The Calculating Method of Rock Compressive Strength Based on Logging Data

Rock compressive strength was a basic lithomechanics parameter. And rock compressive strength affected the drillingability and stability of rock in drilling engineering. So a calculating method of stratum rock compressive strength was needed to raise the reliability of stratum information acquired. Then the bit selection, well design and reservoir stimulation design could be more accurate. By analyzing the experiment data of rock 3-axis compressive strength, a logging interpretation method of confining pressure has been established, and by considering the influence of confining pressure, a quantitative calculating method of rock compressive strength based on the logging data has been given. This model was used to analyz an exploration well. The results showed that the rock compressive strength was fit to the drilling time, which indicates that this model may accurately recognize the rock compressive strength in the researched area. The result also showed that confining pressure can strongly influence mechanical properties of formation rocks, so if we analyzed the rock mechanical properties, the confining pressure must be taken into account. Besides the method can calculate rock compressive strength in some old well with regular logging data only.


Introduction
Rock compressive strength is a basic lithomechanics parameter. The rock compressive strength is closely related to rock drillability, it is also an important factor which affects sediment yield of oil wells, and it is an important parameter for drilling design, bit optimization, reservoir transformation measures and program design(Li Zhiguo

Model of Triaxial Compressive Strength of Rock
Some empirical relationships between uniaxial compressive strength and elastic modulus of sedimentary rocks have been obtained from accumulated engineering data. So there is a fuzzy positive correlation between uniaxial compressive strength and elastic modulus of rock (Farmer,I.W., 1988;Tang Daxiong and Sun Suwen, 1987). In addition, triaxial compressive strength of rock is directly related to uniaxial compressive strength of rock. Therefore, there is an inherent correlation between rock compressive strength and rock lithologic modulus (Li Yu, 2004).
ΔT P --the P-wave interval transit time,μs/m; ΔT P --the S-wave interval transit time, μs/m; ρ--the rock density, g/cm 3 ; β--conversion coefficient. Therefore, rock compressive strength can be measured by logging parameters, such as interval transit time. According to the relationship between compressive strength and elastic modulus, the interpretation method of rock triaxial compressive strength based on interval transit time is obtained through experiments. The triaxial rock mechanics test is carried out by applying equal liquid confining pressure in the horizontal two principal stress directions and mechanical axial pressure alone in the longitudinal direction. The experiment was completed on "High temperature and pressure rock triaxial apparatus". The result shows that rock compressive strength is closely related to rock density, rock porosity and confining pressure. Considering the consistency between conventional logging parameters and laboratory measurement parameters(including triaxial compressive strength, strength, Poisson ratio, modulus of elasticity, interval transit time, et.al), the interval transit time is used as the main measurement parameter. Therefore, ultrasonic testing is carried out simultaneously during the experiment, and finally 12 groups of rock compressive strength and interval transit time test results under confining pressure are obtained (Table 1).
σ bc --the compressive strength of rock, MPa; ΔP--the confining pressure, MPa; a, b--constant, which is related to lithology. As showed in formula (1) , the compressive strength of actual rock can be characterized by interval transit time, which is mainly affected by lithology and confining pressure. Confining pressure is related to drilling fluid density, depth, rock density, porosity, formation compaction and other factors(Sun Yeheng,2010). Therefore, the key is to establish a rock confining pressure calculation model based on logging data.

Calculation of Confining Pressure
In drilling, the confining pressure exists at bottom, which is determined by formation horizontal stress and formation pore pressure. In drilling conditions, confining pressure related to the minimum horizontal principal stress and pore pressure.
σ h --the minimum horizontal principal stress, MPa; P P --the pore pressure, MPa. There are many inversion methods for calculating the minimum horizontal principal stress. Pro.Huang's is adopting for calculating in-situ stress(Huang Rongzun and Zhuang Jinjiang, 1986).
γ --constant; σ--the effective force, MPa; μ--Poisson's ratio; α--Biot coefficient (effective stress coefficient). γ is a constant reflecting the magnitude of tectonic stress in horizontal direction, and it is a fixed value for a given area, but it varies with the area.
ρ--rock mass density, kg/m 3 . The model formula (1)~ (7) shows that rock compressive strength is directly related to rock density, rock mechanical properties (Poisson's ratio), rock porosity, formation depth, lithology and other parameters. Therefore, to study the mechanical properties of formation rocks, the calculation model of rock mechanical parameters established by considering only one parameter will inevitably deviate from the actual situation, but the confining pressure is a comprehensive parameter, which can synthesize the above parameters, and can be easily combined with experiment data.

Application
Well HS2 is located in the Piedmont structural zone of Junggar Basin, and its strata are basically in the Permian-Carboniferous of Upper Paleozoic. Its lithology is dense and dominated by large igneous rocks with high hardness, difficult fragmentation and low penetration rate. Laboratory rock mechanics experiments show that the formation has high compressive strength and poor drillability, but limited by the penetration rate and drilling cycle, the formation coring is less, which can not fully reflect the formation. The mechanical state increases the difficulty of speed-up plan formulation. Therefore, compressive strength calculation method based on logging data is used to process the logging data in the range of 90m-2000m in well HS2, and the data processing results are interpreted.   Fig. 2). This is mainly due to the rock compaction increases with well depth, the energy required to destroy rock increases due to the confining pressure. Therefore, to increase the penetration rate, not only increase the energy supply, but also change the stress state and rock breaking mode. then reducing confining pressure or even underbalanced drilling technology can be used to change the stress state of rock. And impact effect such as air hammer, torsional impact tool, etc can improve instantaneous rock breaking energy. It shows that rock compressive strength has a good correlation with drilling time(as Fig. 2 ). Drilling time becomes slower as the rock compressive strength increase. The air drilling method is adopted in the 90m-375m section and the compressive strength is relatively low (80 MPa-140 MPa), so the average drilling time is about 30 minutes, while the later gas change to drilling fluid, the formation The main reason for the difference is that the calculation method in the literature simply regards hydrostatic pressure as confining pressure, thus confining pressure becomes a single factor function of well depth, which is inconsistent with the actual situation of formation. Therefore, the confining pressure of actual formation rock is affected by many factors, so many factors must be taken into account in calculating and interpreting the mechanical parameters of formation to improve the prediction accuracy.

Conclusion
(1) Based on the analysis of experimental data, the method takes interval transit time as the main identification method of rock compressive strength, and takes the influence of confining pressure into account, so as to improve the accuracy of calculation.
(2) Application shows that the calculation results of this method are in good agreement with drilling time and laboratory test results, which proves that this method is an effective method for calculating the compressive strength of underground rock.
(3) The method uses conventional logging data to calculate compressive strength, which provides a new idea for the analysis of formation rock mechanics characteristics of some old wells with conventional logging data. (4) This method uses data regression to establish the numerical relationship between compressive strength and confining pressure, which lacks the corresponding theoretical basis. Further research is needed in this direction.