Scaleup to full field miscible flood behavior

The objective of scaleup is to take the behavior predicted from detailed, fine-grid reference models that at best represent only a few wells and a tiny part of the reservoir and transfer it to a model that attempts to represent many wells and the integrated behavior of the entire compositionally enhanced solvent flood (or at least a significant portion of it).

Types of scaleup methods

Three scaleup methods are available:

1. Development of pseudorelative permeability relations and pseudoproperties for use in coarse-grid, full-field, numerical reservoir simulators
2. Development of segment models that estimate the behavior of pattern-repeating elements and add up the behavior of all the segments of a pattern, as well as the behavior of all the patterns
3. Development of areal streamtube or streamline models that incorporate 2D vertical cross-section solutions into the streamtubes or streamlines and integrate behavior for all the streamtubes or streamlines

Pseudorelative permeability relations and pseudoproperties

Jerauld is a good example of the application of this method. Several reference models describe different areas of the field. Water/oil, solvent/oil, and solvent/water pseudorelative permeability relations are developed, along with pseudotrapped-solvent and solvent-flood residual oil values, so that the relevant behavior of the reference models is reproduced by corresponding models that have the same coarse grids as the full-field model. The coarse-grid models, of course, represent the same parts of the full-field model that the reference models represent. The pseudorelative permeability relations may be developed by trial and error, or they may be estimated by various methods from the fluid-flow and saturation values in the reference-model gridblocks.

In practice, the pseudorelative permeability relations and pseudoproperties reproduce behavior of one particular fine-grid simulation (e.g., a particular slug size, WAG ratio, injection-solvent composition, start of injection relative to waterflooding, etc.).

Of course, an objective of full-field-model simulations is to study different operating scenarios to optimize the flood; to have much utility, the pseudoproperties must predict behavior for conditions other than those of the particular fine-grid simulation that was used to derive them.

Fig. 1 shows how well behavior in one of the coarse-grid models of Jerauld reproduced the behavior of the corresponding fine-grid model for both the waterflood and the compositionally enhanced solvent flood. The fine-grid and corresponding coarse-grid models represented one-fourth of a nine-spot pattern. The grid of the reference model was 30×30×31, which contained layers that ranged from 4 to 8 ft thick. This 3D reference model already contained pseudorelationships that had been derived from cross sections with 1-ft layers by the method described previously. The grid of the coarse-grid model was 5×5×17. Both the timing and level of waterflood and WAG-flood oil recovery are predicted very well.

• 

  Fig. 1 – Example of predicting reference-model behavior in a corresponding model with full-field-model grid using pseudorelative permeability and pseudoproperties (after Jerauld).

Although the pseudorelations were developed for a single slug size, water-alternating-gas (WAG) ratio, and solvent composition in the reference-model simulation, they reproduced the effect of these variables surprisingly well in subsequent coarse-grid simulations, as seen in Figs. 2 and 3. The reader is cautioned that this degree of predictability of the pseudorelations may result from the fact that the coarse-grid model still has a relatively large number of gridblocks, especially in the vertical direction, for a full-field model, and thus still retains a large degree of description detail and ability to resolve solvent tongues.

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  Fig. 2 – Effect of enrichment on recovery in a reservoir study. After Jerauld (solid lines are the reference model, and dashed lines are the scaleup model).

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  Fig. 3 – Comparison of reference-model and full-field model predictions (after Jerauld).

Scaleup with segment models

When there are too many patterns to allow a sufficient number of gridblocks between wells for adequate scaleup and predictions by the pseudofunction method, segment-model scaleup may be a suitable choice. This was the case for the enriched-solvent flood at Prudhoe Bay, where there are more than 200 enhanced oil recovery (EOR) and waterflood patterns.

The segment model is best suited for regular, repeating patterns. Segment-model scaleup divides each pattern into injector/producer segments, as illustrated in Fig. 4, for a nine-spot pattern. The dimensionless behavior of each segment is computed using information from suitable reference-model simulations (e.g., dimensionless recovery and solvent production vs. dimensionless injection such as HCPV or displaceable pore volumes). Time rating is accomplished with assumed rates, rates calculated by some other model, or actual injection and production data.

