Abstract
Micro-tube experiment has been implemented to understand the mechanisms of governing microcosmic fluid percolation and is extensively used in both fields of micro electromechanical engineering and petroleum engineering. The measured pressure difference across the microtube is not equal to the actual pressure difference across the microtube. Taking into account the additional pressure losses between the outlet of the micro tube and the outlet of the entire setup, we propose a new method for predicting the dynamic capillary pressure using the Level-set method. We first demonstrate it is a reliable method for describing microscopic flow by comparing the micro-model flow-test results against the predicted results using the Level-set method. In the proposed approach, Level-set method is applied to predict the pressure distribution along the microtube when the fluids flow along the microtube at a given flow rate; the microtube used in the calculation has the same size as the one used in the experiment. From the simulation results, the pressure difference across a curved interface (i.e., dynamic capillary pressure) can be directly obtained. We also show that dynamic capillary force should be properly evaluated in the micro-tube experiment in order to obtain the actual pressure difference across the microtube.
Highlights
With the advancement in the extraction technologies, more oil/gas is being produced from low and ultra-low permeability oil/gas fields over the world[1,2]
Measurement tube diameter, the pressure loss caused by the capillary pressure tends to be increased
The pressure loss caused by the capillary force cannot be ignored and the measured pressure difference across the microtube should be corrected by taking into account the capillary pressure effect
Summary
The dynamic capillary calculation method applied to Hydrodynamic theory cannot be used in the micro-tube experiment. The basic idea is that the interfaces of two phases are represented as zero level set function[23]. Solving the location of two phase interface is equivalent of solving the function φ or the time step. The zero level set equation is considered as a function of the two-phase interface in a higher dimensional space, and the shape of the interface is obtained through solving Eq (5) at each time step. Using the Level-set method, we can transform the interface tracking problem into the problem of solving the zero-level set of the level set function. No previous research has examined the suitability and accuracy of Level-set method in studying the seepage law of oil and gas in microscopic pore spaces
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