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CHOPS simulation

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Numerical simulation of cold heavy oil production with sand (CHOPS) is particularly challenging because of several unusual factors:

  • There is a solid-to-liquid phase transition (liquefaction) of the matrix.
  • Stresses and stress changes play a major role in sand destabilization and liquefaction.
  • Conventional assumptions of phase equilibrium (i.e., compositional simulation) are not justified.
  • Much of the process is dominated by slurry flow in situ, rather than diffusional flow.
  • Geometrical boundary conditions (altered zone size) change continuously.
  • A significantly greater number of physical parameters must be specified than in conventional simulation.
  • Reservoir parameters change continuously over time and space.
  • There are sampling and testing difficulties for unconsodlidated sandstones (UCSS).
  • The processes involved (phase transition, slurry behavior, etc.) are all strongly nonlinear.

Nevertheless, a decade of efforts has achieved substantial progress toward the correct physical simulation of CHOPS. Adequate simulation models are now available,[1] and progress continues. This section discusses the major physical processes in an attempt to identify first-order controls on CHOPS.

Nonconventional processes in CHOPS

Sand liquefaction

Sand liquefaction accompanies all CHOPS processes. In this solid-to-fluid phase transition, porosity plays the same role as temperature in the melting of a solid. In fact, porosity should be treated as a thermodynamic state variable in a manner similar to temperature. As in a melting alloy, there is no specific "melting porosity" that defines liquefaction; the process is more complicated.

The reservoir porosity is approximately 30%. The outflow at the wellhead contains approximately 1 to 10% sand and substantial quantities of free gas and, therefore, has a porosity greater than 90%. The system must pass through all intermediate porosities, and the liquefied state is defined as the condition at which grains do not form a continuously linked array (i.e., liquefaction implies that σ = 0, σ = p, and no shear stresses can be sustained).

Fig. 1 attempts to show how the dominant physical processes change with porosity. To achieve the liquefaction porosity of approximately 50%, the sand fabric must dilate. After liquefaction, dense slurry exists where substantial internal energy dissipates through collisions and sliding between grains. With time, dilute slurry is generated; then, grain collision energy dissipation is negligible compared with the viscous energy dissipation in the fluid phase. Even neglecting the complication of a dispersed bubble phase, one phase transition and three separate regimes exist in the porosity domain encountered in CHOPS.

  • Fig. 1-Porosity and processes in CHOPS production.

    Fig. 1-Porosity and processes in CHOPS production.

Dense sands cannot spontaneously liquefy. Under stress, the grains are held in a dense 3D array with high contact forces (normal and shear forces) that cannot be overcome by seepage forces (Fig. 2). This fabric must be perturbed and dilated, and stresses must drop to allow liquefaction, reinforcing the first-order importance of geomechanics processes.

Permeability-enhanced zone

Permeability cannot be defined near the wellbore in liquefied sand. In the approximately 45% porosity zone, it exceeds 10 to 15 darcy for a 100 to 150 μm sand; in intact sand, a typical permeability is 1 to 3 darcy. Perhaps of equal importance, as sand dilates, pore blockages (clays, asphaltenes, gas bubbles) have much less effect on permeability.

If a compact growth zone exists, an average permeability can be linked to porosity (k ∝ φn, where n is an empirically determined exponent). Choosing such a function implies that the mathematical simulation gives a reasonable estimate of porosity and that the porosity is homogeneous (not channeled) at the scale of modeling. These assumptions remain unsubstantiated. Alternatively, some simple function of radius may be used. Fig. 3 shows permeability as a function of radius. If the k-enhanced zone is highly irregular, defining a "block-averaged" permeability at an instant is not only difficult; the values also change with time.

  • Fig. 3-Permeability as a function of radius: two models.

    Fig. 3-Permeability as a function of radius: two models.

