Reservoir models

The other parameters used in the calculation of STOMP and GIIP have been discussed in Section 5.4 (Data Interpretation). The formation volume factors (B and Bg) were introduced in Section 5.2 (Reservoir Fluids). We can therefore proceed to the quick and easy deterministic method most frequently used to obtain a volumetric estimate. It can be done on paper or by using available software. The latter is only reliable if the software is constrained by the geological reservoir model. 

It should be noted that our example used a very simple reservoir model to show the principle. NOS mapping is usually a fairly complex undertaking. 

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). 

At the development planning stage, a reservoir mode/will have been constructed and used to determine the optimum method of recovering the hydrocarbons from the reservoir. The criteria for the optimum solution will most likely have been based on profitability and safety. The model Is Initially based upon a limited data set (perhaps a seismic survey, and say five exploration and appraisal wells) and will therefore be an approximation of the true description of the field. As development drilling and production commence, further data is collected and used to update both the geological model (the description of the structure, environment of deposition, diagenesis and fluid distribution) and the reservoir model (the description of the reservoir under dynamic conditions). 

The reservoir model will usually be a computer based simulation model, such as the 3D model described in Section 8. As production continues, the monitoring programme generates a data base containing information on the performance of the field. The reservoir model is used to check whether the initial assumptions and description of the reservoir were correct. Where inconsistencies between the predicted and observed behaviour occur, the model is reviewed and adjusted until a new match (a so-called history match ) is achieved. The updated model is then used to predict future performance of the field, and as such is a very useful tool for generating production forecasts. In addition, the model is used to predict the outcome of alternative future development plans. The criterion used for selection is typically profitability (or any other stated objective of the operating company). 

Modeling biogeochemical cycles normally involves estimating the spatial and temporal averages for concentrations and fluxes in and out of reservoirs (i.e., reservoir modeling). The... 

Table 4-2 Steady-state carbon contents (unit Pg = lO g) for the four-reservoir model of Fig. 4-11 (a) during the imperturbed (pre-industrial) situation (b) after the introduction of 1000 Pg carbon and (c) after the introduction of 6000 Pg carbon...

For the more mathematically inclined Investigate the dynamic behavior of a coupled linear three reservoir model using the technique outlined in Section 4.3.1. 

Keeling, C. D. (1973a). The carbon dioxide cycle. Reservoir models to depict the exchange of atmospheric carbon dioxide with the oceans and land plants. In "Chemistry of the Lower Atmosphere" (S. Rasool, ed.), pp. 251-329. Plenum Press, New York. 

Keeling, C. D. and Bolin, B. (1967). The simultaneous use of chemical tracers in oceanic studies I. General theory of reservoir models. Tellus 19, 566-581. 

Once wells have been drilled into the formation, the local properties of the reservoir rocks and fluids can be determined. To constmct a realistic model of the reservoir, its properties over its total extent— not just at the well sites—must be known. One way of estimating these properties is to match production histories at the wells with those predicted by the reservoir model. This is a classic ill-posed inverse problem that is very difficult to solve. 

Figure 1.142. The computed result of the relationship between dissolved silica (H4Si04) concentration of mixed fluid and temperature based on four reservoirs model (Shikazono et al, 2002). Open triangle solubility curve for quartz, Open square solubility curve for a-cristabalite, Solid triangle Hishikari Lower Andesite lava (drilling core), Cross Relatively fresh Hishikari Lower Andesite lava (drilling core). H.S. hydrothermal solution G.W. ground water.

Figure 1.143, Four reservoirs model. H.S. hydrothermal solution, G.W. groundwater (Shikazono et al., 2002).

The calculations based on four reservoir models were made using equations (1-62)-(l-67) and precipitation rate constant k) for Si02 minerals by Rimstidt and Barnes (1980). 

Figure 1.144 shows the results of calculation based on multireservoirs (40 reservoirs) model in which each reservoir corresponding to each alteration zone is divided into... 

K. Holing, J. Alvestad, and J. A. Trangenstein. The use of second-order godunov-type methods for simulating EOR processes in realistic reservoir models. In Proceedings Volume, pages 101-111. 2nd Inst Franc Du Petrol Math of Oil Recovery Europe Conf (Arles, France, 9/11-9/14), 1990. 

Petroleum and chemical engineers perform oil reservoir simulation to optimize the production of oil and gas. Black-oil, compositional or thermal oil reservoir models are described by sets of differential equations. The measurements consist of the pressure at the wells, water-oil ratios, gas-oil ratios etc. The objective is to estimate through history matching of the reservoir unknown reservoir properties such as porosity and permeability. 

The discretized reservoir model can be written in the general form presented in Section 10.3. The state variables are the pressure and the oil, water and gas satu-... 

Unlike the permeability runs, the results showed that, the observed data were not sufficient to distinguish all fifteen values of the porosity. The ill-conditioning of the problem was mainly due to the limited observability and it could be overcome by supplying more information such as additional data or by a re-parameterization of the reservoir model itself (rezoning the reservoir). 

In practice when reservoir parameters such as porosities and permeabilities are estimated by matching reservoir model calculated values to field data, one has some prior information about the parameter values. For example, porosity and permeability values may be available from core data analysis and well test analysis. In addiction, the parameter values are known to be within certain bounds for a particular area. All this information can be incorporated in the estimation method of the simulator by introducing prior parameter distributions and by imposing constraints on the parameters (Tan and Kalogerakis, 1993). 

Next, the probability, Pb(r) that the rth model is the correct one, can be used to compute the expected overall field production rate based on the production data from Nm different reservoir models, namely... 

On the debit side, the linearization method is quite sensitive to the form of the network element model. Jeppson and Tavallaee (J2) reported that convergence rate was slow when the usual pump and reservoir models were incorporated, but they obtained significant improvements after the models had been suitably transformed. Although the number of iterations required is small using formulations A and B, the dimension of the matrix equation is substantial. Hence, it becomes essential to use sparse computation techniques if the method is to retain its competitive edge in larger problems. 

Houtermans, J. C., Suess, H. E., Oeschger, H., Reservoir models and production rate variations of natural radiocarbon,... 

Figure 7.9 A three-reservoir model. Vj represents the volume of the reservoir j, Cj the concentration in this reservoir of the element investigated, Q j the material flux from reservoir i to reservoir j.

Weber, K. J., 1982, Influence of Common Sedimentary Structures on Fluid Flow in Reservoir Models Journal of Petroleum Technology, March, 1982, pp. 665-672. 

An alternate model to the ML2 model is the reservoir model, where the catalytic species ML/ and ML are monomeric and in equihbrium with an inactive dimeric meso complex (ML/ )(MLs) (Figure 7.3). In this model the inactive meso complex acts as a racemic trap, consequently decreasing the amount of active catalyst. 

Blackmond pointed out that asymmetric amplification always has, as a consequence, a decrease in reactivity when compared to the enantiopure catalyst. This can be calculated on the various models proposed for the interpretation of nonlinear effects. It is qualitatively visible in the reservoir model above as well as in the ML2 model, where the asymmetric amplification given by g < 1 (low reactivity of the meso catalyst) has as consequence the overall slowdown in reaction rate. The generalized model ML has been discussed (for n = 2,3,4) when the various species are in equilibrium. The complexity of the curve can increase sharply as soon as n > 2. 

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