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Reformulation of the of elliptic flow governing equation for a more complete well test data interpretation in horizontal wells
Javier Andrés Martinez,Freddy Humberto Escobar,Matilde Montealegre Madero
Journal of Engineering and Applied Sciences , 2012,
Abstract: Before year 2000, elliptical flow regime was considered as a transition period found in a horizontal well transient test. It is recognized by a 0.36-slope (or 0.35-slope) tendency on the pressure derivative plot. Few researches have been conducted on the transient analysis for such flow regime. Since the first model does not provide a practical way of obtaining the reservoir horizontal permeability, a new model which is function of the reservoir length along the x-direction, reservoir thickness, horizontal wellbore length, well radius and horizontal reservoir permeability, was presented in 2004. Our experience, however, has indicated to us that this model sometimes fails to provide accurate values of horizontal permeability. Therefore, the first model presented in the literature, which depends upon the permeabilities in the horizontal direction, has been retaken in this study with a slight modification and successfully tested in many scenarios. The conventional straight-line and TDS methods are used as interpretation techniques for crude and gas flow. Both real time and pseudotime were implemented for gas flow.
Niveles de 25 hidroxivitamina D y su correlación clínica con diferentes variables metabólicas y cardiovasculares en una población de mujeres posmenopáusicas
Molina,José Fernando; Molina,Javier; Escobar,Jorge Andrés; Betancur,Juan Felipe; Giraldo,Andrea;
Acta Medica Colombiana , 2011,
Abstract: introduction: osteoporosis is the most common metabolic bone disease. vitamin d deficiency is an important cause of secondary osteopenia and osteoporosis. it predisposes to fragility fractures and increases the risk of falling, while augmenting the risk of developing cardiovascular disease and diabetes mellitus type 1 and 2. objective: the objective of this study was to determine the levels of vitamin d in our population study and to correlate them with bone density, vertebral fractures, and other cardiovascular and laboratory variables. methods: we conducted a cross-sectional study of a cohort (n=205) of postmenopausal colombian women diagnosed with osteoporosis and osteopenia. we analyzed 46 variables. descriptive statistics were used, and multiple linear regressions were analyzed in order to determine correlations. results: it was found that the prevalence of insufficient levels of vitamin d was 55.1% (n=113), deficient levels 16.6% (n=34), and adequate levels in only 28.29% (n=58) of patients. comparing poor and inadequate levels, we found that deficient levels of vitamin d are a risk factor for vertebral fractures, with an rr of 1.02 (ic: 0,96 a 1.06) and for high blood pressure. with an rr of 1.47 (ic: 1.36 a 1.58). conclusions: our study shows that inadequate levels of vitamin d are common in our population. this is associated with low bone mass, vertebral fractures, and hypertension. further studies are needed in our country to confirm our findings (acta med colomb 2011; 36: 18-23).
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 INJECTION TESTS WITH VARIABLE TEMPERATURE WITHOUT TYPE-CURVE MATCHING
Escobar,Freddy-Humberto; Martínez,Javier-Andrés; Montealegre-M.,Matilde;
CT&F - Ciencia, Tecnología y Futuro , 2008,
Abstract: the analysis of injection tests under nonisothermic conditions is important for the accurate estimation of the reservoir permeability and the well's skin factor; since previously an isothermical system was assumed without taking into account a moving temperature front which expands with time plus the consequent changes in both viscosity and mobility between the cold and the hot zone of the reservoir which leads to unreliable estimation of the reservoir and well parameters. to construct the solution an analytical approach presented by boughrara and peres (2007) was used. that solution was initially introduced for the calculation of the injection pressure in an isothermic system. it was later modified by boughrara and reynolds (2007) to consider a system with variable temperature in vertical wells. in this work, the pressure response was obtained by numerical solution of the anisothermical model using the gauss quadrature method to solve the integrals, and assuming that both injection and reservoir temperatures were kept constant during the injection process and the water saturation is uniform throughout the reservoir. for interpretation purposes, a technique based upon the unique features of the pressure and pressure derivative curves were used without employing type-curve matching (tds technique). the formulation was verified by its application to field and synthetic examples. as expected, increasing reservoir temperature causes a decrement in the mobility ratio, then estimation of reservoir permeability is some less accurate from the second radial flow, especially, as the mobility ratio increases.
