Straightforward applications of fractional-flow theory and material-balance calculations demonstrate that, if zones are not isolated during gel placement in production wells, gelant can penetrate significantly into all open zones, not just those with high water saturations. Unless oil saturations in the oil-productive zones are extremely high, oil productivity will be damaged even if the gel reduces water permeability without affecting oil permeability. Also, in field applications, capillary pressure will not prevent gelant penetration into oil-productive zones. An explanation is provided for the occurrence of successful applications of gels in fractured wells produced by bottomwater drive. With the right properties, gels could significantly increase the critical rate for water influx in fractured wells. Introduction Coping with excess water production is always a challenging task for field operators. The cost of handling and disposing produced water can significantly shorten the economic producing life of a well. The hydrostatic pressure created by high fluid levels in the well also is detrimental to oil production. The two major sources of excess water production are coning and channeling. Water coning is common when a reservoir is produced by a bottomwaterdrive mechanism. Fractures and high-permeability streaks are the common causes of premature water breakthrough during waterfloods. Polymer gels have been applied to many wells to reduce excess water production without adversely affecting oil production. l-6 Moffitt reported that polymer gels are particularly effective in suppressing water coning. In many cases, however, gel treatments have not been successful. Part of the reason for the sporadic success was problems with gel placement. During gel placement in production wells, much of the gel formulation will enter zones responsible for the excess water production. However, some of this fluid may enter and damage oil-productive strata. The objectives of this study are to model gel placement in production wells mathematically and to examine the potential effect of gelant invasion into oil-producing zones. Particular attention is paid to the importance of two phenomena. The first is hysteresis of oil/water relative permeability curves during the "pump-in, pump-out" sequence used during gel placement in production wells. The second phenomenon is that gels (or polymers) can reduce the relative permeability to water more than to oil. Sensitivity studies covering most known field and laboratory applications are discussed. In particular, we study permeability contrasts from 1 to 1000, oil/water viscosity ratios ranging from 0.1 to 100, endpoint water relative permeabilities ranging from 0.1 to 0.7, water saturations ranging from 0.2 to 0.8, and fractured and unfractured wells. Therefore, our conclusions should be applicable to most field applications of gels in production wells. Examples are provided to illustrate and contrast situations where gels are or are not expected to damage oil productivity. In these example...

The purpose of this study is to examine Biot's two-phase (fluid and rock), isothermal, linear poroelastic theory from the conventional porous fluid-flow modeling point of view. Biot's theory and the published applications are oriented more toward rock mechanics than fluid flow. Our goal is to preserve the commonly used systematic porous fluid-flow modeling and include geomechanics as an additional module. By developing such an approach, complex reservoir situations involving geomechanical issues (e.g., naturally fractured reservoirs, stress-sensitive reservoirs) can be pursued more systematically and easily. We show how the conventional fluid-flow formulations is extended to a coupled fluid-flow-geomechanics model. Consistent interpretation of various rock compressibilities and the effective stress law are shown to be critical in achieving the coupling. The "total (or system) compressibility" commonly used in reservoir engineering is shown to be a function of boundary conditions. Under the simplest case (isotropic homogeneous material properties), the fluid pressure satisfies a fourth-order equation instead of the conventional second-order diffusion equation. Limiting cases include nondeformable, incompressible fluid and solid, and constant mean normal stress are analyzed. Introduction All petroleum reservoir problems involve two basic elements: fluid and rock. We are interested in two particular processes associated with them: fluid flow and geomechanics. Fluid flow is essential in a petroleum reservoir study. Geomechanics is believed to be important in the study of naturally fractured reservoirs and in reservoirs exhibiting stress-sensitivity. The theory describing fluid-solid coupling was first presented in a series papers by Biot. Biot's theory and the published applications are oriented more toward rock mechanics than fluid flow. Extension of Biot's theory to reservoir studies is not straightforward, especially to nongeomechanical or fluid-flow oriented engineers. The purpose of this paper is to describe how the conventional fluid-flow modeling can be extended to a coupled fluid-flow and geomechanical modeling. Identification of the linkages and consistent interpretations between the flow and deformation fields are emphasized. Several excellent reviews or re-interpretations of Biot's poroelasticity have been presented in, e.g., Refs. 8 through 15. Among these references, the works by Verruijt and Bear are the two most pertinent to this study. They also considered porous fluid-flow modeling approach coupled with Biot's theory. Both works, however, assumed incompressible solid phase in both flow and deformation fields. The solid phase compressibility, although not the primal mechanism in rock deformations, is a necessity for a complete interpretation of Biot's theory. Specifically, the solid compressibility is implicit in the so-called effective stress coefficient which, as will be shown, is the most important and critical concept in the theory of poroelasticity. The assumption of incompressible solid phase effectively eliminates the consideration of effective stress coefficient and greatly simplifies the problem. P. 507

