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R.T. Kelly, SPE, Ranger Oil (U.K.) Limited Abstract The analysis of well test pressure data can often result in a non-unique solution, particularly as a result of the mathematical complexity of matching late-time derivative data and the limitations of well test analysis software. Other frequent faux-pas are the inappropriate use of the radial composite model and p*, these issues are discussed. A series of case studies are presented and discussed with a view to establishing that non-uniqueness is sometimes a reality. Furthermore, it is demonstrated (through examples) that starting with one mathematical match to pressure data and deriving a geological model is the reverse approach and may be fraught with danger. Introduction Few health warnings have been published concerning the abuse of the plethora of assumptions underlying well test analysis theory, the over-ambitious use of well test analysis software, and in particular the application of a single, non-unique 'model' to the evaluation of a field. Save for the efforts of Ershaghi and Woodbury, few forthright statements have been made to keep the unwary within the realms of reasonableness. By way of analogy and contrast, simulation literature is full of warnings by an august body of authors, led perhaps by Coats's offering of realism. The advent of type curve matching and use of the pressure derivative analysis have been both an enhancement and a source of frustration. Enhancement because the extraction of more reservoir information has been made possible, and source of frustration because it is frequently impossible to obtain unique solutions and the wealth of underlying simplifying assumptions are too often forgotten. These last points are exacerbated by the fact that not only do we no longer require graph and tracing paper to perform our analyses, but the software in use is only as safe as the underlying theory, which remains heavily assumption-laden. Furthermore, the reservoir 'models' offered in modem software packages are simplified idealisations of pressure response, none of which can be as complex as the underground systems one is usually dealing with. The case studies presented herein will demonstrate that several of these models may mathematically match the pressure data, and that selecting just one of them can be very dangerous, especially if this non-unique model is then used to predict long-term reservoir performance (for example if it is used as the basis of a reservoir simulator). Much emphasis is placed on collating the physical evidence which the well test analysis must match (not the converse), namely logs, core, the depositional model, and don't forget adjacent or analogous fields. These sentiments are expressed by Streltsova as she sets the scene to her treatment of complex problems, stating that "…models of the depositional environment derived from geological… studies of logs and core data can assist in the quality of well test interpretations". The word must should perhaps replace can in this latter statement, the caveat being that well test interpretation requires an appreciation of the dynamics of the reservoir which static geology alone cannot provide. Validity Of The Assumptions If any one or more of the assumptions (underlying the theory in use) is wholly or partially invalid, then the derived solution suffers accordingly. Well test theory is adequately covered in the industry standard works, in related areas of science, and in the appropriate sections of standard, general textbooks. Accordingly, the theory itself will not be discussed here save for a review of the plethora of underlying assumptions. Solutions to the basic radial flow equation form the building blocks of well test theory, but the basis of this equation is purely horizontal flow of a monophase fluid to a well centred in a circular volume. P. 381
- North America > United States (1.00)
- Europe > United Kingdom > North Sea (0.29)
- Geology > Sedimentary Geology > Depositional Environment (0.49)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.47)
Abstract A two-region composite reservoir model is used to analyze well-test data from a variety of enhanced oil recovery projects, geothermal reservoir, and acidization projects. Dynamic phenomena, such as phase changes and multi-phase flow effects in a region near the front, can cause a sharp pressure drop at the front. Such a sharp pressure drop can be modeled as a thin frontal skin. This study considers interference testing in a two-region composite reservoir with a thin frontal skin. Wellbore storage and skin at the active well are also included in the analytical solution to the problem. Correlating parameters are established in the presence of a frontal skin for type-curve marching analysis of interference data from such reservoirs. Our results indicate that for an observation well in the inner region surrounding the wellbore, the effects of storativity ratio (i.e. Φc, ratio) and frontal skin on interference tests are similar. Thus, frontal skin cannot be estimated independently of storativity ratio from an interference test on an observation well in the inner region. However, interference test data collected at an observation well located in the outer region beyond the front helps estimate storarivity ratio and frontal skin independently of each other. The information presented in this paper should be useful in obtaining a consistent analysis of well tests conducted in composite reservoir situations. Introduction This study considers interference pressure and pressure derivative responses in a two-region composite reservoir with an infinitesimally thin skin at the discontinuity. The observation well may be located in any region. Figure 1 shows a schematic diagram of a radial, two-region composite reservoir with an observation well located in the outer region (region 2) at a distance a from the active well. Region 1 (inner region) extends to a radius R, and a thin skin sr may occur at the discontinuity. Ambastha and Ramey presented an analytical solution for transient pressure behavior at any point in a reservoir depicted by Figure 1. Their analytical solution as presented in the Appendix of this paper has been used to investigate interference test analysis in a radial, two-region composite reservoir with a frontal skin. All results presented in this study are for an infinite reservoir. FIGURE 1: Two-region composite reservoir. (Available in full paper) Correlating Parameters Satman presented an study of interference responses in radial, two region infinite composite reservoir. He did not consider the effects of a thin skin at the discontinuity. He correlated transient interference pressure responses using CD/aD, CDe, a/R, M and F as correlating parameters. He defined dimensionless pressure and time using the properties in the outer region, and considered the interference pressure responses for the observation wells located in the outer region only. This study also considers the same correlating parameters as used by Satman. A thin skin at the discontinuity, Sr is an additional correlating parameter, Figure 2 through 7 verify the selected correlating parameters under different conditions. Figure 2 through 7 are for M = 10 and Fs = 100. TABLE 1: Parameters used to generate responses shown on Figures 3, 6 and 7. (Available in full paper)
- Energy > Renewable > Geothermal > Geothermal Resource (1.00)
- Energy > Oil & Gas > Upstream (1.00)
