This paper presents a method to determine the present condition of a refracturing candidate gas present condition of a refracturing candidate gas well and allows the operator to decide if further stimulation is warranted. This method involves the use of type curves, computer analyses of the original treatment, and a logical comparison of the results. By using constant pressure and constant rate-type curves to analyze actual well performance and build-up data, the effective performance and build-up data, the effective fracture lengths and fracture conductivities created by the original fracturing treatments were calculated. Computer analyses of these original treatments were used to estimate created fracture lengths and, in conjunction with laboratory data, fracture flow capacities. A comparison of these fracture parameters allowed a better understanding of the current performance and resulted in successful refracturing treatments. Lack of agreement between type curves and computer analyses would have indicated potential problem areas such as proppant transport or lack of fracture confinement. proppant transport or lack of fracture confinement
Restimulation efforts in low permeability gas wells generally have met with only limited success. Frequently, restimulation is based solely on the fact that unsatisfactory performance has been obtained and the most logical solution is to retreat the well, often with the operator realizing the marginal chance for success. To make an evaluation of restimulation potential, it is necessary to evaluate current performance in light of the original fracture treatment. Knowledge of fracture length and fracture conductivity, in conjunction with formation permeability, reservoir pressure and productive sand characteristics, pressure and productive sand characteristics, should allow assessment of the original stimulation and indicate potential for refracturing success. Increased fracture length or higher fracture conductivity may result in better performance from the candidate well.
RESTIMULATION CRITERIA AND GUIDELINES
Determination of the present condition of a refrac candidate should be by two independent techniques arriving at a common indication of fracture length and fracture conductivity. One technique involves the analysis of performance data to determine the "effective" fracture length and conductivity. The other technique involves the use of fracture stimulation design concepts including computer programs to assess the "created" fracture length and conductivity. Agreement between the "effective" fracture length and the "Created" fracture length implies that certain fracture characteristics are known. Lack of agreement implies that potential problem areas exist and that further consideration is necessary prior to restimulation. prior to restimulation. Performance analysis: When considering a refrac treatment for a specific well, one of the first considerations should be to determine if the well responded to the original treatment. This would be dependent primarily upon the resource potential of the reservoir. Restimulation design potential of the reservoir. Restimulation design should always consider the possibility that the well lacks sufficient reservoir energy or economically recoverable reserves to be a viable refrac candidate. If the well responded to an original stimulation, the chance for successful refracturing is enhanced.
Build-up tests had been used for a number of years in restimulation analysis by calculating a damaged condition or a created fracture length, depending on the technique employed. Performance analysis by pressure transient methods using "infinite" conductivity fractures often resulted in shorter fracture lengths than could possibly have been created by the hydraulic fracturing stimulations.
Proper evalation of restimulation potential should include the concept of finite capacity fractures.
A successful miscible flood was initiated during 1966 in the Camp Sand Unit, North Haynesville Field, Claiborne Parish, Louisiana. The Camp Sand Unit is about 3.5 miles (5.6 km) long and 1 mile (1.6 km) wide. Injection of a slug of enriched gas was followed by a buffer of natural gas and then by water. Over 2.4 million barrels (0.38 Mm ) of oil have been recovered from the Camp Sand.
The Upper Jurassic Camp Sand occurs at a depth of 8000 ft (2438 m) and is less than 10 ft (3.05 m) thick, averaging slightly less than 5 ft (1.52 m). Vertical lithology variations indicate the sand was very likely deposited as a marine bar by a regressive sea. The expected reservoir distribution and trends of this type of deposit have been confirmed by the available reservoir data and production. Diagenesis, in the form of cementation and solution, has made minor alterations in the reservoir.
Rock characteristics, log character, and reservoir characteristics are closely interrelated. Similar rock and reservoir properties trend east-west; the same as the reservoir body. Thicker sand along the axis of the trend has the best reservoir quality; progressively poorer quality reservoir occurs toward the edge of the reservoir and with depth. Sand size and permeability decrease with depth. This layering along with horizontally oriented shells minimizes fluid cross flow or fingering by serving as baffles.
