CHOPS physical mechanisms

In cold heavy oil production with sand (CHOPS) production, the two limiting physical mechanisms for sand are compact growth of the remolded zone as a cylindrical (or spherical or ellipsoidal) body or extension of an anastomosing piping channel system comprising a network of tubes (“wormholes”). These lead to different geometries in situ, although the impact on well productivity may not be quantifiable through measurements.

Uniform remolded zone growth concepts

Fig. 1 shows a compact zone growth hypothesis for CHOPS. In compact growth, the ratio of the area of the fully yielded zone to the volume enclosed approaches a minimum because a cylindrical or elliptical shape is spatially more compact than a channel network. Discrete zonal boundaries do not really exist: a gradual phase-transition zone develops, although it may be treated mathematically as a thin front, just as in a melting alloy. The complex and diffuse boundary shape is approximated by a geometrically regular shape and a distinct liquefaction front. A circular 2D assumption is simplest for analysis because the radius of the zone and, hence, the pressure gradient can be scaled directly to sand-production volume with no additional assumptions. Also, overburden stress, σ_v, plays a dominant role in the destabilizing and dilation process, and a 2D model cannot capture this process in a rigorous manner.

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  Fig. 1-Compact zone growth hypothesis for CHOPS

There are arguments that support a compact growth hypothesis. The yielded zones can support little overburden stress; therefore, σ_v must be redistributed outward from the wellbore region (see Stress changes during CHOPS). However, the overburden has elasticity and cannot strain into a sharply bent shape or complex curve. It behaves like a thick, stiff beam to smooth and homogenize deformations. Outward extensions of the disturbed zone will shed σ_v as they yield, whereas stiffer, inward-protruding intact zones will attract σ_v. Fig. 2 illustrates how stress concentrations tend to lead to a compact zone. A high stress concentration cannot be sustained by an unconsolidated sandstone (UCSS). Shear, dilation, and softening will occur and σ_v will be cast outward. The overburden stiffness causes σ_v to be smoothed by shedding stress to the periphery of the yielded zones (Fig. 2 cross sections). Extending this argument to three dimensions, it can be deduced that deformation smoothness is "enforced" by the stiff overburden beam, generating homogenization of yield within a compact growth zone. This keeps the boundary approximately circular to elliptic and suppresses fingering of plastic flow zones.

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  Fig. 2-Stress transfer and yield propagation tend to focus vertical stresses on any protruding intact zones. This causes them to yield, smoothing out deformations and stresses, leading to a more uniform(compact) yielded zone growth, as Fig. 1 shows.

The surface area in compact growth is minimized because forming compact shapes requires less energy than forming fingered boundaries. For a 10-m-thick reservoir that has produced 500 m³ of sand, the disturbed zone volume may be approximately 5,000 to 10,000 m³ (1:10 ratio) with a mean radius of approximately 13 to 20 m and a minimum surface area of approximately 800 m². Any frontal perturbations, but particularly channel growth, will increase this area and are, therefore, less probable.

Piping channel (wormhole) growth concepts

Piping channels are assumed to be stable structures, approximately cylindrical, and of constant cross-sectional area along their length (diameter of approximately 25 to 50 mm). The channel is filled with slowly flowing slurry, and the tips are propagating away from the wellbore. Because the size of the affected zone is influenced more by the impermeable upper and lower reservoir boundaries (cohesive shales), fluid flow will evolve from spherical to cylindrical with radial channel growth. This is analogous to reservoir drainage changes as the radius of influence increases to a value larger than the reservoir thickness.

If the sand-production mechanism is piping-channel growth, there are two reasonable limiting cases for the channel network nature. At one extreme, a number of channels develop outward from the wellbore, and that number is constant with distance. At the other extreme, channels bifurcate and create a 3D anastomosing net in which the volume density of the channels remains constant. These are limiting cases because it is difficult to envision either a decreasing number of channels with distance or an increased channel volumetric density with distance.

For a constant channel-density-per-volume assumption, the channel density is the same within the zone containing channels at all sampling scales larger than the representative elementary volume (REV). Fig. 3 illustrates a dendritic piping channel network hypothesis for CHOPS. The mean flow-path length within this zone remains constant with a characteristic value depending on the density of channels. Furthermore, the process zone properties remain the same with growth if the channel density remains constant. In this limiting case, the REV in the channeled zone has an "equivalent permeability," leading to a flow model that has:

• A far-field permeability, k_o
• A near-field permeability, k_i in the remolded zone
• A diffuse-but-narrow transition zone between the two

New channels must be created continuously as the affected zone grows, and the number of channels scales to the area of the boundary.

