Invention of new cements for effective zonal isolation requires bond strength evaluation of the cement to formation. We present a method to evaluate the cement-to-formation bond strength based on the flow of cement through a formation using image analysis. Most researchers perform image analysis on a single slice. This is the first known nondestructive method devised using a quantitative analysis on a sequence of slices from X-ray computed tomography (CT) scans. The number of CT scan slices in which the porosity changes is used to evaluate the bond strength of cement. Our findings demonstrate that the cement-to-formation bond strength is affected by permeability of a formation and viscosity of cement if other physical (sample preparation and measuring conditions) and chemical (cement additives) variables remain constant.

Cement is a necessary component in the drilling, production, and abandonment of oil wells. The annular gap between an oil well casing and the surrounding rock formations is filled with cement. If the cement adhesion is insufficient, fluids from a producing or abandoned well may leak. Bonding properties of cement to formation are the key indicators of the ability of cement to provide effective zonal isolation (Evans and Carter, 1962). As a result, experimental methods for evaluating bond strengths of cement are needed before pumping cement in a well in the field. Shear bond strength, tensile bond strength, and compressive bond strength are different measurements that can be used to evaluate the cement-to-formation bond strength. Bond strengths are measured by applying a load in a controlled manner until the formation and cement separate. This load when divided by the contact area yields the bond strength. Shear bond strength is measured by applying a load parallel to the contact, whereas, for tensile and compressive bond strength, a load is applied normal to the contact. Cement bond strength has been published based on measurements at laboratory ambient conditions (Ladva et al., 2004; Radonjic and Oyibo, 2014; Liu et al., 2015) and downhole reservoir conditions (Bathija and Martinez, 2020).

With the advent of high-performance computing, digital rock physics has been used to model the effective properties of rocks (Andrä et al., 2013). Digital rock physics is an image-based computational technique used to study the physical properties of rocks (Sengupta and Eichmann, 2021). The method described in this paper is derived from the concept of digital rock physics for drilling and completion applications. X-ray computed tomography (CT) scan image analysis has been utilized by many researchers to evaluate cement bonding (Opedal et al., 2014; van der Tuuk Opedal et al., 2014; De Andrade et al., 2016). Using a series of CT scan slices, we demonstrate that cement-to-formation bond strength is dependent on the permeability of a formation and the viscosity of cement.

Cement-to-formation cross sections can be characterized using X-ray CT (Wellington and Vinegar, 1987). We collected X-ray CT images using an NSI X5000 industrial CT scanner from North Star Imaging Inc. The helical scans were performed at 720 views per rotation with a 50 µm helical pitch and a reconstructed voxel size of 50 × 50 × 50 µm. The CT radiographs were reconstructed using iTomoKFBP software. The changes in effective atomic number and density are related to variations in attenuation coefficient (i.e., grayscale) in reconstructed CT scan slices. Therefore, the mineral matrix of the rocks may be separated from the resolved pores, and the porosity of the rocks can be estimated (Boone et al., 2014). However, the CT-estimated porosity can be inaccurate due to the influence of CT scanning resolution and changes in attenuation coefficients. As a result, it is critical to calibrate the CT-estimated porosity to the porosity determined by other techniques (Cnudde and Boone, 2013). In this study, the average CT-estimated porosity of the studied formations was calibrated to the porosity of the formations measured using a helium porosimeter.

The Herschel-Bulkley fluid is a generalized model of a non-Newtonian fluid, such as cement. Shear stress in the Herschel-Bulkley fluid is related to the fluid's shear rate (Nelson and Guillot, 2006). Based on cement viscosity, the Herschel-Bulkley model determines its resistance to flow. For a Newtonian fluid, Darcy's law links the flow rate in a porous media to pressure gradient, medium properties (porosity, permeability), and fluid viscosity. The flow of cement into a porous medium determines the cement-to-formation bond strength. The interface region is defined as the area near the contact surface between cement and the formation where cement seeps into the formation pores. The reduction in the resolved porosity in this region can be seen on CT scan slices. Thus, cement bond strength σ can be expressed in terms of the number of CT scan slices N where porosity changes


and N can be expressed in terms of permeability of the formation k and viscosity of cement µ:


We intend to demonstrate these two equations. The number of CT scan slices N in which porosity changes can also be expressed as depth of cement invasion in length units by multiplying N by the reconstructed voxel size. Two sandstone samples with different permeabilities were chosen in our study (Table 1). Standard and viscous cement formulations were prepared to study the effect of viscosity of cements.

