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Abstract This paper presents a rigorous theoretical development of long term boundary-dominated flow solutions which involve direct coupling of the stabilized flow equation with the gas material balance equation. Due to the highly non-linear nature of the gas flow equation, pseudopressure and pseudotime functions have been used over the years for the analysis of production rate and cumulative production data. While the pseudopressure and pseudotime functions provide a rigorous linearization of the gas flow equation, these transformations do not provide direct solutions. In addition, the pseudotime function requires the average reservoir pressure history - which in most cases is simply not available. Our approach uses functional models to relate the viscosity-compressibility product with the reservoir pressure (p/z) profile. These models provide approximate, but direct, solutions for modelling gas flow during the boundary-dominated flow period. For convenience, the solutions are presented in terms of dimensionless variables and expressed as type curve plots. Other products of this work are explicit relations for p/z and Gp(t). These solutions can be easily adapted for field applications such as rate prediction. We also provide verification of our new flowrate and pressure solutions using numerical simulation results and we demonstrate the application of these solutions using a field example. Introduction This paper focuses on the development and application of semianalytic solutions for modelling gas well performance - with particular emphasis on production rate analysis using decline type curves. Our emphasis on decline curve analysis arises both from its utility in viewing the entire well history, as well as its familiarity in the industry as a straightforward and consistent analysis approach. More importantly, the approach does not specifically require reservoir pressure data (although pressure data are certainly useful). Decline curve analysis typically involves a plot of production rate, qg and/or other rate functions (e.g., cumulative production, rate integral, rate integral-derivative, etc.) versus time on a log-log scale. This plot is matched against a theoretical model, either analytically as a functional form, or graphically in the form of type curves. From this analysis formation properties are estimated. Production forecasts can then be made by extrapolation of the matched data trends. The specific formation parameters that can be obtained from decline curve analysis areโOriginal-gas-in-place (OGIP), โPermeability or flow capacity, and โThe type and strength of the reservoir drive mechanism. In addition, we can establishโThe future performance of individual wells, and โThe estimated ultimate recovery (EUR). Attempts to theoretically model the production rate performance of gas and oil wells date as far back as the early part of this century. In 1921, a detailed summary of the most important developments in this area was documented in the Manual for the Oil and Gas Industry. Several efforts were made over the years immediately thereafter, and probably the most significant contribution towards the development of the modern decline curve analysis concept is the classic paper by Arps, written in 1944. In this work Arps presented a set of exponential and hyperbolic equations for production rate analysis. Although the basis of Arps' development was statistical, and therefore empirical, these historic results have found widespread appeal in the oil and gas industry. The continuous use of these so-called "Arps equations" is primarily due to the explicit form of the relations, which makes them easy for practical applications.
- North America > United States > Texas > Permian Basin > Yeso Formation (0.99)
- North America > United States > Texas > Permian Basin > Yates Formation (0.99)
- North America > United States > Texas > Permian Basin > Wolfcamp Formation (0.99)
- (21 more...)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reserves Evaluation > Estimates of resource in place (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Production forecasting (1.00)
- (2 more...)
SPE Members Abstract This paper proposes analysis techniques for post-transient flow at constant bottomhole post-transient flow at constant bottomhole pressure. Rate-time decline curves approximate this pressure. Rate-time decline curves approximate this flow regime. Reservoir characteristics for homogeneous reservoirs, vertically-fractured reservoirs, and naturally-fractured reservoirs can be obtained using these techniques. These analysis techniques are based on the exponential, posttransient, constant-pressure radial flow solutions posttransient, constant-pressure radial flow solutions for each case. We show that theory predicts a linear relation between log (rate) and time for these curves. Thus, a straight line on a semi-log rate vs. time plot may be the line predicted by the analytical solution for that reservoir. If so, important formation characteristics can be estimated analytically. Reservoir pore volume is determined directly while other reservoir characteristics are calculated indirectly. These new techniques are a very powerful extension of transient well testing. DESCRIPTION OF PROPOSED DECLINE CURVE ANALYSIS METHODS The need for accurate estimates of formation properties from decline curves led us to develop properties from decline curves led us to develop analysis techniques for post-transient production at constant bottomhole pressure (BHP). We have developed methods for homogeneous reservoirs, naturally-fractured reservoirs, and vertically-fractured reservoirs; these methods are derived in the Appendices and illustrated with examples in this paper. All cases exhibit an exponential rate decline for post-transient flow conditions; however, the reservoir characteristics which can be determined vary from case to case. Knowledge of these reservoir characteristics, which include drainage area size and shape, permeability, fracture half-length, natural fracture pore volume and storage, and the natural fracture dimensionless matrix/fracture permeability ratio gives insight into well spacing efficiency, the need for reservoir development, and well stimulation efficiency. Each of the methods employs the rate-time plot used in decline curve analysis, and each was rigorously developed from the constant rate pseudosteady-state flow equation using superposition. pseudosteady-state flow equation using superposition. These methods are also exact in a material balance sense. This means the same results would be obtained from these methods as would be obtained from more tedious average reservoir pressure material balance calculations. Also, our methods use periodically measured or estimated flowrates instead of formal "test" data, thus eliminating the need to shut-in the well. To use these methods, one must have measurements of flowrates. For homogeneous reservoirs, the slope and intercept of the decline curve plot are used to estimate reservoir pore volume. However, estimates of skin factor and permeability are required to calculate the reservoir shape factor from either the slope or intercept of the decline curve plot. For naturally-fractured reservoirs, there are too many unknowns to allow us to solve for pore volume, so it must be assumed. Reservoir shape is also assumed to be circular. Also, the skin factor must be known to estimate fracture and matrix properties. Therefore, both the homogeneous and naturally-fractured cases require that a short buildup test be performed prior to obtaining the production data so that the prior to obtaining the production data so that the skin factor and permeability can be estimated. For vertically-fractured reservoirs the pore volume can be calculated directly from the slope of the decline curve plot. The fracture half-length and reservoir fracture shape factor can be estimated from either the slope or intercept of the decline curve plot and an empirical correlation. Each method requires production at constant bottomhole pressure and post-transient flow conditions. Each of the three methods is rigorous for constant BHP production. The major limitations of these methods are that the exponential solutions derived are applicable only to single-phase (oil or gas) flow and that measurements or estimates of flowrates are required in the post-transient production period. production period. P. 279
- North America > United States > Texas > Permian Basin > Yeso Formation (0.99)
- North America > United States > Texas > Permian Basin > Yates Formation (0.99)
- North America > United States > Texas > Permian Basin > Wolfcamp Formation (0.99)
- (30 more...)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Naturally-fractured reservoirs (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring (1.00)