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Applying Tiab's direct synthesis technique to dilatant non-Newtonian/Newtonian fluids
Martínez,Javier Andrés; Escobar,Freddy Humberto; Cantillo,José Humberto;
Ingeniería e Investigación , 2011,
Abstract: non-newtonian fluids, such as polymer solutions, have been used by the oil industry for many years as fracturing agents and drilling mud. these solutions, which normally include thickened water and jelled fluids, are injected into the formation to enhanced oil recovery by improving sweep efficiency. it is worth noting that some heavy oils behave non-newtonianly. non-newtonian fluids do not have direct proportionality between applied shear stress and shear rate and viscosity varies with shear rate depending on whether the fluid is either pseudoplastic or dilatant. viscosity decreases as shear rate increases for the former whilst the reverse takes place for dilatants. mathematical models of conventional fluids thus fail when applied to non-newtonian fluids. the pressure derivative curve is introduced in this descriptive work for a dilatant fluid and its pattern was observed. tiab's direct synthesis (tds) methodology was used as a tool for interpreting pressure transient data to estimate effective permeability, skin factors and non-newtonian bank radius. the methodology was successfully verified by its application to synthetic examples. also, comparing it to pseudoplastic behavior, it was found that the radial flow regime in the newtonian zone of dilatant fluids took longer to form regarding both the flow behavior index and consistency factor.
PRESSURE AND PRESSURE DERIVATIVE ANALYSIS FOR VERTICAL GAS AND OIL WELLS IN STRESS SENSITIVE HOMOGENEOUS AND NATURALLY FRACTURED FORMATIONS WITHOUT TYPE-CURVE MATCHING
Escobar,Freddy-Humberto; Cantillo,José-Humberto; Montealegre-M,Matilde;
CT&F - Ciencia, Tecnología y Futuro , 2007,
Abstract: currently, rock mechanics plays an important role in the oil industry. effects of reservoir subsidence, compaction and dilation are being taken into account in modern reservoir management of complex systems. on the other hand, pressure well tests run in stress sensitive formations ought to be interpreted with non conventional techniques. during the last three decades, several studies relating transient pressure analysis for characterization of stress sensitive reservoirs have been introduced in the literature. some of them deal with type curves and/or automated history matching. however, due to the nature of the problem, it does not exist a definitive study focused on the adequate characterization of reservoirs which permeability changes as fluid withdrawal advances. in this paper, the permeability modulus concept introduced by pedrosa (1986) is taken as the starting basis. a great number of type curves were generated to study the behavior of the above mentioned formations under stress influence. it was found that permeability modulus, therefore permeability changes, can be correlated with the slope of the pressure derivative trend during the radial flow regime when the reservoir suffers compaction. it is also worth to mention that the time at which the minimum characteristic point of a naturally fractured formation (or the inflection point of a semilog plot) found on the pressure derivative plot is practically the same for formations without stress influence. this contributes to the extension of the tds technique, tiab (1993), so a new methodology to characterize this kind of reservoirs is proposed here. this was verified by the solution of synthetic problems.
RATE TRANSIENT ANALYSIS FOR HOMOGENEOUS AND HETEROGENEOUS GAS RESERVOIRS USING THE TDS TECHNIQUE
Escobar,Freddy- Humberto; Sánchez,Jairo Andrés; Cantillo,José Humberto;
CT&F - Ciencia, Tecnología y Futuro , 2008,
Abstract: in this study pressure test analysis in wells flowing under constant wellbore flowing pressure for homogeneous and naturally fractured gas reservoir using the tds technique is introduced. although, constant rate production is assumed in the development of the conventional well test analysis methods, constant pressure production conditions are sometimes used in the oil and gas industry. the constant pressure technique or rate transient analysis is more popular reckoned as "decline curve analysis" under which rate is allows to decline instead of wellbore pressure. the tds technique, everyday more used even in the most recognized software packages although without using its trade brand name, uses the log-log plot to analyze pressure and pressure derivative test data to identify unique features from which exact analytical expression are derived to easily estimate reservoir and well parameters. for this case, the "fingerprint" characteristics from the log-log plot of the reciprocal rate and reciprocal rate derivative were employed to obtain the analytical expressions used for the interpretation analysis. many simulation experiments demonstrate the accuracy of the new method. synthetic examples are shown to verify the effectiveness of the proposed methodology.
