Three mechanisms of migration are possible candidates for microseepage or vertical migration; diffusion, transport by water, and buoyant transport. Diffusion represents a minimal loss rate from a reservoir. Rates are slow and occur in all directions in response to a concentration gradient. Diffusion, operating in all directions, results in significant dispersion of the migrating hydrocarbons. Many surface geochemical surveys have demonstrated anomalies closely related to the vertical projection of the reservoir to the surface. Repeated geochemical surveys also show a decline in the intensity of the anomaly with production. These two critical observations are inconsistent with diffusion as a mechanism for vertical migration. Diffusion is a viable mechanism for primary migration.

Water transport of hydrocarbons could be as dissolved constituents, or as a separate gaseous or liquid phase. In this mechanism, the transport is related to the hydrodynamics of a basin and hydrocarbon migration follows the water phase to a suitable reservoir. Lateral offset of anomalies would be the general rule. This mechanism is also inconsistent with the vertical projection of the reservoir and the rapid change in the anomaly with production. Water transport is frequently considered a major factor in the secondary migration process.

Buoyancy of gases is the third proposed mechanism, and the mechanism favored by nearly all practitioners and researchers in surface geochemistry. Buoyancy-driven migration is due to density differences between the gaseous and liquid hydrocarbon phases. Buoyancy driven migration also applies to the density differences between the gaseous hydrocarbon and aqueous phases. Buoyancy tends to drive small bubbles of the gaseous phase in the vertical direction. The light hydrocarbon molecules are of a size that they can pass through the pores of a caprock, though obviously impeded, relative to more permeable formations in the sedimentary column.

Modeling of Vertical Migration by the Buoyancy Process
Figure 1 is from Osborne and Swarbrick, 1997, AAPG Bull., v. 81, pp. 1023-1041, which illustrates the buoyant transport process. The initial pressure at the top of a saturated sediment column is atmospheric pressure, Pa- The potential pressure of the gas being gradually transferred to the top of the column as the bubble rises is shown in the middle figure. When the bubble reaches the top, as shown in the right figure, the total pressure is atmospheric plus the product of fluid density times the height of the sedimentary column times the gravitational constant. The potential pressure is the pressure that would be reached if there were an absolutely leak-proof cap at the top of the system. In a real system, the migrating bubble is transferred into the unsaturated zone and then diffuses vertically and laterally, with potentially significant transport to the atmosphere, if there were no microbial degradation processes operating.

The buoyant transport or vertical migration process has been modeled using a finite-difference computer program. It allows for the accurate numerical solution of the complex partial differential equations describing gaseous transport. This has been coupled to a diffusion model for transport through the unsaturated zone. A diffusion model is appropriate for the unsaturated zone since the pore space is filled with soil air, and buoyant transport due to density differences between aqueous and gaseous phases no longer applies. Since the unsaturated zone may be only 1-10% of the vertical distance from the reservoir to the surface, dispersion usually does not cause a problem, with only minor blurring of the anomaly.

Results of the modeling of microseepage from a moderately dry gas reservoir, at 9000 feet depth, and at hydrostatic pressure will be presented. Five different formations exist above the reservoir in the saturated zone, starting with a caprock 1000 feet thick above the reservoir, porosity of 5%, and permeability of 0.0001 md. The other four formations range in thickness from 200-3000 feet, porosity of 0.10-0.20, and permeability of 0.1-5.0 md. The water table is at a depth of 200 feet below the surface.

Results of Modeling of the Vertical Migration Process in the Saturated Zone
Figure 2 shows the normalized gas saturation of the pore space from the level of the reservoir to the top of the water saturated zone at a depth of 200 feet. The normalized gas saturation represents the theoretical, or ultimate degree of gas saturation of the pore space, if an absolutely tight cap existed at the top of the water table. This ultimate degree of gas saturation is not achieved as gas will be transferred into the unsaturated zone. The reservoir is in a steady state condition with no pressure changes due to natural causes, or due to production. Note the small discontinuities that occur at 2000 feet, 5000 feet, and 400 feet, which are the result of discontinuities in gas transport caused by change in formation properties such as porosity and permeability.

