The main goal of this thesis, *A petrophysical evaluation of tidal heterolithic deposits: application of a near wellbore model for reconciliation of scale dependent well data*, is to give a better and less uncertain estimate of porosity and permeability in a challenging reservoir type. This is accomplished through an integrated study that takes into account both sedimentological and petrophysical well data, that are reconciled in a near wellbore model on which critical factors as sedimentological heterogeneity, biased sampling and scale transitions are evaluated.

A 25 m interval of the lower part of the Tilje Formation in Heidrun Field, Halten Terrace offshore mid Norway is parameterized with focus on factors affecting the petrophysical properties in the near wellbore volume. In tidal deposits, the amount and spatial distribution of low-permeable mud is a critical factor. A geostatistical near wellbore model is then created of this interval. The modelling approach is process- oriented and mimics the depositional process by displacement of mathematical surfaces to simulate deposition and erosion. The volumes between the surfaces are populated with petrophysical properties using a correlated Gaussian field approach. This process-oriented modelling tool is critically reviewed and transformations are proposed that are used to obtain input parameters from core observations such, as the sand and mud laminaset thickness distribution. The porosity and permeability values, that have to be specified at the lamina scale, are obtained from core plugs, which represent an average of several lamina types, through an iterative procedure. The result is a realistic representation of the sedimentological components and the petrophysical distributions in the near wellbore volume on which petrophysical parameters can be calculated on various scales.

In one of the lithofacies the vertical variation in sand laminaset thickness was analysed with time series analysis methods to quantify the degree of tidal influence. Although the data set is noisy, a few periodic components are significant: namely 11-16 and 50-60 sand laminasets per cycle. Furthermore, the internal stratification of the sand laminasets, the transition to the over- and underlying mud laminasets and the mean thickness of the mud laminasets, suggest that the shortest period recorded reflects a semi-annual tidal component. Incorporating vertical, periodic variation in mud fraction is important since it influences the bulk petrophysical properties.

Published flume tank studies are used to create a wide range of ripple-laminated, realistic bedding types with different mud fractions and correlation lengths but with constant petrophysical properties. These models are evaluated as a function of sam**viii **ple volume. A large variation in porosity and permeability between realizations, expressed as the Coefficient of Variation (CV), is observed when the sample volume is small. This indicates that the volume of investigation is not representative. A representative elementary volume (REV) is here defined to correspond to the sample volume that gives a CV below 0.5. For permeability there is observed a relation between the size of the REV and the bedding type (i.e. the correlation lengths of the sedimentological components). This relation is different for vertical and horizontal permeability. Porosity, being an additive property only dependent on the amount and not the spatial distribution of the components, shows no such dependency. From these experimental results, flow regimes and critical thresholds are identified that highlight the uncertainty in scale transition issues in these deposits. The results show that core plugs in general are inadequate to describe the effective permeability at the bedding scale and that this will affect the integration of core and log data.

The model set used to study the dependency with sample volume is expanded and evaluated with different porosity and permeability contrasts between the lithological components at a representative scale. The critical threshold for onset of vertical and horizontal flow is enhanced. The relation between the mud fraction and the effective vertical and horizontal permeability is expressed with different function types that are used to estimate a representative permeability value from a mud fraction estimate. Incorporating physical parameters that can be evaluated independently makes the relationship more generally applicable. The results can be used to guide the focus in data collection in these deposits by quantifying the influence of contrast between sand laminae or between the sand and the mud component in the different flow regimes.

The results form a basis for giving a better estimate of porosity and permeability in the selected interval. One method uses the near wellbore model, based on the detailed study of the interval, and forward models the porosity and permeability anisotropy at various scales. With this method individual lithofacies are studied and biased sampling is evaluated. A continuous estimate along the model is compared with existing estimates of horizontal permeability and porosity. A second method, being more general, uses the equations describing the relation between mud fraction and permeability. Using a wireline-based estimator of mud fraction, a continuous estimate of permeability anisotropy is obtained that differs from the traditional core-log method since the effective properties are calculated at a representative scale.

In summary, this study gives, as well as a contribution to scale transition issues in a difficult tidal heterolithic reservoir type, a formalised basis for analysis of petrophysical properties in a multi-scaled heterogeneous geological system.

Norwegian University of Science and Technology

Student: Kjetil Nordahl

Supervisor: Sverre Ola Johnsen