A large language model(LLM)is constructed to address the sophisticated demands of data retrieval and analysis,detailed well profiling,computation of key technical indicators,and the solutions to complex problems in re...A large language model(LLM)is constructed to address the sophisticated demands of data retrieval and analysis,detailed well profiling,computation of key technical indicators,and the solutions to complex problems in reservoir performance analysis(RPA).The LLM is constructed for RPA scenarios with incremental pre-training,fine-tuning,and functional subsystems coupling.Functional subsystem and efficient coupling methods are proposed based on named entity recognition(NER),tool invocation,and Text-to-SQL construction,all aimed at resolving pivotal challenges in developing the specific application of LLMs for RDA.This study conducted a detailed accuracy test on feature extraction models,tool classification models,data retrieval models and analysis recommendation models.The results indicate that these models have demonstrated good performance in various key aspects of reservoir dynamic analysis.The research takes some injection and production well groups in the PK3 Block of the Daqing Oilfield as an example for testing.Testing results show that our model has significant potential and practical value in assisting reservoir engineers with RDA.The research results provide a powerful support to the application of LLM in reservoir performance analysis.展开更多
Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstr...Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.展开更多
Using gas and rock samples from major petroliferous basins in the world,the helium content,composition,isotopic compositions and the U and Th contents in rocks are analyzed to clarify the helium enrichment mechanism a...Using gas and rock samples from major petroliferous basins in the world,the helium content,composition,isotopic compositions and the U and Th contents in rocks are analyzed to clarify the helium enrichment mechanism and distribution pattern and the exploration ideas for helium-rich gas reservoirs.It is believed that the formation of helium-rich gas reservoirs depends on the amount of helium supplied to the reservoir and the degree of helium dilution by natural gas,and that the reservoir-forming process can be summarized as"multi-source helium supply,main-source helium enrichment,helium-nitrogen coupling,and homogeneous symbiosis".Helium mainly comes from the radioactive decay of U and Th in rocks.All rocks contain trace amounts of U and Th,so they are effective helium sources.Especially,large-scale ancient basement dominated by granite or metamorphic rocks is the main helium source.The helium generated by the decay of U and Th in the ancient basement in a long geologic history,together with the nitrogen generated by the cracking of the inorganic nitrogenous compounds in the basement rocks,is dissolved in the water and preserved.With the tectonic uplift,the ground water is transported upward along the fracture to the gas reservoirs,with helium and nitrogen released.Thus,the reservoirs are enriched with both helium and nitrogen,which present a clear concomitant and coupling relationship.In tensional basins in eastern China,where tectonic activities are strong,a certain proportion of mantle-derived helium is mixed in the natural gas.The helium-rich gas reservoirs are mostly located in normal or low-pressure zones above ancient basement with fracture communication,which later experience substantial tectonic uplift and present relatively weak seal,low intensity of natural gas charging,and active groundwater.Helium exploration should focus on gas reservoirs with fractures connecting ancient basement,large tectonic uplift,relatively weak sealing capacity,insufficient natural gas charging intensity,and rich ancient formation water,depending on the characteristics of helium enrichment,beyond the traditional idea of searching for natural gas sweetspots and high-yield giant gas fields simultaneously.展开更多
Based on the tectonic genesis and seismic data of fault-controlled fractured-vuggy reservoirs,the typical fractured-vuggy structure features were analyzed.A 3D large-scale visual physical model of“tree-like”fracture...Based on the tectonic genesis and seismic data of fault-controlled fractured-vuggy reservoirs,the typical fractured-vuggy structure features were analyzed.A 3D large-scale visual physical model of“tree-like”fractured-vuggy structure was designed and made.The experiments of bottom-water flooding and multi-media synergistic oil displacement after bottom-water flooding were conducted with different production rates and different well-reservoir configuration relationships.The formation mechanisms and distribution rules of residual oil during bottom-water flooding under such fractured-vuggy structure were revealed.The producing characteristics of residual oil under different production