Leverett's capillary J-function has been widely used in the petroleum industry as an effective tool for correlating capillary pressure data with rock properties. The major goals of this study are: (1) to investigate the effect of stress on the calculated values of J-function, and (2) to develop new models capable of obtaining the J-function using in situ measurements in clean and shaly heterogeneous reservoirs.Two models are developed, in which well-logging data, a good source of in situ measurements, are used to calculate the Jfunction. The first model was obtained using Tixier's permeability equation and Archie's equation for water saturation. The second model was derived using Tixier's permeability equation in combination with the Schlumberger shale model for water saturation determination. These models were validated using actual field data from two reservoirs in Oklahoma and Louisiana. FIGURE 3: J-function correlation on capillary pressure data in Edwards formation, Jourdanton Field, Texas (4) . FIGURE 4: Effect of stress on the J-function of Hawken's reservoir rock (Actual data from Reference 3).FIGURE 5: Electric logs from Layton Formation, Oklahoma, USA (Reference 8).

SPE Members Abstract Many flow equations have been developed for horizontal wells but they are complicated in derivation and time consuming in application. A simple productivity equation that incorporates the mechanics of fluid flow in porous media is developed. The equation is based on the drainage area concept. The new equation is validated by using it to study the effect of reservoir height and horizontal well length on the ratio of horizontal well productivity to vertical well productivity when both have the same drainage area. This paper presents the derivation of the equation and its application with several simulated results. Comparisons between the simulated results and results using the more complex equations are provided. Results obtained using the new equation are in agreement with those obtained using Joshi and Borisov equations. The results confirmed the theory that thin reservoirs are good candidates for horizontal wells while thick reservoirs are not. It also showed that an increase in the lateral gives higher ratio of horizontal well productivity to vertical well productivity for the same drainage area. The most advantage of this new equation is that it is very easy to use. The new equation can be used to optimize horizontal well length with respect to horizontal well productivity to vertical well productivity. It is a very useful tool for making decision about application of horizontal well in thin and moderately thick formations. Introduction Many equations have been developed to estimate flow rate in horizontal wells. Researchers used a symmetrical geometric shape to describe the horizontal drainage area to simplify the solution. The resultant equations were based on steady-state solutions, but they were complex. The steady-state solution assumes that pressure at any point in the reservoir does not change with time, dP/dt = 0. Table 1 shows the steady-state flow rate equations for horizontal wells developed by various researchers. Because of their complexities, simplifying assumptions are made in application which may lead to some errors in calculations. These in effect may affect decision or judgment concerning the performance of a horizontal well. The equations in Table 1 can be classified into two groups according to the geometry of the horizontal well. The first group by Borisov and Joshi assumed an elliptical shape, and the second group Giger and Giger et al used a rectangle with two semi-circles on both its sides for the same purpose, Fig.1. The reason for using symmetrical geometries is to simplify the solution, but these geometries do not represent the horizontal drainage areas accurately. The first equation introduced by Borisov was used to calculate steady-state oil flow rate for a horizontal well, but his paper did not show the derivation of that equation. Giger derived his equation and augment the term of replacement ratio to show how many vertical wells can be replaced by horizontal well with the assumption of equal drawdown for horizontal and vertical wells. Joshi introduced an equation with its derivation in his augmentation of well productivity with slant and horizontal wells. The most common feature of all of these equations is that all of them were derived for steady-state and single-phase flow. Development of The Simplified Productivity Equation For Horizontal Wells In order to more realistically represent the drainage area of the horizontal well, this study assumes that the flow to the horizontal well from the toe-end side is not the same that from the heel-end side. Therefore, the drainage area is divided into three parts:a rectangle of length (L) and width 2r, for the horizontal section of the well at the center,a semi-circle of radius r, at the toe-end anda small rectangle of length rL/C, and width 2r, at the heel-side, Fig. 2. P. 617

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Reservoir evaluation of shaly formations and enhancement of reservoir characterization has long been a difficult task. This study is devoted to developing relationships for interpreting the combined effects of subsurface stress and shale on petrophysical properties of reservoir rocks. These new relationships are used to: (1) identify shale types, (2) characterize flow units in shaly formations using in situ measurements, and (3) study the effect of stress on reservoir quality index and fluid flow paths of shaly formations. Several flow unit models have been developed to achieve these goals. The proposed flow unit models are based on current shale models appearing in the literature. These flow unit models introduce unique parameters for reservoir characterization of shaly formations. These parameters include the slope of a traight line (that defines the flow unit) and the stress factor on a log-log plot of in situ reservoir quality index versus in situ porosity of the shaly formations. Finally, these models are used to identify shale types and select a suitable water saturation model for shaly formations. The models are validated using simulated data of porosity and pressure. The new models, in combination with the methodologies developed in this study, represent an effective tool for an enhanced reservoir description of shaly reservoirs. Introduction Characterization of shaly formations has been a difficult task for several reasons. One key factor of this difficulty is that the use of conventional core test data simply does not work. Special equipment or procedures are required to determine the low permeabilities and porosities. A serious, and more fundamental, problem related to studying shaly formations is that of the very heterogeneous nature of shales. In addition, the consideration of the subsurface stress effect will make investigation and characterization of shaly formations much more difficult. With respect to the stress effect, Hilchie(1) used six brine saturated porous samples under simulated conditions of overburden and temperature. The simulated overburden pressure used was up to 68.45 mPa (10,000 psi) and the simulated temperature conditions were up to 232 °CDATA[C (450 °CDATA[F). The results showed that the increase of stress caused an increase of the formation resistivity factor. Longeron(2) investigated the effect of overburden pressure on the electrical properties of sandstone. The results showed that the formation resistivity factor increased by about 15﹪ for sandstone when stress ranging from 276 mPa to 20 mPa (400 psi to 2,900 psi) was applied. Lewis et al.(3) investigated the effects of stress and wettability on the water saturation exponent "n" and the cementation exponent "m." The results showed that changes in stress have a relatively minor effect upon the water saturation exponent "n" and the cementation exponent "m," but trends having an increase in these exponents with increasing stress levels have been observed. Lewis et al. data also showed a slight decrease in these exponents with decreasing stress, but the effectf stress on the water saturation exponent "n"was less clear than that of the cementation exponent "m."Therefore, changes in the cementation and water saturation exponents are probably small enough that they can be neglected.