Monday, January 28, 2019

Measuring Vertical Permeability

Limited Entry Well Test

A well test records the pressure response to a pulse transmitted through the reservoir. One conducted on a well drilled partially into a reservoir or one where a limited portion of the reservoir is perforated- usually the upper portion   - reveals three flow regimes. 

Once wellbore storage subsides, radial flow at the perforations is seen. Transient analysis of this portion of the pressure derivative is used to calculate horizontal permeability, kh, at the perforations and also skin. As the pressure wave propagates away from the well, the second regime, spherical flow , develops. 

The slope of the curve of pressure plotted versus the reciprocal of the square root of time curve allows calculation of spherical permeability. Spherical permeability, ks, is the geometric mean of horizontal and vertical permeability. Hence vertical permeability and anisotropy may be determined. When the third regime- radial flow- develops far from the well, another value for horizontal permeability can be calculated.

If permeability anisotropy is low- vertical permeability approaches horizontal permeability- then wellbore storage effects often mask the early-time radial flow. Spherical flow will also occur earlier and may also be masked. 

Water Coning Analysis

As a reservoir is produced, water or gas coning may develop. Although water or gas production is usually undesirable, records of when this occurs are usseful for future field development. The height of a water cone in any particular well depends on flow rate and vertical permeability. The critical flow rate- above which water comes into the well- and the time taken to initiate water breakthrough are used to calculate vertical permeability. These calculations may lead to adjustment of the reservoir model and influence plans for further field development.

Core Analysis

One of more traditonal ways of measuring permeability is directly on a sample of rock. Small plugs cut from cores are used - the orientation of the plug determines whether horizontal or vertical permeabilities are to be measured. After the core plug is cleaned with a solvent, brine is forced through the plug under constant pressure and the volume of emerging fluid is measured over a period of time. This gives the flow rate through the plug and hece, by Darcy's law, permeability.

If samples are taken freqently, say every 1 ft, then average values of permeability may be computed along the well. Usally harmonic averaging is made for vertical permeability to account for variations in vertical displacement between plugs. Arithmetic averaging is made for horizontal permeabilities unless horizontal displacement needs to be accounted for. Results may be consistent with other ways of measuring permeability anisotropy provided that there is an absence of impermeable barriers, such as stylolites or shales. If these do occur, vertical permeability may be 10 to 100 times lower, making core data measurements unacceptable on a reservoir scale.

Formation Tester Pretests

Both single-probe and multiprobe formation testers check the integrity of packer seals when probes are set against the formation by performing a pretest for each. During a pretest, a small volume of fluid -20 cm3 in the case of the RFT Repeat Formation Tester tool - is withdrawn from the formation. Transient pressure data are acquired and analyzed for drawdown and buildup mobilities. In thick anisotropy formations, the effective permeability determined from such a pretest is the spherical permeability. But horizontal or vertical permeability must be known to calculate anisotropy from spherical permeability. 

A full analysis requires knowledge of porosity, fluid compressibility and fluid viscosity. Because such a small volume of fluid is withdrawn from the reservoir during a pretest, the depth of investigation usually does not extend beyond the damaged zone. As a result, uncertainty arises over whether to use the compressibility and viscosity for mud filtrate or for formation fluid, assuming that these values are known in the first place. To add these difficulties and limitations, the flow regime close to the probe may not be spherical and may be non-Darcy. Other problems, such as probe plugging, damage to the formation resulting from the mechanical setting of a probe or gas evolution in the near-probe region, may invalidate the data before an interpretation can even be attempted.

Formation Tester Vertical Pressure Gradient

Formation tester pressure gradients recorded in depleted reservoirs highlight permeability barriers. Under dynamic conditions, there is a component of pressure attributable to vertical flow, such as rise in water level, within the reservoir. By measuring a dynamic pressure gradient and comparing this to the static pressure gradient- no production from the reservoir - this component can be estimated and the vertical permeability modeled. 

The main drawback of this method is the need for significant production before running the formation tester, so it is not possible to use this technique prior to field development. However, these data are extremely useful when infill drilling is considered later in a field's life.

Formation Tester Pulse Testing

Better use of formation tester pressure profiles can be made with pulse testing. This consists of recording several profiles in an observation well at various stages while a nearby producer or injector is being shut in. The act of shutting in the well generates a pressure pulse that will change the pressure profile at the observation well. These changes are affected by horizontal permeability between the wells and formation heterogeneities,such as faults and impermeable zones. Horizontal and permeabilities are calculated using a three-dimensional (3D) reservoir model for pulse-test simulation and history matching. 

Prior modeling is needed to estimate the duration of the pressure pulse and the timing of the pressure gradient surveys, but the results give permeability estimates over a length and scale comparable to the dimensions of the reservoir. However, the need for two wells and long flow periods makes this method uneconomical for pre-development data collection.


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