Gas-Condensate Flow in Perforated Regions

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 89-99 ◽  
Author(s):  
Mahmoud Jamiolahmady ◽  
Ali Danesh ◽  
Mehran Sohrabi ◽  
Rahim Ataei
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Element Modeling ◽  
Relative Permeability ◽  
Single Phase ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Fractional Flow ◽  
Fluid Properties ◽  
Perforated Completions

Summary The most crucial region with regard to affecting well productivity is the perforated region. Considerable effort has been directed to study this subject mathematically by many investigators, but they have been mainly focused on single-phase flow, while two-phase flow has received less attention. It has been demonstrated, first by Danesh et al. (1994) and subsequently by other researchers (Henderson et al. 1995; Blom et al. 1997; Ali et al. 1997), that the gas and condensate relative permeability (kr) can increase significantly by increasing the flow rate, contrary to the common understanding. This effect, known as positive coupling, complicates the flow of gas and condensate near the wellbore even further when it competes with the inertial forces at higher velocities typical of those around perforation tips. The flow of gas and condensate in the perforated region was studied in this work using a finite-element modeling approach. The model allows for changes in fluid properties and accounts for the positive coupling and negative inertial effects using a fractional-flow-based relative-permeability correlation. A sensitivity analysis on the impact of perforation characteristics such as density, phasing, length, and radius as well as that of fluid properties, rock characteristics, wellbore radius, fractional flow, and rate on well productivity was conducted, resulting in some valuable practical guidelines for optimum perforation design. Introduction The effect of perforation characteristics on the well flow efficiency has been studied by many investigators. Muskat presented the first analytical treatment of the problem (1943). In his analysis, perforations were represented by mathematical sinks distributed spirally around the wellbore but did not extend into the formation. Other early investigators used the finite-difference modeling technique to examine the productivity aspects of perforated completions (Harris 1966; Hong 1975). However, because of the limitations of the finite-difference method, these studies considered mostly unrealistic perforation geometries to avoid mathematical complexities. Later investigators applied the finite-element method, which models the geometry of the perforation with greater precision (Locke 1981; Tariq 1987). Tariq (1987) presented results of finite-element modeling of single-phase steady-state flow in perforated completions with and without the non-Darcy (inertial) effect for a linear core and a full 3D system. Although his results for single-phase flow are widely used, there are reports on lack of required accuracy at large perforation lengths and in the non-Darcy cases (Behie and Settari 1993; Jamiolahmady et al. 2006a).

Multiphase Dispersion and Relative Permeability Experiments

1985 ◽  
Vol 25 (04) ◽  
pp. 524-534 ◽  
Author(s):  
M. Delshad ◽  
D.J. MacAllister ◽  
G.A. Pope ◽  
B.A. Rouse
Keyword(s):  
Relative Permeability ◽  
Single Phase ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Relative Permeabilities ◽  
High Concentration ◽  
High Tension ◽  
Three Phase ◽  
Phase Saturation ◽  
Low Tension

Summary Experiments in both Berea sandstone and sandpacks have been conducted to measure dispersion and steady-state relative permeabilities. Measurements have been made on both high-tension brine/oil and a low-tension, three-phase, brine/oil/surfactant/alcohol mixture. One interesting aspect of these experiments is the amount of microemulsion phase trapping. The endpoint microemulsion saturations for both the oil/microemulsion and brine/microemulsion phase pairs were high even at 10–3 dyne/cm [10–3 mN/m] interfacial tension (IFT). The dispersion was measured for each phase with radioactive and chemical tracers. The dispersivity was found to be a strong function of phase, phase saturation, porous medium, and IFT. Values of the dispersivity varied by two orders of magnitude over conditions investigated to data. Extremely early breakthrough of the tracer used in the oil phase (carbon 14) at high tension is especially remarkable. The brine tracer (tritium) curves were similar to that for 100% brine saturation except for a shift caused by material balance reasons. The classical solution to the convection-diffusion equation for single-phase flow has been generalized to multiphase flow and was used to aid in interpreting these data. This combination of relative permeability and dispersion in each phase of the experiment with a high-concentration, three-phase-microemulsion sulfonate formulation is believed to be new, and more directly applicable to commercial surfactant flooding than previously reported experimental results. Introduction In this paper we report the initial results of a project1 to investigate the transport in porous media of several chemicals used in EOR. Specifically, we are studying the behavior of high-concentration, three-phase micellar formulations in beadpacks, sandpacks, and sandstone. The rheology, relative permeabilities, and dispersion coefficients have been the primary focus of this study to date. In this paper, we report on the last two parameters for a single polymer-free micellar formulation. These results are based on the theses of Delshad2 and MacAllister.3 The rheology of this and other EOR fluids is reported in Ref. 4. Oil recovery and history matching was done by Lin.5 A unique feature of this work was the way in which the relative permeabilities and dispersion experiments were combined into essentially the same experiment (see the section on procedures and materials). Since trapping has a profound effect on the efficiency of micellar/polymer flooding, another important feature is the measurement of microemulsion phase trapping at each relative permeability endpoint. These are believed to be the first direct measurement of this type. Literature Review No attempt will be made here to review the numerous high-tension relative permeability studies reported during the past several decades. Also, only a few of the classical single-phase flow dispersion studies will be mentioned. Low-tension data are much less extensive. Leverett,6 Mungan,7 du Prey,8 Talash,9 Bardon,10 Batycky,11 Klaus,12 and Amaefule and Handy13 are among the few who have reported results as a function of IFT. All of these results were for two-phase fluids. Furthermore, apparently only Talash, Klaus, and Amaefule and Handy used fluids containing sulfonates such as we are primarily concerned with, and then only at very low sulfonate concentrations. The general observations are that the relative permeability curves tend to increase and have less curvature as the IFT decreases or the capillary number increases. The residual saturations decrease simultaneously. Consistent with the capillary desaturation curves and theory reported by others,14–16 the nonwetting-phase saturation decreases first, then the residual wetting phase. It has been speculated for a long time that these curves will eventually become straight lines, but few if any of these experiments attained the ultralow IFT typical of optimal micellar fluids that would be necessary to test this idea.