Apparently, no easy way of determining the permeability exists because of the nonhomogeneity of the region surrounding the well. Some work[2] shows that a simple model can capture most of the permeability-enhancement effects. Sensitivity analyses clearly show that although a model with a continuous change in permeability [ k = f(r)]

gives time-derivative plots that are different from a skin model (zero thickness impedance zone), results can be approximated by multizone composite models. However, each additional zone in a composite model has two additional unknowns, making the analysis (or data inversion) more complex. For example, two cylindrical zones around a well give eight total unknowns: three compressibilities, three permeabilities, and two radii. Fig. 4 shows composite annular models of permeability distribution.

  • Fig. 4-Composite annular models of permeability distribution.

    Fig. 4-Composite annular models of permeability distribution.

Foamy-oil behavior

The physics of foamy oil have been examined in detail.[3][4][5] Many scientific and technical issues now being studied will gradually affect mathematical simulation of foamy-oil behavior in situ. These issues include the following.

  • Obtaining kinetic exsolution rate data for CH4 from cold heavy oils (a challenging task).[6][7]
  • Verification or rejection of the hypothesis that a continuous gas phase does not develop in CHOPS or providing another explanation for the constant gas/oil ratio (GOR) values.
  • Understanding if the bubble-induction zone is linked physically to the zone of dilation (i.e., bubbles are created only when sufficient new local volume is created by the dilation process).
  • Quantifying the effect of bubbles on relative-permeability values.
  • Confirmation of the nature of the physical processes around CHOPS wells in situ.

Slurry flow

The flow mechanics of slurries remains a complex, unresolved issue for high-concentration slurries in which internal energy dissipation through collisions can take place.[8]

Conventional approaches to simulation

Conventional flow simulation without stress coupling attempts to account for the effects of effective stress change, Δσ′ , through the prediction of volume changes, ΔV, with compressibility, Cm, as ΔV = V•Cm •Δσ′. To use this equation, a further assumption is made: Δσ′ = −Δp, where the change in pressure is calculated as part of the mathematical simulation. This is a flawed assumption because a change in pressure does not lead to the identical and opposite change in effective stress. The relationship is more complex and must be calculated in a rigorous manner with phase compressibilities. Also, in conventional flow analysis (e.g., the basic equations of Theis, Muskat, and Gringarten), an implicit assumption is that boundary stresses remain constant: Δσ terms do not even arise in the formula. Consider what happens near a vertical well. With production, the pressure near the wellbore drops; therefore, σ′ increases and a small volume change must occur. The rock near the wellbore shrinks slightly, but the overburden rocks have rigidity, so the vertical total stresses are redistributed (Fig. 5). The total stresses are not constant; therefore, the Δσ′ = −Δp assumption is invalidated. Analyses of this effect[9]* show that errors in flow rate predictions are as high as 50% during early transient testing.

Other assumptions for conventional simulation also should be revisited. For example, the assumption of local equilibrium (compositional model) is probably insufficient for heavy oils because of the slow diffusion rates; hence, a kinetic model is needed.

History matches of the behavior of laboratory sand packs have been carried out with conventional simulators but with a number of uncontrolled or ill-constrained parameter modifications (solubilities, gas contents, bubblepoints, relative permeabilities, compressibilities, etc.).[10][11][12][13] It is uncertain whether these parameters and laboratory processes have a direct and useful relationship with in-situ mechanisms and the large-scale system alterations that take place. Is it valid to history match CHOPS in specific cases if several first-order physical processes such as stress change, sand dilation and liquefaction, and slurry flow are absent from the model? Furthermore, is it valid to use this "calibrated" model to predict the future behavior of the well or other wells in the field? The answer is not clear, but the direction of simulation is clearly away from calibrated conventional simulation to more rigorous coupled geomechanics simulation.


* Rothenburg, L., Bratli, R.K., and Dusseault, M.B.: “A Poro-Elastic Solution for Transient Fluid Flow Into a Well,” available from Dusseault on request (1996).