Fluids preferentially flow in the central portion of the reservoir in areas of thicker and higher quality sand. While it is estimated that waterflooding would have recovered 2 million barrels (0.318 Mm3) over a 16-year period, this project has already recovered 2.4 million barrels (0.382 Mm ) of oil over a 12-year period.
A successful miscible flood was initiated at the Camp Sand Unit during 1966. This unit is located in north Louisiana in the northern portion of the Haynesville Field (Fig. 1). The Haynesville Field was discovered in 1921 and produces from eight formations, ranging between depths of 2800 (853 m) and 11,000 ft (3353 m).
In 1961, during development of a deeper reservoir, the Smackover, oil was discovered in the Camp Sand in the area of the unit. The Upper Jurassic-aged Camp Sand occurs at a depth of 8000 ft (2438 m) and has an average pay thickness of only 4.7 ft (1.4 m). The Camp Sand's basic reservoir data are found in Table 1. Its productive area is about 3.5 miles (5.6 km) long and 1 mile (1.6 km) wide and originally contained 6.83 million STB (1.086 Mm ). The initial pressure of this originally undersaturated volumetric pressure of this originally undersaturated volumetric oil reservoir was 3616 psig (24.9 MPa). Produced oil has an API gravity of 46.30 (795.8 kg/m ) and a viscosity of 1.054 centipoise (0.001 054 Pa s).
Because of the Camp Sand's depth and thin pay section, working interest owners agreed to unitize the reservoir prior to development. Tenneco was elected operator and unitization became effective in February 1965. Between February 1965 and July 1966, five wells produced 132,000 barrels (20 986 m ) of oil. At that time the oil's saturation pressure of 2438 psig (16.8 MPa) was reached and the wells were shut-in, pending completion of pressure maintenance facilities. The first stage of the miscible flood was implemented two months later. Injection of a slug of enriched gas was followed by a buffer of natural gas and then by water. The flood has produced over 2.4 million barrels (0.38 Mm ) of oil produced over 2.4 million barrels (0.38 Mm ) of oil which is 860,000 barrels (136 729 m) above the reservoir's primary recovery estimate.
METHOD OF STUDY
The study procedure used here was to accumulate data to determine the interrelationship of rock characteristics, reservoir characteristics, production characteristics, and log characteristics, and to determine reservoir trends and predict performance.
Core material from six wells was available for study.
A linear stability analysis shows that reverse wet combustion is unstable for nearly all physically realizable operating conditions for the special case of coincident steam and combustion fronts. Expansion effects due to gas generation from combustion and vaporization are found to have a stabilizing influence on reverse wet combustion.
Forward wet combustion is also found to be conditionally stable. Significant expansion effects at the combustion front can overwhelm the stabilizing influence of a favorable mobility ratio and effect destabilization with respect to oscillatory long wavelength modes.
In situ combustion processes are being considered for a variety of recovery schemes for underground fossil fuel deposits. These include combustion processes for secondary recovery of highly viscous crude processes for secondary recovery of highly viscous crude oils, tertiary recovery of lighter oils, in situ retorting of oil shale, oil recovery from tar sands, and in situ coal gasification. It is useful to categorize all in situ combustion processes as either forward or reverse combustion. In the former the combustion front travels in the same direction as the flow of gases, whereas in the latter it travels countercurrent to the direction of gas flow.
Forward combustion is by far the more widely used; in such applications as secondary and tertiary oil recovery, it is effectively the only combustion process us However, reverse combustion offers particular advantages for in situ thermal recovery schemes for relatively impermeable media such as subbituminous coal lignites, and tar sands. The reason for this is that during forward combustion, tars vaporized at the combustion front are convected into cooler regions ahead of the front where they condense and thus reduce the natural permeability of the bed. In contrast, for reverse combustion the vaporized tars, or other high molecular weight compounds generated by the combustion, travel toward the production well through a heated region whose permeability is usually greater than the natural permeability of the bed since the front has passed through it. In technologies such as the linked passed through it. In technologies such as the linked vertical well process for in situ coal gasification, a reverse combustion linking step is used to create a highly permeable link through which the combustion gases from subsequent forward gasification can escape. The use of reverse combustion as a preparatory step prior to forward combustion is also being considered prior to forward combustion is also being considered for tar sands.
