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Summary This paper addresses the problem of pressure transient analysis of a reservoir with spherically discontinuous mobility and hydraulic diffusivity. Such a situation may exist as a result of formation of a burned zone in in-situ combustion, by phase change in a steam flood or geothermal operation, or simply by the formation of a bank of injected fluid with properties different from those of the reservoir fluid. The spherical configuration is expected to represent geothermal applications more closely than does a radial configuration, and is also of interest in hydrocarbon wells with limited entry or partial penetration, or those wells in the vicinity of a pinchout. The problem is solved analytically by using the Laplace transform, which is then inverted using the Stehfest algorithm. The solution is different in detail from the radial case but still shows the important pseudosteady-state behavior at the end of the inner region response (in some cases). It is this pseudosteady-state behavior that permits determination of the distance to the discontinuity (or, in fact, the "burned volume"). Other features of the solution are that the mobility ratio and diffusivity ratio may often be determined from pressure drawdown behavior. The mobility ratio can be calculated from the intercept of a pressure-vs.-reciprocal-square-root-time plot. The diffusivity ratio also may be determined from the ratio of the two straight lines, which appear on the same plot. These methods are not possible in the case of large mobility contrasts in which the outer region is the more permeable. This work was motivated by the need in the geothermal industry to interpret well tests in reservoirs of very large production "thickness," especially in cases where the fluid close to the well may be in a phase different from that further away. Such a configuration occurs frequently since the most commonly performed completion tests involve injection of cold water. However, the application of methods derived in this paper are not restricted to the geothermal area and have applications in in-situ combustion as well. Introduction Discontinuities around a well can occur in a wide variety of reservoir situations. In hydrocarbon reservoirs the inflow or outflow of a fluid bank will result in a compressibility discontinuity, or an in-situ combustion or stimulation program may result in a permeability discontinuity. In a gas condensate or geothermal reservoir, reduction of reservoir pressure in the vicinity of the well will give rise to changes in relative permeabilities as the fluid changes phase, and, in the case of water, enormous changes in compressibility. The same would be true in the case of a steamflood. Recent work by Grant and Sorey indicates that the compressibility of a two-phase steam/water mixture at the boiling point has an effective compressibility four orders of magnitude larger than that of water and two orders of magnitude larger than that of steam. Clearly, the appearance of a flash front in a water region or the start of condensation in a steam region would result in a sharp discontinuity of considerable order. JPT P. 2127^

fax 01-972-952-9435. AbstractGeoscientists and reservoir engineers are very well acquainted with the terms "net-to-gross (NTG)" and "petrophysical cut-offs" or just "cut-offs". The significance of these terms is ultimately to define productive zones in the reservoir for hydrocarbon exploitation. However, there has been marked misunderstanding surrounding the usage of the term, net-to-gross and implicitly, the derivation of cut-offs which are limiting values used in expressing the netto-gross ratio. While the geologist may be concerned with the pay for evaluating hydrocarbon-in-place and the ultimately the estimation of economically producible reserves, the simulation engineer is more concerned with fluid flow for pressure support in the reservoir 1 . The significance of this paper is to consider the different cut-offs selection methods, the varying interpretation of net-to-gross ratios and the implications inherent in such methods. A case study from a field in the NigerDelta is also carried out to reveal the impact of such selection criteria especially in rocks with congenital weak hydraulic properties which cannot be excluded at geologic correlation stage 2 . The effect of cut-off parameters on oilinitially-in-place (OIIP) calculation was also investigated and a sensitivity analysis carried out on the petrophysical parameters to reveal the impact of the dynamically conditioned cut-offs selection on the petrofacies. Multiple Monte Carlo realizations were also employed to obtain probabilistic OIIP estimates rather than a single deterministic result.

The importance of reservoir and well parameters estimated from BHP analysis, has made it necessary to analyze field pressure data as practically as possible. This has lead to the application of numerical solutions to BHP analysis. It involves the proper griding of reservoir and subsequent numerical solution of the resulting partial differential equation. This incorporates heterogeneity of reservoir properties into BHP analysis, thereby broadening its applicability to reservoir description, unlike analytic solution, which does not offer the details it requires. Although, analytical methods give reasonable estimate for simple cases, they are not suitable for real complex cases, due to the limiting assumptions inherent in their development. This paper assessed the applicability of numerical solution to BHP analyses. It solved some field examples analytically and numerically, first for a known simple case and then for real complex cases. Furthermore, test design data were generated using field data in a heterogeneous system. The test was analyzed using both analytical and numerical approaches. The results obtained show that although analytical solutions can be employed for some heterogeneous systems, they are highly idealistic and limited to some convenient cases and that numerical solution models field data realistically. Introduction Welltest analysis involves the interpretation of bottomhole pressure (BHP) data to estimate well and reservoir parameters like permeability, skin, average pressure, etc. The analysis of BHP has been increasingly vital in reservoir management, due to the importance of reservoir and well parameters it offers. Petroleum engineers have since made extensive use of analytical solutions to BHP analyses. This method presents a wide range of models for analyzing BHP tests in homogenous and heterogeneous reservoirs. Although this method is fast, reliable and applicable to a wide range of models, it is developed based on idealized well and reservoir configurations and as such has a limited scope. It's solution presents accurate analysis for some simple cases and highly approximate analysis in modeling real complex geology. In the bid to integrate reservoir heterogeneities into BHP analyses, it became necessary to model field BHP using numerical approach. The application of numerical Welltest analysis solutions has made it possible to model complex cases of BHP analysis. This is based on finite element modeling which is a method of solving partial differential equations in heterogeneous and complex geometry domains.

Reservoir flow zones reflects group of rocks that have similar geologic, physical properties and depositional environment that affect fluid flow. Variations in rock properties result from depositional, diagenetic and post-depositional changes. Aside from a geologic approach, statistical analyses are required to verify the existence of these flow zones. A statistical zonation technique developed by Testerman1 to identify and describe naturally occurring zones in a reservoir and to correlate these zones from well to well was used here. The flow performance is a strong function of the average permeability, and therefore of the statistical flow unit definition method used. Five reservoir flow zones were established based on the geologic litho-stratigraphic correlation using gamma ray and resistivity logs. This is against the two flow zones estimated from statistical correlation. Where this happens, the simulator may lump together several geologic layers. Lumping involve adding layers that have similar physical properties. The number of zones depends on the computing limitation and any other constraints of the simulator. Reconciling these two differences provides a better input into numerical flow simulation. Introduction Accurate well correlations are paramount for a reliable reservoir characterisation. All geologic modelling have their foundation in correlation work. Therefore, it is worth knowing that any geologic correlation that is not consistent with the reservoir's physical properties will give a misrepresentation of different flow units. In constructing an appropriate model, it is important that both the " form" and " function" of the reservoir is honoured as much as possible. The form represents the geologic environment, rock type, and the reservoir architecture. The function represent the petrophysical properties that result in the flow performance. While the former is associated with the geologic zones, the latter on the other hand is associated with the quantitative statistical zonation. In the light of limited well data measured at representative sample point, a statistical technique is used to interpolate the unsampled spaces. Statistics, here provides the quantitative relationship describing the spatial variability of a reservoir property. A quantitative description of reservoir characteristics is necessary for proper statistical reservoir analysis. Quantification of these geological parameters statistically has become expedient in order to achieve a better reservoir zonation. Permeability of a rock is one of the most important flow parameter associated with sub-surface production and injection operations. The importance of the parameter is reflected by the number of sources - well logs, cores and well testing among others - that are employed to estimate permeability.