Novel Forward Model Quantifies Uncertainty of Fracture Networks

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A major portion of the uncertainty found in shale reservoirs is the result of the distribution and properties of the fracture network. However, explicit fracture models are rarely used in uncertainty quantification because of their high computational cost. This paper presents a work flow to match the history of reservoirs featuring complex fracture networks with a novel forward model. The efficiency of the model allows fractures to be characterized explicitly, and the corresponding uncertainty about the distribution and properties of fractures can be evaluated.


For low-permeability unconventional shale reservoirs, the fracture network greatly determines the performance of the wells. Because of the large uncertainty of the fracture distribution, especially for natural fractures, the production behavior might differ dramatically. A possible way to characterize fractures is by use of core data, well-logging data, or seismic data. However, these data are either sparse in nature, and thus cannot be used to determine the exact location of fractures, or low in accuracy because of limited quality. An alternative approach is to use production data and characterize the fractures through history matching.

Various approaches have been proposed for automatic history matching. Most of these were evaluated with conventional reservoir models through upscaling (partially the result of the cost of generating explicit fracture models and performing simulations). For fractured reservoir models, especially when explicit fracture models are used, nonlinearity is even more significant and challenges the applicability of the existing methods. In this work, the authors use the improved compartmental embedded discrete fracture model (cEDFM), combining the level-set approach and the ensemble Kalman filter (EnKF) for history matching. The cEDFM has a much better accuracy compared with the original embedded discrete fracture model (EDFM) in handling flux across the direction of fractures, which is a common case for interwell flow.

The Forward Model

EDFM. The concept of EDFM was first proposed in a work in which the transmissibility between fracture and the matrix is calculated in a manner similar to that used to calculate the well index. By assuming a linear relationship between the pressure in the matrix and the distance to the fracture, an analytical expression of the transmissibility can be obtained. Because the matrix grid does not need to conform to the geometry of the fractures, and the fracture is discretized by the boundary of the matrix gridblocks, this approach is flexible and compatible with traditional orthogonal or corner-point grid systems. In original EDFM implementation, three types of non-­neighbor connections (NNCs) are considered:

  • Between the fracture and the matrix grid it intersects
  • Between two intersecting fracture grids
  • Between two neighboring fracture grids from the same fracture

The cEDFM Formulation. Few publications have validated the accuracy of EDFM in simulating highly conductive fractures. However, for low-permeability fractures, large errors are observed for both single and multiphase flow problems, mostly because of the inability of this method to constrain the flow within the matrix when a flow barrier is present.

In this paper, instead of the fracture grid being embedded within a matrix gridblock, the fracture grid will split the matrix grid that it intersects. The model can be thought of as a variation of the discrete fracture model, while the formulation to calculate the flux between fracture and matrix is inherited from the original EDFM. As a fracture grid splits the matrix grid (m) into m1 and m2, the NNC Type I must be modified. This expression can be derived by assuming a linear pressure profile that moves away from the fracture within the matrix. The difference in pressure between the matrix grid and the fracture grid, therefore, is given by the pressure drop within the matrix.

By performing matrix splitting, all fracture grids are at the boundary of matrix gridblocks. The model is implemented in a full 3D corner-point grid system, which extends the robustness of the approach for field application.

EDFM faces limitations when simulating flux across the fracture. Because the parent matrix is one single gridblock, the flux on the two interfaces is either toward the fracture or toward the matrix when the fracture grid has a higher potential. This unphysical phenomenon can be rectified by performing grid-splitting in cEDFM. When there are multiple fractures intersecting within the same parent gridblock, more than two subgrids can be generated. Because a full 3D approach is taken for the cEDFM model, a tiny grid with small volume might be generated, which potentially would cause convergence issues and slow down the computation. The authors performed node merging for nearby nodes to eliminate these small cells when the bulk volume of a subgrid is below a certain tolerance.

Numerical Results

The model first is benchmarked with an extremely fine explicit model. Both the orthogonal case and the skewed fracture case are compared with the explicit model. Flow barriers exist, as well as highly conductive fractures, for both cases. Water is injected from the left boundary at a constant pressure of 12,000 psi, and gas is produced from the right boundary at a constant pressure of 8,000 psi, which is the same as the initial reservoir pressure. The pressure and water-saturation profiles are compared with the explicit model. After 12 years of injection, for both cases, the cEDFM results are almost identical to those of the explicit case even when flow barriers are present, while the EDFM model has a large discrepancy in those cases.

Sensitivity analysis is then conducted for the cEDFM approach when using different mesh for the matrix. Results from different mesh sizes are compared. A total of 12 fractures are defined in the reservoir; however, the two wells are perforated within the matrix grids.

When considering the case of C1 concentration after 12 months of CO2 flooding, the coarse mesh could not capture the concentration profile for a relatively complex model like this and 6.20% of relative error in cumulative production is observed. A much better result can be obtained by using the medium mesh. The three cases are also simulated without the fractures. The relative error in cumulative production is 3.53% for the coarse mesh and 1.10% for the medium mesh. The results indicate that simulating a fractured reservoir is definitely more challenging. However, when the mesh is too coarse, the error persists even without any fracture. A moderate refinement usually is adequate for the cEDFM approach without the need of further local grid refinement near fractures.

One limitation of the original EDFM is that a consistent mesh needs to be used throughout the reservoir. Therefore, it would be beneficial to use a flexible mesh in different regions of the reservoir to reduce the total cell number. In the authors’ implementation of cEDFM, an automatic grid merging is incorporated to combine grids in those areas.

Another limitation of the original EDFM is the fact that the application is restricted to orthogonal mesh. The authors extended the implementation of cEDFM to work with corner-point models. Fractures can be incorporated easily into existing reservoir models, which makes cEDFM more practical for field application. Fig. 1 shows a synthetic case of five multistage hydraulically fractured horizontal wells completed in the Brugge reservoir. The cEDFM approach can work with existing reservoir grids easily.

Fig. 1—Pressure profile of the synthetic Brugge case with five horizontal wells. (a) 1 month, (b) 3 months, (c) 24 months, (d) 60 months.


In this work, a novel cEDFM fractured-reservoir simulation model is proposed. By performing grid-splitting, the cEDFM model obtained improved accuracy compared with the original EDFM approach. The proposed model is validated with fine explicit models for multiphase-flow problems. The advantages of the new model over the original EDFM approach include:

  • Accuracy is improved for flow across fractures, especially for low-permeability flow barriers.
  • The approach can be incorporated into streamline simulators.
  • The model is extended to work with corner-point gridblocks to improve the applicability of this method in the field.
  • The original EDFM is restricted by a constant refinement level of the mesh. Here, in the proposed model, automatic grid merging is implemented for areas without fractures to reduce the computational cost further.

The explicit model can be used directly in history matching without the need for upscaling. Therefore, the validity of Gaussian distribution for the parameters can be maintained, which is a prerequisite for algorithms such as EnKF. This method is capable of locating fractures (or flow barriers) efficiently, and history matching obtains good accuracy compared with the reference case. Compared with other methods, this approach maintains its accuracy and efficiency even for problems with a larger parameter dimension.

For a limited time, the complete paper SPE 191395 is free to SPE members.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191395, “Uncertainty Quantification of the Fracture Network With a Novel Fractured-Reservoir Forward Model,” by Zhi Chai, SPE, Hewei Tang, SPE, Youwei He, and John Killough, SPE, Texas A&M University, and Yuhe Wang, Texas A&M University at Qatar, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed.

Novel Forward Model Quantifies Uncertainty of Fracture Networks

01 April 2019

Volume: 71 | Issue: 4



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