Study On The Wall Effect In The Yield Stress Measurement Of Waxy Oil Gel

With the precipitation and interaction of wax particles in the crude at low temperature,a sponge-like network entrapping liquid oil within it can form.Yield stress is widely used to characterize the mechanical strength of waxy oil gel.However,there may exist two types of gel fracture in the yield stress measurement for waxy oil gels,either cohesive or adhesive,resulting from the difference between the cohesive strength of gel itself and the adhesive strength at the interface of gel and solid surface.It may contribute to the significant discrepancy between the measured yield stress and the actual gel strength.In this study,the physical insight of the discrepancy in the yield stresses measured with different geometries including smooth/grooved cylinder and the vane is investigated by experiment and numerical simulation.Furthermore,a guideline for the selection of rotor types and its geometric parameters in the yield stress measurement of waxy oil gel is proposed.The yield stresses obtained by smooth or grooved cylinder are close to each other and both are generally below than that obtained by vane.This difference can up to 90%with the increase of the gel strength,which indicates adhesive fracture being the primary mode of gel breakage in cylinder geometries.Consequently,the yield stress determined by vane geometry characterizes the intrinsic strength of waxy oil gels.On the contrary,the apparent yield stress determined by cylinder geometry indicates the adhesive strength between the waxy oil gel and the rheological geometry.Under all test conditions,the difference between the yield stresses measured with the vane geometry and that measured with cylinder geometry(σ_y,v-σ_y,c)greatly correlates with the value obtained with vane geometryσ_y,vfollowing a power law relationship(σ_y,v-σ_y,c=ασ_y,v^β).This correlation is independent of temperature,cooling rate,wax content,size or precipitation of wax particle,PPD dosage,and even the shear loading method.Furthermore,such a correlation can be verified by the published data in literature for waxy oil gels,cement pastes and bentonite suspensions.However,the fitted parameters in the aforementioned empirical relationship vary quantitatively for waxy oils and other systems（α=0.01～0.77,β=1.02～1.91）.This universal correlation indicates that the balance between the adhesive strength versus cohesive strength determines the fracture mechanisms during the yield stress measurement for waxy oil gel,while other factors of oil composition and test conditions may influence one or two of these strengths.Therefore,the previous views on the influence of these factors on the gel fracture types are biased and fail to understand the physical nature.Vane geometry is recommended in the yield stress measurement of waxy oil gel to avoid the adhesive fracture occurred in the interface of gel and solid surface.However,it is found that yield stresses measured by vane with different number,diameter and height of blades can also be inconsistent.It is related to the distribution of stress and deformation for waxy oil gel under certain loading conditions,which may be obviously affected by the geometric parameters of measured rotor.Based on the finite element methodology（FEM）,it has been found that the number of blades n is the key factor determining the shape of yield surface.The radial position of the yield surface is actually affected by the ratio of outer cylinder diameter to blade diameter D_c/D_v.However,the characteristics of yield surface is independent of the height of blade H_vwith H_v/D_v≥2.0.To avoid the adhesive gel fracture adjacent to the wall of outer cylinder（slip）,the used vane-cup geometry is recommended with D_c/D_v>1.1.When n exceeds 15and D_c/D_v is larger than 2.0（H_v/D_v≥2.0）,an approximately circular yield surface circumscribed by the vane blades can be obtained for waxy oil gel.The yield stresses obtained by the equivalent cylinder equation are similar to that obtained by FEM,and the relative deviation can be reduced to within 10%.Based on the improved finite element model,the relationship between the stress distribution of yield surface and geometric parameters of vane-cup geometry（n、D_c/D_v）is quantified by the response surface methodology（RSM）.It contributes to evaluate the discrepancy between the shape of yield surface and the equivalent cylinder hypothesis at certain condition,and the equivalent cylinder equation can be modified when the configuration of rheological geometry deviates from the specific conditions mentioned above.This work can enhance the understanding of the rheological mechanical behavior of waxy oil gels during the yielding process,and provide a methodological guide for the accurate determination of the yield stress.