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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, 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 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.
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.
Fig. 2-Hydrodynamic and static forces on a sand grain. Same as in Fig. 3 in Production rate increase mechanisms in cold heavy-oil production with sand (CHOPS) wells
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.
Apparently, no easy way of determining the permeability exists because of the nonhomogeneity of the region surrounding the well. Some work 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.
The physics of foamy oil have been examined in detail. 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).
- 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.
The flow mechanics of slurries remains a complex, unresolved issue for high-concentration slurries in which internal energy dissipation through collisions can take place.
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* show that errors in flow rate predictions are as high as 50% during early transient testing.
Fig. 5-Tangential and radial stresses around a slurry-filled cavity. Same as in Fig. 9 in Physical mechanisms effects in cold heavy-oil production with sand (CHOPS) wells
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.). 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. These models originated in early attempts to understand stress, dilation, and yield around circular openings. 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 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. 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. These methods promise to generate insight into effects such as capillarity changes 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.
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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
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