Challenges in mathematical modeling of dynamic mass transfer controlled by capillary and viscous forces in spontaneous fluid imbibition processes

Summary: Post-fracturing fluid soaking is believed to significantly affect productivity of hydraulic-fractured horizontal wells in the oil and gas industry. It is highly desirable to know the optimal soaking time period to maximize well productivity. An analytical model was developed in this research to describe the dynamic spontaneous imbibition process in shale cracks owing to fluid soaking. The model was integrated with pressure falloff data to develop a mathematical approach for forecasting the optimal soaking time, which is defined as the time it takes for the fluid to reach the midpoint between two adjacent hydraulic fractures. The optimal soaking time depends on crack and fluid properties, including crack width, fluid contact angle, and interfacial tension (IFT). A case study from the data of Tuscaloosa Marine Shale (TMS) suggests that the optimal soaking time is 2–4 weeks if the fracturing spacing is 4–6 m. This work provides petroleum engineers with a quick-and-easy method for predicting the optimal soaking time to maximize their well productivity.

Cement cracks are one of the most common failures in oil and gas wells. Cracks can reduce cement strength, resulting in a loss of zonal isolation and fluid leak. Placement of gels of nanoparticles (NPs) in the cracks is considered as a promising solution to solve the problem. It is highly desirable to know if the flow behavior of the NPs solutions is predictable when they are squeezed into the cracks. Experimental tests were performed in this study to investigate the flow behavior of nano-silica solutions in ducts of cross-sections of rectangular shape. The linear relationship between flow rate and pressure gradient and the calculated Reynolds number values suggests laminar flow in the ducts. However, the Hagen–Poiseuille correlation for laminar flow does not describe the flow behavior of the nano-silica solution. The classic hydraulic model with hydraulic diameter describes the nano-silica flow behavior with an average error of 12.38%. The cause of discrepancies between the flow models and the measured data is not known. It can be attributed to the NPs–NPs frictions and NPs–wall frictions in the rough ducts that were not considered in the flow models.

The Eclipse simulation model is used in this work to forecast the likelihood of asphaltene deposition near oil wellbore during the waterflooding recovery procedure. Using the default option of the molar weight of asphaltene dissolved in the oil as a function of supplied factors, a data file was made up using Eclipse 300 for the conventional asphaltene option. To ensure precise data collection for the modeling, the simulation was run from January 1st, 2011, to June 6th, 2027. At the end of the simulation work, it was discovered that the asphaltene deposition fraction increased dramatically from 0.0001 to 0.0006, changing the block pressure from 2500 psia to over 4500 psia. The pressure and asphaltene deposition fraction were constant at 4000 psia and 0.0006, respectively, from the third to the eighth year. By the end of the eighth year, the block pressure had significantly decreased from 4000 psia to 2500 psia, causing the asphaltene deposition fraction to rise from 0.0006 to 0.0016. This demonstrates that the thermodynamic changes in temperature and pressure affect the deposition of asphaltene and cause it to obstruct the porous medium in the reservoir. Based on the results, it can be concluded that asphaltene deposition rises as reservoir temperatures change from low to high at lowered pressure, indicating a thermodynamic imbalance. The results of this study can be utilized as a reference for the oil and gas sectors to comprehend the factors that must be considered to prevent asphaltene deposition during recovery operations.

Summary: A cement crack is a typical cause of oil and gas well failure. Cracks weaken cement, reducing zonal isolation and fluid leakage. Nanoparticle (NP) gels are being tested for fracture treatment. When crushed into cracks, the flow behavior of NP problem solutions should be predicted. The potential efficacy of utilizing NP gels as a remedial measure for fractures is currently under investigation. It would be advantageous to determine if the flow behavior of solutions for NP problems can be anticipated when they are compressed into crevices. This study aimed to analyze the behavior of nano-silica solutions as they flow through ducts with rectangular cross-sections and varying crack dimensions. The introduction of NP solutions into the core leads to a decrease in pressure, which suggests that the nano-silica has been effectively transported through the crack. As the size of the fracture decreases, there is a corresponding increase in pressure drops, while the flow rate experiences a concurrent increase. This study presents responses of a pressure gradient to fluid concentration for a range of fracture widths, heights, and flow rates. The prediction of laminar flow in ducts is based on the linear correlation between the flow rate and the pressure gradient. Furthermore, the reduced pressure gradient indicates enhanced fluid flow within the fracture because of the amplified slot width. The fluid flow model proposed by Guo et al. (2022) was utilized to conduct a comparative analysis with the experimental data. Compared with test data, the model differs by roughly 90%. The technical cause of the flow model-observed data discrepancies is unknown. The flow model did not account for friction between NPs-NPs and NPs-walls in rough ducts. An empirical correlation has been found that quantifies the ratio as a function of nonsilica solution flow rate, cross-sectional geometry parameters, and nano-silica concentration. The correlation was calculated using nonlinear regression. The empirical relation and actual ratio have a significant correlation, as shown by R2 = 0.8965. In practice, Guo et al.’s (2022) hydraulic model’s pressure drops should be multiplied by the empirical correlation’s ratio to reduce errors.

Wellbore friction is one of the biggest concerns when drilling due to its relation to the total cost. The catenary concept was introduced to reduce wellbore friction, but it requires detailed analyses. This project would fill this gap. A catenary shape is simply the natural shape of a rope, chain, or drill string. The drill string will then hang freely inside the wellbore. Perfectly, there should be no contact between the hole and the string, and thus no friction. Torque and drag should be minimized this way. A case study is introduced to examine the outcome between Catenary Trajectory Design and traditional 2D Arc design. The calculation procedure of Catenary Trajectory and 2D Arc Design can be found in an MS Excel spreadsheet which is easy to use and reliable for designing catenary well trajectories for extended-reach wells.