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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 Because of the presence of two distinct types of porous media, the assumption of homogeneous behavior is no longer valid in naturally fractured reservoirs.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).
Summary Negative tests, or inflow tests, are conducted to verify the integrity of well barriers in the direction of potential flow, subjecting a barrier to a negative pressure differential, while monitoring for signs of a leak. A common practice is to observe the rate of flowback from the well. Flowback may be a sign of a leak due to an influx of formation fluids into the well. However, even when there is no leak, flowback is commonly observed due to thermal expansion of wellbore fluids. Heat transfer will occur between the wellbore fluids in each annulus and with the surrounding formation until temperatures reach an equilibrium. This behavior is described by the process of thermal diffusion, with the resulting temperature increase causing expansion of wellbore fluids and flowback from the well. Industry guidelines state “Horner” analysis may be used when monitoring flowback or pressure buildup during an inflow test. In doing so, engineers and wellsite supervisors may use a “Horner plot” to determine if flowback or pressure buildup is attributable to thermal effects. Those without a reservoir engineering background may not be aware the method was originally derived from a radial flow equation for the purpose of monitoring pressure buildup in a well when shut in after a period of production. The apparent similarity of the radial flow and thermal diffusion equations is what led Horner's technique to subsequently be applied to the prediction of static formation temperature from well logs. However, although thermal expansion is a function of formation temperature, Horner analysis of flowback or pressure buildup during an inflow test has remained a black box that is poorly understood. For the first time, with support from empirical data from offshore wells, we reveal that Horner analysis of thermal expansion is a practice without theoretical justification. The radial equation on which Horner analysis depends, along with the constraints implied by the boundary conditions, fails to accurately account for the conditions of an inflow test. As a result, the method should not be used for analyzing flowback or pressure buildup during an inflow test. Instead, a new method is proposed to interpret a trend of flowback when monitoring well barriers. The findings of this study can help improve understanding Horner analysis and techniques for interpreting inflow tests.
Decline-curve analysis (DCA) is arguably the most commonly used method for forecasting reserves in unconventional reservoirs. Production data from several US unconventional plays are analyzed, and production forecasting is carried out with the traditional Arps methods as a basis for comparison. The results are compared with analytical models developed for each play to determine the suitability of each DCA method. At the most fundamental level, DCA involves fitting an empirical model of the trend in production decline from a well's history and projecting the trend into the future to determine the well's economic life and forecast cumulative production. The Arps decline model is established from the empirical observation that the loss ratio (the rate of change of the reciprocal of the instantaneous decline rate) is constant with time.
Abstract One way of obtaining water-oil relative permeability curves is from co-injection (of water and oil) experiments at steady-state (SS) condition. The two-phase Darcy Law can be used to calculate the relative permeability directly only when water saturation is constant along the core. However, the capillary end effect (CEE) causes water accumulation or depletion at the end of the core depending upon the wettability. This work describes an improved method for correcting for this effect by modifying the "intercept method" initially proposed by Gupta and Maloney (2014). Similar to their work, we again envisage carrying out a steady-state co-injection experiment. For each ratio of water to oil flowrate (), we require experiments at several different total flowrates to be carried out. From each run, we obtain pressure drop across the core and average water saturation inside the core. We demonstrate mathematically that a plot of pressure difference vs. oil flowrate yields a straight line whose slope gives the oil relative permeability which can be used to calculate water relative permeability. A plot of average water saturation vs. reciprocal of oil flowrate gives a straight line whose intercept is the water saturation associated with the oil/water relative permeability values just obtained. It is necessary to perform the same experiment for at least two values of water and oil flowrates while the ratio is constant since we require at least two points to construct a straight line. The same procedure is used for other values of F to obtain more data points to construct the relative permeability curves. We have also mathematically corrected Gupta and Maloney’s work and other works after them and arrived at a simpler and more rigorous method. The details of how our method builds upon and improves their work will be published in due course (Goodarzian and Sorbie, 2020).