The Dispersive Effect of Variable Layer Lengths on Miscible Displacements in Layered Heterogeneous Porous Media

SPE Members Abstract The process of injecting gas into a gas condensate reservoir during production is vital to maintain the reservoir pressure so that the heavy hydrocarbon fractions will be recovered. One would like to inject a gas into the reservoir that is cheaper than methane, but recent one-dimensional studies have shown that the injection of nitrogen into gas condensate at reservoir conditions will result in the loss of much of the condensate liquid. This is a result from the liquid dropping out of the gas phase when nitrogen mixes with the condensate. A solution to this situation is the initial injection of a slug of methane (or dry gas) followed by the injection of nitrogen for pressure maintenance. If the methane slug is large enough it will separate the nitrogen from the condensate and the liquid recovery will be high. The physical processes that tend to destroy the integrity of the methane slug are mixing due to rock heterogeneity, fluid fingering, and bypassing. This paper studies the two step injection process numerically with a three-dimensional EOS compositional simulator. The gases are injected into a heterogeneous quarter five spot. The recovery of liquid condensate is studied as a function of the composition of the injection gas, the methane slug size, and the magnitude of the permeability variations (heterogeneities) of the porous media. A fine grid involving 8,000 blocks is used to allow the proper description of the heterogeneities and to keep numerical dispersion, which simulates sub-grid block dispersion, at a reasonable level. Monte Carlo simulations are performed on realizations of reservoirs. The results show that the heterogeneities allow the nitrogen to mix with the condensate when the methane slug is small (5% to 10% of a porevolume) but the incremental recovery over the porevolume) but the incremental recovery over the injection of nitrogen is large enough to pay for the cost of the methane. Economics are given to allow one to size a methane slug for a real heterogeneous reservoir so as to maximize the profit of the project. project. Introduction The recovery of liquid hydrocarbons from a gas condensate reservoir is dependent upon maintaining as much of the reservoir as possible as a single phase gas. To accomplish this a fluid must be injected into the reservoir as condensate is produced to replace the reservoir volume, maintaining the reservoir pressure above the dew point pressure, and to displace the condensate towards the producing wells. The obvious choice of injecting dry separator gas (basically methane) plus some make-up gas (usually also methane) has both positive and negative aspects. On the positive side, combining methane with most gas condensates has only a small effect on the mixture's dew point. Thus, no liquid falls out. On the negative side, the injected methane is very expensive since it is not available for sales. A alternate choice is the injection of an inexpensive, inert gas, such as nitrogen. Previous experimental displacements with nitrogen Previous experimental displacements with nitrogen and a gas condensate in a slim tube have shown that liquid recoveries are as high as in displacements with methane, that is, of the order of 98%. However, in a numerical study, Kossack et al have shown that at field scale Peclet Numbers the increased mixing between the nitrogen and the condensate would cause a loss of 30 to 40% of the liquid as compared to a displacement with methane. Their simulations were one-dimensional, and thus, did not include areal sweep, gravity segregation, or viscous fingering. Their results did show that injecting a mixture of nitrogen and methane would increase the recovery over that of pure nitrogen. P. 19

Recovery of Condensate From a Heterogeneous Reservoir by the Injection of a Slug of Methane Followed by Nitrogen

Kossack

Opdal

1988

Nitrogen Injection Into Stratified Gas-Condensate Reservoirs

Sänger

Bjørnstad

Hagoort

1994

Nitrogen injection is an attractive recovery process for gas condensate reservoirs. It maintains the reservoir pressure and thus prevents condensate drop-out as a result of pressure depletion. A disadvantage is that liquid drop-out occurs in the mixing zone between the injected nitrogen and the gas condensate. This occurs not only at the displacement front, but, due to bypassing, also at the boundary between layers of different permeability. This paper presents the results of a detailed, high resolution simulation study of nitrogen flooding of a stratified reservoir. The reservoir simulator used is a fully compositional simulator, based on the Peng Robinson EOS. The gas condensate is a 3 component hydrocarbon system that is representative of a North Sea reservoir. The main result of the study is that in stratified systems severe drop-out (up to 50 percent) may occur at the layer boundaries, in particular just downstream of the trailing displacement front. The latter can be explained by crossflow caused by an unfavourable mobility ratio. It is shown how this mechanism is affected by permeability contrasts, dispersion, aspect ratio and gravity. Introduction Retrograde condensation occurs in gas condensate reservoirs when the pressure falls below the dewpoint pressure. This leads to low recoveries as the liquid dropout is capillary trapped or left behind due to the low relative permeability. Retrograde condensation can be prevented by maintaining the reservoir pressure above the dewpoint pressure by injection of gas. The physical properties of dry hydrocarbon gases make it very suitable for injection gas. Hydrocarbon gas, however, is not always available for (re)injection. Injection of nitrogen gas is an attractive alternative. Nitrogen is cheap, safe, non-corrosive, non-polluting and available everywhere. The disadvantage of nitrogen is that liquid drop-out occurs in the mixing zone between the injected nitrogen and the gas condensate. In a homogeneous reservoir this occurs only at the displacement front. In a stratified reservoir however, additional mixing, and hence drop-out, occurs at the boundary between layers of different permeability. The objectives of this study are to identify the drop-out mechanisms and to quantify the recovery losses due to condensate drop-out. To achieve this objective we have used a fully compositional reservoir simulator. As a prototype reservoir we have used a vertical cross-section of a two-layer reservoir. As a gas-condensate fluid we have taken a simple three component hydrocarbon system. with a phase behaviour similar to gas-condensates encountered in North Sea reservoirs [1]. The simulations have been carried out at 360 bar and 100°C, representative conditions for North Sea reservoirs. In order to study the explicit effect of stratification we have used a two-dimensional reservoir model that consists of two parallel layers of equal thickness. We have investigated the sensitivity towards permeability contrast, aspect ratio and dispersivity, and the effect of gravity.

