|Theme||Visible||Selectable||Appearance||Zoom Range (now: 0)|
Formation damage caused by drilling-fluid invasion, production, or injection can lead to positive skin factors and affect fluid flow by reducing permeability. When mud filtrate invades the formation surrounding a borehole, it will generally remain in the formation even after the well is cased and perforated. This mud filtrate in the formation reduces the effective permeability to hydrocarbons near the wellbore. It may also cause clays in the formation to swell, reducing the absolute permeability of the formation. In addition, solid particles from the mud may enter the formation and reduce permeability at the formation face.
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.
Abstract Theoretical papers have been presented considering the depth of investigation of classic sonic tools, largely focusing on the effects of the source-to-receiver spacing in the case of altered zones. Modern sonic tools use multipole sources (monopole, dipole, and/or quadrupole) at a broad range of frequencies and source-to-receiver offsets. This paper briefly reviews the theoretical discussions of the effects of tool geometry and source characteristics, but focuses primarily on the practical aspects of wellbore profiling with modern sonic tools. We concurrently consider the tool geometry, source order, and frequency effects on the depth of investigation and discuss the differences in wireline and logging-while-drilling environments. Multiple field examples are shown in cases of alteration and invasion. We explore the benefits of reporting sonic logs at multiple depths of investigation, which can yield valuable information about shale reactivity, wellbore stability, and geosteering. A summary of how to recognize the effects of variable depth of investigation on common sonic logs presentations completes the report. Introduction Sonic velocities, like other log properties, often vary according to the distance from the wellbore. This variance can be attributable to near-wellbore alteration caused by the interaction between the drilling mud and the formation, stresses induced by the drilling process, invasion of fluid into the pore space, or formation layering. In the last decade, sonic tools have advanced from relatively simple, high frequency, short-spaced sensors to broad frequency, long-spaced devices capable of measuring velocities in a wide range of formations and differentiating both azimuthal and radial variations in velocities (Market, 2008). We will build upon prior work and show how tool geometry, frequency, and source order interact to affect the depth of investigation of sonic logs. This paper primarily focuses on the practical side, showing examples of common processing techniques and plot displays used throughout the industry. Examples are presented in which the sonic properties vary with depth of investigation and techniques for interpreting the near- and far-wellbore responses are described. We consider both the case for wanting to read as deeply as possible and the reasons that we might want to know the sonic properties over a broad range of investigation depths. Theoretical Background - Depth of Investigation Although there is no simple answer to the question of "What is the depth of investigation of sonic logs?", we can consider the pertinent factors to reach a good understanding of the factors affecting the depth of investigation and distill some general rules of thumb. The factors that we will consider are the source-to-receiver spacing, frequency effects, and source order. A traditional rule of thumb for the depth of investigation of sonic tools is that if the source-to-receiver spacing is n feet, then the depth of investigation is n inches (Baker 1984). These calculations were based on monopole sources at 10 to 20 kHz. Further work (Baker and Winbow 1988) showed theoretically that higher order modes (such as dipole and quadrupole sources) could see deeper into the formation, but only if the velocity of the near-wellbore zone is less than that of the deeper zone. When considering source-to-receiver offset, we should balance the desire to have long enough spacing such that:We see formation arrivals, rather than only the mud response. We see past any mud cake or near-wellbore alteration with the following considerations:○The longer the source-to-receiver spacing, the more attenuated the signal becomes. ○The shorter the tool, the easier it is to handle and the closer to the bit the sonic measurement (and that of any tools above it) may be.
