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In order to truly describe the dynamic characteristics of bottom-hole pressure in the reservoir, in this paper, the elastic outer boundary condition is introduced to replace the three kinds of traditional outer boundary conditions (infinity, constant pressure, closed), and a spherical nonlinear seepage model is established for the dual-porosity reservoir, which takes into account wellbore storage, effective well diameter and quadratic gradient term. The solution of the model in the Laplace space is found, and the similar structural formula of the solution is obtained by combining the Laplace transformation with the similarity construction method. Subsequently, by the Stehfest numerical inversion method, the well test curve is drawn, and the influence of main reservoir parameters on bottom-hole pressure dynamics is analyzed. The introduction of the elastic outer boundary not only breaks the traditional fixed form of the ideal outer boundary condition, but also improves the interpretation accuracy of the reservoir boundary. At the same time, a more general representation of the model is put forward, which provides a more effective theoretical basis for further exploration of the seepage law of the reservoir. Simultaneously, the similarity construction method simplifies the complex calculation process of solving the model and provides a new idea for solving the more complicated percolation model of oil and gas reservoirs. The similar construction method simplifies the complicated calculation process of solving the model and provides a new idea for solving the more complicated percolation model of oil and gas reservoirs. [ABSTRACT FROM AUTHOR]

Compared with the variables separation method and integral-transform method, Green’s function method is much more applicable and thus of great practical significance. Based on the general steps of Green’s function method, a new method is originally raised to get Green’s function in oil and gas flow problems through underground formations. After that, the transient pressure solution is get for flow in a spherical reservoir by using this method. This case enlarged the application of Greenʼs method function, and this work can also be a good foundation for the solution of more and more complicated flow problems in oil and gas reservoirs.

Microbially induced carbonate precipitation (MICP) is an innovative approach to strengthening and improving loose porous media. To advance MICP implementation in various geotechnical applications, the work presented herein investigates the distribution pattern of cementation and quantifies the improved material properties through experimental study. Sand was cemented by MICP via a double wall delivery system under submerged conditions and induced spherical flow in a large-scale box. The assessment on MICP-treated sand was conducted using shear wave velocity, hydraulic conductivity, mass of precipitated mineral, and cone tip resistance measurements. Experimental and numerical results were synthesized to evaluate the distribution of MICP with respect to reaction and transport rates. The shear wave velocity and the cone tip resistance were correlated to identify the level of cementation induced in the treated sand. Results included the general cementation pattern of MICP and the level of cementation as affected by induced seepage velocity and density. The relationship between the measured level of cementation, the shear wave velocity, and the cone tip resistance is presented and discussed. [ABSTRACT FROM AUTHOR]

Often, interpretation of interference tests is performed for systems acting under radial flow regimen conditions by means of conventional straight-line method, type-curve matching and TDS technique. For linear and spherical flow cases, the interpretation of interference tests is performed by the conventional analysis and type-curve matching. These procedures do not allow verification of the estimated parameters; therefore, this paper presents the formulation of a more practical, useful and accurate methodology which is achieved based upon the determination of characteristic features found on the pressure and pressure derivative versus time log-log plot with the purpose of developing analytical expressions for the interpretation of interference tests under spherical and linear flow conditions. These equations were successfully verified by their application on synthetic tests.

There are many equations of steady inflow of fluid to the wells depending on the type of well, presence or absence of artificial or natural fractures passing through the well, different degrees of drilling-in of the wellbores. For some complex cases, analytical solutions describing the inflow of fluid to the well have not yet been obtained. An alternative to many equations is the use of numerical methods, but this approach has a significant disadvantage – a considerable counting time. In this regard, it is important to develop a more general analytical approach to describe different types of wells with different formation drilling-in and presence or absence of fractures. Creation of this method is possible during modeling of fractures by a set of nodes-vertical wells passing from a roof to floor, and modeling of a wellbore (wellbores, perforation) by a set of nodes – spheres close to each other. As a result, based on this approach, a calculation algorithm was developed and widely tested, in which total inflow to the well consists of the flow rate of each node taking into account the interference between the nodes and considering the impermeable roof and floor of the formation. Performed modeling confirmed a number of known patterns for horizontal wells, perforation, partial drilling-in of a formation, and also allowed solving a number of problems.

Often, interpretation of interference tests is performed for systems acting under radial flow regimen conditions by means of conventional straight-line method, type-curve matching and TDS technique. For linear and spherical flow cases, the interpretation of interference tests is performed by the conventional analysis and type-curve matching. These procedures do not allow verification of the estimated parameters; therefore, this paper presents the formulation of a more practical, useful and accurate methodology which is achieved based upon the determination of characteristic features found on the pressure and pressure derivative versus time log-log plot with the purpose of developing analytical expressions for the interpretation of interference tests under spherical and linear flow conditions. These equations were successfully verified by their application on synthetic tests. [ABSTRACT FROM AUTHOR]