Forward and reverse in situ combustion may also be either a dry or wet combustion process. In the former only air is injected into a relatively dry fossil fuel deposit such that any vaporization of water due to conduction of heat from the combustion front, has no effect on the process. In a wet combustion process either water is injected along with air or there is sufficient water naturally present in the deposit, such that the steam front is in relative close proximity to the combustion front. If enough water is present, the steam front can be coincident with the combustion front and thus depress the combustion front temperature to the saturation temperature of steam at the prevailing pressure.
Forward wet combustion has some advantages for secondary recovery processes for highly viscous crude oils because less air is required for the front to traverse a given distance thus making it more economically attractive. The authors are particularly interested in the influence of wet combustion on the sweep efficiency of both the reverse and forward combustion steps for the in situ coal gasification process. This process is being considered for the gasification of process is being considered for the gasification of western subbituminous coal seams which can contain considerable moisture.
The sweep efficiency of many in situ combustion processes is related to the stability of the process. processes is related to the stability of the process. In a stable combustion process any perturbations in the combustion front, due to heterogeneities in the properties of the porous media, flow rate pulsations, properties of the porous media, flow rate pulsations, or a variety of other possible causes, die out very rapidly and the progressing flame front is more or less planar. In an unstable combustion process these perturbations grow rapidly and create a fingered perturbations grow rapidly and create a fingered combustion front which can bypass much of the potentially recoverable fossil fuel, thus making the process quite inefficient. Unstable in situ combustion is not always disadvantageous.
Formic and acetic acids have been used in conjunction with stimulation and cleanout treatments for many years. They have found particular application because of their low corrosiveness on metals and compatibility with crude oils. The organic acids have been used either by themselves or in mixtures containing hydrochloric acid. The mixtures have shown the ability to develop etching of carbonate fractures that is usually representative of acid solutions containing much higher hydrochloric acid concentrations.
Recent laboratory investigations have shown that mixtures of formic acid and hydrochloric acid may have particular application as stimulation fluids in very high temperature environments. While it has been known that formic acid, or compounds that form formic acid through chemical reaction or degradation, can reduce the corrosiveness of HCl, there has been no systematic study to optimize such a system. This paper shows that the low corrosivity of HCl-formic paper shows that the low corrosivity of HCl-formic mixtures can be optimized and is a function of the ratio of HCl to formic acid and highly dependent on the corrosion inhibitor selected for use. It will be shown that mixtures containing as high as 10% HCl can be prepared which maintain low corrosivity at temperatures up to 400 deg. F without the use of inhibitor intensifiers. This low degree of corrosivity can be maintained with reduced concentrations of organic corrosion inhibitor.
This investigation resulted in the development of a retarding system that appears to function synergistically in the presence of formic acid. The reduced reaction rate on carbonates appears to be due to a change in the process controlling reaction kinetics. The retarding system changes the reaction kinetics from a diffusion controlled process to a process that is controlled by the surface reaction process that is controlled by the surface reaction rate. This approach to retardation allows deeper penetration of acid into fracture systems before the penetration of acid into fracture systems before the acid completely spends, and appears to be effective at temperatures to at least 400 deg. F.
The acid system resulting from this investigation has best application in treating wells with bottom-hole temperatures between 250 deg. and 400 deg. F. The mixed acid system can be used to prepare fluids for the following applications: (1) perforating and completion, 12) clay removal with HF/HCl/formic, (3) breakdown fluid ahead of fracturing; (4) retarded acid for fracture acidizing, and (5) scale removal.
Retarded acid systems are considered necessary to stimulate effectively the production of many high temperature formations. Retarded acids are used to achieve an acid penetration distance and a conductive fracture length that approaches the drainage radius of the well.