Stress-flow coupling and physics-based modeling

Attempts to develop analytical and semianalytical solutions to CHOPS well production are hampered by the massive nonlinearities and the complexity of the processes. Nevertheless, some progress has been achieved for compact growth and channel models.[14][15][16][17][18][19] These models originated in early attempts to understand stress, dilation, and yield around circular openings.[20][21][22] The sand-flux models are all based on introducing aspects of stress, shear-induced dilation, and concomitant permeability increases with necessary simplifications such as 2D-axisymmetric geometry, ideal elastoplasticity, local homogeneity, limited provision for slurry flow energy dissipation, and so on. In the simplest case, stress changes and flow behavior are expressed in vertically axisymmetric equations so that overburden stress redistribution is not incorporated explicitly. In this case, flux equations reduce to quasi-1D forms.

The Geilikman family of models[14][15][16][17][18][19] links the drawdown rate of wells to the magnitude of sand flux. His model "predictions" of an initially high then declining sand flux, combined with a slowly increasing then slowly declining oil flux, correspond qualitatively with observed field behavior. However, no semianalytical model can simulate the initiation of sand liquefaction and make an a priori prediction of sand flux and oil rate increases based solely on a set of initial conditions, material parameters, and constitutive laws. Currently, all models must be calibrated repeatedly to sand production history to develop realistic predictions.

Simulator development in the 1990s has been based on a coupled stress-flow formula solved with the finite-element method.[23][24][25][26] These methods are far too complex to discuss here, but most aspects of the CHOPS process, with the exception of the slurry-flow component, are being incorporated into modeling on a relatively sound physical basis.

Finally, issues such as arching, fabric evolution, and slurry flow in discrete granular systems can be studied with the discrete-element method in which individual particles are allowed to interact and fluid-flow forces can be included.[27] These methods promise to generate insight into effects such as capillarity changes[28] and the destabilizing of sand arches, an extremely difficult problem that is not amenable to continuum mechanics approaches. However, these are physics-based models. They are not design models that use volume-averaged properties, and they are not likely to be used in reservoir simulation.

