Exposicion Reserva I Calculos de Reservorio
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RESERVORIO I
INTRODUCCION Durante el desarrollo de los estudios de los yacimientos, modernamente el ingeniero de yacimiento se consigue con la incertidumbre de la validez de los datos disponibles, tanto en yacimientos maduros, como en yacimientos nuevos, la validez o precisión de los datos usados, en el desarrollo de un estudio de ingeniería de yacimiento, es fundamental para la predicción y desarrollo de programas de explotación óptimos de los yacimientos. Modernamente la industria petrolera se ha visto en la necesidad de crear grupos interdisciplinarios (Ingenieros (Ingenieros de petróleos, geólogos, geofísicos, petrofísicos, ingenieros de producción, entre otros), para garantizar la obtención y análisis de los datos que permitan desarrollar estudios de los yacimientos, de forma tal de obtener resultados acordes a las condiciones inherentes a la producción esperadas de las reservas existentes en el yacimiento. Este informe presenta las definiciones de reservas de hidrocarburos, su clasificación, métodos de cálculo, y la productividad de hidrocarburos. Los recursos de hidrocarburos son los volúmenes de petróleo crudo, condensado, gas natural, líquidos del gas natural y sustancias asociadas, identificados identificados o por descubrir, que se estima pueden existir en el subsuelo. Los recursos por descubrirse clasifican en hipotéticos y especulativos y los recursos identificados se denominan reservas de hidrocarburos, las cuales se clasifican en reservas probadas, reservas probables y reservas posibles y se diferencian fundamentalmente en la certidumbre de ocurrencia aportada por la información geológica y de ingeniería disponible y bajo condiciones operacionales, operacionales, económicas y regulaciones gubernamentales específicas. La información requerida sobre estas reservas se presenta a nivel de área, jurisdicción, campo y yacimiento. Las empresas operadoras deberán tomar todas las precauciones para que la información sea manejada en forma estrictamente confidencial. Este informe, donde se presentan las definiciones de los cálculos de reservas de hidrocarburos, es elaborado por un grupo de alumnos de la escuela de ingeniería geológica con el propósito de que pueda servir como un informe base para futuras investigaciones sobre este tema.
RESERVAS DE HIDROCARBUROS. Las reservas están definidas como aquellas cantidades de petróleo las cuales anticipadamente se consideran comercialmente recuperables recuperables de una acumulación conocida en una fecha determinada. Todas las estimaciones de reservas presentan un cierto grado de incertidumbre, la cual depende principalmente principalmente de la cantidad de información de geología e ingeniería confiable y
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RESERVORIO I
El grado relativo de incertidumbre conduce conduce a clasificar básicamente a las reservas en:
Reservas probadas. Reservas probables. Reservas posibles.
CLASIFICACIÓN DE RESERVAS.
RESERVAS PROBADAS. Son aquellas que existen en zonas conocidas y explotadas o sea que han sido descubiertas y desarrolladas, aunque no agotadas. Generalmente están en explotación al momento de su valoración e indican volúmenes de hidrocarburos que se pueden extraer inmediatamente, en base a las condiciones económicas económicas del momento de la evaluación y a información que asegure mucha certeza. Las Reservas Comprobadas pueden ser definidas como aquellas cantidades de petróleo y/o gas que se estima pueden ser recuperadas en forma económica y con las técnicas disponibles, de acumulaciones conocidas (volúmenes (volúmenes in situ) a partir de los datos disponibles en el momento de la evaluación. Pueden a su vez dividirse en Comprobadas Desarrolladas, que se esperan recuperar mediante los pozos y las instalaciones de producción existentes, existentes, y No Desarrolladas, que se esperan recuperar de pozos a perforar e instalaciones de producción futuras y de las cuales se tiene un alto grado de certidumbre. RESERVAS