Chemically retarded and emulsified acid systems utilizing hydrochloric acid have provided adequate retardation at temperatures up to 93-3 deg. C (200 deg. F) and in many applications up to 121.1 deg. C (250 deg. F). Slower reacting and less corrosive acid systems are desirable to stimulate production in wells having temperatures above 121.1 deg. C (250 deg. F).
Formic and acetic acid have been used in conjunction with well completions, cleanout, and stimulation treatments for many years because of their low corrosivity on metals. The organic acids have been used alone, but an important application has been in mixtures with hydrochloric acid.
Organic acids, if reacted individually or as a hydrochloric-organic acid mixture, do not react generally to completion on carbonate formations. A previous investigation with acetic acid and formic previous investigation with acetic acid and formic acid shows 42% and 86% conversion to the calcium salts, respectively." Another investigation with hydrochloric-acetic acid mixtures shows that the acetic acid portion is converted to about the same extent. Fig. 1 shows data obtained with a 7 1/2 HCl-10% formic acid mixture. These data show that 86% of the formic acid in the mixture was converted to calcium formate at a temperature of 121.1 deg. C (250 deg. F).
Experimental and theoretical analyses show that uncontrolled water invasion during underground coal conversion (UCC) is harmful at all stages of UCC. By contrast, if water invasion is prevented, coal porosity can be created for further processing, pyrolysis can yield uniform hydrocarbon products, gasification can produce a uniform product, coal is fully consumed (not bypassed) during combustion, and environmental problems are minimized.
The Four Corners Region of New Mexico has long served as the major source of fossil fuel for the 10% (and growing) of the U.S. population which lives in the American Southwest. Over the long term, assuming continued rejection of the nuclear option, despite a temporary supply of Alaskan oil, and including possible future contributions from the Kaiparowitz possible future contributions from the Kaiparowitz Region of Utah, this fuel source must continue to supply electricity and hydrocarbon fuels for the Southwest. Other regions of the United States, as well, may need hydrocarbons from this Region. However, with the deplation of oil and natural gas supplies, it will be necessary to turn to coal both for electric power and for the hydrocarbon fuels.
Although the coal reserves of the Four Corners and Kaiparowitz Regions are vast, the strippable coal is far more limited--underground mining is already proposed for the Kaiparowitz Region, and the 3 deg. dip of the Four Corners coal seams leaves only relatively small amounts of coal at stripping depth, i.e., less than about 65 m (200 ft). Economic factors thus require that deeper coal be recovered, and safety and environmental factors demand development of new methods to recover that coal. The LASL concept of underground coal conversion (UCC) is one promising new method.
In its complete form (simpler versions are also en visioned, as will be discussed), the LASL advanced concept for subbituminous coals in arid or semi-arid regions involves preliminary physical isolation of the coal from the surrounding aquifers, followed by four chemical steps: (1) The coal is dried at about 120 deg. C to produce greater porosity, to create uniform and reproducible conditions for subsequent processing, to accomplish the drying with low-grade heat, and to recover valuable water. (2) The coal is pyrolyzed at about 300-600 deg. C to recover gaseous and perhaps liquid hydrocarbons. Some hydrocarbons will be sold as fuels or petrochemical feedstocks. Part may be blended with the coal gasification products so that a material of very uniform quality can be supplied. (3) The coal is gasified with O /CO feed to yield an intermediate-Btu fuel. (4) The fuel gas is cleaned and blended. LASL sees the use of this gas at a mine-mouth electricity generation station, but other uses for the fuel can be envisioned.
Because the Navajo Nation is equivocal in its attitude toward recovery of its strippable coal, the longterm fuel supply for present and future Four Corners Region electric generators is uncertain. Other coal supplies must be sought. Conventional underground mining in one expensive possibility. However, chemical recovery of deeper coal by the LASL concept should be reasonably straightforward, if water isolation (as in the previous paragraph) could be accomplished. Once water influx is controlled, successive drying, pyrolysis, then gasification with oxygen/carbon dioxide pyrolysis, then gasification with oxygen/carbon dioxide mixtures would provide a uniform, intermediate-Btu fuel gas with relatively low sulfur content to mix with and augment the powdered coal being burned in the generators. Because of the existing stack-gas cleaning facilities, and because the boilers handle coal pyrolysis gases, such generating stations offer a pyrolysis gases, such generating stations offer a particularly advantageous site for a staged development of particularly advantageous site for a staged development of various concepts ultimately to go into UCC technology for more broad-scale use.