In our investigation, Berea and Torrey sandstone formations were selected. We measured porosity with a Boyles' law helium porosimeter, permeability with flowing nitrogen, and grain density. The average values for each of these rock properties are presented in Table 1. The study utilized Class G cement (Murtaza et al., 2013; Reddy et al., 2016). Class G cement is a Portland cement with more than 95% utilization worldwide in oil well applications compared to other American Petroleum Institute class cements.

To regulate the roughness and angle of the contact surface, cylindrical sandstone samples (1 in diameter × 1 in height) are cored with a fixed cutting speed and the ends paralleled to 1 mm. One of the sandstone core surfaces was coated with oil-based mud for one of the cases. The cement was mixed with water in a 2:1 mass ratio according to the recommended standard procedure (API, 2005) and then cast in a cylindrical mold on top of the cut or coated samples. A fixed amount of free-water cement additive was used to increase the slurry viscosity in one of the test cases. The rheological properties of the standard and viscous cements were measured using a Fann model 35 viscometer to confirm the viscosity. The fitted profiles based on the Herschel-Bulkley fluid model (Nelson and Guillot, 2006), as shown in Figure 1, confirm that the apparent viscosity of cement slurry was increased from 36 centipoise in standard cement to 78 centipoise in viscous cement. The molds were cured for three days at 180°F and 3000 psi. The composite cement and formation specimens were trimmed to achieve a 2:1 height-to-diameter ratio and to center the composite specimen's interface (Figure 2). Special attention was paid to keep all of the cement curing and measurement conditions (temperature, pressure, time, and humidity) constant for consistency.

To confirm our findings, the specimens' shear bond strengths were also evaluated utilizing an experimental method that measures acoustic emission, acoustic velocity, and strain data under downhole reservoir conditions (Bathija and Martinez, 2020). The sample preparation technique of that method was based on the theory of rock strength, which was the key to accurately estimate the failure plane area. Cement was cast on top of the prepared sandstone sample under controlled temperature and pressure conditions in a curing chamber to make the composite specimen. Load was applied on the composite specimen using a triaxial testing system until the sandstone separated from the cement. The acoustic emission counts, acoustic velocity, and strain data help in accurately determining the failure load and thus the shear bond strength of the specimen.

The test cases presented are Berea sandstone with standard viscosity cement (Figures 3 and 7), Torrey sandstone with standard viscosity cement (Figures 4 and 8), and Berea sandstone with higher viscosity cement (Figures 5 and 9). Figures 36 depict representative binary CT scan slices spanning the cement-to-formation interface, with yellow representing solid material and purple representing fluid-filled space inside the specimen boundary. Estimating porosity is based on the quantity of fluid-filled space inside the specimen boundaries. The porosity increases from pure cement (Figures 3A, 4A, and 5A) to clean sandstone (Figures 3D, 4D, and 5D), as indicated by the selected CT scan slices A, B, C, and D across the interface. In CT scan slices B and C of Figures 3, 4, and 5, it can be seen that cement seeps into the pores of the sandstone and creates lower porosity than clean sandstone, resulting in good cement-to-formation bonding.

Figure 6 shows another Berea sandstone test case with standard viscosity cement to demonstrate the effect of contamination on bonding. The layer of oil-based mud at the contact surface prevents bonding between cement and sandstone. Higher porosity than clean sandstone at the interface region (Figure 6b) due to no bonding was observed.