EFFECT OF THE PSEUDOTIME FUNCTION ON GAS RESERVOIR DRAINAGE AREA DETERMINATION
Escobar,Freddy-Humberto; López,Aura-María; Cantillo,José-Humberto;
CT&F - Ciencia, Tecnología y Futuro , 2007,
Abstract: the gas flow equation is normally linearized to allow the liquid solution of the diffusivity equation to satisfy gas behavior when analyzing transient test data of gas reservoirs. when wellbore storage conditions are insignificant, drawdown tests are best analyzed using the pseudopressure function. on the other hand, buildup pressure tests require linearization of both pseudotime and pseudopressure. it is not the case for the tds technique which is indifferently applied to either drawdown or buildup tests. however, whichever the case, pseudotime has certain effect at very long testing times in formations of moderate to high permeability. in this paper, we implemented the tiab’s direct synthesis (tds) technique, to include pseudotime effects, and observe its influence on the interpretation results of gas well test data at early and late time periods. new analytical equations to estimate reservoir permeability, wellbore storage coefficient, pseudoskin factor and reservoir drainage area are presented. then, a comparison of results against rigorous time was carried out for simulated and field cases. we found acceptable results for permeability, pseudoskin factor and wellbore storage coefficient. however, for the case of reservoir drainage area, the deviation error was of 4,1% for a simulated case and 17,9% for a field case. however, the smaller of these deviations may be small if related to pressure transient analysis results. however, this deviation in a gas reservoir with reserves of one tera standard cubic feet is equivalent to a huge difference of 38 gigas of standard cubic feet of gas which may have an economic impact to any oil company.
Pseudotime application to hydraulically fractured vertical gas wells and heterogenous gasreservoirs using the TDS technique
Freddy Humberto Escobar,Laura Yissed Martinez,Leidy Johanna Mendez,José Humberto Cantillo
Journal of Engineering and Applied Sciences , 2012,
Abstract: Contrary to liquid flow, the viscosity and compressibility of gases change substantially as pressure varies. This phenomenon has to be carefully modeled, so the gas flow equation can be adequately linearized to allow the liquid diffusivity solution to satisfy gas behavior when analyzing gas transient test data. The first solution to this problem was the introduction of the pseudopressure function that responds for variations of viscosity, density and compressibility which are combined into a single “pseudopressure” variable. Since, the dimensionless time function is also sensitive to changes in both viscosity and compressibility of gases, then, the pseudotime function was incorporated to combine these simultaneous variations into a single variable. This makes more accurate the estimation of the reservoir parameters. A recent study using the TDS technique has found little differences in estimation of permeability, wellbore storage coefficient and skin factor using either pseudotime or real time. However, the estimation of the drainage area is better determined when using pseudotime. This paper has the objective of extending the TDS technique for hydraulically fractured gas wells and heterogeneous gas formations and conducting a comparative study in the estimation of both the half-length and conductivity of a vertical fracture and the naturally fractured reservoir parameters. The new relationships were successfully tested on synthetic and actual field data. It was found better results when using the pseudotime function.
Applying Tiab’s direct synthesis technique to dilatant non-Newtonian/Newtonian fluids Aplicación de la técnica TDS a un yacimiento compuesto con fluidos dilatantes no newtoniano/newtoniano
Martínez Javier Andrés,Escobar Freddy Humberto,Cantillo José Humberto
Ingeniería e Investigación , 2011,
Abstract: Non-Newtonian fluids, such as polymer solutions, have been used by the oil industry for many years as fracturing agents and drilling mud. These solutions, which normally include thickened water and jelled fluids, are injected into the formation to enhanced oil recovery by improving sweep efficiency. It is worth noting that some heavy oils behave non-Newtonianly. Non-Newtonian fluids do not have direct proportionality between applied shear stress and shear rate and viscosity varies with shear rate depending on whether the fluid is either pseudoplastic or dilatant. Viscosity decreases as shear rate increases for the former whilst the reverse takes place for dilatants. Mathematical models of conventional fluids thus fail when applied to non-Newtonian fluids. The pressure derivative curve is introduced in this descriptive work for a dilatant fluid and its pattern was observed. Tiab’s direct synthesis (TDS) methodology was used as a tool for interpreting pressure transient data to estimate effective permeability, skin factors and non-Newtonian bank radius. The methodology was successfully verified by its application to synthetic examples. Also, comparing it to pseudoplastic behavior, it was found that the radial flow regime in the Newtonian zone of dilatant fluids took longer to form regarding both the flow behavior index and consistency factor. Por muchos a os, los fluidos no Newtonianos, tales como los polímeros, se han usado en la industria del petróleo como agentes de fracturamiento y en lodos de perforación. Estas soluciones las cuales normalmente