Complex reservoir flow problems could be better understood through a study using physical models. The purpose of this paper is to present results of an experimental study of water crest behavior under horizontal wells. This work is made in an effort to better understand the formation and growth of water crest prior to and after water breakthrough. The physical model constructed differs from others in that variation in length and position of the horizontal well can be made. Eighteen different systems with varied oil column thickness and oil viscosity were run. Particularly in systems with viscous oil, the bottom water never reached the tip end of the well even at a producing water cut of almost 100 percent. The end effects defined as the unswept oil are pro- flounced as the well length is reduced and as the oil viscosity is increased. Also, at high water cut, the portion of the wellbore with low productivity increases with well length. These physical occurrences have not been previously reported. Postbreakthrough performance will be presented and discussed. Introduction Oil production from bottom water drive reservoirs is usually followed by water produced through the same well. This situation occurs when bottom water has broken through the well due to a high drawdown applied to the reservoir. The appearance of bottom water in vertical wells is in many cases observed in a relatively short time after the wells are put on production. Once the water enters the wells, a rapid increase in water cut may lead to low oil recovery. The application of horizontal well technology has been widely used in many countries to improve oil recovery from water drive reservoirs. At a low drawdown, a horizontal well can have a larger capacity to produce oil as compared to a conventional vertical well. Thus, the critical rate, below which the flat surface of water-oil contact will not deform, in a horizontal well may be higher than that in a vertical well. But in practice, production rate is usually higher than the critical rate due to economic consideration. When this takes place, high mobility bottom water will invade into the overlying oil zone and moves toward the well. The higher the rate of production the faster the bottom water movement. The period required for the water to reach the well is called as a breakthrough time. As compared to a vertical well for a given rate, a horizontal well requires a lower drawdown and therefore gives a longer breakthrough time. This advantage combined with larger displacement cover- age provided by bottom water result in better oil recovery. A region of oil zone that has been invaded by bottom water may be in the form of a cone for vertical wells and a crest for horizontal wells. Many publications relating to water coning phenomena have been available. The water cone beneath a vertical well is assumed to develop symmetrically with respect to the vertical well axis. This is true because no pressure gradient in the well system is accounted for and the well acts as a point source, eventually. In the context of horizontal well producing oil from bottom water drive reservoirs, many researchers considered no pressure gradient exists along the horizontal wellbore. This implies that bottom water rises uniformly and the crest formed is symmetric with respect to a vertical plane passing through the wellbore axis. Later it has been shown that considerable pressure drops within a horizontal well may affect the production performance. Thus, the pressure gradients create varied potential fields beneath the wellbore The first water would then break through the well at a point below which the potential is the highest. A numerical study has recently shown this phenomenon and also reported that neglecting pressure drop in the wellbore leads to overestimation of the rate of oil production. Unfortunately, no detailed information as to the fluids flow mechanism along and in the vicinity of the wellbore has been presented. Complex mechanisms of fluids flow in a reservoir system containing a horizontal well and in the wellbore itself are not well understood. Tackling such problems through the use of physical models has been appreciated. Particularly, water cresting phenomena were recently investigated by Aulie et al. P. 431

Development of horizontal well technology offers a new approach to reducing gas/water coning effect during oil production. However, further improvement of the oil production rate of horizontal wells is still limited by the encroachment of the water cone when bottom water exists. This paper provides reservoir engineers with a general solution of the gas/water coning problem for horizontal wells. The objectives of this investigation include: (1) to determine the location of the stable water/gas cone, (2) to estimate the critical oil production rate, and (3) to find out .the optimum placement of the horizontal well bore so that the maximum critical oil rate can be obtained.Using conformal mapping method, the location of the stable water/gas cone is determined as a function of oil rate and wellbore location. The critical oil rate is estimated by examining the profile development of the stable cone. It is found that the critical rate is directly proportional to the effective permeability (-.Jkhk v ), thickness of the oil reservoir, and density contrast between oil and the coning fluid, and inversely proportional to the oil viscosity. The critical oil rate also depends upon the well bore location in the oil reservoir and takes its maximum value when the horizontal wellbore is placed at about 70 % of reservoir thickness from the unwanted fluid.

