This paper introduces a new approach for reservoir performance where long horizontal wellbores are extended in the porous media with the existence of closed sections.It focuses on the impact of these sections on the p...This paper introduces a new approach for reservoir performance where long horizontal wellbores are extended in the porous media with the existence of closed sections.It focuses on the impact of these sections on the pressure behavior,flow regimes,and productivity index considering different characteristics for the closed sections in terms of the length and petrophysical properties.The methodology used in this approach includes different tasks.The first is developing analytical models for the pressure drop caused by the production at a constant sandface flow rate from a horizontal wellbore where a part of it is closed.These models are developed based on the fact that the porous media with the existence of the closed sections in the horizontal wellbores consists of three regions.The first represents the porous media in the vicinity of the open section of the wellbore and extends to a distance equal to half the formation thickness while the second is the porous media of the open section that extends beyond the first region and reaches the reservoir boundary.The third region represents the porous media of the closed sections that extend from the wellbore to the reservoir boundary.In the second task,the proposed models are solved for different reservoir configurations,wellbore lengths,and closed and open section characteristics.The impact of closed sections on transient and stabilized pseudo-steady state productivity indices are demonstrated in third tacks while the analytical models of the observed flow regimes in the porous media are presented in the fourth task with a major focus given to those impacted by the closed sections.The outcomes of this study can be summarized in the following points:1)The pressure behavior,flow regimes,and productivity index are significantly influenced by the existence of closed sections.This influence is significant during early production time,but it decreases during intermediate production,however,it is not seen at late production time.2)The impact of closed sections becomes more severe when the petrophysical properties of the closed sections are greatly different from those of open sections.3)The pressure behavior of early production time is not affected by the petrophysical properties of the closed section porous media while pseudo-steady state flow is significantly impacted by these properties.4)The pressure and pressure derivative behaviors of long horizontal wellbores with long closed sections are similar to those developed in reservoirs depleted by hydraulic fractures.5)Reaching pseudo-steady state flow may need a longer time when there is a great difference in the petrophysical properties between closed and open sections,however,the length of the closed sections may not have such impact.The novel point that has reached in this study is observing a new bi-linear flow regime instead of a linear flow regime.This flow regime represents a simultaneous linear flow from the closed section porous media to the open section and from the open section to the porous media in the vicinity of the open section of the wellbore.New analytical models for the pressure and pressure derivative of this flow regime is introduced in this study.展开更多
The applicability of early time data in reservoir characterization is not always considered worthy.Early time data is usually controlled by wellbore storage effect.This effect may last for pseudo-radial flow or even b...The applicability of early time data in reservoir characterization is not always considered worthy.Early time data is usually controlled by wellbore storage effect.This effect may last for pseudo-radial flow or even boundary dominated flow.Eliminating this effect is an option for restoring real data.Using the data with this effect is another option that could be used successfully for reservoir characterization.This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production.The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures.Several analytical models describe early time data,controlled by wellbore storage effect,have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures.The relationships of the peak points(humps)with the pressure,pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients.For horizontal wells,a complete set of type curves has been included for different wellbore lengths,skin factors and wellbore storage coefficients.Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures,spacing between fractures,and wellbore storage coefficient.The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells;early linear flow is the most affected flow regime by wellbore storage effect.The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect.As a matter of fact,this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times.These relationships can be used to properly describe the formations and quantify some of their characteristics.展开更多
The objective of this paper is introducing practical solutions for stabilized pseudo-steady state productivity index and pressure behaviors and flow regimes of multiple vertical wells depleting closed rectangular rese...The objective of this paper is introducing practical solutions for stabilized pseudo-steady state productivity index and pressure behaviors and flow regimes of multiple vertical wells depleting closed rectangular reservoirs.It introduces full understanding of reservoir performance during transient and pseudo-steady state flow using pressure and pressure derivative patterns and productivity index and productivity index derivative schemes.The practical solutions proposed in this study are relied on a new approach for accurate estimation of starting time of pseudo-steady state flow and stabilized productivity index by applying productivity index derivative that converges mathematically to zero at the beginning of this flow.It is also an attempt for pointing out the optimal reservoir configuration that can give maximum stabilized pseudo-steady state productivity index for different wellbore types and distributions in the drainage area.Several analytical models are used in this study for describing pressure drop and productivity index behavior of multiple vertical wells considering different reservoir configurations and different wellbore types and locations.These wells were assumed either fully or partially penetrate the formations.These pressure models are justified to generate two pressure derivatives,one represents the derivative of time dependent pressure drop and the second represents the derivative of time-invariant pressure drop.The two derivatives are used for determining the starting time of pseudo-steady state flow and stabilized productivity index when both converge and mathematically become identical.These models are used also to generate several plots for time-invariant or stabilized pseudo-steady state productivity index for different reservoir geometries considering different wellbore conditions.The maximum stabilized productivity index is illustrated in these plots and several analytical models for the expected flow regimes are developed using pressure and pressure derivative behaviors of different reservoirs and wellbore conditions.The outcomes of this study are summarized in:1)Developing new analytical solutions for pressure distribution in porous media drained by multiple vertical wells.2)Developing new practical solution for estimating