A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. Introduction The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature. When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well' s limit of drainage. Calculations can be made for the producing history both before and after cone breakthroughA typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). SPEJ P. 345ˆ

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis paper describes a Permian evaporite carbonate gas field that has been plagued by severe water problems since it was put on production in the mid-80s. The field is a carbonate complex consisting of three communicating reservoirs that are heterogeneously fractured. Matrix permeability is typically less than 2 mD, except in one highly permeable streak, where it can be as high as 5 D. The permeability of the natural fracture network is extremely heterogeneous, and varies by up to a factor 100 over the field. Complex interaction between fractures, matrix and the highly permeable streak caused a surprising pattern of water breakthrough, which can be explained by a geomechanical model for the heterogeneous natural fracture network. This predictive, field-wide fracture model was validated and constrained by both geological and flow data. First, the stress distribution around seismically visible faults was calculated assuming homogeneous, isotropic, linear elastic rock mechanical properties, and frictionless faults. Second, the calculated stress field was used to simulate the growth of discrete fracture networks, which were constrained by statistically comparing fracture orientation and connectivity with that derived from core, BHI, PLT, mud loss, and well test data. Finally, the fracture networks were upscaled dynamically to the grid of a dual-permeability simulator, enabling fieldscale multi-phase reservoir simulation. The flow model obtained this way matched historical production data from all wells. It also explained the source of water breakthrough and the inflow profile seen on PLTs. Integrating seismic, borehole, well test and production data to constrain and validate such a field-wide model considerably reduced the uncertainty in the final predictions.This integrated, predictive fracture model is presently used to investigate future field development scenarios. To this end, the model is coupled to a surface network simulator, which comprises the whole infrastructure. The fully coupled surface and subsurface models offer the flexibility to optimally plan the position and timing of new wells, the size of compressor units, additional in-field trunk lines and the gas offtake.

A procedure which makes use of both analog and digital computers has been developed for predicting the pressure-production behavior of water-drive reservoirs. The electric analyzer is used for matching the past pressure and production history of the reservoir and inferring the physical characteristics of the aquifer. When the history has been matched, a set of base curves called "influence functions" are derived and the future behavior of the reservoir is calculated from these curves. Introduction Electric analog methods are particularly well-suited for complex water-drive problems. Like all other methods of analyzing water-drive reservoirs, however, analog methods are subject to certain limitations. One of the more obvious and serious of these results from inaccurate or insufficient knowledge about physical characteristics of the reservoir and aquifer. However, it is not insurmountable because the unknown characteristics can usually be inferred from the reservoir's previous behavior. Simons and Spain have shown that even with scant reservoir data and limited production history, electric analyzer studies can provide useful and reliable results. Aside from this limitation on analyzer predictions, the main disadvantage has been lack of a technique for keeping predictions abreast of latest production forecasts. Pressure behavior of a reservoir depends on the rate at which fluid is withdrawn; it is therefore necessary to specify the future withdrawal schedule before the future pressure behavior can be calculated. Conventionally, the electric analyzer predicts pressure behavior for a specific production schedule. If this schedule is abandoned in favor of some new one, as is frequently the case, either the study must be rerun or results adjusted in some manner. The usual procedure is to predict pressures for several different forecasts covering a wide range of production rates. Pressures for specific rates other than those studied can then be approximated by interpolating between the analyzer predicted curves. However, reliability of this type of prediction is doubtful. This paper describes a technique for predicting future behavior of water-drive reservoirs that retains all advantages of electric analyzer analysis and eliminates the main disadvantage. That is, the analyzer is used conventionally to infer unknown reservoir parameters from the pressure history, but not to predict the future behavior directly. Instead, a derived set of base curves, called influence functions, can be used to calculate future behavior for any production schedule.

Efficient development of natural-gas reservoirs requires the participation of many engineering planning and implementation disciplines. When development involves large, remote, offshore gas reservoirs with high H2S and CO 2 content, planning and coordination problems increase rapidly. This paper discusses the time/planning relationships in the evaluation and definition phases of a generalized major gas project typical of resources currently being evaluated in many locations.Project development planning requires an extensive drilling appraisal program to define gas in place, gas productivity, and gas qUality. With this information, marketing potentials can be established, and the interrelated planning and design steps to define commercial feasibility can be undertaken. These steps include gas process optimization studies necessary for project definition and continued reservoir assessments, progressing into early multidimensional analyses. This effort assists in establishing well count, well spacing, and platform siting to yield production performance consistent with equipment constraints and delivery requirements.This study does not discuss the execution phase of the project, but it does stress the importance of having a qualified, multidiscipline project organization to complete the evaluation and definition phases and to serve as the basis of the fully staffed project management team necessary to complete the detailed design and construction phases of the project.