The depletion of gas condensate reservoirs to pressures below the dew point has been studied by reservoir engineers for many years. Pressure decline below the dew point pressure causes condensation to occur which creates a hydrocarbon liquid saturation in the reservoir. This process reduces liquid recovery and may reduce gas productivity and gas recovery. Exxon experience, particularly in low-productivity, high-yield gas condensate fields, suggests that liquid condensate formation can result in severe loss of well deliverability and therefore of gas recovery. This study was undertaken to evaluate the historical frequency and severity of productivity impairment due to near-wellbore condensate buildup and to identify reservoir parameters associated with severe productivity and recovery reduction. This study of gas condensate reservoirs included a survey of Exxon and published industry experience, a review of published laboratory data, and simulations with single well flow models. Data from 17 fields are included in this paper to demonstrate that severe loss of gas recovery occurs primarily in low productivity reservoirs. Production data from two wells were history matched with simple radial models to evaluate the potential range of the critical condensate saturation (the minimum mobile condensate saturation) and its impact on gas recovery. Published laboratory data for gas-condensate relative permeability were used as a starting point for these simulations. The primary conclusion from this study is that productivity impairment results in reductions in gas recovery for wells with a permeability-thickness below 1000 md-ft. The history matched simulations support a range of critical condensate saturations from 10% to 30%, in good agreement with published laboratory values. Introduction The depletion of rich, gas condensate reservoirs to pressures significantly below the dew point is a topic of increasing interest as deeper, hotter hydrocarbon reservoirs are exploited. The cost and risk to develop reservoirs under these extreme conditions highlights the need to be able to confidently predict the recovery of gas and liquids from these reservoirs. In particular, there is a need to better understand the factors controlling the decline of well productivity due to hydrocarbon liquid saturation developing in the near-wellbore region of the reservoir as the flowing pressure declines below the dew point pressure. Reservoir engineers have been concerned about the impact of condensate blocking on productivity for many years. Several examples of severe productivity decline are available in the literature. At Exxon, several fields have been identified in which productivity loss below the dew point has significantly reduced gas recovery by pressure depletion. One example of poor performance is shown in figure 1. This is a moderately rich gas condensate field with an initial condensate-gas ratio of 73 bbl/Mscf. The well produced at initial rates over 1 Mscfd. When the flowing bottom-hole pressure reached the dew point, gas production declined rapidly and the well died. Pressure surveys indicated that the well was full of liquid hydrocarbons. Attempts to swab the well were unsuccessful, even though data from surrounding wells indicated the average reservoir pressure was still over 2000 psi above the dew point pressure. The well appears to have 'locked up' and ceased production shortly alter the flowing bottom-hole pressure passed below the dew point pressure. Eventually the well was successfully fracture stimulated, returning the well to initial production rates. P. 677

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgement of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Sequential solution of the reservoir flow equations has been made to yield the stability of calculations previously associated only with the simultaneous solution previously associated only with the simultaneous solution of the equations. Sequential solution is computationally more efficient than simultaneous solution, and it permits the use of simulation algorithms that are more dependable when applied to irregular-shaped, highly heterogeneous reservoirs. Such reservoirs are often troublesome to simulate. Coning, gas percolation, and other high-flow velocity problems have been made tractable through the use of semi-implicit saturation functions. Introduction Sequential solution of the flow equations in a reservoir simulator has been made to yield the calculational stability previously associated only with simultaneous solution of the equations. This new approach forms the basis of a general-purpose reservoir simulator, GPSIM. Sequential solution is computationally more efficient than simultaneous solution, and it permits the use of algorithms that are more dependable when predicting the performance of irregular-shaped, highly heterogeneous performance of irregular-shaped, highly heterogeneous reservoirs. Such reservoirs, which are frequently encountered in practice, are often quite troublesome to simulate. Well coning problems and fieldwide, multiwell gas percolation problems have been made tractable through the optional use of semi-implicit saturation functions including capillary pressures and portions of the Buckley-Leverett fractional flow terms. The semi-implicit approach used in GPSIM is closely related to the semi-implicit relative permeability approach previously described in the literature. Sequential solution conveniently separates the solution of the pressure equation, which is often predominantly elliptic in nature, from that of the saturation equations, which range between parabolic and hyperbolic in character. This permits approximation of the saturation equations by alternating-direction difference equations, which can be solved by direct elimination, thus avoiding an iterative solution. Optional use of the backwards-in-time difference formulation solved by strongly implicit iteration (SIP) or direct solutions methods is provided in GPSIM for use on especially difficult problems such as coning studies.

The engineering evaluation of thermal recovery processes depends on the ability to predict their behaviour in the field. Such a prediction, whetherbased on physical or mathematical models, requires an accurate accounting of the thermal energy utilized by the process. This paper presents a criticalreview of the important contributions to the literature concerning heattransfer during hot fluid injection into an oil reservoir. The heat transfer mechanisms, the resulting energy balance equation and the restrictive assumptions necessary to obtain analytical solutions of the energy balanceequation are discussed. These solutions yield information relative to the thermal efficiency of the process and the temperature distributions within the reservoir and the surrounding impermeable media. However, to date, the published techniques have been limited to injection into a linear or radial homogeneous sand with constant physical properties and have not considered multidimensional heat transfer completely. We have applied a recently published numerical technique to the solution of the energy balance equation in order to remove these limitations. The accuracy of the numerical method for the case of one-dimensional fluid flow is demonstrated in the paper by comparing the calculated thermal efficiency for hot water injection into a water sand to the corresponding analytical solution. A comparison with published experimenta lresults demonstrates the utility of the method and confirms our understanding and analysis of the heat transfer mechanisms. Introduction Predictions of the field behaviour of thermal recovery processes require anaccurate accounting of the energy that is injected into (or generated within)the reservoir. Numerous heat transfer models of the basic thermal processeshave been formulated and solved analytically (c.f. ref. 6, 7, 8, 14, 16, 19).Although limited in scope because of necessary restrictive assumptions, these solutions have proved useful in the development of interpretative mathematical models of the processes (12, 20, 21). For heat transfer during the forward underground combustion process, numerical (3, 4) as well as analytical solutions have been obtained. The following sections discuss the heat transfer mechanisms that take placeduring the injection of hot fluid into an oil reservoir, the energy balance equation and the assumptions necessary to obtain analytical solutions of the energy balance equation. All of the analytical solutions that have appeared inthe literature are limited to a consideration of one-dimensional incompressible fluid flow in a homogeneous sand with constant physical properties. This paper presents a numerical solution of the energy balance that is not hampered bysuch assumptions, and compares it with published experimental results.

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterflooding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil as continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two- dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few. Even if extensive data were available two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements, laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments - injectivity/productivity tests and pilot floods - results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey and Spillette recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery. Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot- water injection are thatno gas phase is present andthe injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. JPT P. 627ˆ