{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/5396"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/5396","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Performance Evaluation of Wells With Single and Multiple Fractures in Tight Formations","abstract":"Hydraulic fracturing technology together with horizontal wells leads to the exploration and development of unconventional resources economically feasible. Due to complex fracture network and geology nature, evaluating performance of fluids flow in such a hydraulic fracture system is really a challenge. Numerical modeling and simulation usually requires very fine grid to reduce the truncation error and enhance the simulation accuracy. Sometimes even with fine grid, the associated computation accuracy is compromised. On the other hand, numerous studies have been conducted on pressure transient analysis with analytical and/or numerical methods, though some underlying mechanisms have not been well understood since fluid flow in such tight formations can be completely dependent on the fracture network while the matrix only plays a source role. Therefore, it is of fundamental and practical importance to evaluate performance of a well with single and multiple fractures in a tight formation. Theoretically, a semi-analytical method is developed to couple the fluid flow in the matrix and the fracture so as to improve the accuracy and efficiency of pressure transient analysis in a tight formation. As for the semi-analytical method, the fracture is firstly discretized into several small segments. Equations for the matrix and fracture system can be solved in the Laplace domain with source functions, respectively. Continuity equations can be obtained along the fracture interface, leading to a linear system. Solving the linear system, the flux in each segment can be obtained, which is substituted into the first segment to determine the bottomhole pressure in the Laplace domain. Finally, the Stephest inverse algorithm can be employed to convert the solutions in the Laplace domain to those in the real time domain. The widely-accepted point source function is used to describe the fluid flow in the matrix for a vertical well with a single fracture, while a novel slab source function in the Laplace domain is developed to achieve the same purpose for a horizontal well with multiple fractures. Compared to the point source function, slab source function is more general, which attributes geometry in each direction and considers the pressure effect inside the source by superposition principle. The non-Darcy flow effect inside the fracture based on the Barree-Conway model is solved by introducing the pseudo-time and iterative methods. The semi-analytical method using source functions has been validated with numerical simulation method and field case, respectively. Subsequently, two dimensionless parameters, i.e., relative minimum permeability (kmr) and non-Darcy number (FND), have been introduced to incorporate the non-Darcy effect on flow performance for a vertical well with single fracture. Compared with the Forchheimer’s equation, the Barree-Conway model causes a smaller pressure drop at a higher non-Darcy number. The fracture conductivity would be underestimated when non-Darcy flow exists inside the fracture. For a horizontal well with multiple fractures, fracture conductivity, fracture stages, fracture number, and fracture dimension are discussed under consideration of both non-Darcy effect and partially penetrating ratio. Compared to the vertical well with single fracture, non-Darcy effect in a horizontal well with multiple fractures can cause a larger pressure drop as non-Darcy number is increased and relative minimum permeability is decreased. The partially penetrating ratio greatly affects the early well response, which leads to an early radial flow regime when the ratio is set to be a small value. Finally, the newly proposed method has been successfully extended to determine the reservoir and fracture parameters in a real field case.","abstract_html":"Hydraulic fracturing technology together with horizontal wells leads to the exploration and development of unconventional resources economically feasible. Due to complex fracture network and geology nature, evaluating performance of fluids flow in such a hydraulic fracture system is really a challenge. Numerical modeling and simulation usually requires very fine grid to reduce the truncation error and enhance the simulation accuracy. Sometimes even with fine grid, the associated computation accuracy is compromised. On the other hand, numerous studies have been conducted on pressure transient analysis with analytical and/or numerical methods, though some underlying mechanisms have not been well understood since fluid flow in such tight formations can be completely dependent on the fracture network while the matrix only plays a source role. Therefore, it is of fundamental and practical importance to evaluate performance of a well with single and multiple fractures in a tight formation. Theoretically, a semi-analytical method is developed to couple the fluid flow in the matrix and the fracture so as to improve the accuracy and efficiency of pressure transient analysis in a tight formation. As for the semi-analytical method, the fracture is firstly discretized into several small segments. Equations for the matrix and fracture system can be solved in the Laplace domain with source functions, respectively. Continuity equations can be obtained along the fracture interface, leading to a linear system. Solving the linear system, the flux in each segment can be obtained, which is substituted into the first segment to determine the bottomhole pressure in the Laplace domain. Finally, the Stephest inverse algorithm can be employed to convert the solutions in the Laplace domain to those in the real time domain. The widely-accepted point source function is used to describe the fluid flow in the matrix for a vertical well