....................(1)

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  Fig. 3-Dendritic piping-channel network hypothesis for CHOP

The velocity of the affected zone boundary also must be related to the radius.

....................(2)

The other limiting case for the channel network is where the number of channels remains the same, neither growing nor shrinking with distance from the wellbore. (N is constant with radius, Fig. 4). There is no definable REV in this case. The channel density decreases with distance, the mean flow-path length increases, and the equivalent permeability must be defined in a spatially dependent manner, becoming asymptotic to k_o at the "boundary" defining the location of the advancing tips. The velocity of the affected zone boundary remains constant, and the flow equations for the constant-N case differ from the flow equations for the dendritic case.

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  Fig. 4-A constant number of piping-channels hypothesis for CHOPS

Fig. 5 is a schematic plot of the equivalent permeability distribution of the two limiting cases, as well as a reasonable assumption for a compact growth model. One interesting point is that from a flow or well-test perspective, it will be almost impossible to discriminate between these cases as the boundary (or transition zone) moves farther from the wellbore. Strong conclusions as to the physical nature of the processes in the reservoir based solely on tests performed at the wellbore face (Δp or ΔQ well tests) seem problematic.

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  Fig. 5-Equivalent permeability in different CHOPS models

For piping channels, two possible cases exist with respect to fluid flow and drainage in the reservoir:

• Strong piping case
• Thin lens case

Fig. 6 shows the two limiting flow regimes for piping-channel drainage. In the strong piping case, formation fluid flow is channeled strongly within the "wormhole." Solids and liquid flux are dominated by the tip processes and pressure gradients that drain the reservoir beyond the tip. In the thin lens case, individual channels also serve as drains for surrounding oil. The sanding at the tip is dominated by local gradients, but the permeable channels that serve as drains dominate the overall oil production. In more viscous oils (> 10,000 cp), mobility is low and the sand cut remains elevated for a long time, more closely resembling the strong piping case in which most fluid comes from the tip region. In lower-viscosity oils, the slurry is diluted during transit to the well, which more closely resembles the permeable thin lens model.

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  Fig. 6-Two limiting flow regimes for piping-channel drainage. Creation of piping channels changes reservoir drainage patterns.

The reservoir contact area for channel growth is potentially far larger than for compact growth. With the same example of 500 m³ of sand produced in the compact zone, if channels average 3 cm in diameter, the contact area is approximately 66,000 m² rather than approximately 800 m².

Combined compact and wormhole processes

Several arguments suggest that sand production is a result of a combination of mechanisms. Assuming a mean stable-channel diameter of 30 mm, the total channel-network length would exceed 1000 km after 1000 m³ of sand is produced from a well. Stated in another way, in a 10-m-thick reservoir with 10 ha well spacing, each cubic meter of formation will contain approximately 10 m of 30-mm-diameter channels (i.e., only 0.17% of the volume of the reservoir). 1000 km of channels seems improbable, but perhaps the piping channels are substantially larger than 30 mm.

Viscous slurry flowing in small channels with rough walls generates large pressure drops, which limits channel lengths because of the finite Δp available in the reservoir between the liquefaction tip and the wellbore. This is impossible to quantify because no method exists to calculate the number of channels, which is necessary to estimate slurry velocity and pressure drop. Channels of great length seem unlikely, and short channel lengths of approximately 2 to 20 m are assumed.

During early time, when the remolded zone is small and sand production large, it appears that compact growth is dominant. The radius of curvature of the zone is small, and the "intact" wall can sustain higher tangential stresses, σ_θ, that counteract piping-channel development. The sharper the radius of curvature, the greater the stability of the sand face; thus, any perturbation of the surface will tend to self-heal. Fig. 7 shows flowlines focusing and stresses near a perturbation.

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  Fig. 7-Flow lines focusing and stresses near a perturbation.

When the remolded zone is large, a surface perturbation may lead to stable channel development. Such a perturbation focuses the flowlines, increasing the local gradient at the leading tip of the perturbation. The destabilizing forces (Fig. 8) are large because of the spherically convergent flow at the channel tip. However, stabilizing forces linked to friction and arching also increase; a small hole in a granular material is far more stable than a large hole. Finally, the presence of a "free face" will lead to stress concentrations. This favors yield, weakening, and dilation of the sand, which facilitates destabilization and liquefaction.