The first column of Table 1 contains the normalized gas potential for methane through n-pentane for the run used in Figure 2 where the system is at steady state. The second column lists the normalized gas potential for a run where the reservoir pressure was decreased by 1.0 psi/day for 500 days. There is a decline in potential pressure for each component. The third column is the ratio of potential pressures for the two runs. The relative change in potential pressures appears the same for all components. A run with a dP/dt of -0.1 psi/day for 5000 days will reveal a more dramatic decline in the ratio and a greater decline for the more mobile constituents. Time is an important factor in migration even though the total reservoir pressure decline is 500 psi in both cases.

The ratios of potential pressures in the two runs of Table 1 are quite close to 1.0000 suggesting the near-surface response to manipulation of reservoir pressure is small after only 500 days of the perturbation. However, the theoretical model does not take into account enhanced migration rates due to microfractures, but assumes there is no fracture-enhanced migration. Observed rates of change near the surface in surface geochemical surveys are faster than predicted by this model and obviously will vary with the degree of microfracturing in individual formations, and is also sensitive to the depth of the reservoir.

Results of Modeling of the Vertical Migration Process in the Unsaturated Zone
There are complications in modeling the transition between the saturated zone and the unsaturated zone. Oceanographers have used the "two-resistance theory of interphase mass transfer" as a model for the exchange of gases between the ocean and the atmosphere. Extension of this model to the water table has uncertainties related to the impediment of gas transfer imposed by sediments or soils with varying degrees of cementation.

The computations are shown for a steady-state model. Figure 3 shows the concentrations of methane, ethane, propane, n-butane, and n-pentane with depth for the steady-state condition and diffusion as the transport mechanism. The concentrations at the base of the unsaturated zone were determined using the two-resistance model. The depth gradients are determined by the calculated concentration at the base of the unsaturated zone and the concentration of each constituent in the atmosphere. In the absence of any process of generation and/or consumption of the hydrocarbon in the unsaturated zone, the profiles are linear.

Consumption of methane, or possibly other light hydrocarbons by methanotrophic bacteria will result in decreases in observed concentrations in the uppermost portion of the unsaturated zone. These bacteria are aerobic and require oxygen from the atmosphere. This limits the depth where microbial oxidation of hydrocarbons can occur. Microbial consumption of methane and light hydrocarbons can produce a variety of oxidation products, which are the basis of many indirect techniques used in surface geochemistry. The presence of specialized bacteria themselves are used as an indirect indicator of microseepage.

Figure 4 shows the profiles of methane through n-pentane on one semi-logarithmic plot, combining Figures 2 and 3. There is a scale break for depth at the water table. The rapid change in concentrations near the surface for ethane through n-pentane illustrate the loss to the atmosphere that would occur in the absence of microbial degradation. If there is microbial degradation of hydrocarbons in the surface soils, the gradients in concentration may be even more complex because of possible transport in both directions. Wet soils may also produce methane. These complexities are major reasons why ratios of methane to C2+ hydrocarbons are used in interpretation of soil gas data. Stable carbon isotopic ratios can also help sort out hydrocarbon production/consumption relationships in soils.

Summary and Conclusions
These examples illustrate the viability of the buoyancy of microbubbles as the process supporting surface geochemistry in oil and gas exploration. Modeling suggests the system is dynamic and responsive to reservoir pressure changes. Results of the modeling also illustrate the complexity of the processes which affect soil gas composition. Since free soil gas is in a quasi-equilibrium with adsorbed soil gases, adsorbed gas measurements can be expected to respond to reservoir pressure changes as well, but at a slower rate. The microbial oxidation of hydrocarbons are the basis of most of the indirect methods.