References

  1. ↑ Wang, Y., Chen, C.C., and Dusseault, M.B. 2001. An Integrated Reservoir Model for Sand Production and Foamy Oil Flow During Cold Heavy Oil Production. Presented at the SPE International Thermal Operations and Heavy Oil Symposium, Porlamar, Margarita Island, Venezuela, 12-14 March 2001. SPE-69714-MS. http://dx.doi.org/10.2118/69714-MS.
  2. ↑ Zhang, L. and Dusseault, M.B. 1997. Formation Alteration Characterization from Well Test Interpretation. Proc., IACMAG 9th Intl. Conference Comp. Methods and Advances in Geomechanics, Wuhan, China, 2299–2306.
  3. ↑ Geilikman, M.B. and Dusseault, M.B. 1999. Sand Production Caused by Foamy Oil Flow. Transport in Porous Media 35: 259.
  4. ↑ Lillico, D.A. et al. 2001. Gas Bubble Nucleation Kinetics in a Live Heavy Oil. Colloids and Surfaces, A: Physicochemical and Engineering Aspects 192 (1–3): 25.
  5. ↑ Sheng, J., Maini, B.B., Hayes, R. et al. 1999. A Non-Equilibrium Model to Calculate Foamy Oil Properties. J Can Pet Technol 38 (4): 38. http://dx.doi.org/10.2118/99-04-04.
  6. ↑ Kumar, R. and Pooladi-Darvish, M. 2001. Effect of Viscosity and Diffusion Coefficient on the Kinetics of Bubble Growth in Solution-Gas Drive in Heavy Oil. J Can Pet Technol 40 (3): 30–37. http://dx.doi.org/10.2118/01-03-02.
  7. ↑ Greaves, M., Maini, B.B., and A.Chakma, A. 2001. Effects of Temperature on Foamy Oil Flowin Solution Gas-Drive in Cold Lake Field. J Can Pet Technol 40 (3). PETSOC-01-03-04. http://dx.doi.org/10.2118/01-03-04.
  8. ↑ Frankel, N.A. and Acrivos, A. 1967. On the viscosity of a concentrated suspension of solid spheres. Chem. Eng. Sci. 22 (6): 847-853. http://dx.doi.org/10.1016/0009-2509(67)80149-0.
  9. ↑ Charlez, P.A. 1997. Rock Mechanics. Petroleum Applications, first edition. Editions Technip.
  10. ↑ Kraus, W.P., McCaffrey, W.J., and Boyd, G.W. 1993. Pseudo-Bubble Point Model For Foamy Oils. Presented at the Annual Technical Meeting, Calgary, Alberta, May 9 - 12, 1993 1993. PETSOC-93-45. http://dx.doi.org/10.2118/93-45.
  11. ↑ Kumar, R. and Pooladi-Darvish, M. 2000. Solution-Gas Drive in Heavy Oil: Field Prediction and Sensitivity Studies with Low Gas Phase Relative Permeability. Presented at the Canadian International Petroleum Conference, Calgary, Alberta, Jun 4 - 8, 2000 2000. PETSOC-2000-063. http://dx.doi.org/10.2118/2000-063.
  12. ↑ Kumar, R. and Pooladi-Darvish, M. 2001. Solution-Gas Drive in Heavy Oil: Viscosity Effect on Gas Relative Permeability. Proc., CIM Petroleum Society 52nd Annual Technical Meeting, Calgary, paper 2001-152.
  13. ↑ Denbina, E.S., Baker, R.O., Gegunde, G.G. et al. 2001. Modelling Cold Production for Heavy Oil Reservoirs. J Can Pet Technol 40 (3). PETSOC-01-03-01. http://dx.doi.org/10.2118/01-03-01.
  14. ↑ 14.0 14.1 Geilikman, M.B., Dusseault, M.B., and Dullien, F.A. 1994. Sand Production as a Viscoplastic Granular Flow. Presented at the SPE Formation Damage Control Symposium, Lafayette, Louisiana, 7-10 February 1994. SPE-27343-MS. http://dx.doi.org/10.2118/27343-MS.
  15. ↑ 15.0 15.1 Geilikman, M., Dusseault, M.B., and Dullien, F.A. 1994. Sand Production And Yield Propagation Around Wellbores. Presented at the Annual Technical Meeting, Calgary, Alberta, Jun 12 - 15, 1994 1994. PETSOC-94-89. http://dx.doi.org/10.2118/94-89.
  16. ↑ 16.0 16.1 Geilikman, M.B., Dusseault, M.B., and Dullien, F.A.L. 1994. Fluid-saturated solid flow with propagation of a yielding front. Presented at the Rock Mechanics in Petroleum Engineering, Delft, Netherlands, 29-31 August 1994. SPE-28067-MS. http://dx.doi.org/10.2118/28067-MS.
  17. ↑ 17.0 17.1 Geilikman, M.B., Dusseault, M.B., and Dullien, F.A.L. 1995. Dynamic Effects of Foamy Fluid Flow in Sand Production Instability. Presented at the SPE International Heavy Oil Symposium, Calgary, Alberta, Canada, 19-21 June 1995. SPE-30251-MS. http://dx.doi.org/10.2118/30251-MS.
  18. ↑ 18.0 18.1 Geilikman, M.B. and Dusseault, M.B. 1997. Fluid-Rate Enhancement from Massive Sand Production in Heavy Oil Reservoirs. J. of Petroleum Science & Engineering 17: 5.
  19. ↑ 19.0 19.1 Geilikman, M.B. and Dusseault, M.B. 1997. Dynamics of Wormholes and Enhancement of Fluid Production. Proc., CIM Petroleum Society 48th Annual Technical Meeting, Calgary, paper 97-09.
  20. ↑ Risnes, R., Bratli, R.K., and Horsrud, P. 1982. Sand Stresses Around a Wellbore. SPE J. 22 (6): 883–898. SPE-9650-PA. http://dx.doi.org/10.2118/9650-PA.
  21. ↑ Wang, Y. and Dusseault, M.B. 1991. Borehole Yield and Hydraulic Fracture Initiation in Poorly Consolidated Rock Strata—Part I: Impermeable Media and Part II: Permeable Media. Intl. J. Rock Mechanics, Mining Science & Geomechanical Abstracts 28 (2): 235.
  22. ↑ Wang, Y. 1996. The Effect of Nonlinear Mohr-Coulomb Criterion on Stresses and Plastic Deformation Near a Circular Opening in Poorly Consolidated Permeable Media. Intl. J. Rock Mechanics, Mining Science & Geomechanical Abstracts 33 (2): 495.
  23. ↑ Wang, Y. and Lu, B. 2001. A Coupled Reservoir-Geomechanics Model and Applications to Wellbore Stability and Sand Prediction. Presented at the SPE International Thermal Operations and Heavy Oil Symposium, Porlamar, Margarita Island, Venezuela, 12-14 March 2001. SPE-69718-MS. http://dx.doi.org/10.2118/69718-MS.
  24. ↑ Yi, X. 2001. Simulation of Sand Production in Heavy Oil Reservoir. Proc., CIM Petroleum Society 52nd Annual Technical Meeting, Calgary, paper 2001-51.
  25. ↑ Papamichos, E. et al. 2001. Volumetric Sand Production Model and Experiment. Intl. J. Numerical and Analytical Methods in Geomechanics 25 (8): 789.
  26. ↑ Wan, R.G. and Wang, J. 2001. Analysis of Sand Production in Unconsolidated Oil Sand Using a Coupled Erosional-Stress-Deformation Model. Proc., CIM Petroleum Society 52nd Annual Technical Meeting, Calgary, paper 2001-049.
  27. ↑ Thallak, S., Rothenburg, L., and Dusseault, M.B. 1991. Hydraulic Fracture Simulation in Granular Assemblies Using the Discrete Element Method. Alberta Oil Sands Technology and Research Authority 7 (2): 141.
  28. ↑ Han, G. and Dusseault, M.B. 2002. A Quantitative Analysis of Mechanisms for Water-Related Sand Production. Presented at the International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, 20–21 February. SPE-73737-MS. http://dx.doi.org/10.2118/73737-MS.

