A novel constraint-based method for density measurement in cased hole

In recent years, thru-casing measurement has shown high application values in controlling risk and improving production efficiency. However, in cased-hole applications, the investigation depth of gamma density logging is significantly confined due to the impacts of casing and cement, resulting in decreased accuracy of density measurement. Furthermore, the common uncertainty associated with cement bonding quality increases the difficulty of quantitative density evaluation. In order to overcome these challenges, a new thru-casing density measurement method is proposed. The method consists of three aspects: 1) casing correction; 2) simultaneous formation and cement density calculation based on cement constraint characterization; 3) cement thickness correction. The key to the method is step 2), where cement is defined by a set of physical constraints. e.g., volumetric fractions of contaminants such as water, mud, gas. The identification of constraints enables efficient sampling in the constrained phase space and provides the optimal solution to both formation density and cement density. To obtain precise and scenario-based cement constraints, Naive Bayes classifier combined with sliding window technique is used to provide prior information on cement quality. Geant4 is employed to simulate gamma density tools and obtain their responses in various formations, casings, and cements. These models are capable of meeting statistical error requirements. Since the simulation parameters are well-defined, it is useful for validating the proposed method using Monte Carlo simulation data under varying casing, cement, and formation conditions. The method can effectively obtain formation and cement density, as indicated by the calculation error of less than 0.02 g/cm³ and 0.025 g/cm³, respectively. The method is then applied to a well in the Bohai oilfield, and the measured data is processed using the proposed method. A comparison of open-hole and cased-hole density in a 48-m well interval shows that the error of each section increases as the well condition deteriorates. The maximum RMSE is 0.027 g/cm³ in the unstable borehole section (>13.6), while minimum RMSE is 0.016 g/cm³ in the section with good cementing quality and stable borehole. The mean relative error of the entire section is 0.91% and the RMSE of cased-hole density measurement is 0.0245 g/cm³. These results demonstrate the feasibility of the proposed method in the field by effectively correcting casing and cement impacts.