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The fracture clean-up model is made up a number of options specifically developed to allow IMEX to model flow back of fracturing fluids around a newly fractured well.

The option was developed to be used with the polymer option in IMEX as the fracturing fluid is modeled as a water-polymer mixture (Only the velocity and polymer concentration

dependent water viscosity and fracture width correction features actually require the polymer model to be used).

The option is made up of the following features.

Features

Velocity and polymer concentration dependent water-polymer mixture viscosity can be used to model shear thinning/thickening fluids.

Fracture width correction for reservoir condition velocity to be used in the above water-polymer mixture viscosity calculation. A zero value for the correction eliminates the velocity dependency in regions away from the fracture. A correction value of 1.0 uses the block average reservoir condition velocity directly.

Block and direction dependent pressure gradient thresholds to flow in specified regions.

Once a threshold has been exceeded the flow connection will always allow flow regardless of the pressure gradient. This can be used to approximate yield stress

Non equilibrium initial saturation overrides can be entered in user defined regions (e.g. near a fracture) in a model which is initialized everywhere else using a gravity equilibrium

initialization technique. This can be used to set up fracture fluid distributions in the fracture without the need to model fracture fluid injection.

The ability to initiate the pressure gradient threshold option at a restart is added. This allows the model to simulate fracture fluid injection followed by clean-up (after the restart).

All of the above features can be used with or without the non Darcy flow option and can be used independently of each other.

Velocity Dependent Polymer Mixture Viscosity (Component Properties Section) A new option in the *PMIX keyword has been added.

*PMIX *VELTABLE

This signals IMEX to expect velocity dependent polymer-water mixture viscosity data.

IMEX expects to read the keyword VWT followed by an initial velocity value on the same line. Following this at least two relative polymer concentration - relative water-polymer mixture viscosity rows are expected to be read in.

After the entire table at the initial reservoir condition velocity value has been entered the next occurrence of VWT followed by a larger reservoir condition velocity will trigger the reading of the next relative polymer concentration - relative water-polymer mixture viscosity table (at least two rows).

If only a single reservoir condition velocity is entered (only one value of VWT), the table will become velocity independent.

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The relative polymer concentration is the actual polymer concentration divided by the reference polymer concentration *PREFCONC. The relative water-polymer mixture viscosity is the mixture viscosity divided by pure water viscosity.

An example of the *PMIX *VELTABLE keyword is given below for a shear thinning fluid at velocities 0.10, 10.0 and 40.0 ft/day. The velocities used for the table lookup are intrinsic reservoir condition velocities and so are calculated using the average velocity in a gridblock divided by the block porosity. In addition, the velocities are multiplied by a fracture width correction term which will be discussed shortly (Velcor = FRWIDTHCOR * Reservoir Condition Velocity/φ).

For velocities below 0.10 ft/day, the table at 0.10 ft/day is used. For velocities above 40.0 ft/day the table at 40.0 ft/day is used.

Fracture Width Correction (Rock-Fluid Data Section)

The model includes a fracture width correction array *FRWIDTHCOR which is used to enable/disable velocity dependent water-polymer mixture viscosity calculations in portions of the reservoir and to increase the effective velocity in the fractured region due to numerical fracture representation.

*FRWIDTHCOR = 0.0 turns off the velocity dependent viscosity calculation for the block it is defined in. The model will always use the lowest velocity (*VWT) in the *PMIX

*VELTABLE table in this case.

A non zero *FRWIDTHCOR is used to multiply the intrinsic water-polymer mixture velocity for use in the *PMIX *VELTABLE table. For example if a 0.1 millimeter fracture is

represented using a 0.2 meter gridblock a *FRWIDTHCOR of 2000.0 might be used to approximate the much higher velocity along the actual fracture.

When *PMIX *VELTABLE is encountered, a two dimensional interpolation is used. Water-polymer mixture velocity is calculated for each gridblock. The velocity is divided by gridblock porosity and multiplied by a correction factor (*FRWIDTHCOR), or:

Velcor= FRWIDTHCOR * Reservoir Condition Velocity/φ

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Where Velcor is the corrected velocity used in the VELTABLE table, FRWIDTHCOR is the fracture width correction term entered on a block by block basis, Velocity is the average velocity in a block and φ is the block’s porosity

Block and Direction Dependent Pressure Gradient Thresholds (Rock-Fluid Data Section)

The fracture clean-up model approximately accounts for yield stress effects by including pressure gradient thresholds in the three directions. The arrays *PTHRESHI, *PTHRESHJ, and *PTHRESHK define these pressure gradients between every gridblock and its neighbor.