• 

  Fig. 4 – Dividing a pattern into segments (after Martin and Wegner).

The preferred method for dividing the patterns into segments is with a streamline model that honors actual injection and production rates. Such a model calculates the streamline pattern from injectors to producers, and from this the no-flow boundaries can be determined. Typically, the streamlines for a waterflood are used. Such a model does not assume a balanced, closed boundary system and is able to account for the effects of unbalanced patterns, reservoir heterogeneities, and faulting.

Of course, in an actual flood, the streamlines change with time as they are influenced by injection and production rates and fluid-mobility changes, and dividing a pattern into segments on the basis of a snapshot of streamline distribution is an approximation. It also may be prudent to adjust segments further according to engineering judgment.

A simpler, and more approximate, method for dividing into segments is by geometric construction. Segments are constructed by bisecting the area surrounding the producing wells and connecting these segments to the appropriate injector.

Using the reference-model curves directly can become cumbersome quickly because of such factors as:

• Different solvent slug sizes injected into each segment (because of different degrees of throughput into each segment)
• Different amounts of water pre-injection
• Differing WAG ratios

Reference simulations need to be run for all these variations, and schemes must be developed to interpolate between the various reference curves.

Wingard and Redmond proposed a novel way of transforming the dimensionless performance computed by the reference model by making an analogy with the behavior of a series of stirred tanks. In their procedure, segment performance is calculated over a series of timesteps. The solvent injected during a given timestep mobilizes a given amount of incremental oil and creates a given amount of returned solvent that was not effective in mobilizing oil. The incremental oil mobilized during each timestep and the returned solvent are then produced from each segment according to the dimensionless performance of the reference model. The Wingard and Redmond method calculates the incremental oil recovered by solvent injection vs. time. The total recovery is obtained by superimposing this incremental recovery on a waterflood calculation.

Wingard and Redmond give equations that:

1. Represent the type of information shown in Fig. 5 and derived from reference-model simulations for incremental recovery vs. slug size
2. Represent the increment of returned solvent for each increment of solvent slug injected
3. Represent the production of each mobilized-oil increment according to the dimensionless injection vs. production performance derived from the reference-model simulations.

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  Fig. 5 – Example of the relationship between incremental oil and slug size.'

The advantage of the segment model is its simplicity and tractability for a large number of patterns. Its major drawback is the inflexibility in accounting for drastic changes in streamline patterns and, thus, changing segment volumes and creation of new segments as wells are converted from producer to injector (or vice versa), as patterns are reconfigured, as wells are recompleted or shut in, or as new wells are drilled. Wingard and Redman discuss these issues and propose approximations to make.

In addition, if solvent-flood performance depends on factors other than just slug size, such as throughput rate, WAG ratio, degree of prior waterflooding, and changing pressure level, approximations must be made to account for these factors.

Scaleup with streamtube and streamline models

In many respects, scaleup with areal streamtube models is similar to scaleup with segment models. First, segments are assigned from injectors to producers—in this case, the streamtubes. The streamtubes are defined with a special model that calculates streamlines. Typically, the pressure distribution is solved on an underlying grid for a given distribution of total mobility, and the streamlines are calculated for that pressure distribution. Fig. 6 illustrates

• Streamlines calculated for 2D areal flow
• No-flow boundaries between wells
• The resulting streamtubes for several wells.

• 

  Fig. 6 – Scaleup with streamtube or streamline models.

