Interpretation of Pressure-Buildup Responses in Gas-Condensate Wells

Abstract

Summary Methods to analyze buildup responses in gas-condensate reservoirs producing below the dewpoint pressure are examined. Two analogs to compute formation flow capacity and average reservoir pressure are presented. These analogs are based on the steady-state theory (developed by O'Dell and Miller and later modified by Fussell) and the single-phase-flow theory (which ignores the existence of the two phases). The mechanical skin factor can be computed from the derivative response by computing the appropriate dimensionless pseudopressure. Introduction We examine pressure-buildup data in a gas-condensate reservoir where the producing pressure is below the dewpoint pressure. In a recent study, we considered the flowing well response in a gas-condensate reservoir and presented a theoretical foundation for the analysis of well test data. Ref. 1 introduced the concepts of the reservoir and sandface integrals and demonstrated the utility of these integrals in the analysis of well test data subject to multiphase flow. In this work, we show that the buildup correlating function based on the reservoir integral is the proper analog for the analysis of buildup data. As shown by Raghavan, the fundamental problem in the analysis of pressure-buildup data for solution-gasdrive reservoirs involves the determination of the saturation profile at the instant the well is shut in. In the present case, the mole fraction distributions of the vapor and liquid phases are also needed. For solution-gasdrive systems, Raghavan has shown that in many cases the producing GOR at the instant of shut-in may be used to obtain the saturation distribution. Unfortunately, because of the distinct differences between the two systems, this method cannot be used to couple pressure, saturation, and molar distributions. Fortunately, as shown in Ref. 1, it is possible to obtain the saturation and the molar distribution in the reservoir with the steady-state theory for two cases of interest:boundary-dominated flow when the pressure at the outer boundary is held at a pressure greater than the dewpoint pressure, andconstant-pressure production in an infinite-acting reservoir. For these two cases, we show that it is possible to obtain accurate estimates of formation flow capacity, kh, average reservoir pressure, p, and the mechanical skin factor, s. The steady-state theory may also be used to analyze pressure data in circumstances where a significant portion of the reservoir is above the dewpoint pressure at the instant of shut-in; i.e., a significant portion of the reservoir consists of only a single-phase gas region. For these conditions, accurate estimates of kh and p can be determined by use of this theory. Because of the unique characteristics of gas-condensate systems, the single-phase-flow theory may also be used to obtain accurate estimates of kh and p. Estimates of s, however, will be much higher than the mechanical skin factor because the existence of two phases is ignored when this analog is used to analyze pressure-buildup data. It will be difficult to determine the need for or the efficacy of stimulation programs with this analog if the producing pressure falls below the dewpoint pressure. At best, the estimate of this skin factor is an upper bound for the mechanical skin factor. The utility of the steady-state theory is limited in that relative permeability data are needed. If relative permeability data are unavailable, the single-phase-flow analog is the only recourse to obtain formation permeability, average pressure, and skin factor. Thus, the information we present on the applicability of the single-phase-flow analog is particularly useful. Jones and Raghavan have shown (see Eq. 27 of Ref. 1) that it is possible to compute the product of formation permeability and total sandface mobility from drawdown data. In this paper, we extend their observations to the analysis of buildup data. We show that it is possible to predict the formation-permeability/total-mobility product distribution in the reservoir at the instant the well is shut in from the shut-in pressure derivative response. This information can be used to compute the dimensionless pseudopressure change during the buildup period. An accurate estimate of mechanical skin factor can then be computed. Mathematical Model and Assumptions The one-dimensional model considered in this work is identical to that considered in Ref. 1 and thus will not be discussed here. Briefly, the model is similar to that presented by Coats and uses the Redlich-Kwong equation of state as modified by Zudkevitch and Joffe. Extensive details and procedures used to verify the accuracy of the solutions are discussed in Ref. 8 (see also Ref. 1). Three sets of relative permeability data were used in this study (Fig. 1). As in Ref. 1, we assume that the gas is a methane/ n-butane/decane system. We consider two mixtures (Fig. 2), and the initial compositions of the two mixtures are given in Table 1. We examine pressure-buildup data following constant (molar) -rate or constant-pressure production and consider both infinite-acting and boundary-dominated flow (closed or constant pressure equal to the initial pressure). In all investigations, except for the existence of a skin region, the reservoir is assumed to be a horizontal, homogeneous, porous medium of uniform thickness. Gravitational effects are assumed to be negligible; in essence, buoyancy effects resulting from density differences are not considered and the effect of variations in the hydrostatic head on pressure at various elevations is neglected. The well penetrates the formation fully, and the skin region is modeled along the lines suggested by Hawkins. Definitions All results in this study will be presented in dimensionless form for purposes of generality. The dimensionless pressure, PD(rD, tD), dimensionless time, tD, and dimensionless distance, rD, are defined by the following equations: ,...................(1) ...........................(2) and ...........................................(3) The dimensionless pressure change during the buildup period, p sD, is given by ,...................(4) and dimensionless shut-in time, delta tD, is given by ....................(5) Eqs. 1 through 5 assume that we are considering the flow of a slightly compressible liquid. When we consider the flow of the condensates, we follow the method of Al-Hussainy et al. and define dimensionless time on the basis of the viscosity/compressibility product at the initial pressure, pi. The definition of dimensionless shut-in time is modified appropriately, and the modifications will be discussed as needed. We now consider the definitions of pseudopressures. The dimensionless wellbore pseudopressure is given by ,................... (6)

Modelling the Interfering Effects of Gas Condensate and Geological Heterogeneities on Transient Pressure Response

“…Jons and Raghavan (1986) The value of incorporating relative-permeability effects in the pseudo-pressure function is that skin due to condensate banking is already being included within the two-phase pseudo-pressure integral (Osorio et. al 2005) The authors suggested to evaluate the pseudo-pressure function based on a 2-region fluid model proposed by O'Dell andMiller (1966) andFussel (1973).…”

Well Test Analysis of Multiple Hydraulically Fractured Horizontal Wells MHFHW in Gas Condensate Reservoirs

“…Well-test analysis is able to quantify the mobility decrease due to condensate blockage (Jones, et al, 1986), or the increase due to capillary number effects (Gringarten, et al, 2000). After the condensate bank has been formed, the radial composite model is suggested to represent zones of different fluids (Van Pollen, 1984) by considering different mobility regions as two or more circular zones surrounding the well.…”

Relative Permeability Estimation for Rich Gas-Condensate Reservoirs

“…The single-phase gas pseudo-pressure method does not require relative permeability information (Thompson et al, 1993;Marhaendrajana et al, 1999). Multi-phase pseudo-pressure analysis (two phase analogy) accounts for the mobility of both the condensate and gas phases (Jones et al, 1989;Ragahavan et al, 1995;Xu and Lee, 1999). This technique has been shown to provide improved estimates for mechanical skin.…”