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Abstract Characterization of hydraulic fracture system in multi-fractured horizontal wells (MFHW) is one of the key steps in well spacing optimization of tight and shale reservoirs. Different methods have been proposed in the industry including core-through, micro-seismic, off-set pressure data monitoring during hydraulic fracturing, pressure depletion mapping, rate-transient analysis, pressure-transient analysis, and pressure interference test. Pressure interference test for a production and monitoring well pair includes flowing the production well at a stable rate while keeping the monitoring well shut-in and recording its pressure. In this study, the coupled flow of gas in hydraulic fractures and matrix systems during pressure interference test is modeled using an analytical method. The model is based on Laplace transform combined with pseudo-pressure and pseudo-time. The model is validated against numerical simulation to make sure the inter-well communication test is reasonably represented. Two key parameters were introduced and calculated with time using the analytical model including pressure drawdown ratio and pressure decline ratio. The model is applied to two field cases from Montney formation. In this case, two wells in the gas condensate region of Montney were selected for a pressure interference test. The monitoring well was equipped with downhole gauges. As the producing well was opened for production, the bottom-hole pressure of the monitoring well started declining at much lower rate than the production well. The pressure decline rate in the monitoring well eventually approached that of the producing well after days of production. This whole process was modeled using the analytical model of this study by adjusting the conductivity of the communicating fractures between the well pairs. This study provides a practical analytical tool for quantitative analysis of the interference test in MFHWs. This model can be integrated with other tools for improved characterization of hydraulic fracture systems in tight and shale reservoirs.
Abstract The main objectives of field development are to maintain high profitability, as well as to achieve the highest coefficient of oil recovery (COR). One of the ways to ensure a high COR for oil fields is creation of a reservoir pressure decrease system (RPD). So, for example, when create a system of RPD, the COR can reach 0.5 d. q., and without RPD - only 0.1-0.2 d. q In the case of designing the development of oil fields with a complex geological structure (the presence of a gas cap, block structure of the Deposit, a large number of faults), the complexity of the task of choosing the optimal development system increases significantly. In Russia and in the world, there are a considerable number of oil fields that have been developed for a long time on the depletion mode, which has led to the formation of a considerable volume of the free gas phase. Such deposits often pass into the category of problematic and are characterized by low current values of the coefficient of oil recovery (COR), as well as the lack of reliable technological solutions for their effective development. Examples include the Talinsky area of the Krasnoleninsky field, the oil pool in the Jurassic sediments of the Novogodnee Deposit, and others. When the pressure increases further, for example, by pumping water, modeling the development of such deposits requires the use of non-equilibrium hydrodynamic models. Application of the results of the pressure interference test (PIT) allows us to obtain valuable information about the connectivity of inter-well intervals, a quantitative assessment of the conductivity of reservoir faults, and, consequently, reduce risks when planning field development, increase the efficiency of ongoing geological and technical measures and their profitability. Conducting of PIT on a working stock, in comparison with classical methods, allows you to minimize the loss of production during research. Proper planning of field development with the involvement of PIT results, in particular-the introduction of the RPD system, allows to increase the COR and profitability of the development system as a whole. The paper shows the results of the pressure interference test studies for a tectonically complicated structure of an oil and gas condensate field. Based on the results of the research, the efficiency of the existing RPD system was evaluated and decisions were made to transfer production wells to injection, taking into account the assessment of the risks of water breaks through conducting faults. In addition, the results of the pressure interference test were combined with the results of tracer studies. The convergence of research results by both methods is shown.
Abstract There is not yet a defined relationship between stimulation volume and long term producing volume in low permeability (nanodarcy scale) "reservoirs". To quantitatively describe producing volume, we define the distances at which stimulated horizontal wells show sustained connectivity by interpreting field pressure data to understand communication with neighboring wells over a series of time steps at 2, 6, 8, and 12 months after completion. We show how to design and execute pressure transient tests, how these field results yield conclusive evidence of proper well spacing, and how other methods to assess stimulated reservoir volumes compare. Our procedure takes weeks to perform, and may be applied to make unplanned shut-in events useful reservoir characterization tools. Coordination between geology, reservoir engineering, and field engineers is required to successfully execute these tests. The results show we have a powerful tool for tuning of development plans well in advance of years' worth of production commonly used for such decisions. From frac hits, microseismic, and tracer results we observe a continuous reduction in the stimulated volume around horizontal wells from the instant of completion through early production. To describe the continued evolution of the producing volume, we define producing volume half-lengths at 2, 6, 8, and 12 months. Armed with measurements of half-length stabilization in the early months of production, we confidently define the upper limit of well spacing for future development. Although we cannot yet define economically optimal overlap between producing volumes, this upper limit allows operating groups to set the correct length scale for future investigations. Results from our pressure communication studies are compatible with other methods of greater uncertainty, longer timelines, and higher cost. Traced fluid and proppant, microseismic events, and frac hits represent stimulation that may not relate to long term productivity. Pressure communication between stimulated wellbores defines the capability of the stimulation to maintain permeability at the test production time step. However, these other measurements do help bound the evolution of stimulated reservoir volumes in a manner compatible with our pressure communication results.
