Appendix B – Mathematical Extrapolation Technique for Predicting and Assessing Production Performance
In this section developments in graphical methods of assessing water drive performance are presented. An extensive number of graphical and mathematical extrapolation techniques is available in the literature. A number mathematical extrapolation methods were also assessed (not presented here). Mathematical extrapolation technique presented by Dake (1994) was found to be quite effective in predicting future production performance and in assessing the effects of any remedial actions which has taken place. The method was tested on two fields, namely Miller and Maureen. Description of method proposed by Dake is presented below.
Examination of
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Conversion from surface volumes to reservoir pore volumes is performed using the following relationships:
N_pd=(N_p B_o)/(NB_oi )(1-S_wc)
W_id=W_i/(NB_oi )(1-S_wc)
Since 1PV=(NB_oi)/(1-S_wc )
Finally, the dependence of fractional flow at the producing end of the system on fractional flow at reservoir conditions is expressed using the classical Buckley-Leverett fraction flow function: f_we=1/(1+B_o/B_w (1/f_ws -1))
It must be noted that in most water drive reservoirs before the water breakthrough, there is an initial period of depletion. The fractional flow calculations, only take into account the oil recovered by water injection. Therefore calculations can be performed only after the water breaks through in the producing wells.
Prediction of final oil recovery
If injection rates during the latter part of the flood are relatively stable, then 1/Wid function can be approximated by a straight line, which can be fitted by equation of the form:
(δf_we)/(δS_we )=aS_we+b
Where a and b are constants. Integrating the equation results in quadratic function: f_we=a^2/2 S_we^2+bS_we+c
Where c is constant. Predicted values of fwe and Swe obtained by extrapolation of the quadratic equation above are then can be used in Welge equation for predicting Npd as a function of fwe, which are then should be converted to surface conditions.
Miller Field
The data
• The promoters have been trying to promote the concept through press and meeting with retailers.
Next, it is necessary to identify the land that is possibly flooded and this can be calculated as:
1) Which type of function (linear, exponential, or cubic) do you believe will best fit the data? Support your choice.
This paper comprises an appreciation of data representation, its visualization, an outline description of behavior, plus an indication of the use of the equation in engineering.
The purpose of this experiment was to perform a simple distillation as well as a fractional distillation and to determine the composition of an unknown solution using fractional distillation.
The analysis came during the 40 days of the flood and the 150 days it took for the waters to decrease.
The regional storm (Hurricane Hazel) will be adjusted for each catchment to consider the areal reduction factor. The factor will be calculated based on the equivalent circular area and the area reduction factor percentage lookup table given in Technical Guide, River & Stream Systems: Flooding Hazard Limit (Water Resource Section, Ontario Ministry of Natural Resources, 2002). Considering the large number of catchments, Civica will develop a tool to calculate the equivalent circular area and then assign the right reduction factor.
With the purpose of the experiment being to identify the 30 mL of unknown liquid, the theoretical basis of simple and fractional distillation must be deconstructed and applied to the data obtained describing the liquid in question.
The process of the collection of an underground fluid would not be possible without the use of hydraulic fracturing. In the Shale reserves, located about 5,000 feet underground, suffer an extremely low permeability rate. Permeability is the measure of how well a fluid flows through an absorbent material at the depth, and within such nonporous rock, the ability of fluids to travel to the well is greatly limited. Fracturing increases the area of the fluid that is exposed to porous materials and thus greatly increases production. The method of fracturing utilizes a few key components which allow for an economical extraction of resources.
As the terminology of hydraulic fracking suggests, it involves water, a lot of water in fact that in British Columbia, the average volume of water per well is 77 million litres. With the usage of water at both the front end with fracking fluid, the water based chemical cocktail that is injected into the shale, and at the back end where there is flowback water and produced water. (Becklumb et al., 2015) The flow of water back up from the fracking operation (the backflow) is a combination of brine and formulated fracking fluid. This backflow water will persist until it reaches the point where the water and components resembles the local formation of minerals and rock chemically. This is known as produced water, while the well continues in operation.
Class II is the selection given by the EPA for wells that inject below the Underground Source of Drinking Water (USDW) and are consider deep wells, unlike Class V, that are shallow disposal wells such as septic tanks that dispose non-hazardous fluids underground. These salt water disposal wells are used to dispose the produced water from oil and gas extraction activities permanently. The produced water is also called brine. This produced water is extremely saturated with salt, has a high number of total dissolve solids, contains residuals from crude oil, and may contain other chemicals used during the production process. There are other injection activities in this area that inject produce water in the Birds Nest aquifer, which is the enhance recovery activity. The enhance recovery activity injects produced water in the same formation that the oil companies are extracting the oil and gas. These enhance recovery wells will not be used in this study since the water injected will stay in the formation temporary. The produced water from salt water disposal wells will stay in a different formation permanently and can pose a threat to the area and nearby aquifers. The average depth of the injection zones in the Birds Nest average from 3,000 feet below surface level to 10,000 feet below surface level. The average depth of the USDW in this area is 300 feet below surface level. If there is an aquifer that is used or will be used in the future for the purpose of drinking water, then the constructions of these wells need to be rigorously engineered to protect this source of drinking water. These injection wells contain two to three layers of cement to make sure there is no migration of the injected fluid. The permits for these well state that extensive logs and test needs to be done regularly to ensure the mechanical integrity of
The methodology used was to utilize the Recurrence Interval formula (R) = (N+1)/M, to determine the recurrence interval and magnitude of historical floods provided on the Stream Gauge Data of Peak Flood Discharges on Clearwater River in Hazard City. Also, I reviewed the flood insurance map to
A brief homework exercise of 10 problems will be given to reinforce the fractional modeling concepts. The students will model each operation, by drawing the shapes and showing what is being done.
A level pool routing experiment was carried out to determine the adequacy of results obtained through simulated flood routing. The experiment yielded experimental results from which calculations of inflow; storage and discharge over a weir were obtained. The Energy Grade line from the tank to the pipe outlet was observed as well as the relationship between the tank discharge to the square root of height. Noted from this was that height was the driving force of flow from the tank.
Based on the real world functioning of businesses, every organization that deals with the process of manufacturing of certain products operates in accordance with the main principle of maximizing its profits. During the performance of daily activities, many business managers face a series of questions related to planning, control and decision making. In order to give answers to all these questions, an additional analysis needs to be considered. It is very important for managers to plan carefully how they are going to generate sufficient money to pay down costs and, in this way to result with a profit. As managers are interested in having the adequate information about the influence that certain actions might have on the profitability of the business, "Cost Volume and Profit" analysis plays a significant role by being a potential tool in facilitating the process of making the right decisions regarding planning and control in order to add value to the company. (Trifan and Anton, 2011). To further illustrate the essential impact that CVP analysis has on management authorities in making better decisions, I will refer to and analyze the case of the Hampshire Company which follows as below.