Analysis of Pressure Transients in Two-Phase Radial Flow

1963 ◽  
Vol 3 (02) ◽  
pp. 116-126 ◽  
Author(s):  
J.C. Martin ◽  
D.M. James
Keyword(s):  
Finite Difference ◽  
Compressible Flow ◽  
Single Phase ◽  
Numerical Solutions ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Short Term ◽  
Two Phase ◽  
Finite Difference Techniques

Abstract The results are presented of a study of the application of analytical methods to the solution of two phase flow into single wells. Approximate analytical expressions for the pressure distribution in two-phase flow are found for a number of conditions. The results obtained from the analytical solutions are found to be in good agreement with results obtained by finite difference techniques using a high speed digital computer. Mathematical solutions for four sets of boundary conditions are presented. All of these solutions are composed of a short-term transient plus a steady or quasi-steady state. The rates of decay of the short-lived transients are analyzed. It is found that the durations of the short-term transients may be characterized by a parameter defined as the time constant which can be determined from simple relations. It is shown also that if the outer radius is much greater than the radius of the well, the short term transients decay at rates which are proportional to the square of the exterior radius, and the rates of decay are only slightly dependent upon the radius ratio. Numerical solutions based on finite difference techniques are presented for a number of conditions. The numerical solutions are in good agreement with the predictions based on the theoretical analysis for small and moderate drawdowns. Examples involving large drawdowns indicate that the nonlinearities in the equations of flow do not appreciably alter the longevity of the short-term transients. In all cases the time required for the short-term transients to disappear is predicted satisfactorily. Introduction The mechanism by which oil and gas flow into a single well is of vital interest to the petroleum industry. The fundamental equations of two-phase flow which describe this mechanism are nonlinear partial differential equations. Numerical solutions of these equations describing pressure transients have been obtained with the aid of electronic computers. Although solutions obtained in this manner take into account a large number of effects, the reduction of this information to useful generalities is difficult. One method of obtaining generalities is the use of linearized approximations of the nonlinear equations. Since it is possible to obtain explicit solutions of the linearized equation, general properties of the role of pressure in the flow mechanism may be ascertained. Results obtained from this approach are limited to some extent by the linearizing assumptions. The severity of these limitations may be evaluated by comparing solutions of the linear equation with numerical solutions of the more exact nonlinear equations of two-phase flow. In the past considerable amount of work has been devoted to studying pressure build-up using the single-phase flow theory. Unfortunately, most pressure build-up tests involve multiphase flow. A small amount of work has been done studying pressure build-up where the flow is two-phase. The encouraging results of these studies suggest that useful results may be found from additional studies of not only pressure build-up, but also the rapid transients associated with placing a well on production. This paper presents the basic theory of the pressure transients associated with placing a well on production and with closing it in. The paper is concerned chiefly with two-phase compressible flow; however, the results also apply to single-phase flow, The results are based on analytical solutions of the flow equations, and they are verified by numerical solutions using finite difference techniques. Much of the previous work on compressible flow into wells has been confined to single-phase flow. Some work has been done on compressible two-phase steady state flow, and solutions of the equations of flow have been found by finite difference techniques using high-speed computers. Muskat presents some rather general solutions to the equations of single-phase compressible flow into wells. Much work has been done on pressure build-up in wells (see, for example, Refs. 2–6). Almost all of the work on pressure build-up concerns single-phase flow with the exception of Ref. 5 and part of Ref. 2. Some work has been done on pressure fall-off in injection wells. Muskat presents the solution of the equations for radial steady state two-phase compressible flow. SPEJ P. 116^

Critical review on wax deposition in single-phase flow

Fuel ◽  
2021 ◽  
Vol 293 ◽  
pp. 120358
Author(s):  
Charlie van der Geest ◽  
Aline Melchuna ◽  
Letícia Bizarre ◽  
Antonio C. Bannwart ◽  
Vanessa C.B. Guersoni
Keyword(s):  
Critical Review ◽  
Single Phase ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Wax Deposition
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