with a single fracture, while a novel slab source function in the Laplace domain is developed to achieve the same purpose for a horizontal well with multiple fractures. Compared to the point source function, slab source function is more general, which attributes geometry in each direction and considers the pressure effect inside the source by superposition principle. The non-Darcy flow effect inside the fracture based on the Barree-Conway model is solved by introducing the pseudo-time and iterative methods. The semi-analytical method using source functions has been validated with numerical simulation method and field case, respectively. Subsequently, two dimensionless parameters, i.e., relative minimum permeability (kmr) and non-Darcy number (FND), have been introduced to incorporate the non-Darcy effect on flow performance for a vertical well with single fracture. Compared with the Forchheimer’s equation, the Barree-Conway model causes a smaller pressure drop at a higher non-Darcy number. The fracture conductivity would be underestimated when non-Darcy flow exists inside the fracture. For a horizontal well with multiple fractures, fracture conductivity, fracture stages, fracture number, and fracture dimension are discussed under consideration of both non-Darcy effect and partially penetrating ratio. Compared to the vertical well with single fracture, non-Darcy effect in a horizontal well with multiple fractures can cause a larger pressure drop as non-Darcy number is increased and relative minimum permeability is decreased. The partially penetrating ratio greatly affects the early well response, which leads to an early radial flow regime when the ratio is set to be a small value. Finally, the newly proposed method has been successfully extended to determine the reservoir and fracture parameters in a real field case.","abstract_has_math":false,"creators":["Zhang, Feng"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Applied Science (MASc)","degree_level":"Master's","degree_discipline":"Engineering - Petroleum Systems","degree_department":null,"school":null,"contributors":[],"advisors":["Yang, Daoyong (Tony)"],"committee_chairs":[],"committee_members":["Torabi, Farshid","Gu, Yongan (Peter)"],"year":2013,"date_issued":"2013-08","date_published":"2013-08","updated_at":"2026-07-24T04:03:34Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4245"],"render_values":[{"text":"https://doi.org/10.82465/4245","href":"https://doi.org/10.82465/4245","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/5396","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Yang, Daoyong (Tony)"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Torabi, Farshid","Gu, Yongan (Peter)"]},{"key":"dc:creator","label":"Author","values":["Zhang, Feng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-10-17T15:48:34Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-10-17T15:48:34Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-08"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering - Petroleum Systems"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Applied Science (MASc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4245"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/5396"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Petroleum Systems Engineering, University of Regina. xvi, 136 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["Hydraulic fracturing technology together with horizontal wells leads to the exploration and development of unconventional resources economically feasible. Due to complex fracture network and geology nature, evaluating performance of fluids flow in such a hydraulic fracture system is really a challenge. Numerical modeling and simulation usually requires very fine grid to reduce the truncation error and enhance the simulation accuracy. Sometimes even with fine grid, the associated computation accuracy is compromised. On the other hand, numerous studies have been conducted on pressure transient analysis with analytical and/or numerical methods, though some underlying mechanisms have not been well understood since fluid flow in such tight formations can be completely dependent on the fracture network while the matrix only plays a source role. Therefore, it is of fundamental and practical importance to evaluate performance of a well with single and multiple fractures in a tight formation. Theoretically, a semi-analytical method is developed to couple the fluid flow in the matrix and the fracture so as to improve the accuracy and efficiency of pressure transient analysis in a tight formation. As for the semi-analytical method, the fracture is firstly discretized into several small segments. Equations for the matrix and fracture system can be solved in the Laplace domain with source functions, respectively. Continuity equations can be obtained along the fracture interface, leading to a linear system. Solving the linear system, the flux in each segment can be obtained, which is substituted into the first segment to determine the bottomhole pressure in the Laplace domain. Finally, the Stephest inverse algorithm can be employed to convert the solutions in the Laplace domain to those in the real time domain. The widely-accepted point source function is used to describe the fluid flow in the matrix for a vertical well with a single fracture, while a novel slab source function in the Laplace domain is developed to achieve the same purpose for a horizontal well with multiple fractures. Compared to the point source function, slab source function is more general, which attributes geometry in each direction and considers the pressure effect inside the source by superposition principle. The non-Darcy flow effect inside the fracture based on the Barree-Conway model is solved by introducing the pseudo-time and iterative methods. The semi-analytical method using source functions has been validated with numerical simulation method and field case, respectively. Subsequently, two dimensionless