contienen agua, son inyectadas en la formación para la recuperación mejorada de petróleo mediante el mejoramiento de la eficiencia de barrido. Es de resaltar que algunos crudos pesados también tienen comportamiento no Newtoniano. Los fluidos no Newtonianos no exhiben una proporcionalidad directa entre el esfuerzo de corte aplicado y la rata de corte; la viscosidad varía con la rata de corte dependiendo si el fluido es pseudoplástico o dilatante. Para los primeros, la viscosidad decrece con el incremento de la rata de corte. Para los dilatantes ocurre el caso inverso. Por ello, los modelos matemáticos de los fluidos convencionales fallan al aplicarse en fluidos No Newtonianos. En este trabajo descriptivo, se introduce la curva de derivada de presión para un fluido dilatante y se observa su comportamiento. Se usa la metodología TDS como herramienta para la interpretación de transientes de presión de modo que se presentan expresiones nuevas para estimar las permeabilidades efectivas, factores de da o y el radio d
RATE TRANSIENT ANALYSIS FOR HOMOGENEOUS AND HETEROGENEOUS GAS RESERVOIRS USING THE TDS TECHNIQUE ANáLISIS DE PRUEBAS DE CAUDAL VARIABLE PARA YACIMIENTOS DE GAS HOMOGéNEOS Y HETEROGéNEOS MEDIANTE LA TéCNICA TDS
Freddy- Humberto Escobar,Jairo Andrés Sánchez,José Humberto Cantillo
CT&F - Ciencia, Tecnología y Futuro , 2008,
Abstract: In this study pressure test analysis in wells flowing under constant wellbore flowing pressure for homogeneous and naturally fractured gas reservoir using the TDS technique is introduced. Although, constant rate production is assumed in the development of the conventional well test analysis methods, constant pressure production conditions are sometimes used in the oil and gas industry. The constant pressure technique or rate transient analysis is more popular reckoned as "decline curve analysis" under which rate is allows to decline instead of wellbore pressure. The TDS technique, everyday more used even in the most recognized software packages although without using its trade brand name, uses the log-log plot to analyze pressure and pressure derivative test data to identify unique features from which exact analytical expression are derived to easily estimate reservoir and well parameters. For this case, the "fingerprint" characteristics from the log-log plot of the reciprocal rate and reciprocal rate derivative were employed to obtain the analytical expressions used for the interpretation analysis. Many simulation experiments demonstrate the accuracy of the new method. Synthetic examples are shown to verify the effectiveness of the proposed methodology. En este estudio se introduce el análisis de pruebas de presión en pozos de gas que fluyen a presión de fondo constante en formaciones homogéneas y naturalmente fracturadas usando la técnica TDS. Aunque normalmente se considera la producción de un pozo a caudal constante en el desarrollo de los métodos convencionales de interpretación de pruebas de pozos, el caso de producción de un pozo a condiciones de presión constante se usa en algunas ocasiones en la industria de los hidrocarburos. La técnica de presión constante o análisis de transientes de caudal se conoce más popularmente como "análisis de curvas de declinación" en la cual se permite que la rata de flujo decline en vez de hacerlo la presión del pozo. La técnica TDS se vuelve más popular cada día incluso en la mayoría de los programas comerciales que aunque sin usar su nombre de pila, usan el gráfico log-log para analizar datos de presión y la derivada de presión para identificar características únicas de las cuales se derivan relaciones analíticas exactas para estimar fácilmente los parámetros del yacimiento y el pozo. Para este caso "las huellas digitales" características procedentes del gráfico log-log del recíproco del caudal y la derivada del recíproco del caudal se emplearon para obtener expresiones analíticas que se usan para propósitos de
PRESSURE AND PRESSURE DERIVATIVE ANALYSIS FOR VERTICAL GAS AND OIL WELLS IN STRESS SENSITIVE HOMOGENEOUS AND NATURALLY FRACTURED FORMATIONS WITHOUT TYPE-CURVE MATCHING Analisis de la presión y derivada de presión para pozos verticales de gas y petróleo en formaciones homogéneas y naturalmente fracturadas sensibles a los esfuerzos
Freddy-Humberto Escobar,José-Humberto Cantillo,Matilde Montealegre-M
CT&F - Ciencia, Tecnología y Futuro , 2007,
Abstract: Currently, rock mechanics plays an important role in the oil industry. Effects of reservoir subsidence, compaction and dilation are being taken into account in modern reservoir management of complex systems. On the other hand, pressure well tests run in stress sensitive formations ought to be interpreted with non conventional techniques. During the last three decades, several studies relating transient pressure analysis for characterization of stress sensitive reservoirs have been introduced in the literature. Some of them deal with type curves and/or automated history matching. However, due to the nature of the problem, it does not exist a definitive study focused on the adequate characterization of reservoirs which permeability changes as fluid withdrawal advances. In this paper, the permeability modulus concept introduced by Pedrosa (1986) is taken as the starting basis. A great number of type curves were generated to study the behavior of the above mentioned formations under stress influence. It was found that permeability modulus, therefore permeability changes, can be correlated with the slope of the pressure derivative trend during