methods after bottom-water flooding were discovered.The results show that the remaining oil in"tree-like"fractured-vuggy structure after bottom-water flooding mainly include the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones.There exists obvious water channeling of bottom-water along the fault at high production rate,but intermittent drainage can effectively weaken the interference effect between fault zones to inhibit water channeling.Compared with the vertical well,horizontal well can reduce the difference in flow conductivity between fault zones and show better resistance to water channeling.The closer the horizontal well locates to the upper part of the“canopy”,the higher the oil recovery is at the bottom-water flooding stage.However,comprehensive consideration of the bottom-water flooding and subsequent gas injection development,the total recovery is higher when the horizontal well locates in the middle part of the“canopy”and drills through a large number of fault zones.After bottom water flooding,the effect of gas huff and puff is better than that of gas flooding,and the effect of gas huff and puff with large slug is better than that of small slug.Because such development method can effectively develop the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones transversely connected with oil wells,thus greatly improving the oil recovery.展开更多
The Liaohe Oil Field has passed peak production and correct discrimination of hydraulic units(HU) has vital significance for forecasting remaining oil distribution in a petroleum reservoir, enhancing the recovery ra...The Liaohe Oil Field has passed peak production and correct discrimination of hydraulic units(HU) has vital significance for forecasting remaining oil distribution in a petroleum reservoir, enhancing the recovery ratio and adjusting development plans. A unified multi-parameter cluster analysis and fuzzy quality synthetic evaluations have been used for the identification of reservoir hydraulic units. This paper analyzes three predictions within Block Shen-95: intersection of multiple well-logs, independent mulitple well-logs and mutually exclusive multiple well-logs. HU has been delineated to conveniently compute permeability and serve as the basis of a structural model for enhanced simulation study. HU has been defined by the flow zone indicator concept using a modified Kozeny-Carmen equation. The Bayesian method was used to predict HU at uncored wells by constructing a probability database and then integrating established HU and well-log responses at cored wells. HU has then been inferred from the database using well-log responses. Estimated permeability from predicted HU gave an overall improved permeability match when compared with traditional statistical methods. The method proved most favourable when using mutually exclusive multiple well-logs, most significant by integrating reservoir performance with HU distribution and indicating that reasonable prediction had been obtained at uncored wells using this mutually exclusive approach. The distribution pattern was revealed by interwell HU correlation using modified depositional cycles as a framework, an integration step that qualitatively examines prediction accuracy. Detailed analysis has been carried out to determine and verify the characteristics of each kind of flow unit, providing a detailed geological basis for control of the oil field.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
基金Supported by the National Talent Fund of the Ministry of Science and Technology of China(20230240011)China University of Geosciences(Wuhan)Research Fund(162301192687)。
文摘A large language model(LLM)is constructed to address the sophisticated demands of data retrieval and analysis,detailed well profiling,computation of key technical indicators,and the solutions to complex problems in reservoir performance analysis(RPA).The LLM is constructed for RPA scenarios with incremental pre-training,fine-tuning,and functional subsystems coupling.Functional subsystem and efficient coupling methods are proposed based on named entity recognition(NER),tool invocation,and Text-to-SQL construction,all aimed at resolving pivotal challenges in developing the specific application of LLMs for RDA.This study conducted a detailed accuracy test on feature extraction models,tool classification models,data retrieval models and analysis recommendation models.The results indicate that these models have demonstrated good performance in various key aspects of reservoir dynamic analysis.The research takes some injection and production well groups in the PK3 Block of the Daqing Oilfield as an example for testing.Testing results show that our model has significant potential and practical value in assisting reservoir engineers with RDA.The research results provide a powerful support to the application of LLM in reservoir performance analysis.
文摘Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.