In considering any coal recovery scheme for arid regions, one must recognize the overriding importance of water conservation.
It is, perhaps, obvious that coal cannot burn if it is too wet. Control of water influx into coal beds during underground coal gasification (UCG) has seldom been attempted, and underground processing yields have been degraded accordingly. Uncontrolled water influx has implications throughout both the combined steps of simple gasification (UCG) and the individual steps of LASL's UCC.
Parameter estimation techniques that allow quantitative treatment of thermal data from an in situ coal gasification experiment are presented. After a discussion of the important aspects of using parameter estimation, the specific models used for parameter estimation, the specific models used for the Hanna II and Hanna IV test data are outlined. In particular, conduction models have been useful for describing the reverse combustion process and a formal mapping procedure has provided quantitative detail of cavity growth during forward gasification.
Since 1973 Sandia Laboratories has been associated with a series of Underground Coal Gasification (UCG) experiments conducted by the Laramie Energy Technology Center (LETC) at Hanna, Wyoming. There has been a variety of instrumentation fielded by Sandia for these tests. The instrumentation has included the conventional in situ diagnostic tools, gas sampling and thermometry, in addition to remote monitoring techniques such as electrical resistivity, seismic and acoustic. An assessment of these various techniques has been compiled. This paper limits itself to a discussion of the techniques developed to analyze thermocouple data from UCG experiments.
Sandia Laboratories' approach to in situ thermometry has been shaped to a large degree by two simple facts of life regarding measurements for UCG. First, the test environment is extremely hostile with severe chemical, thermal, and mechanical effects. Thermocouple failure is almost inevitable. Extreme attempts to prolong thermocouple lifetime with the often accompanying loss of measurement resolution are not cost effective. A different approach is to accept thermocouple failure and instead of survivability, emphasize thermocouple diagnostics and accurate data. Thus the experimenter knows when his data is reliable and because it is accurate he can use it quantitatively. Sandia Laboratories fielded a diagnostic oriented thermometry system on the Hanna IV experiment. Results indicate that appropriate diagnostics are not a luxury for UCG experiments; they are a necessity. The second fact of life is that thermal instrumentation from vertical boreholes is expensive. The number of wells, and consequently spatial resolution, is often limited by cost considerations. Thus every effort must be made to maximize the information from the available instrumentation. This necessity naturally leads to using the data for quantitative analysis. Such an approach can extend the information obtained from the data base. It also can rule out some of the erroneous explanations for data sequences that can be made on the basis of purely qualitative inspection of the data.
In-situ temperature data poses a natural inverse problem. That is one desires to describe a source, problem. That is one desires to describe a source, be it a reverse combustion path or an expanding gasification cavity, by observation of its output. Parameter estimation or non-linear least squares is a Parameter estimation or non-linear least squares is a very effective method for solving the non-linear inverse problems the data presents. For work in UCG this author has found parameter estimation useful in two areas; first, for the analysis of low temperature ( less than 100 deg. C) responses and, second, for mapping cavity growth during forward gasification. The models are described in detail, herein, and results from both the Hanna II and Hanna IV experiments are given.
PARAMETER ESTIMATION PARAMETER ESTIMATION Before discussing the particular models appropriate for UCG, it is useful to point out some of the problems associated with parameter estimation in a problems associated with parameter estimation in a more general sense. Of course, parameter estimation has been the subject of considerable work with respect to both the statistical inferences of least squares problems and solution techniques. The reader is referred to one of the many texts on the subject . For the engineer engaged in data analysis two problem areas standout; parameter identification and model appropriateness. Let us consider these with practical examples of germane to UCG data.
