# Borehole Condition and Limit Pressure Differential Analysis in Carbonate Reservoirs
## 4 Determination of Limit Test Pressure Differential  
In the actual testing, maintaining the hundreds-of-meters-long rock surrounding the wellbore in a uniformly safe elastic or plastic state is fraught with challenges, given the along-axis heterogeneity of the formation. It is pragmatically tolerated for isolated segments of the wellbore to encounter localized wall collapse, provided the collapse remains within manageable limits and does not compromise the overarching safety of the horizontal open-hole section. Domestic and international researchers alike have delved into wellbore stability issues on localized wall collapse. [PERSON] and [PERSON] postulated that wellbore instability was highly probable when the plastic zone circumference twice exceeded the wellbore's cross-sectional area [10]. Conversely, [PERSON] and [PERSON] inferred that wellbore stability prevailed until the failure angle surpassed 90\({}^{\circ}\), beyond which the collapse progressed uncontrollably, triggering instability [11; 12]. While these perspectives find credence in selected engineering datasets, they are confined to instability at discrete points within a well section under plane strain assumptions, inadequately addressing the comprehensive wellbore instability dynamics encountered in practical testing. Consequently, building upon methodologies alluded to in references [10; 11; 12], a novel approach was devised to scrutinize the open-hole wellbore wall condition as a function of depth, thereby facilitating the determination of a critical test pressure differential. This  
Figure 5: The calculation results of horizontal wellbore state in different directions. innovative method entails quantifying the extent of the elastic, plastic, and post-failure residual zones adjacent to the wellbore throughout the testing phase, alongside estimating the magnitude of the failure angle along the wellbore perimeter. A scenario wherein the test pressure differential is substantial, accompanied by excessive fractions of the plastic and failure zones, coupled with a pronounced failure angle on the wellbore wall, is indicative of an unsafe testing environment. Considering the reservoir interval spanning 7350 m to 7600 m in a vertical well as a case study, Figures 6 and 7 illustrate, respectively, the variations in the ratios of the failure zone volume, plastic zone volume to the wellbore volume, and the dependency of the wellbore wall failure angle on depth under differing test pressure differentials. Longitudinally, the reservoir exhibits a depth-dependent dichotomy characterized by frail strata susceptible to failure intermixed with robust, resilient layers. This stratigraphic heterogeneity gives rise to localized formation collapse at specific differential pressures, whereas other strata maintain stability. In the lateral context, increments in the test pressure differential correlate with proportional escalations in the plastic zone extent, the ratio of failure zone volume to wellbore volume, and the wellbore collapse angle. Delineating the threshold of wellbore failure is pivotal for ascertaining the maximum tolerable test pressure differential. Based on the analysis of actual test data from the well, the maximum test pressure differential is approximately 20 MPa, and no significant wellbore instability issues have been observed. According to the calculation results, when the test pressure differential is 20 MPa, the ratio of the plastic zone volume to wellbore volume is generally within 20%, and the ratio of the failure zone volume to the wellbore rock volume is within 10%. The majority of well sections have a wellbore wall failure angle smaller than 80\({}^{\circ}\), which is consistent with the criterion mentioned in references [11, 12] stating that the well wall failure angle should be smaller than 90\({}^{\circ}\).