Simulation of tight fluid flow with the consideration of capillarity and stress-change effect

www.nature.com/scientificreports OPEN Received: 31 December 2018 Accepted: 19 March 2019 Published: xx xx xxxx Simulation of tight fluid flow with the consideration of capillarity and stress-change effect Yuan Zhang1,2, Yuan Di3, Pengcheng Liu1,2 & Wanzhen Li1,2 The horizontal wells and multi-stage hydraulic fracturing technologies play a significantly important role in developing unconventional reservoirs. Due to the nanopore effects and stress deformation in tight formations, the fluid equilibrium and thermodynamics become more complex and the conventional reservoir simulation models cannot accurately handle these mechanisms. Hence, the objective of this work is to propose a comprehensive simulation model considering the effects of confined space and stress-dependent deformation. We first evaluated the phase envelope and fluid properties in the confined nanopores. Results show that bubble-point pressure and oil viscosity decrease, while formation volume factor and gas-oil ratio increase. The heavy components cause large deviation on the P-T phase envelope at the reservoir condition. Subsequently, a reservoir simulation model of the Bakken tight oil reservoir was built including the effect of stress-dependent deformation. The proposed phase behavior model was applied into the reservoir simulator to predict the hydrocarbon production from the Bakken tight oil reservoir. Finally, the role of the confined space and the stressdependent deformation on the production are examined in detail. This novel simulation approach can shed light on the better understanding of the key parameters affecting well production of in developing tight oil reservoirs in the future. Unconventional reservoirs, including tight oil, shale gas, and tight gas are key to meeting the increasing demand for hydrocarbon fuels in the world1,2. Tight oil reservoirs have recently become a hotspot for development in unconventional oil and gas resources3,4. As reported, the production of tight oil reservoirs will increase to more than double from the 2015 to the 2040 all over the world. Hydraulic fracturing has played a prominent role in the improvement of the oil and gas production5. Due to the characteristics of low permeability and low porosity, the combination of horizontal wells and multi-stage hydraulic fracturing has been applied to improve the contacted volume and flow capacity in developing tight oil reservoirs6–9. In spite of great achievement, the mechanisms such as confinement in nanopores and geomechanics are still not well understood10,11. Recent studies have shown that phase behavior and fluid transport exhibit deviation from the bulk fluid due to the nanopores in tight oil reservoirs. Sigmund et al. demonstrated that the effects of curvature cannot be neglected at high surface curvatures12. Brusilovsky investigated the phase behavior of binary mixture experimentally, concluding that the dew point pressure increases because of the surface curvature13. Nojabaei et al. also pointed out that the capillary pressure leads to the significant suppression on the bubble point pressure14. Similar conclusions were also reported in others literatures15–21. In Nojabaei et al.’s work, they then developed a compositionally-extended black-oil simulator to evaluate the capillarity effect on the well production14. However, pore characterization and geomechanics were not considered. Teklu et al. observed the minimum miscibility pressure (MMP) decreases in the confined space22. Luo et al. conducted experiments of phase behavior in nanopores and also pointed out that the bubble point pressure of confined fluid deviates from the bulk fluid23. Equation of state, such as Peng-Robinson (PR) and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was implemented to represent the fluid-phase equilibria in nanosized pores24–26. Dong et al. systemically analyzed the capillary pressure effect, adsorption and the critical shifts on the behavior of the confined fluid27. They found that bubble-point pressure is overestimated if neglecting the adsorption film. Haider and Aziz explored 1 School of Energy Resources, China University of Geosciences (Beijing), Xueyuan Rd. 29#, Haidian district, Beijing, 100083, China. 2Beijing Key Laboratory of Unconventional Natural Gas Geology Evaluation and Development Engineering, Xueyuan Rd. 29#, Haidian district, Beijing, 100083, China. 3College of Engineering, Peking University, Yiheyuan Rd. 5#, Haidian district, Beijing, 100871, China. Correspondence and requests for materials should be addressed to P.L. (email: ) Scientific Reports | (2019) 9:5324 | https://doi.org/10.1038/s41598-019-41861-3 1 www.nature.com/scientificreports www.nature.com/scientificreports/ the key parameters of nano-porous media in shale reservoirs28. Their findings showed that the fluid properties and well production are both influenced in the confined space. Cui et al. modified the Peng-Robinson equation of state considering the reduced mole number of fluids caused by adsorption29. Zuo et al. first applied SRK-EOS for the phase behavior calculations in the confined phase and investigated the impact of capillary pressure and nanopore confinement on the phase behaviors of shale gas and oil30. These methods are mainly based on the pressure-temperature flash calculation, which uses the pressure, temperature, and fluid composition as the primal state variables (NVT-flash)31–35. An algorithm for calculating phase equilibrium at specified moles, volume, and temperature was proposed in recent years; additionally, Kou and Sun incorporated the capillarity into the NVT-flash. This method can be used to predict the phase properties of pure substance and mixture systems36. The impacts of the physical mechanisms on the well performance have received more attention. Du and Chu17 used a commercial reservoir simulator to investigate the influences of PVT variations on well performance. However, they only considered the single pore size and assumed the matrix permeability as a fixed value. Considering the change of porosity and permeability with effective stress, Wang et al. concluded that the well performance was affected due to the capillary pressure in the nanopores37. Nojabaei et al. took the pore size distribution into account and incorporated the capillarity effect in their simulation model, but the variation of permeability and stress sensitivity were not included38. Sanaei et al. developed a correlation between pore size and permeability based on mercury injection capillary pressure (MICP) tests on Eagle Ford core plugs, but there are still some limits on the field-scale application39. Rezaveisi et al. implemented the capillarity equilibrium in an in-house simulator and observed obvious difference on the production40. However, stress sensitivity was not considered in their model. Yan et al. developed a fully compositional model considering the effect of nanopores, in their approach, capillary pressure is c (...truncated)