stabilized pseudo-steady state productivity index.3)Understanding pressure,pressure derivative,and productivity index behavior of finite acting reservoir depleted by multiple vertical wells during transient and pseudo-steady state production.4)Investigating the impacts of different reservoir configurations and wellbore sizes and locations as well as partial penetration on stabilized pseudo-steady state productivity index.The novel points in this study are:1)The optimum reservoir configuration that gives the maximum stabilized productivity index is the rectangular shape reservoir with reservoir length to width ratio of(2-4).2)Starting time of pseudo-steady state and stabilized productivity index are impacted by wellbore numbers,sizes,and locations.3)Starting time of pseudo-steady state flow is not affected by partial penetration ratio,however,stabilized productivity index is affected by this ratio.4)Five spots pattern gives the maximum productivity index compared with other wellbore distribution patterns.5)Productivity index of diagonally distributed wellbores is greater than the index of wellbores distributed along reservoir length.展开更多
This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs.This approach demonstrates the impact of v...This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs.This approach demonstrates the impact of variable Sand face flow rate on reservoir performance.A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response.The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume.Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study.This model depicts,instead of van Everdingen model,indirectly the declining rate with time by using pressure responses with production time.Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model.Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions.The results are interpreted and analyzed for better understanding pressure behaviors,flow regime types,and productivity index trends for continuously changing flow rate especially at early production time.Estimating stimulated reservoir volume(Vsrv)is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached.The outcomes of this study can be summarized as:1)Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time.2)Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution.3)Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior.4)Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response.5)Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume.The most interesting points are:1)The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time,however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure.2)A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime.3)Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate.4)The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate.5)The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.展开更多
The objective of this paper is studying the impact of the hydraulic flow unit and reservoir quality index(RQI)on pressure profile and productivity index of horizontal wells acting in finite reservoirs.Several mathemat...The objective of this paper is studying the impact of the hydraulic flow unit and reservoir quality index(RQI)on pressure profile and productivity index of horizontal wells acting in finite reservoirs.Several mathematical models have been developed to investigate this impact.These models have been built based on the pressure distribution in porous media,depleted by a horizontal well,consist of multi hydraulic flow units and different reservoir quality index.The porous media are assumed to be finite rectangular reservoirs having different configurations and the wellbores may have different lengths.Several analytical models describing flow regimes have been derived wherein hydraulic flow units and reservoir quality index have been included in addition to rock and fluid properties.The impact of these two parameters on reservoir performance has also been studied using steady state productivity index.It has been found that both pressure responses and flow regimes are highly affected by the existence of multiple hydraulic flow units in the porous media and the change in reservoir quality index for these units.Positive change in the RQI could lead to positive change in both pressure drop required for reservoir fluids to move towards the wellbore and hence the productivity index.展开更多
文摘This paper introduces a new approach for reservoir performance where long horizontal wellbores are extended in the porous media with the existence of closed sections.It focuses on the impact of these sections on the pressure behavior,flow regimes,and productivity index considering different characteristics for the closed sections in terms of the length and petrophysical properties.The methodology used in this approach includes different tasks.The first is developing analytical models for the pressure drop caused by the production at a constant sandface flow rate from a horizontal wellbore where a part of it is closed.These models are developed based on the fact that the porous media with the existence of the closed sections in the horizontal wellbores consists of three regions.The first represents the porous media in the vicinity of the open section of the wellbore and extends to a distance equal to half the formation thickness while the second is the porous media of the open section that extends beyond the first region and reaches the reservoir boundary.The third region represents the porous media of the closed sections that extend from the wellbore to the reservoir boundary.In the second task,the proposed models are solved for different reservoir configurations,wellbore lengths,and closed and open section characteristics.The impact of closed sections on transient and stabilized pseudo-steady state productivity indices are demonstrated in third tacks while the analytical models of the observed flow regimes in the porous media are presented in the fourth task with a major focus given to those impacted by the closed sections.The outcomes of this study can be summarized in the following points:1)The pressure behavior,flow regimes,and productivity index are significantly influenced by the existence of closed sections.This influence is significant during early production time,but it decreases during intermediate production,however,it is not seen at late production time.2)The impact of closed sections becomes more severe when the petrophysical properties of the closed sections are greatly different from those of open sections.3)The pressure behavior of early production time is not affected by the petrophysical properties of the closed section porous media while pseudo-steady state flow is significantly impacted by these properties.4)The pressure and pressure derivative behaviors of long horizontal wellbores with long closed sections are similar to those developed in reservoirs depleted by hydraulic fractures.5)Reaching pseudo-steady state flow may need a longer time when there is a great difference in the petrophysical properties between closed and open sections,however,the length of the closed sections may not have such impact.The novel point that has reached in this study is observing a new bi-linear flow regime instead of a linear flow regime.This flow regime represents a simultaneous linear flow from the closed section porous media to the open section and from the open section to the porous media in the vicinity of the open section of the wellbore.New analytical models for the pressure and pressure derivative of this flow regime is introduced in this study.
