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The Merriam-Webster Dictionary defines simulate as assuming the appearance of without the reality. Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behavior assumes the appearance of actual reservoir behavior. The model itself is either physical (for example, a laboratory sandpack) or mathematical. A mathematical model is a set of equations that, subject to certain assumptions, describes the physical processes active in the reservoir. Although the model itself obviously lacks the reality of the reservoir, the behavior of a valid model simulates--assumes the appearance of--the actual reservoir. The purpose of simulation is estimation of field performance (e.g., oil recovery) under one or more producing schemes. Whereas the field can be produced only once, at considerable expense, a model can be produced or run many times at low expense over a short period of time. Observation of model results that represent different producing ...
Reservoir engineers use relative permeability and capillary pressure relationships for estimating the amount of oil and gas in a reservoir and for predicting the capacity for flow of oil, water, and gas throughout the life of the reservoir. Relative permeabilities and capillary pressure are complex functions of the structure and chemistry of the fluids and solids in a producing reservoir. As a result, they can vary from place to place in a reservoir. Most often, these relationships are obtained by measurements, but network models are emerging as viable routes for estimating capillary pressure and relative permeability functions. Before defining relative permeability and capillary pressure, let us briefly review the definition of permeability.
Reservoir simulation is a widely used tool for making decisions on the development of new fields, the location of infill wells, and the implementation of enhanced recovery projects. It is the focal point of an integrated effort of geosciences, petrophysics, reservoir, production and facilities engineering, computer science, and economics. Geoscientists using seismic, well-log, outcrop analog data and mathematical models are able to develop geological models containing millions of cells. These models characterize complex geological features including faults, pinchouts, shales, and channels. Simulation of the reservoir at the fine geologic scale, however, is usually not undertaken except in limited cases.
The Haft Kel field is located in Iran. Its Asmari reservoir structure is a strongly folded anticline that is 20 miles long by 1.5 to 3 miles wide with an oil column thickness of approximately 2,000 ft. The most probable original oil in place (OOIP) was slightly 7 109 stock tank barrels (STB) with about 200 million STB in the fissures; numerical model history matching resulted in a value of 6.9 109 STB. The matrix block size determined from cores and flowmeter surveys varied from 8 to 14 ft. The numerical simulation model considered matrix permeabilities from 0.05 to 0.8 md.
The Empire Abo field, located in New Mexico, US, covers 11,000 acres (12.5 miles long by 1.5 miles wide) and contains approximately 380 million stock tank barrels (STB) of original oil in place (OOIP). This reservoir is a dolomitized reef structure (Figure 1) with a dip angle of 10 to 20 from the crest toward the fore reef. The oil column is approximately 900 ft thick, but the average net pay is only 151 ft thick. The pore system of this reservoir is a network of vugs, fractures, and fissures because the primary pore system has been so altered by dolomitization; the average log-calculated porosity was 6.4% BV. Numerical simulations of field performance and routine core analysis data have indicated that the horizontal and vertical permeabilities are about equal.
Smith and Hannah documented the evolution of hydraulic fracturing in high-permeability reservoirs since the 1950s. The first fracture treatments in the 1950s were pumped in moderate- to high-permeability formations. Those treatments were designed to remove formation damage that usually occurred during the drilling and completion operations. Low-permeability reservoirs were fracture treated in the 1950s and 1960s, but, at low oil and gas prices, low-permeability reservoirs were generally not economic, even after a successful fracture treatment. The values of high, moderate, and low permeability need to be defined on the basis of both the formation permeability and the reservoir fluid viscosity, or the k/μ ratio, where k is the formation permeability in md, and μ is the formation fluid viscosity in cp.
There are many factors that the engineer must consider when analyzing the behavior of a well after it has been fracture treated. The engineer should analyze the productivity index of the well both before and after the fracture treatment. Other factors of importance are ultimate oil and gas recovery and calculations to determine the propped fracture length, the fracture conductivity, and the drainage area of the well. Post-fracture treatment analyses of the fracture treatment data, the production data, and the pressure data can be very complicated and time consuming. However, without adequate post-fracture evaluation, it will be impossible to continue the fracture treatment optimization process on subsequent wells. Many of the early treatments in the 1950s were designed to increase the productivity index of damaged wells.
The most important data for designing a fracture treatment are the in-situ stress profile, formation permeability, fluid-loss characteristics, total fluid volume pumped, propping agent type and amount, pad volume, fracture-fluid viscosity, injection rate, and formation modulus. It is very important to quantify the in-situ stress profile and the permeability profile of the zone to be stimulated, plus the layers of rock above and below the target zone that will influence fracture height growth. There is a structured method that should be followed to design, optimize, execute, evaluate, and reoptimize the fracture treatments in any reservoir. The first step is always the construction of a complete and accurate data set. Table 1 lists the sources for the data required to run fracture propagation and reservoir models.
Petroleum reservoir management is a dynamic process that recognizes the uncertainties in reservoir performance resulting from our inability to fully characterize reservoirs and flow processes. It seeks to mitigate the effects of these uncertainties by optimizing reservoir performance through a systematic application of integrated, multidisciplinary technologies. It approaches reservoir operation and control as a system, rather than as a set of disconnected functions. As such, it is a strategy for applying multiple technologies in an optimal way to achieve synergy. Reservoir management has been in place in most producing organizations for several years.
This section discusses the impact of vertical variations in permeability and the effect of gravity on simple 2D reservoir situations in which the areal effects are ignored. Gravity effects always are present because for any potential waterflood project, oil always is less dense than water, even more so after the gas is included that is dissolved in the oil at reservoir conditions. The discussion below does not include the Pc effects on vertical saturation distributions. Through countercurrent imbibition, Pc effects help to counteract nonequilibrium water/oil saturation distributions. The mathematics of including Pc effects makes the problems too complicated for inclusion here.