The array value *PTHRESHI *IJK I, J, K defines the pressure gradient (pressure drop / unit of length) required to initiate flow between block I, J, K and I+1, J, K.

The array value *PTHRESHJ *IJK I, J, K defines the pressure gradient (pressure drop / unit of length) required to initiate flow between block I, J, K and I, J+1, K.

The array value *PTHRESHK *IJK I, J, K defines the pressure gradient (pressure drop / unit of length) required to initiate flow between block I, J, K and I, J, K+1.

The pressure gradient threshold is a one time switch. Once it is exceeded between two blocks in a specific direction, the interblock connection remains open to flow thereafter.

A zero value of the thresholds indicates the connection is always open to flow.

Regions in and around the fracture may have non zero values of *PTHRESHI, *PTHRESHJ, and *PTHRESHK, while regions in the reservoir might have zero values for thresholds.

Non Equilibrium Initial Saturation Override (Initial Conditions Section)

In cases where the initial injection of fracturing fluid into the fracture is not modeled, it would be convenient to be able to initialize the entire reservoir to a gravity-capillary pressure equilibrium state and just override this state in the region in and around the fracture which has just had fracturing fluid pumped into it.

This can be done using the keywords *SONEQ and *SWNEQ. These keywords override the gravity-capillary pressure equilibrium saturations determined when using the *VERTICAL

*BLOCK_CENTER or *VERTICAL *DEPTH_AVE equilibrium options in specified regions.

*SONEQ and *SWNEQ should only be defined (using the *IJK array reading option) in the region around the fracture the user wishes to override saturations in. Normally around the fracture we expect a high saturation of the fracturing fluid, this is modeled as water with a high polymer concentration. Using high initial *POLYCONC (polymer concentration) and high *SWNEQ (low *SONEQ) in this region is a convenient way to do this.

Initiating the Pressure Gradient Threshold Option at a Restart

On occasion it may be necessary to also model the fracturing fluid injection period of the fracture clean-up process. It is possible to accomplish this by restarting from the end of the injection period (or shutin period) before the flow back period and only introducing pressure gradient threshold calculations in the restarted run.

The fracture cleanup model can determine if the *PTHRESHI, *PTHRESHJ, *PTHRESHK keywords were in the data set of the model to be restarted from. If they were not, and the pressure gradient threshold keywords are encountered in the current data set, then the

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pressure gradient threshold option is initiated on the restart. On the restart, the pressure field read from the restart record is set as the initial pressure field. A pressure gradient that will initiate flow in the I direction is then defined as:

DP = [(P(I+1,J,K) – Prestart(I+1,J,K)) - (P(I,J,K) – Prestart(I,J,K))]/[Distance_I]

Distance_I is the distance between block centers in the I direction Prestart is the initial pressure field read from the restart.

P is the current pressure field

DP is compared with *PTHRESHI, when DP is greater than *PTHRESHI (defined in block I,J,K) flow is initiated between blocks I,J,K and I+1,J,K.

On restarts before or after the introduction of the pressure gradient threshold keywords, the model restarts normally.

As the introduction of the pressure gradient threshold keywords on a restart can only be done once per run, this model cannot be used when wells are fractured at different times.

It is also possible and desirable to change the water-polymer mixture viscosity during the restart which separates the injection period from the flow back period. In the injection portion of the run, the fracturing fluid is a very high viscosity fluid. During flow back the water-polymer mixture fluid has a very much lower viscosity. Similarly, it is also possible to alter *FRWIDTHCOR on the restart.

When the mixture viscosity is altered on a restart, it is critical that the *PMIX *VELTABLE table be used both for injection and production periods. The values in the table, the number of points in each table, and the number of velocity tables may be altered as required, but the

*VELTABLE option must be used.

Output of Pressure Thresholds and Fracture Width Correction (Input/Output Control Section)

The *RES list of input arrays has been expanded to include FRWIDTHCOR and the three pressure threshold arrays (PTHRESHI, PTHRESHJ, PTHRESHK).

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