Aqueous solutions of two synthetic petroleum sulfonates, nonyl and dodecyl orthoxylene sulfonates with tertiary amyl alcohol as cosurfactant, were studied with the polarizing microscope. Surfactant concentrations of 2-10%, the approximate range being considered for injection in surfactant processes, were used, while salinities in each system ranged from well below to well above the optimum salinity for a particular mixture of refined oils. The solutions were also studied as a function of temperature and time.
Both these surfactants showed the same pattern of structure variation with salinity. At low salinities there was a dispersion of liquid crystalline particles in brine. At high salinities a single liquid crystal-line phase was present. over a narrow range of intermediate salinities a mixture of these two structures was seen. The generality of this behavior was confirmed by observation of solutions of two conventional petroleum sulfonates, which also exhibited a transition petroleum sulfonates, which also exhibited a transition between structures over a narrow salinity range.
The mean salinity of the transition region was found to increase as a surfactant's optimum salinity increases for a given oil. Since optimum salinity is associated with the lowest interfacial tensions, this result indicates that structure of an injected surfactant solution is related to its ability to produce low tensions on contacting oil. Solution viscosity should also be affected by the structural changes.
A major portion of current research on enhanced oil recovery deals with chemical flooding processes employing surfactants. In many proposed processes the surfactant is injected as a "slug" which is an aqueous saline solution containing the surfactant and often an alcohol cosurfactant as well. Surfactant concentration in the slug is typically in the range of 2-10% by weight.
Both the slug's flow behavior within the reservoir and its interaction with trapped oil globules, especially its ability to produce ultralow interfacial tensions and mobilize such globules, are very important for process performance. To obtain information which will help in understanding and predicting such aspects of slug behavior, we have used the polarizing microscope to study the macroscopic structure of aqueous saline solutions of some petroleum sulfonate surfactants. As discussed below, we have found that structure variation with composition, especially with salinity, follows a general pattern in these systems. in particular, there exists a narrow salinity range for each surfactant-cosurfactant mixture where a change occurs from one type of structure to another. The salinity where this transformation in structure occurs increases as the optimum salinity of the surfactant-cosurfactant mixture increases for a given oil. Since the lowest interfacial tensions occur at optimum salinity, these results suggest that the structure of the injected surfactant slug is related to its ability to produce low tensions upon contact with oil.
The synthetic petroleum sulfonates used were mono-ethanolamine alkyl orthoxylene sulfonates, which were supplied by Exxon Chemical Company. In PDM-337, which contains 84% active sulfonates, the alkyl chain is predominantly dodecyl. In PDM-484, which is 85% predominantly dodecyl. In PDM-484, which is 85% active, the alkyl chain is mainly nonyl. Conventional petroleum sulfonates used were TRS 10-410, which was petroleum sulfonates used were TRS 10-410, which was supplied by Witco Chemical Corporation, and Mahogany AA, which was supplied by Amoco Production Company. ate former contains 61.5% active sulfonates and has an equivalent weight of 424, while the latter contains about 60% active sulfonates and has an equivalent weight of 430.
Reagent grade isopropanol, isobutanol, and tertiary amyl alcohol were used as cosurfactants. The surfactant-cosurfactant mixtures were added to brines of the appropriate compositions made from distilled water and reagent grade NaCl.
This study has looked into the feasibility of operating a floating methanol plant in a North Sea environment. The plant was fed with associated gas from an oil field.
Both the technical and economical results are promising. This indicates that such projects might promising. This indicates that such projects might be an alternative solution for otherwise reinjected gas; however, more work needs to be done to evaluate their attractiveness.
By now the floating production facility approach is a well recognized concept. Its major advantages are savings in capital investments, shorter development time, and increased flexibility because parts of the facility can be easily relocated.
So far the interest has focused mostly on floating gas processing plants; however, to the author's knowledge none is planned yet for the North Sea.
The purpose of this study was to do a technical/ economical feasibility study of gas-to-methanol conversion aboard a converted oil tanker in the North Sea.
The methanol plant would be of Imperial Chemical Industries (ICI) design. Close contacts were established with their contractors in order to find what is critical when operating a plant under such adverse conditions.
