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Keywords: intercept

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Permian Basin Oil and Gas Recovery Conference, March 23–26, 1998

Paper Number: SPE-39810-MS

... upon the permeability equation used. The straight line (representing the flow unit) yields various unique slopes for the different models. This depends upon the porosity exponent that appeared in the permeability equation. In addition, each flow unit model possesses a characteristic

**intercept**...
Abstract

Abstract The purpose of this study is to develop new models capable of providing better description of the reservoir through the use of the concept of Reservoir Quality Index (RQI) combined with the available permeability models appearing in the literature. Six enhanced reservoir characterization models have been developed that incorporate core and/or conventional well-logging derived-data to identify hydraulic (flow) units. Two models are developed based on equation of Nuclear Magnetic Resonance (NMR) to identify flow units using core data. In addition, three flow unit models are developed based on Timur, Wyllie and Rose, and a generalized permeability equations. The sixth model is developed using Jorgensen permeability equation. It is found that each flow unit can be represented by a straight line on a log-log plot of the RQI versus porosity,, or versus the parameter()depending upon the permeability equation used. The straight line (representing the flow unit) yields various unique slopes for the different models. This depends upon the porosity exponent that appeared in the permeability equation. In addition, each flow unit model possesses a characteristic intercept on the NMR Decay time- # log-log plot, or on the RQI- # log-log plot, or on RQI() log- log plot. The new flow unit models are validated by using actual and simulated data. Use of the new models in combination with the systematic technique developed, 2. Is correlative and mappable at the interwell scale; represents effctive tools for enhancing reservoir characterization. P. 505

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 27–29, 1996

Paper Number: SPE-35197-MS

... and the superposition time function, ?t sup , is defined as Equation 4 According to Eq. 1, a plot of inverse injectivity, (p i -p w )/q N , versus the superposition time function, ?t sup , will yield a straight line with a slope of m and an

**intercept**of b. During an acid treatment, all of the parameters defining...
Abstract

Abstract The use of an inverse injectivity versus superposition time plot to diagnose the changing skin factor in a matrix acidizing treatment has been presented previously by Hill and Zhu 1 . The model has been extended to calculate skin factor as a function of injection time or injected volume directly to help the operator monitor and optimize the treatment. A Windows program based on the theory has been developed to provide a pretreatment test to evaluate the permeability and the initial skin factor of the formation when they are not available before the acid treatment, to calculate and plot the evolving skin during the treatment in real-time, and to evaluate treatments afterwards. It converts surface pressure, when measured, to the bottomhole pressure for the calculation, and handles fluid density and viscosity changes in real time. Several field examples showed that the technique can be used conveniently to monitor skin changes and diversion effects during matrix acidizing treatments. The program is reliable and flexible in acquiring and processing data, calculating skin, and diagnosing matrix acidizing treatments. Introduction To monitor changing skin during a matrix acidizing treatment, the theory for a standard injectivity test using the approximate line source solution for transient flow during injection has been adopted 1,2 . The pressure transient response to injection for multiple injection rates is Equation 1 where, Equations 2 and 3 and the superposition time function, ?t sup , is defined as Equation 4 According to Eq. 1, a plot of inverse injectivity, (p i -p w )/q N , versus the superposition time function, ?t sup , will yield a straight line with a slope of m and an intercept of b. During an acid treatment, all of the parameters defining the slope, m, do not change, leaving m a constant. Among the parameters defining the intercept, b, the only one that changes as acid is injected is the skin factor, s. As a result, each inverse injectivity/superposition time point will l ie on a straight line having a slope, m, with its intercept depending on the skin factor at the moment. Thus, a family of constant skin curves can be calculated and plotted on a diagnostic chart of inverse injectivity versus superposition time function before the treatment, and the skin change can be monitored by locating the inverse injectivity as a function of superposition time on the chart. This method is easy to apply in the field and the result is comparable with other more complicated methods developed before 3,4,5 , but it requires the user to read from the diagnostic chart and interpolate between lines of constant skin to obtain the skin factor in real time. The model has been extended so that the evolving skin is calculated directly in real time as the treatment proceeds, allowing the operator to monitor and optimize the treatment more conveniently.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 27–29, 1996

Paper Number: SPE-35245-MS

... drillstem testing characteristic time straight line horizontal transmissibility transmissibility formation pore pressure well control upstream oil & gas sidpp flow rate annular pressure drilling mud density wellbore permeability practical application mud weight