PROBADAS DESARROLLADAS .Las Reservas Probadas Desarrolladas están representadas por el volumen de hidrocarburos comercialmente recuperable del yacimiento por los pozos e instalaciones de producción disponibles. Dentro de esta definición se incluyen las reservas detrás de la tubería de revestimiento r evestimiento que requieren un costo menor y generalmente g eneralmente no requieren uso de taladro para incorporarlas a producción. También se incluyen lasque se esperan obtener por la aplicación de métodos comprobados de recuperación suplementaria cuando los equipos necesarios hayan sido instalados. RESERVAS PROBADAS NO DESARROLLADAS. Las Reservas Probadas No Desarrolladas son los volúmenes de reservas probadas de hidrocarburos que no pueden ser recuperadas comercialmente comercialmente através de los pozos e instalaciones de producción disponibles. Incluye las reservas detrás de la tubería de revestimiento que requieren un costo mayor para incorporarlas a producción (RA/RC) y las que necesitan de nuevos pozos e instalaciones o profundización de pozos que no hayan penetrado el yacimiento. Las empresas deben mantener actualizada la información sobre la proporción entre las Reservas Probadas No Desarrolladas y Las Reservas Probadas Desarrolladas y además deben realizar un esfuerzo significativo en desarrollar estas
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RESERVORIO I
RESERVAS PROBABLES. Son las reservas que no disponen de la suficiente información geológica y de reservorios como para asegurar el volumen de fluidos a recuperar, aunque estén identificados los volúmenes del yacimiento en general. Son atribuidas a acumulaciones acumulaciones conocidas y cuya estimación se basa en información similar a la que se requiere para las reservas comprobadas, pero la certidumbre de su existencia no es suficiente para clasificarlas como tales. Las Reservas Probables pueden definirse como aquellas a las que tanto los datos geológicos como de ingeniería dan una razonable probabilidad de ser recuperadas de depósitos descubiertos, aunque no en grado tal como para estimar específicamente los volúmenes a recuperar en forma rentable y ser consideradas como comprobadas. RESERVAS POSIBLES. Están determinadas por la información elaborada disponible, pero no existe la seguridad ni de su volumen total, ni de las condiciones y cantidad de hidrocarburos que se pueden recobrar en forma económica. Así definidas las reservas, debe tenerse en cuenta un concepto fundamental: el requisito de viabilidad económica de la recuperación, establecida por las condiciones imperantes en el momento en que se hace la estimación. La ausencia de este requerimiento es suficiente para que los volúmenes estimados no puedan ser considerados como reservas. Por lo tanto, las estimaciones económicas y las proyecciones de producción de un campo se hacen, generalmente, en base a las reservas comprobadas.
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RESERVORIO I
El 85% de la producción mundial de petróleo se obtiene actualmente por métodos de recuperación primaria y secundaria con un recobro promedio del 35% del Petróleo In Situ.
RESERVAS POR RECUPERACIÓN PRIMARIAS. Son las cantidades de Hidrocarburos que se pueden recuperar con la energía propia o natural del yacimiento. RESERVAS POR RECUPERACIÓN SUPLEMENTARIAS. Son las cantidades adicionales de hidrocarburos que se pudieran recuperar, como resultado de la incorporación de una energía suplementaria al yacimiento a través de métodos de recuperación suplementaria, suplementaria, tales como inyección de agua, gas, fluidos miscibles o cualquier otro fluido o energía que ayude a restituir r estituir la presión del yacimiento y/o a desplazar los hidrocarburos para aumentar la extracción del petróleo.
MÉTODOS VOLUMÉTRICOS PARA EL CÁLCULO DE VOLUMEN ORIGINAL DE HIDROCARBUROS A CONDICIONES DE YACIMIENTOS. Para calcular reservas se utilizan distintas metodologías, o sus combinaciones, combinaciones, de acuerdo a la información disponible y el estado de desarrollo de los yacimientos.