Summary This paper presents an extension for linear and spherical flow conditions of the El-Khatib method for the analysis of pressure interference tests through the use of the pressure derivative. For linear flow a graph shows a straight line with slope and intercept, which can be used to estimate the formation permeability and porosity; similarly, for spherical flow a graph shows a straight line with slope and intercept, which can be used to estimate the same previously discussed parameters. A friendly computer code for the automated analysis of pressure interference tests is also discussed. Two field cases are presented to show the use of this program. The first deals with the interference tests conducted in the naturally fractured Klamath Falls geothermal field, and the second is a test carried out in a river-formed bed, dominated by linear flow conditions.
Today reservoir engineers are faced with the challenge of evaluating well tests in heterogeneous, complex reservoirs which may include fractures. For such reservoirs analytical methods are not available so numerical simulation is required. We present a finite element simulation system for gas well test analysis in such reservoirs. An automatic finite element grid generation technique provides grid refinement only in regions where it is needed. In this way wells and fractures are rigorously represented. Also wellbore storage and skin effects can be included in the model. Analytical coupling of fracture flow equations with reservoir flow equations, and nonlinear treatment of gas viscosity and compressibility, make the model ideal for gas well testing in fractured reservoirs. Also included in this 2-D model is the capability of simulating multi-layer, 2-D reservoirs with crossflow only at the wells in a numerically efficient way. The model has been validated against analytical solutions for liquid flow in homogeneous media and has been shown to he correct to high order accuracy.
Analytical solutions to linearized approximations of the equation of flow for single phase flow in reservoirs have been exploited for many decades in the design and evaluation of transient pressure well tests. These, by definition, can be exploited by pressure well tests. These, by definition, can be exploited by the principle of superposition, for example, to represent variable flow rate histories [Collins, Earlougher, Lee]. Clearly, these are only approximations to reality and severely limit the types of physical systems that can he represented. Even the semi-analytic physical systems that can he represented. Even the semi-analytic method, based upon superposition of simple solutions obtained in the LaPlace transform domain using inversion by numerical techniques, is limited to linear forms of flow problems [Gringarten et al., Heber et al., Kucuk and Brigham ]. Thus one must turn to numerical solutions if the more realistic, non-linear formulations for single phase flow are to he treated, especially for flow of real gases.
Now it is true that an almost-linear differential equation for flow of a real gas is obtained if one introduces the real gas pseudo pressure [Dake] pressure [Dake]
as the dependent function in lieu of pressure. Specifically this is
where non-linearity still arises in the dependence of u and ct on P, or m. Furthermore, even if one accepts the linear P, or m. Furthermore, even if one accepts the linear approximation of K, ,u and Ct, all independent of variation in P, or m, analytical, or semi-analytical, solutions can be obtained P, or m, analytical, or semi-analytical, solutions can be obtained only for cases of reservoirs having very simple geometry and uniform properties. Thus numerical solutions must still be invoked for complex, heterogeneous reservoirs.
As one turns to numerical solutions there are two options, finite difference methods or finite element methods. In block-centered finite difference techniques a well representation is required [Aziz and Settari]. Usually well models are based on the approximation of pseudo steady-state flow near the well; this causes error in well pressures. Furthermore, the common use of rectangular, orthogonal grids introduces grid limitations on the representation of reservoir geometry and the configuration of reservoir heterogeneities. An even greater difficulty arises in the use of finite difference techniques for reservoirs with heterogeneities in permeability; significant grid refinement is required in the neighborhood of any large discontinuity in permeability. Local grid refinement is possible permeability. Local grid refinement is possible [von Rosenberg] but is generally impractical in finite difference methods. Thus the finite element method is preferred.
Now one might well ask, why require numerical solutions of great accuracy? The answer is that if one wishes to exploit the high precision of modern pressure gauges then one requires solutions as precise as analytical solutions.
This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Computer graphics were used to analyze dynamic pressure responses from short-term interference tests that were conducted in an attempt to outline the natural and induced fracture systems in a petroleum reservoir. By use of a time-programmable data acquisition system, pressure responses from 40 wells arranged in 16 regular 5-spots were monitored during 74 water injection tests that resulted in over 120,000 individual pressure readings. To aid in the interpretation of the complex field behavior, the data were transferred to computer cards. Software was then developed using cathode ray tubes (CRT), drum plotter, and on-line printers to reduce and evaluate the data. Pressure-time plots were generated for each well in a test. From these plots, tests that indicated evidence of existing fracture systems were selected for more detailed analysis. Of the selected tests, sequenced delta pressure contour maps were used to show the dynamic behavior of the field due to the interference test. Graphic three-dimensional perspective views of the changing field perspective views of the changing field pressures were also used in the interpretation pressures were also used in the interpretation of the reservoir behavior. Results of two specific tests are shown. Introduction A series of experiments was designed in an effort to map existing fracture systems in an oil reservoir. The delineation of natural and induced fractures in a petroleum reservoir is important in the determination of potential flow characteristics. Knowing these potential flow characteristics. Knowing these characteristics can result in a more efficient recovery of oil through the planning and operation of secondary and tertiary recovery projects. A 36-acre test site owned and operated by the Minard Run Oil Company was selected near Bradford, Pa. The test site included 25 injection and 16 producer wells that had been fractured and used in a waterflooding operation. The spacing of the wells was arranged in 16 regular 5-spots and is shown in figure 1. The porosity of the producing formation averaged porosity of the producing formation averaged about 16 percent and had an average permeability of 6 millidarcys. The depth of the wells ranged from 1,950 to 2,000 feet.