With few exceptions the contractors outlined the same points as critical. Based on this information and knowledge about the limitations on other parts of the facility, it was possible to arrive at parts of the facility, it was possible to arrive at an expected "on time" plant availability.
The methanol producer was treated as a separate company, buying associated gas from the field operators.
A computer model was written to perform the economic evaluations. Both a base case calculation and a sensitivity analysis were treated in this model.
2. DESCRIPTION OF EQUIPMENT AND PROCESSES
Fig. 1 shows a principle view of the thought facility. The associated gas arrives at the SALM base, rises through it, and feeds into flexible lines to the plant. The 1000 M.T./day methanol plant is ICI's L.P. (low pressure) design.
In the plant the gas is first desulphurized. It is then combined with superheated steam (prepared from seawater) and fed to a reformer. There, synthesis gas, comprising hydrogen and carbon oxides, is formed. This mixture is further compressed and fed to the reactor where the methanol reaction takes place. This methanol is thereafter distilled and place. This methanol is thereafter distilled and stored in the tanker.
The processing tanker, together with the shuttle tanker when loading occurs, is free to weathervane 360 degrees around the SALM. The shuttle tanker then brings the methanol to a shore base for further distillation into grade AA before being stored.
The methanol facility is self-sufficient with energy and has an overall thermodynamic efficiency of approximately 60%. As a rule of thumb, it can be said the production of 1 M.T. of methanol requires approximately 31 MMSCF of natural gas.
3. TECHNICAL FEASIBILITY
The mooring unit is of Exxon's SALM type. It is able to permanently moor a 50-60000 DWT tanker in a northern North Sea environment, and should therefore not represent operating limitations.
The Exxon SALM is built in modules for rapid connections/disconnections when maintenance or repairs are performed at the field site.
An investment risk analysis by the probability distribution technique was proposed and published by Hillier in a 1963 issue of Management Science. His work was quite theoretical. A simplified form of the method was presented in petroleum literature by Davidson and Cooper in 1975. However, their work did not extend to using the method in practical decision making. Both of these works critically discussed why this approach is preferable to earlier methods. In as much as the main value of such an innovation and the ultimate need for its publication is its application, discussion of the practical aspects of the method is important. The purpose of this paper is to fulfill this need.
Regardless of what criterion an investor uses to determine the profitability of his venture, the amount of risk involved must be considered for a sound, final decision. As such, many techniques have evolved over the years for quantifying risk. Among the older techniques which have been used are: 1) Payback Period - The length of time required to Payback Period - The length of time required to recover an investment through the net cash flows from the project. 2) Expected Monetary Value - Sum of the products of investment outcomes and their respective products of investment outcomes and their respective chances of occurrence. 3) The Certainity Equivalent - A method of discounting cash flow by a risk-free interest rate. 4) Sensitivity Analysis - Determining the profitability measure by varying an uncertain parameter. For reasons well discussed in parameter. For reasons well discussed in literature, all of these techniques are weak and are inadequate for proper risk portrayal. The more recent and certainly more sophisticated method of risk analysis is the probability distribution of the profitability index. One form of this is the Monte profitability index. One form of this is the Monte Carlo simulation which uses randomly selected parameters from appropriate ranges of values to generate parameters from appropriate ranges of values to generate a series of possible outcomes. While this technique is a quite reliable tool, it does not lend itself to routine application because of the computer work involved. Another form is the, analytical technique proposed by Fredrick Hillier . This approach adopts proposed by Fredrick Hillier . This approach adopts well know statistical theories and assumes the distribution of the profitability index to derive the probability distribution. Hillier's work, though probability distribution. Hillier's work, though amenable to hand calculators, was quite theoretical. A simplified form of the method was presented in petroleum literature by Davidson and presented in petroleum literature by Davidson and Cooper in 1975. However, their work did not extend to using the method in practical decision making.