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RESERVORIO I
1. MÉTODOS DETERMINÍSTICOS. DETERMINÍSTICOS. Utiliza valores puntuales que representan el mejor estimado de cada parámetro geológico, de ingeniería y económico en la estimación de las reservas para cada caso específico. Este método trata cada parámetro como un rango de valores, los cuales son representados por variables aleatorias que permiten describir eventos futuros cuyos resultados son una incertidumbre. Dichas variables se representan mediante distribuciones estadísticas. 2. MÉTODO VOLUMÉTRICO. Se utiliza para calcular el Hidrocarburo Original En Sitio (POES, GOES y COES) con base en el modelo geológico que geométricamente describe el yacimiento y a las propiedades de la roca y de los fluidos. El Método Volumétrico es el adoptado por el Ministerio de Energía y Petróleo como Método Oficial para el cálculo de las reservas. Estos cálculos pueden estar apoyados por cualquier otro método.
1. PETRÓLEO Y GAS ASOCIADO
Cálculo del Petróleo Original En Sitio (POES): (POES): El Petróleo Original En Sitio se calcula usando la siguiente ecuación: POES = 7.758 x A x e x x Soi x 1/Boi Una vez obtenido el POES, al aplicarle el Factor de Recobro, se obtienen las Reservas de Petróleo Recuperables Originales. Cálculo del Gas en Solución Original En Sitio (GOES): El Gas en Solución Original En Sitio se obtiene en función de la Relación Gas, Petróleo Original (Rsi): GOES = POES x Rsi Cálculo del Gas Original en Sitio de la Capa de Gas (GOES): El Gas Original En Sitio de la Capa de Gas se obtiene mediante la siguiente relación: GOES = 43.560 x V x x Sgi x 1/Bgi
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RESERVORIO I
Para el cálculo del Gas No Asociado debe hacerse hincapié en la determinación de las características intrínsecas de dicho gas (composición, (composición, gravedad específica, etc). 3. CONDENSADO
Cálculo del Gas Condensado Original En Sitio (GCOES): La cantidad de Gas Condensado Original En Sitio (a condiciones estándar) se calcula mediante la siguiente relación: GCOES= 43.560 x A x e x X Sgci x 1/Bgci Or iginal en Sitio (GSOES): Cálculo del Gas Seco Original El Gas Seco Original en Sitio, proveniente del Gas Condensado, se calcula mediante la siguiente ecuación: GSOES = GCOES x Fg Cálculo de los líquidos del Gas Condensado Original En Sitio(COES): COES= GCOES x (1 –Fg) x 1/Rgci 4. CÁLCULO POR BALANCE DE MATERIALES. Uno de los principios fundamentales utilizados en ingeniería es la ley de la conservación de la masa. La aplicación de este principio a un yacimiento con el propósito de realizar la deducción cuantitativa del volumen de hidrocarburos presentes originalmente en dicho yacimiento y para la predicción del comportamiento del
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fluido y la presión en el mismo, es lo que se conoce como “El Método de Balance de Materiales”.
Cuando el yacimiento ha producido durante un periodo de tiempo, y se dispone de historia, tanto de producción como de presión, el ingeniero de yacimientos, tiene la opción de recurrir a otras herramientas, que son complementarias para cotejar y validar las reservas disponibles del yacimiento a su responsabilidad. Un Balance de Materiales de los fluidos presentes y producidos, le permita determinar el POES y/o el GOES. Luego puede hacer una comparación, cotejando con el método volumétrico para verificar con el Geólogo el verdadero volumen del yacimiento, haciendo los ajustes pertinentes en el tiempo. El método de balance de materiales provee un simple, pero efectiva alternativa para la estimación volumétrica no solamente del POES (petróleo original en sitio) y el GOES (Gas
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RESERVORIO I
que en balance de materiales; es que en balance de materiales se asume un promedio, un modelo tipo tanque, una presión promedio, una temperatura promedio, una porosidad promedio; es decir, tiene muchas limitaciones, pero con una ecuación obtengo los resultados necesarios; ya que se tiene una solución analítica a ese problema, una solución exacta a un programa aproximado. Simulación numérica no aproxima un modelo, lo que se hace es un modelo lo más real que se pueda, haciendo que la porosidad varíe, que la presión varíe con profundidad, etc. colocando todos los parámetros para que el modelo sea el más real. Este modelo, tiene que ser discretizado temporal y parcialmente en cero que sería la discretización espacial y en tiempo que sería la discretización temporal, para cada una de