Well Test Interpretation in Heterogeneous Reservoirs With Skin and Afterflow: Some New Theoretical Solutions and General Field Experience

Some new analytical solutions for dimensionless pressure vs. dimensionless time are presented. It is deomonstrated how these new solutions, together with existing ones, can be used for unravelling reservoir heterogeneity patterns, quantitative interpretation of selected field tests, and well test design. The field tests cover both naturally fractured carbonates and layered sandstones. Two examples of well test interpretation in naturally fractured formations reinforce the conclusions of other authors, namely that well test interpretation based only on 2 parallel semi-log straight lines is questionable in cases with afterflow. The new analytical solutions refer to stratified and heterogeneous systems with inter layer crossflow. In both cases after-flow and skin factor are included. It is shown how the type curve can be used in certain long pressure build-ups to gain information on the average reservoir pressure in a stratified system. In the pressure behaviour of a heterogeneous system with inter layer crossflow, there is often quite a long transition zone bemore the system behaves like a single reservoir. This requires careful planning of test duration. In particular, the early part of the transition zone. looked at in isolation, may give a false impression of pressure stabilisation, which could lead to the interpretation of small drainage areas or a gross over-estimation of the system permeability. INTRODUCTION Over the past few years, there has been an increasing trend in industry to develop tighter and more heterogeneous reservoirs. Simultaneously, detailed studies of old fields often demonstrated that reservoirs are not as homogeneous as they were originally thought to be. In both cases, the petroleu~ engineer should be in a position to characterise and define the nature of these heterogeneities, in order to select the best production policy for the field, be it primary or enhanced. References and illustrations at end of paper. There has also been a significant upsurge of industry interest in well testing recently. The reasons are two-fold. First, the advent of fast computers together with the development of analytical and numerical (=simulator based) flow models has greatly enhanced our theoretical base of well test interpretation. Secondly, the introduction of precision pressure gauges, continuous downhole pressure recording etc. has vastly improved the quality of pressure data available for analysis. The main types of heterogeneities that may be encountered in reservoirs are summarised in ig. 1, comprising (i) natural fractures, (ii) stratified formations with sealing shale layers, (iii) heterogeneous formations with interlayer cross-flow. Combinations of these three main types of heterogeneities are also possible. The factors which usually complicate well test interpretation are near well-bore effects such as skin and bore hole compressibility, and influences of reservoir boundaries such as faults or gas caps/ aquifers. Although much has been published on well testing in recent years, gaps still exist. For instance, there were significant contributions to the well testing theory in heterogeneous formations during 1982, which did not, however, include the effect of well bore storage. There is thus the need for a study which tries to close some of these gaps. The other, perhaps even more important, objective of the present study is to demonstrate the use of well testing theories for interpretation in realistic field cases and for well test design. In this context, field examples are presented for naturally fractured carbonates. stratified formations and heterogeneous reservoirs with interlaye cross-flow. All equations were originally solved with the help of a micro computer (HP-85). In order to use these analytical models efficiently for well test design and interpretation, running on faster computers is obviously required. WELL TEST INTERPRETATION IN HETEROGENEOUS RESERVOIRS WITH SKIN AND AFTERFLOW: 2 SOME NEW ANALYTICAL SOLUTIONS AND GENERAL FIELD EXPERIENCE SPE 11964 NATURALLY FRACTURED FORMATIONS Fractured formations contain many of today's known oil fields. Such formations have a so-called dual porosity system: a matrix porosity and a fracture porosity. Fractures are either solution cracks or tectonic fractures. The objective of well testing in fractured formations is to obtain: (i) the permeability of the fracture system, (ii) the skin factor, (iii) average reservoir pressure, (iv) the secondary porosity parameter w, and (v) the matrix-fracture cross-flow coefficient A. Both w 'and A are dimensionless numbers.