parameters, i.e., relative minimum permeability (kmr) and non-Darcy number (FND), have been introduced to incorporate the non-Darcy effect on flow performance for a vertical well with single fracture. Compared with the Forchheimer’s equation, the Barree-Conway model causes a smaller pressure drop at a higher non-Darcy number. The fracture conductivity would be underestimated when non-Darcy flow exists inside the fracture. For a horizontal well with multiple fractures, fracture conductivity, fracture stages, fracture number, and fracture dimension are discussed under consideration of both non-Darcy effect and partially penetrating ratio. Compared to the vertical well with single fracture, non-Darcy effect in a horizontal well with multiple fractures can cause a larger pressure drop as non-Darcy number is increased and relative minimum permeability is decreased. The partially penetrating ratio greatly affects the early well response, which leads to an early radial flow regime when the ratio is set to be a small value. Finally, the newly proposed method has been successfully extended to determine the reservoir and fracture parameters in a real field case."]},{"key":"dc:title","label":"Title","values":["Performance Evaluation of Wells With Single and Multiple Fractures in Tight Formations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Yang, Daoyong (Tony)"],"dc:contributor.committeemember":["Torabi, Farshid","Gu, Yongan (Peter)"],"dc:creator":["Zhang, Feng"],"dc:date.accessioned":["2014-10-17T15:48:34Z"],"dc:date.available":["2014-10-17T15:48:34Z"],"dc:date.issued":["2013-08"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Petroleum Systems Engineering, University of Regina. xvi, 136 p."],"dc:description.abstract":["Hydraulic fracturing technology together with horizontal wells leads to the exploration and development of unconventional resources economically feasible. Due to complex fracture network and geology nature, evaluating performance of fluids flow in such a hydraulic fracture system is really a challenge. Numerical modeling and simulation usually requires very fine grid to reduce the truncation error and enhance the simulation accuracy. Sometimes even with fine grid, the associated computation accuracy is compromised. On the other hand, numerous studies have been conducted on pressure transient analysis with analytical and/or numerical methods, though some underlying mechanisms have not been well understood since fluid flow in such tight formations can be completely dependent on the fracture network while the matrix only plays a source role. Therefore, it is of fundamental and practical importance to evaluate performance of a well with single and multiple fractures in a tight formation. Theoretically, a semi-analytical method is developed to couple the fluid flow in the matrix and the fracture so as to improve the accuracy and efficiency of pressure transient analysis in a tight formation. As for the semi-analytical method, the fracture is firstly discretized into several small segments. Equations for the matrix and fracture system can be solved in the Laplace domain with source functions, respectively. Continuity equations can be obtained along the fracture interface, leading to a linear system. Solving the linear system, the flux in each segment can be obtained, which is substituted into the first segment to determine the bottomhole pressure in the Laplace domain. Finally, the Stephest inverse algorithm can be employed to convert the solutions in the Laplace domain to those in the real time domain. The widely-accepted point source function is used to describe the fluid flow in the matrix for a vertical well with a single fracture, while a novel slab source function in the Laplace domain is developed to achieve the same purpose for a horizontal well with multiple fractures. Compared to the point source function, slab source function is more general, which attributes geometry in each direction and considers the pressure effect inside the source by superposition principle. The non-Darcy flow effect inside the fracture based on the Barree-Conway model is solved by introducing the pseudo-time and iterative methods. The semi-analytical method using source functions has been validated with numerical simulation method and field case, respectively. Subsequently, two dimensionless parameters, i.e., relative minimum permeability (kmr) and non-Darcy number (FND), have been introduced to incorporate the non-Darcy effect on flow performance for a vertical well with single fracture. Compared with the Forchheimer’s equation, the Barree-Conway model causes a smaller pressure drop at a higher non-Darcy number. The fracture conductivity would be underestimated when non-Darcy flow exists inside the fracture. For a horizontal well with multiple fractures, fracture conductivity, fracture stages, fracture number, and fracture dimension are discussed under consideration of both non-Darcy effect and partially penetrating ratio. Compared to the vertical well with single fracture, non-Darcy effect in a horizontal well with multiple fractures can cause a larger pressure drop as non-Darcy number is increased and relative minimum permeability is decreased. The partially penetrating ratio greatly affects the early well response, which leads to an early radial flow regime when the ratio is set to be a small value. Finally, the newly proposed method has been successfully extended to determine the reservoir and fracture parameters in a real field case."],"dc:identifier.doi":["https://doi.org/10.82465/4245"],"dc:identifier.uri":["https://hdl.handle.net/10294/5396"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Performance Evaluation of Wells With Single and Multiple Fractures in Tight Formations"],"dc:type":["master thesis"],"thesis:degree_discipline":["Engineering - Petroleum Systems"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Applied Science (MASc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:34Z"}