CONVENTIONAL PRESSURE ANALYSIS FOR NATURALLY FRACTURED RESERVOIRS WITH TRANSITION PERIOD BEFORE AND AFTER THE RADIAL FLOW REGIME
Escobar,Freddy-Humberto; Martinez,Javier-Andrés; Montealegre-Madero,Matilde;
CT&F - Ciencia, Tecnología y Futuro , 2009,
Abstract: it is expected for naturally occurring formations that the transition period of flow from fissures to matrix takes place during the radial flow regime. however, depending upon the value of the interporosity flow parameter, this transition period can show up before or after the radial flow regime. first, in a heterogeneous formation which has been subjected to a hydraulic fracturing treatment, the transition period can interrupt either the bilinear or linear flow regime. once the fluid inside the hydraulic fracture has been depleted, the natural fracture network will provide the necessary flux to the hydraulic fracture. second, in an elongated formation, for interporosity flow parameters approximated lower than 1x10-6, the transition period takes place during the formation linear flow period. it is desirable, not only to appropriately identify these types of systems but also to complement the conventional analysis with the adequate expressions, to characterize such formations for a more comprehensive reservoir/well management. so far, the conventional methodology does not account for the equations for interpretation of pressure tests under the above two mentioned conditions. currently, an interpretation study can only be achieved by non-linear regression analysis (simulation) which is obviously related to non-unique solutions especially when estimating reservoir limits and the naturally fractured parameters. therefore, in this paper, we provide and verify the necessary mathematical expressions for interpretation of a vertical well test in both a hydraulically-fractured naturally fractured formation or an elongated closed heterogeneous reservoir. the equations presented in this paper could provide good initial guesses for the parameters to be used in a general nonlinear regression analysis procedure so that the non-uniqueness problem associated with nonlinear regression may be improved.
PRESSURE AND PRESSURE DERIVATE ANALYSIS FOR A WELL IN A RADIAL COMPOSITE RESERVOIR WITH A NON-NEWTONIAN/NEWTONIAN INTERFACE
Escobar,Freddy-Humberto; Martínez,Javier-Andrés; Montealegre-Madero,Matilde;
CT&F - Ciencia, Tecnología y Futuro , 2010,
Abstract: in many activities of the oil industry, engineers have to deal with completion and stimulation treatment fluids such as polymer solutions and some heavy crude oils which obey a non-newtonian power-law behavior. when it is required to conduct a treatment with a non-newtonian fluid in an oil-bearing formation, this comes in contact with conventional oil which possesses a newtonian nature. this implies the definition of two media with entirely different mobilities. if a pressure test is run in such a system, the interpretation of data from such a test through the use of conventional straight-line method may be erroneous and may not provide a way for verification of the results obtained. in this work, the signature of the pressure derivative curve is investigated to understand and ease the interpretation of the well test data in reservoirs with non-newtonian power-law fluids. specifically, the tiab's direct synthesis (tds) technique is implemented using some characteristics features found on the pressure and pressure derivative curves. hence, new equations are introduced to estimate permeability, non-newtonian bank radius and skin factor. permeability can be verified. the proposed methodology was successfully verified by its application to an example reported in the literature and a synthetic case.
Niveles de 25 hidroxivitamina D y su correlación clínica con diferentes variables metabólicas y cardiovasculares en una población de mujeres posmenopáusicas Levels of 25-hydroxyvitamin D and their clinical correlation with several metabolic and cardiovascular variables in a population of postmenopausal women
José Fernando Molina,Javier Molina,Jorge Andrés Escobar,Juan Felipe Betancur
Acta Medica Colombiana , 2011,
Abstract: Introducción: la osteoporosis es la enfermedad ósea metabólica más común. Entre sus causas secundarias se encuentra la deficiencia de vitamina D (VD), la cual predispone además a fracturas por fragilidad e incrementa el riesgo de caídas. También confiere un riesgo incrementado de desarrollar enfermedad cardiovascular, diabetes mellitus tipo 1 y 2. Objetivo: el objetivo principal del estudio fue determinar los niveles de vitamina D en la población y correlacionarlos con diferentes variables clínicas, de laboratorio y densitométricas. Métodos: se realizó un estudio descriptivo de corte transversal, de una cohorte de pacientes donde se analizaron datos secundarios de mujeres posmenopáusicas colombianas con diagnóstico de osteoporosis y osteopenia (N=205). Se analizaron 46 variables donde se calcularon estadísticos descriptivos y regresiones lineales múltiples para determinar correlaciones. Resultados: la prevalencia de niveles insuficientes de vitamina D fue 55.1%, (n=113), deficientes 16.6% (n=34), y adecuados sólo 28.29% (n=58). Al comparar los pacientes con niveles deficientes e insuficientes, se encontró que los pacientes con niveles de vitamina D deficientes fue un factor de riesgo para la presencia de fracturas vertebrales, RR de 1.02 (IC: 0.96 a 1.06) y para la hipertensión arterial RR de 1.47 (IC: 1.36 a 1.58). Conclusión: dos terceras partes de nuestra población de pacientes tienen niveles inadecuados de vitamina D, y se encontró correlación con fracturas vertebrales e hipertensión arterial (Acta Med Colomb 2011; 36: 18-23). Introduction: osteoporosis is the most common metabolic bone disease. Vitamin D deficiency is an important cause of secondary osteopenia and osteoporosis. It predisposes to fragility fractures and increases the risk of falling, while augmenting the risk of developing cardiovascular disease and diabetes mellitus type 1 and 2. Objective: the objective of this study was to determine the levels of vitamin D in our population study and to correlate them with bone density, vertebral fractures, and other cardiovascular and laboratory variables. Methods: we conducted a cross-sectional study of a cohort (n=205) of postmenopausal Colombian women diagnosed with osteoporosis and osteopenia. We analyzed 46 variables. Descriptive statistics were used, and multiple linear regressions were analyzed in order to determine correlations. Results: it was found that the prevalence of insufficient levels of vitamin D was 55.1% (n=113), deficient levels 16.6% (n=34), and adequate levels in only 28.29% (n=58) of patients. Comparing poor and inadequate