This paper discusses the practical aspects of Hillier's approach. Although Davidson and Cooper suggested log-normal distribution assumption for analysis of petroleum investments, this work is based on the validity of normal distribution when the random variable is the cash flow. Both assumptions are compared in the discussion. Arriving at a decision to accept or reject an investment proposal on the basis of the method requires the use of utility theory. Therefore, the concept of the theory is reviewed. Its use in conjunction with the probability distribution of net present value is then shown. Finally, a decision present value is then shown. Finally, a decision concerning two or more risky investments may be influenced by the skewness of normal distribution. Hence, the semi-variance equation for testing the normality or magnitude and direction of skewness is presented and its application discussed.
DERIVATION OF PROBABILITY DISTRIBUTION
In his work, Hillier assumed that under conditions of uncertainity, cash flows from an investment are random variables which can be characterized by their means and variances. Therefore, by the central limit theorem, the distribution of these means will be approximately normal. Moreover, their sum will approach a normal distribution. Based on these, he derived the probability distributions of net present values and internal rate of return for three possible cases of cash flows from an investment. These cases include (1) statistically independent cash flows (2) perfectly correlated cash flows and, (3) combined independent and correlated cash flows. This paper considers the second case only.
A comprehensive numerical model of the under-ground coal gasification process via the stream method was developed for a two-dimensional geometry. Seven reactions, involving carbon, carbon dioxide, carbon monoxide, oxygen, water/steam, hydrogen, and methane are accounted for. Nitrogen is the seventh gas component. As a result of gasification, the channel diameter increases with time, and a combustible gas is produced. The model accounts for all of these factors.
Considering the fact that vast known coal reserves occur in the United States, much research has been directed toward producing synthetic liquids and gases via above ground gasification and liquefaction of coal which lends itself to large scale operations. The current federal and state pollution control regulations and the enormous cost of mining, transporting and processing make this process commercially unfeasible. Furthermore a low quality coal cannot be used in this process. Some of these problems can be avoided if gasification of coal in situ is utilized.
This process, known as underground gasification of coal, is defined as the controlled burning of coal seam in the presence of gas mixture consisting of mainly nitrogen, oxygen and steam, to produce gasification reactions. A combustible gas mixture containing nitrogen, carbon monoxide, steam, hydrogen, methane and carbon dioxide is formed, which can be used in the generation of electricity on a commercial scale.
This method possesses many advantages over conventional mining and synthetic fuel operations in that it minimizes health hazards to miners, improves process safety, provides ecological benefits in that process safety, provides ecological benefits in that the land surface is left intact, and eliminates much of the need for aboveground plant requirements. Furthermore, it offers a technically simple and feasible method for producing the vast bituminous and low rank coal reserves in the United States (much of which can neither be economically mined nor is acceptable in rank for commercial synthetic fuel operations), and if designed properly can be very economical.
In order to increase the understanding of this process, a series of steady state analytical models process, a series of steady state analytical models by the stream methods were developed by Magnani, by Magnani and Farouq Ali, and by Farouq Ali and Pasha. The steady state assumption of the process enabled the extraction of closed form solutions, which, though complex, were useful for carrying out parameter sensitivity studies. Furthermore, these models were of considerable value for carrying out pseudosteady state simulation of unsteady state underground coal gasification process.
The present model is a numerical extension of the previous models, and as a result is considerably more general. A two dimensional axisymmetrical coal seam is assumed to be ignited at one end and thereafter a mixture of air and steam (or a mixture of oxygen enriched air and steam) is injected. As a result, the combustion zone advances in both axial and radial directions and the channel wall recedes resulting in the production of a combustible gas mixture.
It should be mentioned that while this study has been devoted to the stream method of underground coal gasification, a number of other simulation studies has been reported which consider other gasification processes. These include the works of Kotowski and processes. These include the works of Kotowski and Gunn, Gunn and Whiteman, Winslow, Thorsness and Rosza, and Dinsmoor, Galland and Edgar.
1. The coal bed consists of 100% carbon. However, the model allows for source terms in all components considered and thus the influx of any of these as a function of distance and time may be simulated.
2. The gasification channel is initially assumed to be of cylindrical geometry, one extremity of which is ignited.