The bond strength of the test cases is studied by the change in CT-estimated porosity for a sequence of CT scan slices (i.e., cross sections) traveling from the cement end of the specimen to the formation. Figures 79 show the porosity of each CT scan slice versus the CT scan slice location (in length units) from the cement end to the formation end of the specimen. The horizontal black dashed lines depict the average porosity of pure cement and clean formation. In comparison to the formation, cement on the left has a low porosity. The vertical double end arrow shows the difference in average porosity between the formation and cement. The beginning of the interface region (left tip of the horizontal double end arrow) can be determined at the CT scan slice, B, with a porosity greater than the average porosity of the cement, close to the center of the specimen, and is sequentially followed by CT scan slices whose porosities are higher than the average porosity of the cement. The end of the interface region (right tip of the horizontal double end arrow) may be established at the first CT scan slice that has a porosity greater than or equal to the average porosity of the formation. The total number of CT scan slices in the interface region (N) or the depth of cement invasion (multiply N by the voxel size) is an evaluation of the cement bond strength (equation 1). Figures 7b, 8b, and 9b are zoomed in on the x-axes of Figures 7a, 8a, and 9a, respectively, for better visibility of the depth of cement invasion. According to equation 2, N is proportional to the formation's permeability and inversely proportional to the cement's viscosity. Next, the validity of the two proposed equations is explained with our observations.

The increased permeability allows the cement to fill more connected pore space during bonding. As a result, the rock with greater permeability will have a thicker interface region. Adding cement into a porous rock increases the rock's strength by replacing part of the pore fluid. A well-connected pore system in the host rock allows cement to displace more pore fluid. Because a well-connected pore system corresponds to high permeability, it is expected that cement will bond better with permeable rocks. The Berea sandstone has a permeability of 785 mD. Torrey sandstone has a permeability of 2.74 mD (Table 1). Therefore, the cement-Berea specimen should have a higher cement bond strength. This phenomenon is observed by the depth of cement invasion being 1.35 mm for the cement-Berea specimen (Figure 7), which is higher than the 0.45 mm in the cement-Torrey specimen (Figure 8).

The viscous cement invades to a lesser extent than the standard cement in the Berea sandstone specimen with a depth of cement invasion of 0.25 mm as shown in Figure 9, compared to 1.35 mm with the standard cement (Figure 7). Increasing viscosity of cement reduces cement flow and pore filling in the porous media, which reduces the depth of cement invasion in the interface region and thereby decreases the cement bond strength.

The layer of oil-based mud at the contact surface prevents bonding between cement and sandstone in the last case. Note the porosity at pure cement (A) to clean sandstone (C), with B showing a middle CT scan slice with high porosity (Figure 10).

As shown in Table 2, the specimen's cement-to-formation shear bond strength was determined using an experimental approach that included acoustic emission, acoustic velocity, and strain measurements under downhole reservoir conditions (Bathija and Martinez, 2020). Each specimen type included measurements from three samples. The cement-Berea specimen has a higher shear bond strength than the cement-Torrey specimen. The viscous cement-Berea specimen has a weaker shear bond strength than the standard cement-Berea specimen. This agrees with the average depth of cement invasion (Table 2) trend in terms of permeability and viscosity. As a result, the proposed equations' validity is demonstrated by the CT scan image analysis. Here, shear bond strength measurements have been used to validate the observations from image analysis, but other types of bond strength measurements can be used for future studies. Also, the proposed equations establish the proportionalities and are used for making qualitative inferences. The proportionality constants to calculate the numerical values of cement bond strength are not reported due to small data set and large number of controlling factors. The main known controlling factors are physical (rock sample preparation techniques, cement curing and measurement conditions) and chemical (cement additives).

The quantitative analysis on a sequence of CT scan slices reveals that the porosity changes as cement invades the pores in sandstone. Cement flows into the connected pores of a sandstone and changes the cement-to-formation bond strength.

An array of CT scan slices can be used for cement-to-formation bond strength evaluation. Cement-to-formation bond strength increases as the permeability of a porous medium increases. Also, the cement-to-formation bond strength evaluated from CT scan slices decreases as the viscosity of cement increases. The key to consistent results is to keep physical (sample preparation and acquisition conditions) and chemical (cement additives) factors constant. The equations proposed for evaluating cement-to-formation bond strength are validated based on our CT scan image analysis data. Laboratory measurements from a different method for cement-to-formation shear bond strength evaluation confirm our CT scan image analysis observations. Thus, a method derived from digital rock physics has been applied successfully to studying cement-to-formation bond strength in the drilling and completion engineering domain.

The authors thank Qiushi Sun for acquiring X-ray CT data and Roland Martinez for sample preparation and acoustic measurements.

Data associated with this research are available and can be obtained by contacting the corresponding author.

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