基金Supported by the National Natural Science Foundation of China(42141022,42272189)Project of Ministry of Natural Resources of China(QGYQZYPJ2022-1)CNPC Core Project(2021ZG12)。
文摘Using gas and rock samples from major petroliferous basins in the world,the helium content,composition,isotopic compositions and the U and Th contents in rocks are analyzed to clarify the helium enrichment mechanism and distribution pattern and the exploration ideas for helium-rich gas reservoirs.It is believed that the formation of helium-rich gas reservoirs depends on the amount of helium supplied to the reservoir and the degree of helium dilution by natural gas,and that the reservoir-forming process can be summarized as"multi-source helium supply,main-source helium enrichment,helium-nitrogen coupling,and homogeneous symbiosis".Helium mainly comes from the radioactive decay of U and Th in rocks.All rocks contain trace amounts of U and Th,so they are effective helium sources.Especially,large-scale ancient basement dominated by granite or metamorphic rocks is the main helium source.The helium generated by the decay of U and Th in the ancient basement in a long geologic history,together with the nitrogen generated by the cracking of the inorganic nitrogenous compounds in the basement rocks,is dissolved in the water and preserved.With the tectonic uplift,the ground water is transported upward along the fracture to the gas reservoirs,with helium and nitrogen released.Thus,the reservoirs are enriched with both helium and nitrogen,which present a clear concomitant and coupling relationship.In tensional basins in eastern China,where tectonic activities are strong,a certain proportion of mantle-derived helium is mixed in the natural gas.The helium-rich gas reservoirs are mostly located in normal or low-pressure zones above ancient basement with fracture communication,which later experience substantial tectonic uplift and present relatively weak seal,low intensity of natural gas charging,and active groundwater.Helium exploration should focus on gas reservoirs with fractures connecting ancient basement,large tectonic uplift,relatively weak sealing capacity,insufficient natural gas charging intensity,and rich ancient formation water,depending on the characteristics of helium enrichment,beyond the traditional idea of searching for natural gas sweetspots and high-yield giant gas fields simultaneously.
基金Supported by the National Natural Science Foundation of China(52074344)。
文摘Based on the tectonic genesis and seismic data of fault-controlled fractured-vuggy reservoirs,the typical fractured-vuggy structure features were analyzed.A 3D large-scale visual physical model of“tree-like”fractured-vuggy structure was designed and made.The experiments of bottom-water flooding and multi-media synergistic oil displacement after bottom-water flooding were conducted with different production rates and different well-reservoir configuration relationships.The formation mechanisms and distribution rules of residual oil during bottom-water flooding under such fractured-vuggy structure were revealed.The producing characteristics of residual oil under different production methods after bottom-water flooding were discovered.The results show that the remaining oil in"tree-like"fractured-vuggy structure after bottom-water flooding mainly include the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones.There exists obvious water channeling of bottom-water along the fault at high production rate,but intermittent drainage can effectively weaken the interference effect between fault zones to inhibit water channeling.Compared with the vertical well,horizontal well can reduce the difference in flow conductivity between fault zones and show better resistance to water channeling.The closer the horizontal well locates to the upper part of the“canopy”,the higher the oil recovery is at the bottom-water flooding stage.However,comprehensive consideration of the bottom-water flooding and subsequent gas injection development,the total recovery is higher when the horizontal well locates in the middle part of the“canopy”and drills through a large number of fault zones.After bottom water flooding,the effect of gas huff and puff is better than that of gas flooding,and the effect of gas huff and puff with large slug is better than that of small slug.Because such development method can effectively develop the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones transversely connected with oil wells,thus greatly improving the oil recovery.
基金supported by the National Important Special of China (No. 2011ZX05016-002)
文摘The Liaohe Oil Field has passed peak production and correct discrimination of hydraulic units(HU) has vital significance for forecasting remaining oil distribution in a petroleum reservoir, enhancing the recovery ratio and adjusting development plans. A unified multi-parameter cluster analysis and fuzzy quality synthetic evaluations have been used for the identification of reservoir hydraulic units. This paper analyzes three predictions within Block Shen-95: intersection of multiple well-logs, independent mulitple well-logs and mutually exclusive multiple well-logs. HU has been delineated to conveniently compute permeability and serve as the basis of a structural model for enhanced simulation study. HU has been defined by the flow zone indicator concept using a modified Kozeny-Carmen equation. The Bayesian method was used to predict HU at uncored wells by constructing a probability database and then integrating established HU and well-log responses at cored wells. HU has then been inferred from the database using well-log responses. Estimated permeability from predicted HU gave an overall improved permeability match when compared with traditional statistical methods. The method proved most favourable when using mutually exclusive multiple well-logs, most significant by integrating reservoir performance with HU distribution and indicating that reasonable prediction had been obtained at uncored wells using this mutually exclusive approach. The distribution pattern was revealed by interwell HU correlation using modified depositional cycles as a framework, an integration step that qualitatively examines prediction accuracy. Detailed analysis has been carried out to determine and verify the characteristics of each kind of flow unit, providing a detailed geological basis for control of the oil field.
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.