Abstract
The study is motivated by monitoring the space orientation of a hydrolic fracture used in oil production. Streaming potential arises due to the leakage of ionic fracking fluid under the rock elastic forces which make the fracture disclosure disappear after pumping stops. The vector of electric field correlates with the fracture space orientation since the fluid leakage is directed normally to the fracture surfaces. We develop a mathematical model for the numerical evaluation of the streaming potential magnitude. To this end, we perform an asymptotic analysis taking advantage of scale separation between the fracture disclosure and its length. The contrast between the virgin rock fluid and the fluid invading from the fracture is proved to be crucial in a build up of a net charge at the invasion front. Calculations reveal that an increase of the viscosity and resistivity contrast parameters results in an increase of the streaming potential magnitude. Such a conclusion agrees with laboratory experiments.
Highlights
In applying hydraulic fracturing treatment of rocks, one should prepare for execting the size of a fracture and its space orientation
We formulated a mathematical model to evaluate the streaming potential induced by ionic fracture fluid leak-off after shut-in of a water injection well
The contrast between the virgin fluid and the fluid invading from the fracture is proved to be crucial in a build up of net charge at the invasion front
Summary
In applying hydraulic fracturing treatment of rocks, one should prepare for execting the size of a fracture and its space orientation. The onset of fluid flow perturbs the distribution of the ions present in that layer and induces a current, which is the source of the streaming potential. This electrokinetic mechanism has been tested and employed in the laboratory to monitor the evolution of an oil–water encroachment front over time during hydrocarbon recovery Earlier, the streaming potential dynamics were studied near the production well during water-flood of an initially oil-filled [6,7]. To evaluate the electric field near the fracture, we apply an asymptotic technique assuming that the contrast between the invasion zone and the virgin rock is small. The proposed mathematical model explains the laboratory experiments [10] and set theoretical tools for the streaming potential method applied both in the tracking the water front during production operations and the hydro-fracture development
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