las celdas se tiene que resolver una ecuación; es decir, que para todas las celdas se tendría que resolver para cada tiempo una matriz o un sistema de ecuaciones, mientras más celdas tenga más ecuaciones se tienen, esas ecuaciones parten de un balance de masa, que dice que la masa que entra en la celda menos la que sale es igual a la que se acumula en cada paso de tiempo; pero esa ecuación llega a la ecuación de difusibilidad y se genera una ecuación en derivadas parciales de segundo grado que no tiene t iene solución exacta. Entonces; estas ecuaciones diferenciales en derivadas parciales de segundo grado no tiene t iene solución exacta tienen que ser resueltas por métodos numéricos, esto significa que ya no se va a obtener una solución exacta y se tiene que hallar un parámetro de convergencia para que esa ecuación en ese momento converge, porque se obtiene un valor aproximado en función al parámetro de convergencia que se esté utilizando y se va calculando eso para cada paso de tiempo hasta que se llegue al final; es decir, se va a tener un problema real pero con una solución aproximada, ya no va hacer un problema aproximado con una solución real, entonces, en este caso se tiene que hacer que el modelo sea visto como algo matemático, que pueda ser resuelto; es decir, que el yacimiento va hacer un modelo matemático y se va a resolver por un sistema de ecuaciones a través de métodos numéricos, ese modelo matemático y esos métodos numéricos que resuelven es un simulador de yacimiento; y este se encarga de agarrar ese modelo matemático y resolverlo de forma numérica y se observan los resultados. Por otro lado; con un simulador de yacimiento puedo decir que es lo va pasar dentro de 10
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RESERVORIO I
Factor de recobro de petróleo De todo el volumen de hidrocarburos presente en un yacimiento, sólo una fracción puede ser conducida o producida hasta superficie. Es el porcentaje que puede ser producido de petróleo que se encuentra en el subsuelo. Está relacionado directamente con la economía, porque la economía va generar o va determinar cuáles son las condiciones de abandono, ósea la condición final a la que se va a llegar, porque si se pone a ver el valor al que se llego, nos lo va a determinar exclusivamente la economía; es decir, la curva de producción la puedo llegar hasta abajo, pero a lo mejor no es rentable llegarla hasta abajo porque por que hasta cierto punto es rentable; luego se puede complicar y lo que se esté produciendo no va a pagar la inversión. Por consiguiente; el factor de recobro está relacionado directamente con la economía, pero se sabe que las condiciones de abandono si está relacionado con la determinación del índice; de forma difícil, por otro lado, la rentabilidad del proceso está relacionada con el factor de recobro. El factor de recobro no es más que la relación de petróleo producido y el volumen de hidrocarburo de yacimiento que puede ser generado a través de métodos m étodos volumétricos o a través de balance de materiales, que se pueda calcular y sin saber lo que se tiene de balance. Npr = FR * N declinación utiliza 6. Método de curvas de declinación de producción. El método de curvas de declinación los datos de producción para ajustarse a una curva de descenso y estimar la producción pr oducción futura de petróleo. Las tres formas más comunes de curvas de declinación son exponenciales, exponenciales, hiperbólicas y armónico. Se supone que la producción se reducirá en una curva razonablemente suave, y por lo derechos de emisión deben ser hechas para los pozos cerrados y en las restricciones de producción. La curva se puede expresar matemáticamente o representa en una gráfica para estimar la producción futura. Tiene la ventaja de incluir todas las características del yacimiento. Se requiere una historia suficiente para establecer una tendencia estadísticamente significativa, idealmente cuando la producción no se ve limitado por las condiciones artificiales reguladoras u otras.
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RESERVORIO I
Al elaborar cualquier tipo de mapa se deben tener en cuenta las siguientes precauciones:
Los datos deben ser representados según una escala y un intervalo apropiado. Los mapas no deben estar sobrecargados de datos. Son un documento de trabajo tr abajo de carácter informativo, por esta razón existen patrones, convenciones estándar y escalas. Los mapas geológicos deben guardar relación con las áreas adyacentes, así como con los mapas geofísicos.
