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The purpose of this paper is to document transient behavior at a well that produces a fractured reservoir by solution-gas drive. The authors consider the dual-porosity model Barenblatt et al. and Warren and Root introduced and the dual-permeability model Bourdet presented. These idealizations are considered to demonstrate the consequences of production from the matrix system. They document pressure and saturation behaviors in the fracture and matrix systems. The interaction between the matrix and the fracture systems under multiphase flow conditions also is discussed. For convenience, they refer to the Warren and Root model as the dual-porosity model and to the Bourdet idealization as the dual-permeability model.

This paper analyzes the influence of gravity segregation effects on inflow performance relationship (IPR) curves, with both totally and partially penetrated vertical wells. Using synthetic responses from a finite difference simulator, the effects of different parameters, such as vertical to radial permeability ratio, production mode, position of productive interval, oil rate, and mechanical skin, on the shape of IPR curves are documented. It is shown that greater flow potentials are obtained when the ratio of gravity to viscous forces increases. It is shown that for the case of partially penetrated wells, the IPR curve generated at constant bottomhole pressure does not coincide with the IPR generated at constant oil rate. Also, the presence of gravity segregation affects the values of absolute open flow potential, obtaining big differences with the corresponding values when gravitational effects are ignored. The values of the exponent n of Fetkovich IPR and the coefficients of the quadratic equation proposed by Jones et al. are functions not only of time but also of production rate, position of productive interval, and other parameters. The consequence of the above results is that the interpretation of IPR curves is affected by the presence of gravitational effects and therefore the use of traditional methods, such as those of Vogel , Fetkovich, or Jones et al., is restricted to the specific conditions considered by these authors.

Summary This paper presents procedures to obtain reservoir parameters from constant-pressure drawdown data in solution-gas-drive reservoirs. A novel procedure to determine the mechanical skin factor is introduced. Examples, including a field case, illustrate the use of this procedure. An estimate of the drainage area can be obtained with the derivative of rate data. A theoretical basis for analyzing data by the pressure-squared, p2, approach is presented; this procedure permits the approximate determination of sandface effective permeabilities in the transient flow period. For damaged wells, it is possible to obtain rough estimates of the size of the skin zone and the ratio of reservoir/skin-zone permeability when early transient data are available. The expression of the appropriate dimensionless rate in terms of physical properties for solution-gas-drive systems is presented. Finally, this paper presents a procedure to obtain an estimate of the change in sandface saturation during the transient flow period.

This work examines the well and reservoir performance under both solution gas-drive and gravity drainage in homogeneous systems. Based on synthetic information obtained with a fully implicit black-oil simulator, the influence of different parameters like oil rate, position of the producing interval, wellbore pressure level, skin factor, and vertical permeability, for both constant oil rate and constant pressure production modes are documented. Analytical results for the reservoir performance during the boundary dominated flow period are derived. An approximate expression that describes the variation of oil saturation with average pressure is presented. For constant oil rate production, the influence of gravity drainage on the inflow performance relationships curves is studied, and a new correlation is presented. For constant pressure production, the decline curve behavior is analyzed and it is found that under favourable gravitational effects, the production behavior shows two decline stages such as double porosity systems; however, it does not follows the typical decline type curves for naturally fractured reservoirs. At certain backpressure values during the first stage an exponential decline behavior could be observed, while during the second stage values of the decline exponent less than zero are observed.

Abstract The effect of capillary pressure on well test is investigated. Solution gas-drive, homogeneous and naturally fractured reservoirs are considered. A numerical simulator, with a Warren and Root formulation for the case of fractured reservoirs, is used to generate synthetic data. For homogeneous reservoirs the procedures of Perrine-Martin and pseudo-pressure are evaluated under the presence of capillary pressure. As expected the influence of capillary pressure is more pronounced in buildup tests than in drawdown tests. A capillary pressure number is proposed to evaluate the importance of capillary forces over viscous forces in different regions in the reservoir. For naturally fractured reservoirs, the effects of including capillary pressure in the fracture and matrix systems are investigated. It is observed that, under certain conditions, both drawdown and buildup tests show capillary pressure effects in different flow periods under transient conditions. Also, the influence of capillary pressure on the flow transfer between matrix and fracture is documented, observing that the oil flow rate per unit volume from the matrix to the fracture system is lower when capillary pressure is taken into account. P. 421

A computer program has been developed for simulating two-phase flow in horizontal and inclined pipes. This program is based on the mechanistic model of Xiao et al., extending the inclination angle from ± 15° to the range: ± 45°, using the works of Barnea and Hasan and Kabir. With this hybrid model it is determined the flow pattern, under stationary conditions, and hydrodynamic characteristics of the flow pattern, mainly hold-up and pressure gradients. An analysis of synthetic information, generated with the computer program, has been done. Based on statistical parameters, the mechanistic model performance has been compared with that of Beggs and Brill correlation, observing similar trends, with both procedures for the whole range of pipe inclination angles. Finally, through 3-D graphs, performance of principal hydrodynamic parameters has been presented. Mechanistic models for multiphase flow in pipes consider the basic physical phenomena for their development. The inclination angle is one of the main parameters that control flow characteristics. One of these models is that of Xiao et al., developed for horizontal and close to horizontal pipes.