Emanuel et al. describe a procedure for superimposing fine-grid reference-model solvent-flood simulations on 2D areal streamtubes as follows:

• Construct a detailed fine-grid geostatistical cross-section reference model that characterizes the permeability and porosity heterogeneity and correlation between wells in the reservoir area of interest. The wells chosen should typify the flow path of the displacing fluid. This selection is judgmental and will depend on reservoir characteristics. The reference model should be highly detailed in the vertical direction to represent measured log or core data as closely as possible. Layers should be 1 or 2 ft thick. The number of gridblocks between wells should be 20 to 100 depending on computational tractability. Although only one gridblock wide, the cross section should be of variable width to represent the shape of the streamtube. This geometry is intended to model the transition from radial flow near the wells to more linear flow midway through the pattern.
• Simulate the behavior of the process of interest in the reference model. The results of these simulations are reduced to correlations of phase fractional flow at the producer and the total mobility vs. distance from injector to producer as a function of pore volumes or HCPV injected.
• Map the fractional-flow solution onto each streamtube by:

1. Determining the total mobility in each tube for the cumulative HCPV injected into each tube

1. Allocating injected volume to each streamtube according to its total mobility (the fluid rate for each injection well can be specified or calculated from the imposed pressure drop and total resistance to flow of all the streamtubes)
2. Calculating the incremental HCPV injected into each streamtube for the timestep selected
3. Determining the fractional phases of the produced fluid for the cumulative HCPV injected according to correlations
4. Summing up the contributions from all the tubes connected to a producing well.

The primary advantage of streamtube models over segment models is that the effect of well-rate changes and changing mobility on the streamlines and resulting areal sweep can be accounted for, provided that the streamlines and streamtubes are updated with time. Even if they are not updated, such a model still gives an estimate of the effect of short streamlines and long streamlines on areal sweep, provided that areal sweep is dominated by viscous forces (i.e., a sufficiently high viscosity/gravity ratio) or by areal heterogeneity. In addition, throughput rates can be estimated from the total mobility of the streamtubes rather than being assumed as in segment models. Otherwise, limitations are similar to those encountered with segment models.

Giordano et al. propose a novel method of mapping the behavior computed by a reference model directly on the streamlines. Their method makes an analogy between oil mobilization and solvent trapping with tracer adsorption and desorption. They convert the incremental solvent EOR performance computed for a 2D cross-section reference model to 1D tracer-model equations that represent adsorption and desorption of the tracer as it flows through the reservoir:

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

where

• C_i and A_i are the flowing and adsorbed concentrations of component i
• x_s is the distance along the streamline from the injection well
• ϕ_i is the accessible pore volume of component
• i, which is used as a parameter to scale breakthrough times.

Giordano et al. present equations that for a series of timesteps:

1. Calculate the solvent that is effective in mobilizing incremental oil and leaves it trapped according to an adsorption curve
2. Calculate additional ineffective solvent that is left trapped according to another adsorption curve
3. Calculate production of the remaining solvent that is not adsorbed
4. Calculate the oil mobilized by a given increment of solvent injected according to a desorption curve.

Injected water is calculated as the difference between the total injection rate and the injected-solvent rate; produced water is the difference between the total production rate and the sum of the produced solvent, EOR oil, and waterflood oil.

The power of the Giordano et al. method is its ability to:

• Account for the effect of well conversions and shut-ins, infill drilling, and changing well rates on streamline patterns, as well as its ability to
• Avoid the complications of having to recalculate streamtubes.

Its limitations, similar to those for streamtube models, are in the complexity of accounting for changes in performance caused by changes in:

1. WAG ratio
2. Throughput rate
3. Pressure level
4. Injected-solvent composition
5. Other operating conditions.

Nomenclature

Ci	=	flowing concentration of component i
xs	=	distance along the streamline from the injection well
ϕi	=	accessible pore volume of component
i,	=	a parameter to scale breakthrough times.

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

Adepoju, O. O., Lake, L. W., & Johns, R. T. (2013, January 30). Investigation of Anisotropic Mixing in Miscible Displacements. Society of Petroleum Engineers. doi:10.2118/159557-PA

Johns, R. T., & Garmeh, G. (2010, October 1). Upscaling of Miscible Floods in Heterogeneous Reservoirs Considering Reservoir Mixing. Society of Petroleum Engineers. doi:10.2118/124000-PA

External links

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

See also

Miscible flooding

Compositional simulation of miscible processes

Solvent saturation in miscible flooding

Reservoir simulation

PEH:Miscible_Processes