A simple parameter estimation procedure, designated as integration-based estimation (IBE), was introduced to determine the hydraulic properties of an aquifer using slug test models subjected to certain flow geometries such as radial and spherical flows. The basic idea behind the proposed IBE approach is to link an integration value at pre-defined normalized head levels for field data with that of a theoretical type curve. The IBE method removes the need for the implementation of the classical graphical matching process which would be ineffective to acquire aquifer parameters for non-ideal aquifer conditions. As the second aspect of this study, a new decision tool was suggested to determine the suitable slug test model to be utilized for the site data since diagnosing the flow character properly is of crucial importance for following a convenient analysis procedure. The estimation performance and limitation of the proposed IBE method were tested for several slug test scenarios including radial and spherical flow models with a number of synthetically generated data sets as well as a field application. Results reveal that the IBE together with the identification methodology not only is able to retrieve aquifer parameters as reliable as the existing techniques in the literature but also diagnoses the flow character precisely as demonstrated in this study. [ABSTRACT FROM AUTHOR]

it has been long recognized that in some reservoirs the flow does not follow the expected radial cylindrical pattern. Spherical flow may take place in systems with wells completed in thick reservoirs where a short completion interval is open to flow yielding a unique and more complex early-time pressure behavior. Some of the main reasons for partial penetration are to avoid coning of water and minimize sand production. A similar early-time pressure behavior may be due to the presence of plugged perforations. Such well completions are referred to as limited-entry, restricted-entry or partially penetrating wells. A typical case of spherical propagation of pressure transients occurs during the repeat formation tester measurements. Such a test measures spot formation pressures and recovers formation fluid samples for gaining an insight into the reservoir flow mechanics. The purpose of this study is to identify on the pressure and pressure derivative curves the unique characteristics for different flow regimes resulting from these type of completions and to determine various reservoir parameters, such as vertical, horizontal permeability, and various skin factors. The interpretation is performed using Tiab’s Direct Synthesis (TDS) Technique, introduced by Tiab (1993), which uses analytical equations obtained from characteristic lines and points found on the log-log plot of pressure and pressure derivative to determine permeability, skin and wellbore storage without using type-curve matching. The extension of this methodology for the case under study includes wellbore storage and skin effects. It is applied to both drawdown and buildup tests. We found that a spherical or hemispherical flow regime occurs prior to the radial flow regime whenever the penetration ratio of about 20%. A half-slope line on the pressure derivative is the unique characteristic identifying the presence of the spherical/hemispherical flow. The typical half-slope line of theses flow regimes is used to estimate spherical permeability and spherical skin values. These parameters are then used to estimate vertical permeability, anisotropy index and skin. Results of TDS technique where successufully compared to those of conventional technique for field and simulated examples.Desde hace mucho tiempo se sabe que en algunos yacimeintos el flujo no sigue la trayectoria cilíndrica esperada. El flujo esférico puede ocurrir en sistemas con pozos completados en formaciones con mucho espesor con una pequeña porción de intervalo perforado abierto al flujo dando lugar a una única y más compleja respuesta de presión temprana. Algunas de las principales razones para acudir a penetración parcial es evitar la conificación de agua y minimizar la producción de arena. Un comportamiento similar de la presión a tiempos tempranos podría deberse al taponamiento en las perforaciones. Tales completamientos se denominan entrada limitada, entrada restringida o pozos con penetración parcial. Un caso típico de propagación esférica del transiente de presión ocurre durante medidas de RFT. Dicho registro mide presiones de formación y muestrea los fluidos de la formación para tener una idea de la mecánica de flujo en el yacimiento. El propósito de este estudio es identificar características únicas en le gráfico de la presión y la derivada para diversos regimenes de flujo que resultan de este tipo de completamientos y determinar los distintos parámetros del yacimiento. Tales como permeabilidad vertical, permeabilidad horizontal, y diversos factores de daño. La interpretación se lleva a cabo usando la Tiab’s Direct Synthesis (TDS) Technique, introducida por Tiab (1993), la cual usa ecuaciones analíticas obtenidas de líneas y puntos característicos hallados en el gráfico log-log de presión y derivada de presión para determinar permeabilidad, daño y almacenamiento sin emplear curvas tipo. La extensión de esta metodología para el caso en estudio incluye almacenamiento y daño. La técnica se aplica tanto a pruebas de restauración como de declinación de presión. Encontramos que el flujo hemisférico o esférico toma lugar antes del flujo radial siempre que la relación de penetración sea aproximadamente menor del 20%. Una pendiente negativa de ½ en la curva de la derivada es la característica única para identificar la presencia de flujo hemisférico/esférico. Esta línea típica de pendiente -½ se usa para determinar la permeabilidad esférica y los daños esféricos, para luego estimar la permeabilidad vertical y el índice de anisotropía. Los resultados de la TDS fueron satisfactoriamente comparados con casos de campo y casos simulados.

The article focuses on the flow of non-Newtonian power-law fluids and high viscosity crude in a homogenous petroleum reservoir and well. It states that the viscous crude oil is characterized with spherical flow behavior through porous medium and mentions that the slope of non-Newtonian fluids is a function of its flow behavior index. It presents the assumptions made while designing a mathematical model for non-Newtonian fluids such as validity of Darcy's flow and Laminar flow.