Modeling Conformance as Dispersion

Coats

Whitson²,

Thomas

2004

Summary For decades the effect of physical dispersion (in-situ mixing) in porous media has been of interest in reservoir engineering and groundwater hydrology. Dispersion can affect the development of multi-contact miscibility and bank breakdown in enriched gas drives and miscible solvent floods of any mobility ratio. The magnitude or extent of dispersion is quantified by the rock property physical dispersivity (a) which is the order of 0.01 ft for consolidated rocks and several times smaller for sand-packs, from many laboratory measurements. Numerical studies of the effect of dispersion on enriched gas drives and field tracer tests often use input values of dispersivity 100 to 1000 or more times larger than ~0.01 ft. These large input dispersivity values stem from large apparent dispersivities (aa) determined by matching the one-dimensional convection-diffusion (1D CD) equation to production well effluent tracer concentration profiles observed in field tracer tests. The large apparent dispersivities reflect conformance or other behavior not governed by the 1D CD equation and should not be used to justify large physical dispersivity as input to numerical studies. This paper shows that large apparent dispersivities observed in field tests can result with physical dispersivity no larger ~0.01 ft lab-measured value. Heterogeneity alone (no physical dispersivity or molecular diffusion) causes no in-situ mixing and cannot explain observed large apparent echo dispersivities. Large apparent echo dispersivities for two reported field tracer tests are shown to result from the effect of drift alone with no dispersion. The widely reported scale-dependence of apparent dispersivity is a simple and necessary consequence of mis-applying the 1D CD equation, with its single parameter of Peclet number L/a, to conformance it does not describe. Apparent dispersivity is scale-dependent but physical dispersivity is a rock property independent of scale and time. Introduction This paper differentiates between the rock property physical dispersivity (a), associated with dispersion (in-situ mixing), and apparent dispersivity (aa) associated with conformance. Apparent dispersivities aa are determined by a best-fit match of the 1D CD equation to effluent concentration profiles C vs pore volumes injected QD from field tracer tests or numerical simulations. For the assumptions used in this paper, conformance reflects the combined effects of heterogeneity, well areal pattern and completion intervals, and drift (regional flow gradient). The aa values derived from field tracer test data appear to be strongly scale-dependent1,2, with log-log plots of aa vs scale L showing a slope of roughly1. Field-scale aa values are orders of magnitude larger than lab-measured dispersivities3 a~0.01 ft which have no scale dependence. Our concern, and the reason for this paper, is the use of large apparent dispersivity values as input physical dispersivity in numerical studies2,4–8 designed to quantify the impact of dispersion on reservoir processesa. The above-referenced studies use input dispersivity values as large as 8000 times larger than a physical dispersivity ~0.01 ft. Nearly 40 years ago, Mercado9 showed that large apparent dispersivities from transmission (two-well) field tracer tests reflected conformance (heterogeneity), not dispersion. We argue that dispersivity ~0.01 ft should be input in studies designed to quantify the impact of physical dispersion on reservoir processes. We show in this paper that apparent dispersivities are approximately the sum of physical dispersivity (a) and apparent dispersivity due only to conformance (aac), aa˜a+ aac. For all cases of practical interest, aac>>a, making aa˜ aac an excellent approximation. We also show that aac˜ aap+ aas, where aap is the apparent dispersivity due to pattern (areal) sweep alone, and aas is the apparent dispersivity due to stratification (vertical) sweep alone.