Wellbore geometry

Wellbore geometry is another reason. In kick-off or well curvature, the drillstring has more flexibility when tripping in than when tripping out and the friction may increase to the point of getting stuck. 

The dissolution channels (wormholes), obtained under certain conditions of attack of carbonate rocks by hydrochloric acid, have been recently proven to have a fractal geometry. An equation was proposed, relating the increase of the equivalent wellbore radius (i.e. the decrease of the skin) to the amount of acid injected, in wellbore geometry and in undamaged primary porosity rocks. This equation is herein extended to damaged double porosity formations through minor modifications. 

Similarly, in 3D-radial geometries of interest for petroleum engineers, an equivalent wellbore radius re is defined. The near-wellbore region, including radially distributed wormholes from rw up to re, is infinitely permeable and therefore becomes a mere radial extension of the wellbore itself. Equation 2 can be used to calculate the pseudodecrease of the skin when an undamaged primary porosity formation of permeability k0 includes wormholes as described hereabove ... 

The borehole is assumed to be infinitely long and inclined with respect to the in-situ three-dimensional state of stress. The axis of the borehole is assumed to be perpendicular to the plane of isotropy of the transversely isotropic formation. Details of the problem geometry, boundary conditions and solutions for the stresses, pore pressure and temperature are available in [7], The solution is applied to assess the thermo-chemical effects on stresses and pore pressures. Both the formation pore fluid and the wellbore fluid are assumed to comprise of two chemical species, i.e., a solute fraction and solvent fraction. The formation material properties are those of a Gulf of Mexico shale [7] given as E = 1853.0 MPa u = 0.22 B = 0.92 k = 10-4 md /r = 10-9 MPa.s Ch = 8.64 x 10-5 m2/day % = 0.9 = 0.14 cn = 0.13824 m2/day asm = 6.0 x 10-6 1°C otsf = 3.0 x 10-4 /°C. A simplified example is considered wherein the in-situ stress gradients are assumed to be trivial and pore pressure gradients of the formation fluid and wellbore fluid are assumed to be = 9.8 kPa/m. The difference between the formation temperature and the wellbore fluid temperature is assumed to be 50°C. The solute concentration in the pore fluid is assumed to be more than that in the wellbore fluid such that mw — mf> = —1-8 x 10-2. 

When a well is drilled, the stress state of the rock around the wellbore is altered. The stresses around the wellbore are a function of position and, because of geometry, can be expressed in cylindrical coordinates (Figure 3b). The general solutions for the wellbore stresses can be quite complicated depending on the orientation of the well and the axes of... 

Early modeling of wellbore stresses assumed that the rock behaved elastically (52). Bratli and Risnes (27) and Risnes et al. (53) included a plastic zone around the wellbore with variable permeability (Figure 11). In unconsolidated sands, the plastic zone is of the order of about 1 m radius consolidated formations have a smaller plastic zone. For stress solutions with fluid flowing into an uncased wellbore (cylindrical geometry around the wellbore), a stability criterion that equates fluid flow parameters to rock strength parameters is found ... 

The completion of a well in an unconsolidated sandstone is more complicated than in a consolidated sandstone because of wellbore instability and the need to install solids control. Perforation geometry is an important consideration (3). At low fluid production rates, small quantities of solids may be produced, whereas at high fluid production rates, large quantities of solids may be carried in the production stream. 

Simple porosity determination. In wells where mudcake controls the overall flow into the formation, and where Ar/r j. < 0.20 is satisfied, a lineal mudcake model suffices. This being so, we unwrap the cake layer adhering to our wellbore and view the buildup process as a lineal one satisfying the Vt law. But the invasion into the formation, of course, is highly radial in this farfield, the effects of borehole geometry and streamline divergence must be considered in order to conserve mass. Now consider a well with a radius r // and an axial... 

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