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  Fig. 8-Hydrodynamic and static forces on a sand grain.

Whether a perturbation will self-heal or propagate depends on the force balance and whether the energy rate will be positive (self-healing) or negative (propagation). If it is negative, it generates its own high-permeability channel that advances into less depleted zones of the reservoir, accessing (and indeed perhaps seeking) zones in which a higher tip gradient can be maintained. This is the realm of stable channel growth, although components of compact growth nearer the wellbore must still take place because of stress redistribution that helps trigger sand yield. It is unlikely that stable channel growth occurs in intact formations. Even at a porosity of 30%, sands under stress are extremely strong and resistant to piping stresses, so channels likely only propagate in preyielded zones.

This transition between compact and channel growth is not entirely speculative. In the field, communication between wells has been observed repeatedly, mainly for mature wells that have produced appreciable amounts of sand. Furthermore, mathematical perturbation analysis of sand-production models, which couple both flow and stress, confirm that stable channel growth is favored energetically late in the well life. Compact growth is favored in early time.

Stress changes during CHOPS

Natural and induced stresses drive CHOPS processes. Sand removal leads to high shear stresses that yield and dilate the sand before it is liquefied and flows toward the wellbore as slurry. Fig. 9 illustrates the tangential and radial stresses around a slurry-filled cavity. The material adjacent to the void must carry the stresses originally supported by the solid material, leading to concentration of tangential stress, σ_θ↑, and reduction of radial stress, σ_r↓, near the boundary. The same effect occurs for vertical and horizontal stresses. In 30% porosity sand, this leads to shear yield, which alters the stress distribution and promotes dilation because σ_r is low and cannot prevent the sand from dilating.

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  Fig. 9-Tangential and radial stresses around a slurry-filled cavity.

Implications for reservoir behavior are interesting. A CHOPS reservoir contains regions in which the static sand matrix is stressed greater than originally, regions in which shear has softened and dilated the sand massively, and liquefied regions in which sand grains are not in contact and can transmit no effective stress. The detailed distribution of these zones is unknown, but some inferences can be made from geomechanical analysis.

Stresses in the wellbore region

Yield and dilation of the sand matrix will generate stress distributions around a CHOPS well similar to those around a cavity. Four "zones" with diffuse boundaries may be postulated. Fig. 10 shows the distribution of stresses around a compact growth zone.

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  Fig. 10—Distribution of stresses around a compact growth zone.

In the liquefied zone (slurry zone), effective stresses are zero; therefore, the total stress is equal to the fluid pressure and is isotropic. Porosity in this zone must be greater than approximately 50%. Permeability is extremely high, and compressibility is dictated by the slurry composition (oil, sand, water, and gas bubbles).

In the fully remolded plastic flow zone, not yet liquefied, the ratio of effective stresses after shearing and dilation is limited by the residual friction angle for sands (≈ 30° at approximately 40 to 45% porosity); therefore, σ′₁/σ′₃ ≈ 3.0. The major principal stress, σ′₁, is σ′_v because of downward force from the overburden, and σ′₃ = σ′r because of the geometry of sand removal. Porosity in this zone changes from approximately 35% at the yielding zone boundary to more than 50% at the liquefaction front. Permeability increases by an order of magnitude across this zone, and rock stiffness gradually disappears as φ → 50%.

Farther from the wellbore where high-shear stresses exist, the formation experiences shear, and strength and cohesion are degraded. This is the yielding zone, and it carries a higher σ′_v, and the σ′_r is low from continuous sand removal. Intact dense UCSS (φ~ 30%) can withstand a σ′₁ /σ′₃ ratio as high as 5 to 6 before yield, but once failure has occurred, the sand continues to yield and weaken. Gradually, σ′₁/σ′₃l_max → ~3. Porosity in the yielding zone increases to approximately 35%, and permeability may double across this zone during shear and dilation before the fabric is totally disrupted by plastic flow. There is not much grain crushing if individual grains are strong because the confining stress is decreasing rather than increasing. It is believed that bubble nucleation begins at the 35% porosity region, triggered by the pressure drop enforced at the wellbore and by the fabric dilation, which cannot be accommodated by oil inflow because of the high oil viscosity.