Abstract Most composite solutions used in modern well test interpretation use the "step-permeability" model where the altered formations are divided into two or more concentric zones, each with constant permeability. Depending on the causes of alteration or variation, this model can deviate significantly from the real condition. A formation can be altered because of stress redistribution, drilling damage, solids co-production, mineral precipitates, and drilling mud invasion, each factor more likely to generate spatially-varying permeabilities rather than constant k zones. Experimental data confirm that a continuous permeability model is more realistic than the step permeability model. A new semi-analytical solution with smooth radius-dependent permeability has been developed to analyze well test results from such altered formations. The altered formation is approximated as a concentric two-zone composite model: an exterior intact zone that retains the original unaltered permeability, and an interior zone where the permeability values have been altered and change as a function of radius. The permeability in this near-well zone can change continuously to the original permeability or to a different value at the boundary with the exterior zone, where there is a step-change in permeability. The choice of an increase or decrease of permeability with radius within the altered zone depends on the nature of the actual alteration. The permeability can also be simulated as a step-wise function if appropriate parameters are used; in such situations, the model collapses to conventional step-wise composite models. Other parameters such as formation porosity and compressibility of each zone can also be different, but they are assumed constant for this derivation. The new solution is derived in Laplace space, and numerical Laplace inversion is used. Introduction Well test interpretation is widely used in estimating formation parameters such as permeability. Early well test solutions by Muskat assumed a fully penetrating well in a homogeneous, isotropic, and infinite formation; the condition of constant permeability, however, has been recognized as inadequate in many field applications (Sabet, Freeze and Cherry). Non-uniformity of permeability arises mainly from two factors. The first is natural heterogeneities inherited from existing geological structures in the formation being tested; Streltsova has a fairly detailed discussion on this category. The second factor is formation alterations caused by engineering development processes. In this paper, we focus on the latter. Near-wellbore permeability can be altered as the result of physical processes such as sand production, drilling-induced stress redistribution, drilling damage, fine-grained material migration, carbonate or asphaltene precipitation, drilling mud invasion, thermal injection effects such as formation shear dilation, or some combination of these. Different methods have been proposed to assess permeability alteration effects on well productivity and well test interpretation. The "skin term" model first presented by Hawkins, and used extensively by reservoir engineers (Robert), is probably the earliest attempt to quantify permeability alteration. The skin term was introduced as a small, zero-thickness flow impedance factor, which is positive or negative depending on whether well productivity is decreased (+ve) or increased (-ve). The skin term is obtained by assuming that steady-state pressure conditions exist in the skin, which in reality, with a significantly thick altered zone, may only be true at late stages of well tests, when the unaltered zone dominates production. As noted by Abbaszadeh et al, depending on the size of the altered zone, times to steady-state can be very different. A weakness of skin term interpretation is that it gives little useful information to determine the nature of the permeability alteration. Hence, composite models have been proposed, such as those of Olarewaju et al., Butler, and Novakowski[10,11]. These models are based on an axisymmetric, two-annulus altered formation around the wellbore; permeability is assumed constant in each zone, with an abrupt change at the interface between zones. We refer to these as "step-permeability" models because permeability varies as a step-wise function with radius.
SPE Members Abstract This work deals with well productivity reduction due to altered formation permeability and other flow restrictions around a vertical wellbore. This near-wellbore formation change can be caused by liquid dropout in a gas condensate reservoir, for example. The corresponding reduction in well productivity can be quantified as an increase in the total skin (St). According to the conventional method, the total skin is given by a sum of individual components: St = Sm + Sp + Sd + Sa, where Sm represents flow restrictions from mechanical damage, Sp from partial completion, Sd from non-Darcy flow effect, and Sa from permeability reduction due to liquid dropout. The key finding of this work is that the total skin with condensate dropout can be much bigger than (Sm+Sp+Sd+Sa) due to nonlinear multiplicative fluid- dynamic interactions among skin components. These interactions have not been fully recognized and accounted for in literature. Two correct methods are presented for the total skin calculation in a multi-layered formation: direct simulation and heuristic analytical approximation. The analytical approximation equation is simple, but very accurate in most cases under the pseudo-steady state condition, when compared to the direct simulation method. The new equation developed here has significant implications in various engineering analyses. The conventional method can grossly overestimate well deliverability, if the total skin value is computed from individual components. Conversely, when an individual component (such as Sm) is back-calculated from the total skin obtained from pressure transient analysis, the conventional method can grossly overestimate Sm. Also, this new equation can be used to predict simulation impacts of different wellbore description and of adjustments made in permeability distributions and skin components during history matching. Introduction This paper deals with well deliverability changes induced by fluid-dynamic interactions among various flow impairments around a wellbore. In quantifying the effects of these interactions on well productivity in general, liquid dropout effects on gas flow in a retrograde gas condensate reservoir are considered as a specific example. Well deliverability calculation requires proper modeling of near-well gas flow behavior. As the pressure around a wellbore drops below dew point, liquid dropout appears in the formation which in turn forms a liquid bank choking gas flow into the wellbore. This liquid bank reduces well productivity drastically through various fluid dynamic interactions: altering formation permeability and porosity, changing relative permeabilities, increasing non-Darcy flow effects, and fluid PVT behaviors. Numerous studies have been conducted on various aspects of these interactions. This work quantifies well productivity as productivity index (PI). P. 607