**intercept**pressure...
Abstract

Abstract This paper describes a new method for prediction of pore pressure and formation permeability from a kicking Well. Getting reliable and accurate information about reservoir parameters (when the formation damage is minimal) is of critical importance for making proper well completion decisions. In addition, when a awell kicks, inaccurate estimation of the formation pressure may cause loss of equipment and possibly the well and human lives. To combat the above problems, a conventional pressure analysis method is modified to predict the formation pore pressure and estimate directional formation permeabilities from a kicking well. The method is simple, and the only prerequisite is that the buildup data be collected upon shutting-in a kicking well. Examples of using simulated as well as actual field data, are provided to demonstrate the practical application of the method. Introduction During regular rotary drilling operations the bore-hole pressure is higher than the formation pore pressure resulting in positive pressure differential. The positive value of pressure differential is required to prevent formation fluid influx into the wellbore. When the wellbore pressure drops below the formation-fluid pressure, formation fluids enter the well. If the formation pore pressure is known, one can calculate the required drilling fluid density to create the desired bottom hole pressure. Designing the correct value of mud density is of critical importance and requires information about pore pressure. If the mud density is too low, influx of formation fluid, frequently called a kick, may occur. It is a well known fact that the influx of formation fluid into the wellbore may be dangerous. If timely actions are not taken to shut-in and kill the well (using proper procedure), a blowout or other complications may result. Once the kick is detected at the surface, the well is shut-in and proper well control technique is undertaken to establish the desired pressure conditions in the wellbore. Upon shutting-in the well, casing and drillpipe pressures increase as a function of time due to compressibility of formation fluid. Surface pressure on the drillpipe (shut-in drill pipe pressure - SIDPP) and casing (shut-in casing pressure - SICP) are recorded to establish "stabilized pressures". The pressure buildup data, recorded during the shut-in time, can be used for determination of formation pore pressure and flow properties, if a proper data interpretation technique is available. Arbitrary determination of shut-in pressures can lead to errors in estimating formation pressure, which in turn, leads to improper mud density calculation and further complications.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 13–15, 1986

Paper Number: SPE-15018-MS

... 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...
Abstract

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

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 13–15, 1986

Paper Number: SPE-15028-MS

... of petroleum engineers rate case relation graph

**intercept**SPE 15028 Variable-Rate Reservoir Limits Testing by T.A. Blasingame and W.J. Lee, Texas A&M U. SPE Members Copyright 1986, Society of Petroleum Engineers SPE Society of Petrolet.m Engineers of AIME This paper was prepared for presentation...
Abstract

SPE Members Abstract This paper presents a new method of estimating drainage area size and shape from production data (bottom-hole pressures and flowrates). The method is a rigorously derived approximation for variable-rate flow in a closed reservoir. This method requires a graph of Ap/qm vs. the superposition plotting function (which is easily calculated by plotting function (which is easily calculated by hand). The slope and intercept of the graph are used to provide the desired estimates of drainage area size and shape. The method that we propose is an approximation, however it has been proved to be very accurate for the constant rate, constant pressure, exponential rate, logarithmic rate, hyperbolic rate, sinusoidal rate, and discrete rate cases. The method also gives acceptable results for square wave rate and random rate cases. The new method is derived for the time after the initial pressure transient has reached the outer boundary. The changes in flowrate cause additional transients, but we assume that this effect is negligible when compared to the influence of the outer boundary. Therefore, if the change in flowrate does not dominate the influence of the outer boundary, the new method should give acceptable results. Also, at present, this method is only derived for single-phase flow of a liquid of small and constant compressibility. Introduction The purpose of this paper is to present a simple, but accurate method of predicting reservoir drainage area size and shape from variable-rate production data. Previous works have dealt with production data. Previous works have dealt with constant or cyclically constant rate and constant bottom-hole pressure production. A summary of these methods is shown graphically in Figure 1. Earlougher defined the cyclically constant or square wave rate case in Figure 2. Rather than focus on a particular rate scheme, we develop a general variable-rate approximation that should give accurate results for typical production situations. Without a variable-rate solution we would have use the more tedious material balance methods that require average reservoir pressures to estimate reservoir pore volume. This would require the well to be shut-in, which results in lost revenue. However, with the new method, the reservoir pore volume and shape can be estimated directly from the production data, without shutting-in the well. production data, without shutting-in the well. The problem of variable-rate flow in bounded systems isolimited in the literature t work by Earlougher-' and the "stabilized flowing,- U methods (which use average reservoir pressures). Though both approaches give acceptable results for their specific application, Earlougher's case is not realistic and the "stabilized flow" methods again require the well to be shut-in for average reservoir pressure determinations. This suggests the need for a general solution for variable-rate flow in a bounded reservoir. In the "Description of the New Method" section we will present the general variable-rate solution and the reservoir characteristics which can be derived from it. Also, we will verify the general variable-rate equation (Eq.(2)) using analytical and finite-difference simulation. Then a step-by-step procedure for applying our method and a complete example will be shown in the "Method of Application" section. Finally, we will present the derivation of the exact solution for variable-rate flow in a bounded circular reservoir and the approximate solution for variable-rate flow in any shape reservoir in the Appendix of this report. P. 361