the radial flow regime when the reservoir suffers compaction. It is also worth to mention that the time at which the minimum characteristic point of a naturally fractured formation (or the inflection point of a semilog plot) found on the pressure derivative plot is practically the same for formations without stress influence. This contributes to the extension of the TDS technique, Tiab (1993), so a new methodology to characterize this kind of reservoirs is proposed here. This was verified by the solution of synthetic problems. Actualmente la mecánica de rocas juega un papel importante en la industria del petróleo. Los efectos de subsidencia, compactación y dilatación del yacimiento se están tomando en cuenta para la administración adecuada de yacimientos complejos. Por otro lado, las pruebas de presión corridas en formaciones sensibles a esfuerzos deben interpretarse con técnicas no convencionales. Durante las últimas tres décadas, numerosos estudios relacionados con el análisis del transiente de presión para la caracterización de los yacimientos sensibles a esfuerzos han sido introducidos en la literatura. Algunos de ellos tratados con curvas tipo y/o por ajuste histórico. Sin embargo, debido a la naturaleza del problema, no existe un estudio definitivo enfocado a la caracterización adecuada de yacimientos de permeabilidad variable. En este artículo, el concepto de módulo de permeabilidad introducido por Pedrosa (1986)
EFFECT OF THE PSEUDOTIME FUNCTION ON GAS RESERVOIR DRAINAGE AREA DETERMINATION Efecto de la función de pseudotiempo en la determinación del área de drene de un yaciemiento de gas
Freddy-Humberto Escobar,Aura-María López,José-Humberto Cantillo
CT&F - Ciencia, Tecnología y Futuro , 2007,
Abstract: The gas flow equation is normally linearized to allow the liquid solution of the diffusivity equation to satisfy gas behavior when analyzing transient test data of gas reservoirs. When wellbore storage conditions are insignificant, drawdown tests are best analyzed using the pseudopressure function. On the other hand, buildup pressure tests require linearization of both pseudotime and pseudopressure. It is not the case for the TDS technique which is indifferently applied to either drawdown or buildup tests. However, whichever the case, pseudotime has certain effect at very long testing times in formations of moderate to high permeability. In this paper, we implemented the Tiab’s Direct Synthesis (TDS) technique, to include pseudotime effects, and observe its influence on the interpretation results of gas well test data at early and late time periods. New analytical equations to estimate reservoir permeability, wellbore storage coefficient, pseudoskin factor and reservoir drainage area are presented. Then, a comparison of results against rigorous time was carried out for simulated and field cases. We found acceptable results for permeability, pseudoskin factor and wellbore storage coefficient. However, for the case of reservoir drainage area, the deviation error was of 4,1% for a simulated case and 17,9% for a field case. However, the smaller of these deviations may be small if related to pressure transient analysis results. However, this deviation in a gas reservoir with reserves of one tera standard cubic feet is equivalent to a huge difference of 38 gigas of standard cubic feet of gas which may have an economic impact to any oil company. Normalmente, la ecuación de flujo de gas se linealiza para permitir que la solución de difusividad de los líquidos satisfaga el comportamiento del gas cuando se analizan pruebas de presión en yacimientos gasíferos. Las pruebas de declinación de presión se analizan mejor usando la función pseudopresión, cuando los efectos de almacenamiento de pozo son insignificantes. Por otra parte, las pruebas de restauración de presión requieren la linealización tanto de la pseudopresión como del pseudotiempo. Sin embargo, cualquiera que sea el caso, la función de pseudotiempo presenta ciertos efectos a tiempos de prueba muy largos en formaciones de permeabilidad moderada a alta. En este artículo, implementamos la técnica de Síntesis Directa de Tiab, (TDS), para incorporar los efectos del pseudotiempo, y observar su influencia en los resultados de interpretación de pruebas de presión en yacimientos de gas a tiempos tempranos y tardíos
STRAIGHT-LINE CONVENTIONAL TRANSIENT RATE ANALYSIS FOR LONG HOMOGENEOUS AND HETEROGENEOUS RESERVOIRS
FREDDY HUMBERTO ESCOBAR,MARGARITA MARIA ROJAS RODDRIGUEZ,JOSE HUMBERTO CANTILLO SILVA
DYNA , 2012,
Abstract: El flujo lineal es un régimen de flujo muy importante que se presenta en pozos fracturados, horizontales y yacimientos alargados. Tanto el análisis de pruebas de presión como de transitorio de caudal podrán verse afectados por la presencia del flujo lineal. Para el caso de producción a caudal variable, la mayor parte del análisis se realiza mediante ajuste de curvas de declinación y poca atención ha recibido el análisis transitorio de caudal. Este artículo presenta las ecuaciones gobernantes usadas para análisis transitorio de caudal en sistemas alargados y proporciona ejemplos mediante el método convencional. La metodología permite la estimación de la permeabilidad, el ancho del yacimiento y los factores de da o geométricos. Si la prueba es lo suficientemente larga se puede estimar el área de drenaje del yacimiento y la posición del pozo dentro del mismo. La metodología se verificó satisfactoriamente mediante su aplicación a pruebas sintéticas.
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