Improved Calculation of Effective Permeability for Pore Network Models Using the Diffuse Source Methodology
- Sherry Liu (Texas A&M University) | Michael J. King (Texas A&M University)
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- Society of Petroleum Engineers
- SPE Europec featured at 81st EAGE Conference and Exhibition, 3-6 June, London, England, UK
- Publication Date
- Document Type
- Conference Paper
- 2019. Society of Petroleum Engineers
- Diffuse Source Upscaling, Pore Network Models
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- 91 since 2007
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In this study, we have extended and applied the diffuse source upscaling methodology to sandstone and carbonate pore network models in order to evaluate their effective transmissibility and permeability. The proposed method allows us to find transmissibility values for sub-volumes of the pore network during the transition from transient to pseudo steady state flow. The pore network models utilize a lattice grid construction, consisting of nodes and bonds that connect the nodes. The Eikonal equation is solved on the lattice using Dijkstra's method to obtain the diffusive time of flight, which is then used to model the transition from transient to pseudo steady state flow. The solution uses the concept of a transient drainage volume, which increases with time as pressure propagates into the nodes of the pore network. The diffuse source upscaling approach allows us to calculate the transmissibility of the drainage volume as it increases with time. The calculated results can be compared to the analytical results, where the sample is assumed to be internally homogeneous. A synthetic model was created to illustrate how the calculated lattice model and the analytic reference results compare for a homogeneous model. The comparison of the carbonate analytical and calculated results showed that there exists a high degree of internal heterogeneity while the more homogeneous sandstone model showed a close agreement with the synthetic model. For both samples, the late time pseudo steady state permeability showed a good correspondence with other permeability evaluations. The diffuse source method has more directional information available than the steady state method. Hence, the new method of analysis can be viewed as an extension of pseudo steady state concepts of permeability to transient flow, with increased spatial resolution corresponding to the transient drainage volume. Instead of obtaining only the steady state transmissibility from a pore network model, the diffuse source approach provides us with the ability to better characterize the internal heterogeneity of a model and to explain the wide range of permeability values obtained by other approaches.
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