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Abstract Market-induced production shut-downs and restarts offer us an opportunity to gather step-rate and shut-in data for pressure transient analysis (PTA) and rate transient analysis (RTA). In this study, we present a unified transient analysis (UTA) to combine PTA and RTA in a single framework. In this new approach continuous production data, step-rate data, shut-in data and re-start data can be visualized and analyzed in a single superposition plot, which can be used to estimate both and infer formation pore pressure in a holistic manner by utilizing all available data. Most importantly, we show that traditional log-log and square root of time plots can lead to false interpretation of the termination of linear-flow or power-law behavior. Field cases are presented to demonstrate the superiority of the newly introduced superposition plot, along with discussion on the calibration of long-term bottom-hole pressure with short-term measurements.
Abstract An explicit solution to the general 3D point to target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multi-valued and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact, or polynomial type solution methods to be employed. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point to target problem can be represented as a 10 order self-intersecting geometric surface, characterised by the trajectory's start and end points, the radii of the two arcs and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided and together these indicate the most convenient solution method for each case. In the presence of a tangent section the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point to target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.
A method of computing depreciation under which equal annual amounts are set aside for the ultimate retirement of the property at the end of its service life. For a property with an assumed 25-year life, the annual charge would be 4% per year, usually applied to the cost of the property less estimated net salvage (From AGA).
This article focuses on interpretation of well test data from wells completed in naturally fractured reservoirs. Because of the presence of two distinct types of porous media, the assumption of homogeneous behavior is no longer valid in naturally fractured reservoirs. This article discusses two naturally fractured reservoir models, the physics governing fluid flow in these reservoirs and semilog and type curve analysis techniques for well tests in these reservoirs. Naturally fractured reservoirs are characterized by the presence of two distinct types of porous media: matrix and fracture. Because of the different fluid storage and conductivity characteristics of the matrix and fractures, these reservoirs often are called dual-porosity reservoirs.
Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. Fig 1 illustrates a flow-after-flow test.
Diagnostic plots are a log-log plot of the pressure change and pressure derivative (vertical axis) from a pressure transient test vs. elapsed time (horizontal axis). They are typically divided into three time regions: early, middle, and late. Two different method types, one using data from the middle-time region and the second using data from the late-time region (LTR), are commonly applied in estimating average reservoir pressure. The middle-time region methods are the Matthews-Brons-Hazebroek (MBH) method and the Ramey-Cobb method. The MTR methods are based on extrapolation of the middle-time region and the correction of the extrapolated pressure.
There are several known methods of computing directional survey. The five most commonly used are: tangential, balanced tangential, average angle, curvature radius, and minimum curvature (most accurate). This method uses the inclination and hole direction at the lower end of the course length to calculate a straight line representing the wellbore that passes through the lower end of the course length. Because the wellbore is assumed to be a straight line throughout the course length, it is the most inaccurate of the methods discussed and should be abandoned completely. Modifying the tangential method by taking the direction of the top station for the first half of the course length, then that of the lower station for the second half can substantially reduce the errors in that method.
Productivity estimates in horizontal wells are subject to more uncertainty than comparable estimates in vertical wells. Further, it is much more difficult to interpret well test data because of 3D flow geometry. The radial symmetry usually present in a vertical well does not exist. Several flow regimes can potentially occur and need to be considered in analyzing test data from horizontal wells. Wellbore storage effects can be much more significant and partial penetration and end effects commonly complicate interpretation. In vertical wells, variables such as average permeability, net vertical thickness, and skin are used. Horizontal wells need more detail. Not only is vertical thickness important, but the horizontal dimensions of the reservoir, relative to the horizontal wellbore, need to be known. Evaluation of data from a vertical wellbore will generally center on a single flow regime, such as infinite-acting radial flow, known as the MTR. However, a pressure-transient test in a horizontal well can involve as many as five major and distinct regimes that need to be identified. These regimes may or may not occur in a given test and may or may not be obscured by wellbore storage effects. Each flow regime can be modeled by an equation that can be used to estimate important reservoir properties.
This article discusses the basic concepts of single-component or constant-composition, single phase fluid flow in homogeneous petroleum reservoirs, which include flow equations for unsteady-state, pseudosteady-state, and steady-state flow of fluids. Various flow geometries are treated, including radial, linear, and spherical flow. Virtually no important applications of fluid flow in permeable media involve single component, single phase 1D, radial or spherical flow in homogeneous systems (multiple phases are almost always involved, which also leads to multidimensional requirements). The applications given in this Chapter are based on a model that includes many simplifying assumptions about the well and reservoir, and are interesting mainly only from a historical perspective See "Reservoir Simulation" for proper treatment of multi-component, multiphase, multidimensional flow in heterogeneous porous media. The simplifying assumptions are introduced here as needed to combine the law of conservation of mass, Darcy's law, and equations of state to obtain closed-form solutions for simple cases. Consider radial flow toward a well in a circular reservoir. Combining the law of conservation of mass and Darcy's law for the isothermal flow of fluids of small and constant compressibility yields the radial diffusivity equation,  In the derivation of this equation, it is assumed that compressibility of the total system, ct, is small and independent of pressure; permeability, k, is constant and isotropic; viscosity, μ, is independent of pressure; porosity, ϕ, is constant; and that certain terms in the basic differential equation (involving pressure gradients squared) are negligible.
The main reason for testing an exploration well is to take a fluid sample. Further reasons are to measure the initial pressure, estimate a minimum reservoir volume, evaluate the well permeability and skin effect, and identify heterogeneities and boundaries. Testing producing wells aims at verifying permeability and skin effect, identifying fluid behavior, estimating the average reservoir pressure, confirming heterogeneities and boundaries, and assessing hydraulic connectivity. We create a step change in rate--for instance, by closing a flowing well or an injection well (buildup or falloff, respectively); by opening a well previously shut in (drawdown); or by injecting in a well previously closed (injection). This rate change creates a change in pressure in the same well (exploration or production testing) or in a different well (interference testing).