文摘The applicability of early time data in reservoir characterization is not always considered worthy.Early time data is usually controlled by wellbore storage effect.This effect may last for pseudo-radial flow or even boundary dominated flow.Eliminating this effect is an option for restoring real data.Using the data with this effect is another option that could be used successfully for reservoir characterization.This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production.The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures.Several analytical models describe early time data,controlled by wellbore storage effect,have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures.The relationships of the peak points(humps)with the pressure,pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients.For horizontal wells,a complete set of type curves has been included for different wellbore lengths,skin factors and wellbore storage coefficients.Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures,spacing between fractures,and wellbore storage coefficient.The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells;early linear flow is the most affected flow regime by wellbore storage effect.The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect.As a matter of fact,this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times.These relationships can be used to properly describe the formations and quantify some of their characteristics.
文摘The objective of this paper is introducing practical solutions for stabilized pseudo-steady state productivity index and pressure behaviors and flow regimes of multiple vertical wells depleting closed rectangular reservoirs.It introduces full understanding of reservoir performance during transient and pseudo-steady state flow using pressure and pressure derivative patterns and productivity index and productivity index derivative schemes.The practical solutions proposed in this study are relied on a new approach for accurate estimation of starting time of pseudo-steady state flow and stabilized productivity index by applying productivity index derivative that converges mathematically to zero at the beginning of this flow.It is also an attempt for pointing out the optimal reservoir configuration that can give maximum stabilized pseudo-steady state productivity index for different wellbore types and distributions in the drainage area.Several analytical models are used in this study for describing pressure drop and productivity index behavior of multiple vertical wells considering different reservoir configurations and different wellbore types and locations.These wells were assumed either fully or partially penetrate the formations.These pressure models are justified to generate two pressure derivatives,one represents the derivative of time dependent pressure drop and the second represents the derivative of time-invariant pressure drop.The two derivatives are used for determining the starting time of pseudo-steady state flow and stabilized productivity index when both converge and mathematically become identical.These models are used also to generate several plots for time-invariant or stabilized pseudo-steady state productivity index for different reservoir geometries considering different wellbore conditions.The maximum stabilized productivity index is illustrated in these plots and several analytical models for the expected flow regimes are developed using pressure and pressure derivative behaviors of different reservoirs and wellbore conditions.The outcomes of this study are summarized in:1)Developing new analytical solutions for pressure distribution in porous media drained by multiple vertical wells.2)Developing new practical solution for estimating stabilized pseudo-steady state productivity index.3)Understanding pressure,pressure derivative,and productivity index behavior of finite acting reservoir depleted by multiple vertical wells during transient and pseudo-steady state production.4)Investigating the impacts of different reservoir configurations and wellbore sizes and locations as well as partial penetration on stabilized pseudo-steady state productivity index.The novel points in this study are:1)The optimum reservoir configuration that gives the maximum stabilized productivity index is the rectangular shape reservoir with reservoir length to width ratio of(2-4).2)Starting time of pseudo-steady state and stabilized productivity index are impacted by wellbore numbers,sizes,and locations.3)Starting time of pseudo-steady state flow is not affected by partial penetration ratio,however,stabilized productivity index is affected by this ratio.4)Five spots pattern gives the maximum productivity index compared with other wellbore distribution patterns.5)Productivity index of diagonally distributed wellbores is greater than the index of wellbores distributed along reservoir length.
文摘This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs.This approach demonstrates the impact of variable Sand face flow rate on reservoir performance.A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response.The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume.Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study.This model depicts,instead of van Everdingen model,indirectly the declining rate with time by using pressure responses with production time.Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model.Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions.The results are interpreted and analyzed for better understanding pressure behaviors,flow regime types,and productivity index trends for continuously changing flow rate especially at early production time.Estimating stimulated reservoir volume(Vsrv)is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached.The outcomes of this study can be summarized as:1)Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time.2)Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution.3)Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior.4)Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response.5)Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume.The most interesting points are:1)The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time,however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure.2)A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime.3)Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate.4)The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate.5)The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.
文摘The objective of this paper is studying the impact of the hydraulic flow unit and reservoir quality index(RQI)on pressure profile and productivity index of horizontal wells acting in finite reservoirs.Several mathematical models have been developed to investigate this impact.These models have been built based on the pressure distribution in porous media,depleted by a horizontal well,consist of multi hydraulic flow units and different reservoir quality index.The porous media are assumed to be finite rectangular reservoirs having different configurations and the wellbores may have different lengths.Several analytical models describing flow regimes have been derived wherein hydraulic flow units and reservoir quality index have been included in addition to rock and fluid properties.The impact of these two parameters on reservoir performance has also been studied using steady state productivity index.It has been found that both pressure responses and flow regimes are highly affected by the existence of multiple hydraulic flow units in the porous media and the change in reservoir quality index for these units.Positive change in the RQI could lead to positive change in both pressure drop required for reservoir fluids to move towards the wellbore and hence the productivity index.