This paper presents a new approach for the simultaneous estimation of relative permeability and capillary pressure curves from two-phase laboratory corefloods. The new technique enables us to retrieve a discrete representation of the flow functions by using a discrete optimization method called simulated annealing. The number of discrete points for each flow curve can be very high and yet will not affect the convergence of the algorithm specially designed for multidimensional optimization problems. Moreover, the algorithm is totally independent from the forward model; therefore, changes in the objective function, boundary conditions, or numerical scheme do not affect the formulation of the optimization problem. Simulated annealing as a global optimization method does not require the evaluation of objective function gradients. Hence, costly gradient computations by finite differences or lengthy derivations of adjoint equations for the optimal control theory are not necessary. The flow functions are estimated after minimizing a least-squares objective function containing all available and reliable experimental data obtained from standard drainage or imbibition experiments. The automatic history-matching code is demonstrated with actual and synthetic experiments, and good matching is obtained for various cases tested. Since the convergence of the algorithm is no longer the major concern, other physical problems such as end effect and the dependence of relative permeability curves on the flow rate are addressed.References and illustrations at end of paper SPE 24870 AHMED OUENES, GUY FASANINO and ROBEFtT LEE 7

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The correct explanation for the non-Darcy behavior (or effect) on gas flow through porous media has been debated for decades. Non-Darcy behavior (i.e. extra pressure drop) has been more logically ascribed to fluid inertia (caused when gas under high flow rate is forced through tortuous rock) than to turbulence. This high flow rate, non-Darcy concept has been adopted and extended to explain the concave upwards nature of the back-pressure plot. However, two anomalies arise:the laboratory determined values are much lower than the field observations, in other words, the field gas velocity is much less than the gas velocity used in laboratory;there are numerous experimental data showing that the rock permeability is a function of the net-stress (mainly, overburden pressure minus pore pressure) regardless of the gas flow rates. We define this permeability reduction due to net-stress decrease as the net-stress effect. During the gas production, we believe that the non-Darcy behavior should be caused by both the effect and the net-stress effect. By combining these two effects, the scale of the non-Darcy observed in fields is in the range of laboratory experimental values. This paper also shows the applications of using these two effects to analyze the back-pressure test data. Introduction While measuring gas permeability in the laboratory at atmospheric conditions, researchers have found that gas no longer follows Darcy's law in the high gas flow regime. An extra term is added to the Darcy equation to account for this non-Darcy behavior. In this paper, we refer the extra pressure drop due to high velocity as the effect. Most states in the US require a back-pressure test for all gas wells to estimate the deliverability of the wells. The results of back-pressure tests are plotted in the form of p 2 vs. Qsc. Usually, the slope of the back-pressure plot is greater than one. This means that the well exhibits non-Darcy behavior. The logical explanation is the high velocity effect experienced in the laboratory. The effect was originally mistaken as the turbulent effect. Later, it was recognized and accepted as the effect of inertia. It is almost impossible to have turbulent flow in a consolidated rock. Laboratory experimental values of k, the product of permeability and coefficient, are in the range of 104 to 106 darcy/cm. In many gas wells, even at low production and flow velocity, their corresponding back-pressure curves still give slopes greater than one. Rarely does a back-pressure curve give an unit slope. To match the field data, sometimes, the value must be increased 100 times or more. Compared to laboratory estimates, the factor may increase in high pressure environments such as in gas fields. Only one study (Warpinski et al.) shows the measurement of the factor under high pressures. The interpreted data indicates that the k values are still in the same range of the data observed under atmospheric conditions. Actually, their data shows the factor increases when the net-stress increases, however, their k values were relatively insensitive to the net-stress. It is well known that the gas permeability may reduce during drawdown. This is particularly true for naturally fractured reservoirs. The reduction of pore pressure increases net-stress. If no new fractures are induced during this stress alternation process, the increase of the net-stress may restrict the flow path, therefore, reduces the gas effective permeability. This gas permeability reduction is referred to as the net-stress effect in this paper. This net-stress effect has not been incorporated in many petroleum engineering practices including in analyzing the back-pressure data. Back-Pressure Test In many states of the US, the back-pressure test is required for a gas well and is documented by the regulatory agency. P. 191^

E ABSTRACTA method is presented by which permeability, skin, and turbulence can be analyzed by interpretation of an open flow potential test. The method is based on a variation in the method suggested by Odeh and Jones, and allows a direct calculation of the turbulence factor from well test data. The method also utilizes the continuous record of bottom hole pressure now recorded for many well tests.To facilitate interpretation of high permeability data, an optimization scheme is used to arrive at values of permeability, skin, and turbulence factor. Data from an open flow potential test and subsequent build-up are presented; analysis results in a favorable comparison. The optimized permeability, skin, and turbulence values also predicted, with reasonable accuracy, the measured well performance.