DEFINICIÓN. Es un tipo de mapa del subsuelo cuyas curvas de contorno representan la elevación de una determinada formación, yacimiento o marcador geológico en el espacio, de modo que los pliegues, fallas y otras estructuras geológicas se muestran con claridad. Su apariencia apariencia es similar a la de un mapa topográfico, salvo que este último muestra las elevaciones de la superficie terrestre en tanto que un mapa estructural exhibe la elevación de una determinada capa de roca, generalmente por debajo de la superficie. Un mapa estructural es la proyección en el plano horizontal del tope o la base de un cuerpo de arena o nivel estratigráfico de interés
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RESERVORIO I
ELABORACION DE MAPAS ESTRUCTURALES. Una curva estructural es una línea imaginaria que conecta puntos de igual posición estructural en el subsuelo, por consiguiente un mapa estructural muestra la configuración de un horizonte o estrato. Los datos para su construcción deben ser referidos a una línea base, que por lo general es el nivel del mar. Información Requerida:
Ubicación exacta de cada punto de observación. Profundidad de los marcadores bajo la superficie. Composición conocida de las rocas. Marcadores estratigráficos seleccionados.
CONSTRUCCION:
Interpolación. Trazado. Interpretación. Utilización.
Interpretación: Los datos litológicos y paleontológicos son utilizados en la determinación del tope de una unidad, si el propósito del mapa es mostrar la estructura geológica. Cuando no se dispone de ripios o núcleos para evaluarlos, se utilizan los registros de pozos. Trazado: el intervalo entre las curvas depende de la diferencia de elevación dentro del área de estudio, lográndose proporcionar un suficiente número de isolíneas que muestren una interpretación razonablemente clara de la estructura del subsuelo. NORMAS DE CONSTRUCCION: CONSTRUCCION:
Son mapas similares a los de curvas de nivel y siguen las normas generales del trazado de isolíneas. Curvas juntas representan buzamientos pronunciados y viceversa.
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RESERVORIO I
Es conveniente mantener el buzamiento constante y mostrar gradualmente los cambios de rumbo, a menos que las cotas obliguen a cambios marcados de rumbo o buzamiento. Las áreas donde no se presenten cambios anómalos deben ser cuidadosamente estudiadas en busca de posibles fallas. La geología regional proporciona indicadores del tipo de estructuras que pueden encontrarse en el área. En los sinclinales cuyo eje no es horizontal las curvas de nivel están subiendo por un flanco, cruzan el eje y regresan bajando por el blanco opuesto, formando una V con el extremo abierto hacia la caída del pliegue. En los mapas estructurales, una falla normal suele originar una zona donde el horizonte clave no se presenta y esta zona es mayor cuanto menor es el buzamiento del plano de falla. La zona vacía puede ser determinada en los mapas estructurales cuando existe suficiente control para fijar la posición del marcador encada bloque y por lo menos tres pozos deben haber cortado el plano de falla. A medida que se obtiene más información las curvas estructurales deben ir siendo modificadas.
ERRORES EN EL TRAZADO DE MAPAS
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RESERVORIO I
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RESERVORIO I
Un mapa isópaco de arena total t otal es la representación en el plano horizontal de los espesores de un cuerpo de arena, los cuales son medidos en los perfiles de pozos (registros eléctricos, densidad, micro log, etc.). El espesor de cada cuerpo de arena se determina estableciendo el tope y la base del cuerpo completo, la interpretación de este mapa informa sobre la orientación del cuerpo de arena y su distribución en el área. Un mapa isópaco de arena neta representa el espesor de la roca con calidad de yacimiento dentro de un intervalo o unidad particular. El espesor de arena se determina estableciendo un límite de arena permeable, donde solo se seleccionan las arenas que contengan un volumen de arcilla menor o igual que el 50%. Un mapa isópaco de arena neta petrolífera representa la geometría de la arena neta saturada de hidrocarburos, se elabora a partir del mapa de arena neta al cual se le integran los límites del yacimiento que generalmente son una o más fallas sellantes y el contacto agua petróleo. Es a partir de este mapa que se evalúan los volúmenes de arena neta con hidrocarburos. CONSTRUCCION DE UN MAPA ISOPACO: Luego de elegir la unidad estratigráfica que se va a representar con el mapa isopaco, se determina el espesor en cada pozo y su número se coloca en el mapa base encima o debajo del símbolo del pozo. Después se trazan las isopacas siguiendo las normas generales del dibujo de isolíneas. El intervalo empleado depende de la calidad del mapa,
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RESERVORIO I
ser atravesada por la broca y el horizonte superior o capa clave, se utiliza como plano de referencia a representar. Los mapas isopacos se pueden utilizar para expresar el grado de hundimiento que ocurrió durante la acumulación de un depósito sedimentario, según la paleo estructura, y también pueden ser usados como mapas paleo geomorfológicos.