Abstract A study was made of the behavior of reservoirs composed of horizontal layers with fluid banks, unconnected except at the well and filled with a slightly compressible fluid. The new solution described in this paper is an analytical solution for a circular well with a skin effect and wellbore storage. Each layer has a composite system with a circular inner region whose diffusivity is different from the one in the outer region. There may be either a constant pressure, closed, or infinitely-distant outer boundary. pressure, closed, or infinitely-distant outer boundary. The solution method is Laplace transformation followed by a numerical inversion scheme. A recent study of transient flow in one layer systems with radial discontinuities, paper SPE No. 9399, indicated that it was possible to measure the volume of the gas filled displaced region with accuracy and the method did not depend upon regular geometry for the displaced region. There appeared to be very important potential application for enhanced oil recovery and geothermal reservoirs with phase boundaries. This paper is an extension of that study to the reservoirs composed of horizontal layers and investigates the effects of various reservoir and fluid parameters including the shape of the fluid front. Theoretical injectivity and falloff curves from such reservoirs are presented, and the influence of a skin effect and wellbore storage are also evaluated. The results of injectivity and falloff tests are given. The study of injectivity tests indicate a short duration wellbore storage effect, followed by a semilog straight line whose slope is related to the average permeability-thickness of the swept volume. The permeability-thickness of the swept volume. The semilog straight line is then followed by a pseudosteady Cartesian straight line characteristic of the swept volume. Finally, a second semilog straight line appears, characteristic of the average permeability thickness of the unswept region. It is possible to find the nearest distance to the front and also average distance to the front by evaluating the first a few hours of the injectivity test data. The analysis of the falloff tests also shows a short duration wellbore storage effect, followed by a semilog straight line. It is then followed by a transition region. To detect the nearest distance to the front may be possible but the falloff tests do not show any pseudosteady state behavior. Detecting the nearest distance to the front is not always possible due to the fact that the producing time makes possible due to the fact that the producing time makes the analysis of a falloff test for such a system more complex as indicated in the literature. When the producing time is not long enough a flattening region following the first semilog straight line masks the portion of the data whose characteristic is used to detect the nearest distance. Introduction An extensive literature exists on the pressure transient testing on homogeneous and single layer reservoirs. The conventional pressure build-up and drawdown techniques and the reservoir limit tests have been widely used to estimate the important parameters of the reservoirs. Particularly reservoir parameters of the reservoirs. Particularly reservoir limit tests have been accepted as very convenient tools to determine the size of drainage volume associated with the well and possibly the distance to the boundary of the reservoir. Due to the complexity of the environment in which sediments were deposited, and as a result of subsequent physical and chemical changes, many type of heterogeneities are present in all reservoirs. A common type of heterogeneity is the presence of impereable laminations within the producing formation separating the formation into two or more layers. The layers can have different rock and fluid properties. This type of systems can be divided into two properties. This type of systems can be divided into two groups;layered systems with crossflow, and layered systems with no crossflow (also called commingled systems). As the pressure transient behavior of the systems in the first group is analogous to that of a single layer reservoir with the average properties of the layered system, the behavior of properties of the layered system, the behavior of the second group could be different. The reservoir systems in the second group can have two or more layers but the communication between the layers is only through wellbores.
Abstract The fluid flow in porous media has been addressed in literature for obvious reasons. A large portion of petroleum engineering literature was focused on developing solutions for different flow/well models. Composite reservoir model has drawn attention of well testing researchers. The complexity of oil reservoirs in the field make the use of developed models limited. A composite reservoir is made up of two or more regions. Each region has its own rock and fluid properties. A composite system can occur naturally or may be artificially created. Aquifers with two different permeabilities forming two regions, oil and water regions or gas and oil regions with different properties in a reservoir are examples of naturally occurring two-region composite systems. For a well in a radial composite reservoir, the reservoir model usually considered is the radial composite model, in which the well is centered in a circular region of mobility M1 and storativity S1. Beyond this inner zone, the reservoir has mobility M2 and storativity S2. The outer zone mobility may be either higher or lower than that of the inner zone. Field engineers are inclined to use oil flow models for interpreting well tests as long as these wells produce dry. The fluid fractional flow in formation, however, changes as more water encroaches toward the producing well. This paper presents a study focusing on an important application of the use of analytical solutions of composite reservoir model to evaluate the impact of non-unit mobility flow. This is of paramount importance in fields with big differential of mobilities of oil and water as in this study. This research work is to highlight the significance of consideration of water flow impact in formation before wells start cutting water. The solutions were validated with other semi analytical solution and supported by field data.
- North America > United States > California (0.28)
- Asia > Middle East > Saudi Arabia > Eastern Province (0.28)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Pressure transient analysis (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)
Abstract The theories and models of well testing analysis of dual porosity reservoirs with uniform thickness have been discussed in detail in the literature. In order to completely describe the situations of real reservoirs, this paper first studies the pressure behavior of dual-porosity composite reservoirs with non-uniform thickness and lateral heterogeneity. In this paper, the dual-porosity composite reservoir with non-uniform thickness and lateral heterogeneity is defined as the dual-porosity reservoir that consists of many zones with non-uniform thickness, different fluid and formation properties. A new effective radius mathematical model of this composite reservoir in the presence. of skin, wellbore storage and phase redistribution is presented. Laplace-space solutions for this mathematical model with outer constant pressure boundary or outer impermeable boundary are obtained by Laplace transformation and the typical curves for the modern welltesting analysis are given by numerically inverting method. The mathematical model has improved the welltesting analysis theories and the pressure behavior of this reservoir is discussed. The model and solution can be used in the fractured reservoir with variable formation properties or containing water injection wells, gas injection wells, polymer injection wells or finite damaged zone. P. 235