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CO2 minimum miscibility pressure (MMP) calculator based on machine-learning-based model

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At constant temperature and composition, MMP is the lowest pressure at which multiple-contact miscibility (dynamic miscibility) can be achieved. In a multiple-contact miscibility (MCM) gas and oil mix in repeated contacts that are either forward (Fig. 1a, equilibrium gas at a given location or cell moves forward to contact. fresh oil), backward (Fig. 1b, vapor with the injection composition contacts the equilibrium liquid phase left behind when equilibrium gas moves forward), or a combination of both (Fig. 1c). [1] [2] Miscibility in MCM floods is developed when the phase compositions that form in each contact move toward a critical point. That is, MCM is an achieved state at MMP that requires multiple contacts between an oil and the injected gas. There are an infinite number of critical points, but given an injection-gas composition, reservoir-oil composition, and reservoir temperature, there is a specific critical point that is reached.

Fig. 1: Relative location of the critical point achieved by displacement of reservoir oil by injection gas, where L5 liquid phase, G5 gas/vapor phase (Johns and Dindoruk 2013).

Purpose

The use of Minimum Miscibility Pressure (MMP) is broad in the E&P business, from getting more oil from the subsurface to getting rid of CO2 more efficiently using hydrocarbon reservoirs. It is one of the key design parameters for broader gas injection processes and as well as CCS projects. This physical parameter is a measure of local displacement efficiency, while subject to some constraints due to its definition. It is also used to tune compositional models, coupled with proper fluid description constrained with other available basic phase behavior data, such as bubble point pressure and other volumetric properties.

MMP determination methods

The best method for MMP determination is slim-tube experiments which is most coherent with definition of multi-contact miscibility, followed by calculated MMPs with the Analytical Methods [3] [4] [5] or Physics-Based Correlations [6] [7] [8] (Alston et al. 1985) or Mixing Cell Method [9] [10] [11] [12] [13] or Compositional Simulations. Ideally, these methods should agree before doing compositional simulation. The advantage of the calculated MMPs is that they reduce the cycle time as well as the cost as compared to the Slimtube experiments[14].


In Sinha et al. 2021[15] a physics augmented machine learning model was developed to predict MMP during CO2 injection. They developed an analytical physics based MMP correlation which they combined with a machine learning model to form a hybrid model aka Super-Learner (or Stacked Ensemble Model) to predict the CO2 MMP. Further, they applied minute correction on their MMP predicted by the Super-Learner model to obtain the final value of the predicted MMP (MMP corrected).

The model required easy to obtain inputs such as fluid composition, plus fraction molecular weight and reservoir temperature. It captures an extremely wide range of CO2 MMP (MMP as high as 4900 psia and as low as) with extremely high predictive accuracy (Average Absolute Relative Error = 4.18%).

This workflow is summarized and packed into an interactive and extremely simple to use yet powerful tool called UH MMP Calculator, with free public access.

Figure 2- Cross plot of MMP Corrected (predicted using Sinha et al. 2021 model) vs the experimental MMP.
Figure 3 – Statistical performance of the Sinha et al. 2021 model.

References

  1. ↑ Zick, A. A. (1986). A Combined Condensing/Vaporizing Mechanism in the Displacement of Oil by Enriched Gas. Paper presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 5–8 October. SPE-15493-MS. https://doi.org/10.2118/15493-MS
  2. ↑ Johns, R. T. and Dindoruk, B. (2013). Gas Flooding. In Enhanced Oil Recovery: Field Case Studies, ed. J. J. Sheng, Chap. 1. Waltham, Massachusetts,USA: Gulf Professional Publishing.[1]
  3. ↑ Jessen, K., Michelsen, M. L., & Stenby, E. H. (1998). Global approach for calculation of minimum miscibility pressure. Fluid Phase Equilibria, 153(2), 251-263. https://doi.org/10.1016/S0378-3812(98)00414-2
  4. ↑ Orr, F. M., Johns, R. T., & Dindoruk, B. (1993). Development of miscibility in four-component CO2 floods. SPE reservoir engineering, 8(02), 135-142. https://doi.org/10.2118/22637-PA
  5. ↑ Wang, Y., & Orr Jr, F. M. (1997). Analytical calculation of minimum miscibility pressure. Fluid phase equilibria, 139(1-2), 101-124.https://doi.org/10.1016/S0378-3812(97)00179-9
  6. ↑ Cronquist, C. (1978, August). Carbon dioxide dynamic miscibility with light reservoir oils. In Proc. Fourth Annual US DOE Symposium, Tulsa (Vol. 1, pp. 28-30).
  7. ↑ Yuan, H., Johns, R. T., Egwuenu, A. M., & Dindoruk, B. (2005). Improved MMP correlation for CO2 floods using analytical theory. SPE Reservoir Evaluation & Engineering, 8(05), 418-425. SPE-89359-MS.https://doi.org/10.2118/89359-MS
  8. ↑ Emera, M. K., & Sarma, H. K. (2005). Use of genetic algorithm to estimate CO2–oil minimum miscibility pressure—a key parameter in design of CO2 miscible flood. Journal of petroleum science and engineering, 46(1-2), 37-52.
  9. ↑ Jaubert, J. N., Arras, L., Neau, E., & Avaullee, L. (1998a). Properly defining the classical vaporizing and condensing mechanisms when a gas is injected into a crude oil. Industrial & engineering chemistry research, 37(12), 4860-4869. https://pubs.acs.org/doi/10.1021/ie9803016
  10. ↑ Jaubert, J. N., Wolff, L., Neau, E., & Avaullee, L. (1998b). A very simple multiple mixing cell calculation to compute the minimum miscibility pressure whatever the displacement mechanism. Industrial & engineering chemistry research, 37(12), 4854-4859.
  11. ↑ Zhao, G. B., Adidharma, H., Towler, B., & Radosz, M. (2006). Using a multiple-mixing-cell model to study minimum miscibility pressure controlled by thermodynamic equilibrium tie lines. Industrial & engineering chemistry research, 45(23), 7913-7923. https://doi.org/10.1021/ie0606237
  12. ↑ Zhao, G., Adidharma, H., Towler, B. F., & Radosz, M. (2006a, September). Minimum miscibility pressure prediction using statistical associating fluid theory: Two-and three-phase systems. In SPE Annual Technical Conference and Exhibition. SPE-102501-MS. https://doi.org/10.2118/102501-MS
  13. ↑ Ahmadi, K., & Johns, R. T. (2011). Multiple-mixing-cell method for MMP calculations. SPE journal, 16(04), 733-742. SPE-116823-PA. https://doi.org/10.2118/116823-MS
  14. ↑ Dindoruk, B., Johns, R., & Orr, F. M. (2021). Measurement and Modeling of Minimum Miscibility Pressure: A State-of-the-Art Review. SPE Reservoir Evaluation & Engineering, 24(02), 367-389. SPE-200462-PA.
  15. ↑ Sinha, U., Dindoruk, B., & Soliman, M. (2021). Prediction of CO2 Minimum Miscibility Pressure Using an Augmented Machine-Learning-Based Model. SPE Journal, 1-13. SPE-200326-PA. https://doi.org/10.2118/200326-PA
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