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RESERVORIO I
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RESERVORIO I
Elaborar conjuntamente un mapa isopaco y uno estructural en el tope de la misma unidad es recomendable ya que nos proporciona la profundidad, forma y posición geográfica del sitio de interés. Cuando se trabaja con mapas isopacos e isocoros, los espesores obtenidos en base a núcleos o perfiles deben ser corregidos cuando los pozos no son verticales a la superficie de estratificación.
CALCULO VOLUMEN BRUTO DE LA ROCA. Para poder calcular el volumen de roca, existen dos métodos:
Método de ISOPACAS Método de CIMAS Y BASES
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RESERVORIO I
total o bruto = Prof. Base-prof. Cima H=DB-DC Espesor neto Espesor total – suma esp. Compactos h=H- (e1+e2) METODO DE CIMAS Y BASES Este método tiene t iene como base la configuración de mapas con curvas de igual profundidad tanto de las Cimas como las Bases de la formación para cuya preparación será necesario disponer de planos con las localizaciones de todos los pozos que constituyen el campo en estudio. Por medio de registros geofísicos, se puede determinar la Cima y la Base de la formación productora pare cada uno de los pozos. En el plano de localización de los pozos se anotan en cada uno de ellos, la profundidad de la cima de la formación correspondiente y se hace la configuración por interpolación o extrapolación de datos para t ener curvas con valores cerrados, tal como se observa en la Fig. (3-8). Las áreas encerradas por las diferentes curvas se miden, sea con la ayuda de un planímetros sea
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RESERVORIO I
de roca. Una vez construida la tabla 3-IV, se grafican los valores contenidas en ella en un plano de coordenadas cartesianas, tomando como ordenadas a las profundidades y como abcisas a los volúmenes correspondientes correspondientes (Fig. 3-10). A partir del volumen medio de roca total (1/2 Vb), se baja una línea vertical hasta intersectar la curva; desde este punto, se traza otra otr a línea horizontal en forma tal que intersecte al eje de coordenadas. El valor sobre las ordenadas dará la profundidad del plano de referencia. Del ejemplo anterior; (Fig. 3-l0), se puede apreciar que la profundidad del plano es de: D = 2529 m.b.n.m. Antes de continuar es conveniente puntualizar algunos aspectos relacionados con las “base" de la
formación del yacimiento. No siempre es conocida la "base de una formación productora. En una estructura acumuladora de hidrocarburos de tipo cerrada, la "base" puede ser perfectamente diferenciada a partir de los registros geofísicos tomados en cada uno de los pozos perforados durante el desarrollo del campo, cuando se pasa de una formación porosa y permeable (arenas,
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RESERVORIO I
la porosidad media de la formación y por la saturación media de hidrocarburos, da precisamente el volumen de hidrocarburos que se trata de conocer.
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RESERVORIO I
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RESERVORIO I
La definición anterior se puede expresar matemáticamente como sigue:
∅
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RESERVORIO I
- Cálculo a partir de registros eléctricos. - Núcleos tomados en pozos perforados ( afectados por: cambios de presión, desplazamiento de fluidos, manejo y movimiento de las muestras de Corazón) Debido al desplazamiento de fluidos innatos al momento de corazonar la formación,
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Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
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