In the intact zone, porosity is still approximately 30%, and the sand has not yet experienced shear distortion, cohesion loss, dilation, or shear yield, although stresses have changed. This zone may be under higher shear stresses than in the virgin state, but it possesses all the properties of intact virgin rock. It is believed that pore pressures remain largely unaffected in the yielding and intact zones because of high oil viscosity (immobility). Infill wells drilled into intact reservoirs often have virgin reservoir pressures even though the fracture gradient (i.e., σ_h) has diminished.

Stress distributions for such models may be calculated from a combination of nonlinear elastic theory in intact zones and plasticity or damage theory in the weakening and plastic flow zones. Predictions depend strongly on the choice of constitutive law. Because the process is 3D, such a constitutive law must account for the material behavior in a fully 3D stress field, and this is not simple mathematically.

Reservoir-scale stress changes

Both compact and channel growth lead to development of a region of softer material that can carry less of the overburden stress. The total overburden load must still be supported to maintain overall stress equilibrium; therefore, the interwell σ_v value rises. Fig. 11 shows vertical stress trajectories at the interwell scale. At the same time, the lateral stresses, σ_h, within the reservoir drop because of continuous sand removal. The reservoir is thin (5 to 15 m) compared with its area (hundreds of meters); therefore, σ_h equilibrium is maintained by redistributing σh stresses into overlying and underlying strata. Fig. 12 illustrates horizontal stress trajectories at the reservoir scale.

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  Fig. 11—Vertical stress trajectories at the interwell scale.

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  Fig. 12—Horizontal stress trajectories at the reservoir scale.

A major macroscopic effect of sanding is the lowering of σ_h in the reservoir. Attempts to inject fluids into wells that have produced large amounts of sand show that the fracture gradient has dropped from approximately 17 to 22 kPa/m to as low as 7 to 9 kPa/m, approximately one-third of the vertical stress. In the plastic zone surrounding the well, σ′_v /σ′_h ≈ 3.0. Pore pressures are also low, which suggests that the lower limit of σ′_h is controlled by frictional plastic flow. CHOPS wells cannot be maintained full of liquid. Undiluted fluids break through to nearby producing wells, indicating either open channels or the generation of induced hydraulic fractures. Carefully monitored field tests suggest the flow mechanism is fracturing. The formation acceptance of fluid ceases suddenly, implying fracture closure when p_i = (σ_h)_min , whereas in channel flow, a gradual pressure decline is expected (Fig. 13).

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  Fig. 13—Falling head-flow test indicates fracturing at low stresses around a CHOPS well, rather than channel flow or Darcy flow.

In a reservoir-scale perturbed stress field with low σ_h, fractures will propagate toward zones of lowest σ_h, leading to rapid interwell communication during injection. Communication does not take place with a well that has not produced sand. This behavior is an alternative explanation to the "wormhole" hypothesis, which, although widely believed, remains conjectural. All phenomena explained in terms of wormholes can be explained in terms of stress and dilation, but the converse is not true: wormholes do not explain all the phenomena observed. Horizontal stress concentrations above and below the zone (Fig. 12) lead to excellent fracture containment if fluids are injected at a later date. However, large-scale injection of hot fluids eventually will result in both repressurization and restressing so that fracture gradients can return and even exceed original values.

Stresses around a channel

The stress distributions of channels in UCSS are governed by a combination of frictional yield and nonlinear elastic response. (The modulus of sand is also a function of the effective stress.) Fig. 14 shows how the effective stresses around a channel are distributed. At the wall, both the radial and tangential effective stresses must be small if there is no cohesion. (Cohesion likely has been destroyed by yielding and dilation.) A small amount of arching may occur, and capillary effects may exist because of fractional water saturation giving apparent cohesion but of a few kPa at most. The stress reduction is balanced by redistribution farther from the opening, where the confinement effect allows the fabric to withstand larger stresses. This distribution is similar to that around the large zone (Fig. 10), except at a smaller scale.

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  Fig. 14—Stresses at the small scale around a hypothesized channel.

A channel causes a general softening (partial loss of structural rigidity) of a large volume around the channel, which also may be a zone of dilation and enhanced permeability. In a reservoir, many channels lead to an overall softening effect (the "Swiss Cheese" effect), causing large-scale stress redistributions (similar to the compact growth model) between intact reservoir zones and zones containing channels.

