Permeability distributions

The flow of groundwater in an actively filling basin is greatly influenced by the space- and time-dependent hydraulic conductivity of the subsurface. 

Mechanical compaction is the dominant process responsible for porosity reduction in argillaceous sediments (Rieke and Chilingarian, 1974). The porosity reduction in coarse-grained sediments like sands may be influenced by mechanical compaction, pressure solution and cementation (Bj0rlykke et al.. 

1989 Houseknecht, 1987). The porosity of carbonate sediments and rocks is reduced by cementation, recrystallization, and mechanical and chemical compaction (Mazzullo and Chilingarian, 1992). 

The remaining porosity in sandstones with early diagenetic silica or carbonate cement may be preserved relatively better during subsequent burial (Bj0rlykke et al., 1989). Secondary porosity may also have a greater preservation potential than primary porosity during subsequent burial (Bj0rlykke et al., 1989). 

During deeper burial of newly deposited carbonate sediments, the primary and secondary porosity is decreased by cementation and chemical compaction. At these deeper hurial depths pressure solution causes the sedimentary grains to dissolve and cement, and stylolites to form. Stylolites may start to form at depths of 1 to 2 km (Bjorlykke, 1989). Early formed carbonate cement may hamper later pressure solution, i.e. carbonate sediments which have been subject to relatively early cementation may retain their remaining porosity better with depth (Bj0rlykke, 1989). Aqueous dissolution of carbonates may also create secondary porosity in carbonate rocks at deeper burial. The complex evolution of porosity in carbonate sediments and rocks is reflected in the extreme lateral and vertical heterogeneity of carbonate rocks (Mazzullo and Chilingarian, 1992). 

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The average nonuniform permeability is spatially dependent. For a homogeneous but nonuniform medium, the average permeability is the correct mean (first moment) of the permeability distribution function. Permeability for a nonuniform medium is usually skewed. Most data for nonuniform permeability show permeability to be distributed log-normally. The correct average for a homogeneous, nonuniform permeability, assuming it is distributed log-normally, is the geometric mean, defined as ... 

History matching in reservoir engineering refers to the process of estimating hydrocarbon reservoir parameters (like porosity and permeability distributions) so that the reservoir simulator matches the observed field data in some optimal fashion. The intention is to use the history matched-model to forecast future behavior of the reservoir under different depletion plans and thus optimize production. 

We have developed a method to spatially resolve permeability distributions. We use MRI to determine spatially resolved velocity distributions, and solve an associated system and parameter identification problem to determine the permeability distribution. Not only is such information essential for investigating complex processes within permeable media, it can provide the means for determining improved correlations for predicting permeability from other measurements, such as porosity and NMR relaxation [17-19]. 

We use a conventional experimental design, in that fluid is flowed at a constant flow rate through a sample. We measure the pressure drop and the distribution of velocity within the sample, as described in the following section. We then estimate the permeability distribution from the measured data, as described in Section 4.1.4.2.2. 

We formulate an identification problem to determine the permeability distribution from the measured superficial velocity distribution. In this section, we first develop the model for our experiment, and present the estimation method. 

The estimate for the permeability distribution obtained using the velocity data shown in Figure 4.1.7 is presented in Figure 4.1.8. For this example, we used 30... 

Fig. 4.1.8 Determined permeability distribution for the thin Bentheimer sample. The vertical axis represents the permeability value for the corresponding point.

We presented a novel method to determine spatially resolved permeability distributions. We used MRI to measure spatially resolved flow velocities, and estimated the permeability from the solution of an associated system and parameter identification problem. 

Our approach was demonstrated by determining multiphase flow functions from displacement experiments. Spatially resolved porosity and permeability distributions can be incorporated to mitigate errors encountered by assuming that the properties are uniform. We developed measures of the accuracy of the estimates and demonstrated improved experimental designs for obtaining more accurate estimates of the flow functions. One of the candidate experimental designs incorporated MRI measurements of saturation distributions conducted during the dynamic experiments. 

Defining the movement of water in rocks of low permeability by chemical methods, such as the use of tracers, age dating of water, and isotope ratios, has met with limited success for the same reasons as have the physical methods. That is, they are incapable of describing the permeability distribution in an adequately large area. 

Megascopic Dispersivity. The megascopic scale is the full-aquifer dispersivity whose value determines the volumetric sweep in numerical simulation blocks. Figure 3 shows the behavior of (expressed as inverse Peclet number) as a function of time for miscible displacements in a two-dimensional stochastic permeability field. The parameter V is the Dykstra-Parsons coefficient, a dimensionless measure of the spread of the permeability distribution to which the flow field was conditioned. = 0 corresponds to a... 

The Dykstra-Parsons coefficient is a normalized measure of the spread of a permeability distribution that is bounded between zero and one. The formal definition is... 

The system of hydrodynamic secondary hydrocarbon migration, whether the hydrocarbons move in separate phase, in very fine suspension or in aqueous solution, is influenced by the porosity and permeability distribution in a sedimentary basin, and the magnitude and direction of the net driving force for groundwater flow. As a consequence, the different processes and associated forces that are responsible for the hydrodynamic conditions in a sedimentary basin also determine to a greater or less extent the characteristics of the hydrocarbon migration system in a hydrodynamic basin (Sections 4.3.4.1, 4.S.4.2 and4.3.4.3). 

Permeabilities in sedimentary basins are known to vary with the scale of observation (e.g. Bredehoeft et al., 1983,1992 Chapman et al, 1991 Neuzil, 1986). Different techniques are being developed to estimate reservoir- and basin-scale permeabilities, e.g. computer-aided techniques based on relations between characteristics of depositional systems and permeability distribution (Weber, 1982,1987 Stam, 1989 Stam et al., 1989 Mijnssen, 1991), and techniques based on numerical simulations of basin-scale groundwater flow in combination with known groundwater pressure distributions (e.g. Bredehoeft et al., 1983, 1992 Burrus et al., 1991), techniques that use numerical models of coupled groundwater flow/heat flow and known thermal characteristics to estimate basin-scale permeabilities (Chapman et al., 1991). 

The present-day groimdwater flow systems in the selected study area may not be in accordance with the relief of the present-day water table, and as a consequence the characteristics of the flow system cannot be reliably inferred solely from water table relief and subsurface permeability distribution. A direct determination of the quantitative characteristics of the present-day gravity-induced groundwater flow system, requires data on pressure, density and viscosity of groundwater and data on the permeability distribution... 

Determination of permeability distributions from experimental velocities 138... 

To determine permeability distributions, experiments are conducted whereby fluid is injected into saturated samples. A pulsed-field-gradient stimulated-echo technique is used to resolve the velocity field within the sample. An inverse problem is formulated and solved to determine the permeability distribution. 

Our goal is to determine the permeability with millimeter resolution, approaching an intrinsic scale that corresponds to the minimum representative volume element. To do so, we first use NMR velocity-imaging experiments to determine the velocity distributions within a saturated porous medium undergoing a constant injection of water. Then, we solve an associated inverse problem to determine the permeability distribution. 

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