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
CONVENTIONAL PRESSURE ANALYSIS FOR NATURALLY FRACTURED RESERVOIRS WITH TRANSITION PERIOD BEFORE AND AFTER THE RADIAL FLOW REGIME
Freddy-Humberto Escobar,Javier-Andrés Martinez,Matilde Montealegre-Madero
CT&F - Ciencia, Tecnología y Futuro , 2009,
Abstract: It is expected for naturally occurring formations that the transition period of flow from fissures to matrix takes place during the radial flow regime. However, depending upon the value of the interporosity flow parameter, this transition period can show up before or after the radial flow regime. First, in a heterogeneous formation which has been subjected to a hydraulic fracturing treatment, the transition period can interrupt either the bilinear or linear flow regime. Once the fluid inside the hydraulic fracture has been depleted, the natural fracture network will provide the necessary flux to the hydraulic fracture. Second, in an elongated formation, for interporosity flow parameters approximated lower than 1x10-6, the transition period takes place during the formation linear flow period. It is desirable, not only to appropriately identify these types of systems but also to complement the conventional analysis with the adequate expressions, to characterize such formations for a more comprehensive reservoir/well management. So far, the conventional methodology does not account for the equations for interpretation of pressure tests under the above two mentioned conditions. Currently, an interpretation study can only be achieved by non-linear regression analysis (simulation) which is obviously related to non-unique solutions especially when estimating reservoir limits and the naturally fractured parameters. Therefore, in this paper, we provide and verify the necessary mathematical expressions for interpretation of a vertical well test in both a hydraulically-fractured naturally fractured formation or an elongated closed heterogeneous reservoir. The equations presented in this paper could provide good initial guesses for the parameters to be used in a general nonlinear regression analysis procedure so that the non-uniqueness problem associated with nonlinear regression may be improved. Se espera en formaciones naturalmente fracturadas que el periodo de transición de las fisuras a la matriz tome lugar durante el flujo radial. Sin embargo, dependiendo del valor del parámetro de flujo interporoso, esta transición puede ocurrir antes o después del flujo radial. El primer caso, en una formación heterogénea que ha sido sometida a un tratamiento de fracturamiento hidráulico, la transición puede interrumpir el flujo bilineal o lineal tempranos. Una vez existe depleción de flujo en la fractura hidráulica, éste es restablecido por flujo procedente de la red de fracturas naturales. En el segundo escenario, en una formación alargada, para parámetros de flujo aproxima
PRESSURE AND PRESSURE DERIVATE ANALYSIS FOR A WELL IN A RADIAL COMPOSITE RESERVOIR WITH A NON-NEWTONIAN/NEWTONIAN INTERFACE
Freddy-Humberto Escobar,Javier-Andrés Martínez,Matilde Montealegre-Madero
CT&F - Ciencia, Tecnología y Futuro , 2010,
Abstract: In many activities of the oil industry, engineers have to deal with completion and stimulation treatment fluids such as polymer solutions and some heavy crude oils which obey a non-Newtonian power-law behavior. When it is required to conduct a treatment with a non-Newtonian fluid in an oil-bearing formation, this comes in contact with conventional oil which possesses a Newtonian nature. This implies the definition of two media with entirely different mobilities. If a pressure test is run in such a system, the interpretation of data from such a test through the use of conventional straight-line method may be erroneous and may not provide a way for verification of the results obtained. In this work, the signature of the pressure derivative curve is investigated to understand and ease the interpretation of the well test data in reservoirs with non-Newtonian power-law fluids. Specifically, the Tiab's Direct Synthesis (TDS) technique is implemented using some characteristics features found on the pressure and pressure derivative curves. Hence, new equations are introduced to estimate permeability, non-Newtonian bank radius and skin factor. Permeability can be verified. The proposed methodology was successfully verified by its application to an example reported in the literature and a synthetic case. En algunas actividades de la industria petrolera, los ingenieros tienen que tratar con fluidos de estimulación y completamiento tales como polímeros y algunos crudos pesados que obedecen un comportamiento no Newtoniano. Cuando se requiere un tratamiento con un fluido no Newtoniano en una formación productora de crudo, éste entra en contacto con el crudo convencional que posee naturaleza Newtoniana. Esto implica la definición de dos medios con movilidades completamente diferentes. Si allí se corre una prueba de presión, su interpretación mediante el método convencional de la línea recta podría conducir a resultados erróneos y tampoco permitiría la verificación de los resultados obtenidos. En este trabajo se estudió la huella de la derivada de presión para entender y facilitar la interpretación de pruebas de presión en yacimientos con fluidos no-Newtonianos que obedecen la ley de potencia. Específicamente, se implementó la Síntesis Directa de Tiab (TDS) usando algunas características específicas halladas en la curva de la presión y la derivada de presión, de modo que se introdujeron nuevas ecuaciones para estimar permeabilidad, radio de la zona no Newtoniana y el factor de da o. La permeabilidad se puede verificar. La metodología propuesta se verificó satisfactoria
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