Changes in physical properties during CHOPS

During CHOPS, all physical properties change at all relevant scales within the affected zone: dilation, stress redistribution, and even gas bubbles affect the macroscopic system response (e.g., with respect to seismics, electromagnetics, gravity, etc.).

In compact growth, permeability and compressibility increase with dilation. Intact 30% porosity UCSS has a solid skeleton compressibility of approximately 10^–6 kPa^–1, but once yielded and dilated to φ~ 40% under reduced stress, the compressibility may be approximately 10^–4 to 10^–3 kPa^–1. As final liquefaction takes place, the matrix compressibility becomes indefinable, but the slurry becomes more compressible as gas bubbles grow. Permeability increases dramatically, and hydraulic conductivities may show an even greater increase because of phase saturation changes.

Acoustic velocities drop and the shear wave disappears in the remolded zone as the shear modulus disappears and the bulk modulus is degraded. Acoustic wave attenuation becomes severe in the presence of a large gas-bubble fraction, and the reduction of effective stress also contributes to velocity reduction and attenuation. In Alberta, intact acoustic compressional wave velocities are approximately 3.1 to 3.5 km/s for overburden and 2.5 to 3.0 km/s for oil sands. After sanding, large elliptical zones of low velocity (< 1.5 km/s) and high attenuation develop in the reservoir. Fig. 15 illustrates low seismic velocities around CHOP wells. Similar effects would occur for a dendritic channel network. Around each channel, stresses are altered and the presence of a viscous fluid with gas bubbles in discrete channels will degrade seismic velocity and increase attenuation as well.

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  Fig. 15—Low seismic velocities around CHOPS wells.

In disturbed material, all high-frequency waves are filtered rapidly out of wave trains, eliminating seismic monitoring as a means of deciding whether the dominant process is compact growth or channel growth. However, seismic probing can identify the approximate boundaries of the affected zone and help decide if the boundary is relatively sharp. If the boundary is diffuse and the seismic velocity changes slowly with position, either the compact growth zone has a broad diffuse boundary, or the channels are not growing in a dendritic manner with an identifiable front. Conversely, a sharp velocity and attenuation boundary reduces the probability that growth is occurring through propagation of a constant number of channels with distance. More data are needed to address and hopefully resolve these issues.

Nomenclature

ki	=	near-field (altered) permeability, L2, darcy
ko	=	far-field (unaltered) permeability, L2, darcy
r	=	radius (from the center of a circular opening or well), L, m
v	=	velocity, L/t, m/s
vD	=	Darcy velocity, L/t, m/s
Δp	=	pressure drops
ΔQ	=	change in rate
φ	=	porosity, %
σ	=	stress, m/Lt2, MPa
σh	=	horizontal (lateral) stress, m/Lt2, MPa
σr	=	radial stress, m/Lt2, MPa
σv	=	vertical stress, m/Lt2, MPa
σθ	=	tangential stress, m/Lt2, MPa
σ′	=	effective (matrix) stress, m/Lt2, MPa
σ′h	=	effective horizontal stress, m/Lt2, MPa
σ′n	=	effective normal stress, m/Lt2, MPa
σ′r	=	effective radial stress, m/Lt2, MPa
σ′v	=	effective vertical stress, m/Lt2, MPa
σ1	=	major principal stress, m/Lt2, MPa
σ2	=	intermediate principal stress, m/Lt2, MPa
σ3	=	minor principal stress, m/Lt2, MPa

Noteworthy papers in OnePetro

Dusseault, M., Hayes, K., Kremer, M., & Wallin, C. 2004. Workover Strategies in CHOPS Wells. Petroleum Society of Canada. http://dx.doi.org/10.2118/04-09-GE

Rangriz Shokri, A., & Babadagli, T. 2012. An Approach To Model CHOPS (Cold Heavy Oil Production with Sand) and Post-CHOPS Applications. Society of Petroleum Engineers. http://dx.doi.org/10.2118/159437-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

DU, Z., Chan, C., & Zeng, F. 2013. An Experimental Study of the Post - CHOPS Cyclic Solvent Injection Process. Society of Petroleum Engineers. http://dx.doi.org/10.2118/165524-MS

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

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 production rate increase mechanisms

Combining CHOPS and other production technologies

CHOPS operational and monitoring issues

CHOPS reservoir assessment and candidate screening

CHOPS sand management

PEH:Cold_Heavy-Oil_Production_With_Sand

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Cenk Temizel, Reservoir Engineer