Noteworthy papers in OnePetro

Jayaraman, B., Zhang, D., Vanderheyden, W. B., & Ma, X. 2013. Multiscale Simulation of CHOPS Wormhole Networks. Society of Petroleum Engineers. http://dx.doi.org/10.2118/163603-MS

Tremblay, B. 2009. Cold Flow: A Multi-Well Cold Production (CHOPS) Model. Petroleum Society of Canada. http://dx.doi.org/10.2118/09-02-22

Rangriz Shokri, A., & Babadagli, T. 2012. Evaluation of Thermal/Solvent Applications With And Without Cold Heavy Oil Production with Sand (CHOPS). Society of Petroleum Engineers. http://dx.doi.org/10.2118/158934-MS

Ma, X., Vanderheyden, W. B., & Zhang, D. 2013. Closure Modeling Of Sub-grid-scale Effects For Well-drainage-scale Prediction Of CHOPS. Society of Petroleum Engineers. http://dx.doi.org/10.2118/165536-MS

Arnold, W. A., Graham, R., & Wagg, B. 2012. Enhanced CHOPS Using SuperSump To Reduce Environmental Footprint and Increase Oil Recovery. Society of Petroleum Engineers. http://dx.doi.org/10.2118/157940-MS

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Cold heavy oil production with sand

CHOPS reservoir assessment and candidate screening

CHOPS physical mechanisms

CHOPS production rate increase mechanisms

PEH:Cold_Heavy-Oil_Production_With_Sand

Page champions

Cenk Temizel, Reservoir Engineer

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