Invasion Zones in Lateral Drilling

A mathematical model for mud filtrate invasion in lateral drilling is proposed. The main assumption is that the difference in density between the invading and formation fluids is insignificant. Gravitational asymmetry of the invasion front is determined, and it is established that with time one of its points becomes abnormal and the entire invasion zone loses convexity. The main reason for the asymmetry is the density difference. If a lighter drilling mud is injected, the front “floats up” if the mud is heavier, the front “floats down.” The abnormal point of the front appears below or above the borehole, depending on the drilling mud weight. In the case where the mud is lighter than the formation fluid, the point of the front directly under the center of the borehole has the special property that with time it is less advanced downward than the neighboring left and right points of the front if the advance is reckoned from the horizontal axis through the center of the borehole. This property is the most pronounced for a small pressure difference between the borehole and formation equal to a certain critical value: under such conditions, the indicated point of the front does not move at all. For large pressure differences, the frontal advance is nearly equal in all directions.