Cumulative production

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

Once production commences, data such as reservoir pressure, cumulative production, GOR, water cut and fluid contact movement are collected, and may be used to history match the simulation model. This entails adjusting the reservoir model to fit the observed data. The updated model may then be used for a more accurate prediction of future performance. This procedure is cyclic, and a full field reservoir simulation model will be updated whenever a significant amount of new data becomes available (say, every two to five years). 

Cumulative production in countries outside the former USSR, Eastern Europe, and China since the late 1930s has totaled about 1 x 10 t U. A majority of this production came from the United States, Canada, Germany, Namibia, Niger, and South Africa. In addition, some 218,500 t U, 102,245 t U, 16,700 t U, and 16,850 t U have been produced, respectively, in the former GDR, former C2echoSlovakia, Hungary, and Romania. It is estimated that about 72,000 t U have been produced in Ka2akhstan. Reflable cumulative production data for the rest of the CIS, other Eastern European countries, and China, however, are not available (26). 

Perhaps the biggest contribution that technological advancement in petroleum production will make is bringing large volumes of unconventional petroleum resources, eg, heavy oil and tar sands, into a viable economic realm by lowering the unit cost of production. Compared to the inventory of conventional petroleum reserves and undiscovered resources, the physical inventories of such unconventional petroleum resources are extremely large for example, the Athabasca tar sands in Alberta, Canada, are estimated to contain 360 x 10 m (2250 x 10 bbl) of in-place petroleum (19). This volume is equivalent to the total inventory, ie, the combined cumulative production, reserves, and undiscovered resources, of world conventional cmde petroleum. In... 

The cost c>i,4E of the last unit of a block bringing the cumulative production toX units is, from Eq. (9-63),... 

If the batch units are capable of continuous subdivision, we proceed as follows. We substitute the given values of the cumulative-average cost Y and cumulative production X for the first batch into Eq. (9-63) to give, by taking logarithms of each side,... 

It is noted that the partial derivatives in the above variance expressions depend on time t and therefore the variances should be computed simultaneously with the state variables and sensitivity coefficients. Finally, the confidence intervals of the cumulative production of each well and of the total reservoir are calculated by integration with respect to time (Kalogerakis and Tomos, 1995). 

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

Based on estimated continuous world annual metal production, the cumulative world production of these trace metals was calculated (Table 9.2, Figs. 9.5-9.7). However, the cumulative production of Pb and of Cu are greater than the estimates presented here since both metals were utilized by... 

The cumulative production of Cu, Zn and Cd dramatically increased after 1960-1970, as did the cumulative Cr production after the 1980 s... 

Table 9.2. Global industrial age cumulative production of selected trace elements and heavy metals in 1880,1900,1950,1990 and 2000 (million tons)a...

Cd > Hg. However, Pb has the highest total cumulative production if the pre-industrial output is included. Compared to the cumulative world trace element production in 1900, Cr and Ni had the highest increase, while Hg had the lowest increase. The ratios of cumulative production in 2000 to that in 1900 for the eight trace elements followed the trend Cr (643) > Ni (110)... 

Global industrial age annual production of selected trace elements and heavy metals in 1880, 1900, 1950, 1990 and 2000 (million tons) (Data extracted from Han et al., 2002a, 2003b). Global industrial age cumulative production of selected trace elements and heavy metals in 1880, 1900, 1950, 1990 and 2000 (million tons)a. 

The cumulative probability of dying, C equal to the cumulative product of... 

The following terms are often used in the context of quantifying reserves and resources of fossil fuels the Estimated Ultimate Recovery (EUR), also called Ultimate Recoverable Resources (URR), is the sum of past cumulative production, proved reserves at the time of estimation and the possibly recoverable fraction of undiscovered resources. The remaining potential, i.e., the sum of reserves and resources, is the total amount of an energy source that is still to be recovered. The mid-depletion point is the point of time when approximately 50% of the EUR (at field, country or world level) has been produced. 

Table 3.3. Crude bitumen - reserves, resources and cumulative production, end 2006...

Country Crude bitumen in-place (Gb) Reserves (Gb) Resources (Gb) Cumulative production (end 2006) (Gb)... 

Resource estimates and current production The vast majority of the world s oil-sand deposits is located in Canada. Of the total in-place volume of around 1700 Gb of bitumen, only slightly less than 20% is assumed to be recoverable. The EUR of Canadian crude bitumen, i.e., reserves, resources and cumulative production as of the end of 2006, amounted to around 316 Gb. Taking the remaining reserves of around 174 Gb into account, Canada ranks second following Saudi Arabia in global oil reserves (see Table 3.3). However, the practice of including oil sands in official... 

Cumulative production, end 2005 Remaining potential (conventional) 0 Unconventional reserves... 

Figure 3.20 shows the distribution of the EUR, i.e., cumulative production, reserves and resources of conventional natural gas for different world regions. 

Table 3.9 shows the distribution of world hard coal reserves and resources in 2005. Total reserves amounted to 728 Gt (626 Gtce), of which the vast majority are located in the USA and China, followed by India and Russia. The top ten countries represent 85% of total reserves. Considering the production of 2005, the static lifetime of hard coal can be calculated at around 150 years however, we should acknowledge the simplicity of this approach, as coal use is expected to increase significantly in the future. As for hard coal resources, whose quantification is more uncertain, Russia is leading, followed by China and the United States. Figure 3.22 shows the geographical distribution of cumulative production, reserves and resources of hard coal. 

In all oil fields it is necessary, to some degree, to control production rates, monitor individual well performance and determine the cumulative production on an individual well basis. In Prudhoe Bay, this is of particular importance for the following two principal reasons ... 

Figure 9-1 gives production pressure history data for a typical black oil reservoir. The reservoir in this case does not have a gas cap and is not connected to an aquifer. The conventional method of plotting these data is against time. However, the trends we want to see are more apparent when the data are plotted against cumulative production, as in Figure 9-2. 

Although the producing gas-oil ratio data show some scatter, the initial trend is constant. The producing gas-oil ratio will start to increase very soon after bubble-point pressure is reached in the reservoir. Figure 9-2 shows that producing gas-oil ratio starts its increase at about the same cumulative production as the pressure line changes slope. This gives a check on the estimate of bubble-point pressure. 

The production data from a volatile oil reservoir exhibit the same trends as those from a black oil, but reservoir pressure above the bubble point for a volatile oil does not decrease as rapidly as for a black oil. And the change in slope of the plot of pressure against cumulative production for a volatile oil is not as sharp as it is for a black oil. The bubble-point pressure is often hard to identify. 

Producing gas-oil ratio from a retrograde gas reservoir is also constant during early production and then increases. When reservoir pressure is above the dew point, the gas carries a constant quantity of components which will liquefy at surface conditions. However, at reservoir pressures below the dew point some of these components condense in the reservoir. This liquid does not flow to any appreciable degree. Thus, the produced gas carries fewer condensable components to the surface and producing gas-oil ratio increases. Dew point pressure cannot be determined from a plot of pressure versus cumulative production the change in slope at the dew point is rarely apparent. 

These studies demonstrated that DNA-binding can be a reliable probe of metabolic activation. In contrast to studies of metabolites per se, which usually involve large numbers of metabolite intermediates, DNA-binding monitors only chemically reactive metabolites. Also, if there is no selective repair of specific adducts, DNA-binding monitors the cumulative production of metabolites over time, while direct measurement of metabolites can show the metabolite spectrum only at the time observed. This can be particularly critical for studies of activation of complex chemicals such as polycyclic aromatic hydrocarbons whose primary metabolites are subject to secondary and tertiary metabolism (8). 

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