Abstract The aim of this work is to examine the well bore pressure behavior in reservoirs with single phase non-Darcy flow conditions produced at a constant sandface rate. The transient flow period is analyzed by means of results generated with a finite difference model. Analytical expressions of pressure drop and its semilog-arithmic slope are presented for the first time. These equations contain the laminar flow solution as a particular case and they provide means to evaluate the total skin factor. Another use of the analytical solution to the non-Darcy flow problem is to be able of identifying the presence of inertial effects by using a diagnostic plot which consists of graphing the derivative of the pressure data. versus the inverse of the square root of time on a cartesian paper. In this way, an analyst can easily predict the magnitude of the skin due to non-laminar flow under any condition of mechanical skin and rate. Furthermore, better stimulation jobs can be designed if non-Darcy flow conditions during a transient test are properly identified through the methodology presented in this study. The use of the methodology obtained in this work is illustrated with synthetic examples for homogeneous and naturally fractured reservoirs. Also, a field example of an undersaturated reservoir and a dry gas case (taken from the literature) show the application of this technique. For the case of naturally fractured reservoirs new insights are provided.

This paper presents the results of a systematic st.udy of the influen'~e of highvelocity flow on the interpretation of t.ransient gas condensat.e well t.ests. A one dimensional radial fully implici t compositional model using the Forchheimer equation was used t.o obtain the results present.ed in this work, Dra.wdown anel buildup tests at const.ant. ma'.>s rate were simulated. The simulator wa'.> carefully checked, since no solut.ions for gas condensate flow are available in the literature t.hat consider high-velocity flow, Among these tests, in accordance to the met.hod of Camacho et.. al, multiphase highvelocity result.s were graphed in terms of d Pl'wd/dIn l D vs 1/(tD)1/'!., presenting a posit.ive slope, characterist.ic of high-velocit.y flow, t.hat extrapolat.es c.orrec t.Iy to the 0,5 int.ercept.ion value corresponding to Darcy flow. It. was found that drawdown solut.ions graphed in t.errns of the sandface dimensionless pseudopressme vs log tD show for large times the characterist.ic one phase slope of 1.151. As expected, high-velocit.y effects result in an earlier appearance of the condensate phase in the reservoir. It was also found, as alrea.dy mentioned, that. results of this study when properly expressed ill t.erms of pseudo.pressure show the characteristic behavior for the high-velocit.y monophasic flow rnet.hod of Camacho et.. aI., which allows the estimat.ion of the high-velocit.y pseudoskin fador and flow capacity. Thus, this met.hod is also valid for condit.ions of t.his st.udy as a diagnostic References and illustrat.ions at. the end of paper tool for high-velocity flow. It is also demonstrated that the mobility function ).t(Pw) can be estimated from the derivative of the pressure data.

Abstract Most of theoretical work on decline curves considering non-laminar flow is related with dry gas systems. The purpose of this study is to analyze decline curves considering non-Darcy flow effects in the reservoir for both slightly compressible liquid flow and solution gas-drive systems keeping the wellbore pressure constant. The transient and boundary-dominated flow periods are examined by means of computer results generated with a finite difference black-oil reservoir simulator with a variable bubblepoint formulation. The consequences of this formulation under non-Darcy flow are studied. The influence of the mechanical skin factor on the rate response is documented. For the case of liquid flow, it is presented for the first time an expression to evaluate the total skin factor which is a function of the mechanical skin and the skin due to inertial forces. This expression is given in terms of physical properties of the system, it is proportional to the square root of the pressure drop, and it is also equal to the square root of the Reynolds number. This is one of the main findings of this work. It is investigated the possible presence of a semilogarithmic straight line of reciprocal rate for both liquid and solution gas-drive systems, and new insights are provided. In general, when the inertial effects are important and the bottomhole wellbore pressure is kept constant, a true semilogarithmic straight line of the inverse of oil rate does not develop. This result is valid for both liquid and solution gas-drive systems, and it is an important difference with the case of liquid flow under constant oil rate production mode, where a semilog straight line of the pressure drop is evident during the transient period for a big enough drainage area. For liquid flow an apparent straight line may be fitted and its ordinate to the origin is approximately equal to the value of total skin computed with the expression mentioned above. The presence of inertial effects distort the shape of the laminar decline curves for both multiphase and slightly compressible liquid flow, causing that type curve analysis yield wrong estimates of the wellbore and reservoir parameters. Also, if someone attempts to do a history match with data affected by non-Darcy flow using a conventional simulator, that uses Darcy's law in its formulation, an alteration of the reservoir properties will be necessary. Introduction In several activities of reservoir engineering the employment of a graph of production versus time is been used routinely to forecast production decline. This technique is also used as a type curve analysis procedure. The decline curves can be grouped into two sets, empirical and analytical. The empirical curves presented by Arps are applicable during the boundary-dominated flow period for saturated reservoirs under different driving mechanisms. The analytical curves, designed for undersaturated reservoirs, are applicable for both transient and boundary-dominated flow periods considering laminar flow. M. Fetkovich has proposed to combine these two sets of curves, yielding in this way a single set of type curves to predict production decline. P. 301^

Summary The performance of wells in solution-gas-drive reservoirs during the boundary-dominated flow period is examined. Both constant-wellbore-pressure and constant-oil-rate production modes in closed systems are considered. For the constant-wellbore-pressure production mode, Arps' performance-prediction equations are examined, and predictions of future performance are shown to be strong functions of well spacing, well condition, and fluid properties. The parameters b (the decline exponent) and di (the initial decline rate) in the Arps equations are expressed in terms of physical properties. The conditions under which these equations can be used are specified. An empirical procedure to predict production rates is also presented. In the case of constant-oil-rate production, an expression to correlate the pressure distribution in the reservoir is presented. The correlating function permits us to extend the definition of pseudosteady-state flow to solution-gas-drive systems. Its use also allows the simultaneous computation of average properties (pressure and saturation) during boundary-dominated flow from wellbore information.