the magnetic permeability of the material surrounding the solenoid coils increases, the mutual inductance between coils increases. Eddy current effects on mutual inductance measurements can be minimized by reducing the interrogation frequency of the measurement, such that fluid conductivity changes have no effect on the measurement of interest. The radial responsivity of the mutual inductance is a function of the axial separation between pairs of coils. Thus, measuring mutual inductance across multiple pairs of coils enables the system to map the radial distribution of magnetic permeability surrounding the sensor. An analytical model of the system response to radial distributions of magnetic permeability was developed. A linearized algorithm relating the coil pair response to various radial distribution of magnetic permeabilities is created from the analytical model. Data from this linearized algorithm is inverted to create a radial image of magnetic permeability surrounding the tool system. A laboratory mockup of the coil array measurement is demonstrated, and radial images from the laboratory demo are compared to the analytical model response.