Fluid prediction

Figure 8.8 shows the resulting saturation indices for halite and anhydrite, calculated for the first four samples in Table 8.8. The Debye-Hiickel (B-dot) method, which of course is not intended to be used to model saline fluids, predicts that the minerals are significantly undersaturated in the brine samples. The Harvie-Mpller-Weare model, on the other hand, predicts that halite and anhydrite are near equilibrium with the brine, as we would expect. As usual, we cannot determine whether the remaining discrepancies result from the analytical error, error in the activity model, or error from other sources. 

The influence of fillers has been studied mostly at hl volume fractions (40-42). However, in addition, it is instructive to study low volume fractions in order to test conformity with theoretical predictions that certain mechanical properties should increase monotonlcally as the volume fraction of filler is Increased (43). For example, Einstein s treatment of fluids predicts a linear increase in viscosity with an increasing volume fraction of rigid spheres. For glassy materials related comparisons can be made by reference to properties which depend mainly on plastic deformation, such as yield stress or, more conveniently, indentation hardness. Measurements of Vickers hardness number were made after photopolymerization of the BIS-GMA recipe, detailed above, containing varying amounts of a sllanted silicate filler with particles of tens of microns. Contrary to expectation, a minimum value was obtained (44.45). for a volume fraction of 0.03-0.05 (Fig. 4). Subsequently, similar results (46) were obtained with all 5 other fillers tested (Table 1). 

FIGURE 5.8. Liquid/vapour coexistence curve of the Lennard-Jones fluid predicted by the lOZ/LMBW theory in the KHM, KH and VM approximation (solid, short-dash and long-dash lines, respectively). Monte Carlo (MC) simulations are shown by the open circles. 

Figure 21. Comparisons of experimental and predicted K values for two gas condensate fluids (----), predicted. (A) (O, , A), Data of Hoff-...

Empirical relationships between gas character and fluid properties allow the prediction of the phase and fluid properties of untested (and sometimes unlogged) hydrocarbon-bearing zones. The 5 C and dryness (e.g. C / XlCi... C3) of associated and free gases correlate with a number of fluid properties, including phase, API gravity and saturation pressure. These same trends can be recognized in the mud gas hydrocarbon and dryness data and, once calibrated with the MDT information, predictions can be made for untested zones. When integrated with ancillary information (when available) such as reservoir pressure, show information and wireline log data, these empirically based phase and fluid predictions are extremely accurate. 

In addition to the studies mentioned here, Mentzer, et a/. summarized extended corresponding-states results for phase equilibrium especially for systems containing hydrogen and common inorganics. They found accurate pure-fluid predictions for non-polar compounds up to about C7H16. For mixtures they found a strong dependence on the binary interaction parameters but once those parameters were optimized for phase equilibrium, they could be used to represent a variety of properties accurately, without further optimization. 

This viscosity is extremely extension thickening, since it rises to infinity as k approaches 1/2X. Recall that the second-order fluid equation predictsonlyalinearriseof t)u withe, while the Newtonian fluid predicts no dependence of on e. 

Tsuneyama et al. (2014) conducted a case study of lithology and fluid prediction from seismic data. In an RPT, they could separate carbonates from sandstone and shale. 

Tsuneyama, F., Takahara, K., Nagatomo, A., Tanioka, K., Enomoto, M., Nishizuka, T., 2014. Characterization of hitherto unseen reservoirs a case study of lithology and fluid prediction using QI. First Break 32, 49-59. July. 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

As the conditions of pressure and temperature vary, the phases in which hydrocarbons exist, and the composition of the phases may change. It is necessary to understand the initial condition of fluids to be able to calculate surface volumes represented by subsurface hydrocarbons. It is also necessary to be able to predict phase changes as the temperature and pressure vary both in the reservoir and as the fluids pass through the surface facilities, so that the appropriate subsurface and surface development plans can be made. 

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

Figure 5.21 helps to explain how the phase diagrams of the main types of reservoir fluid are used to predict fluid behaviour during production and how this influences field development planning. It should be noted that there are no values on the axes, since in fact the scales will vary for each fluid type. Figure 5.21 shows the relative positions of the phase envelopes for each fluid type. 

In addition, the separator temperature and pressure of the surface facilities are typically outside the two-phase envelope, so that no liquids form during separation. This makes the prediction of the produced fluids during development very simple, and gas sales contracts can be agreed with the confidence that the fluid composition will remain constant during field life in the case of a dry gas. 

Oil viscosity is an important parameter required in predicting the fluid flow, both in the reservoir and in surface facilities, since the viscosity is a determinant of the velocity with which the fluid will flow under a given pressure drop. Oil viscosity is significantly greater than that of gas (typically 0.2 to 50 cP compared to 0.01 to 0.05 cP under reservoir conditions). 

In Section 5.2.8 we shall look at pressure-depth relationships, and will see that the relationship is a linear function of the density of the fluid. Since water is the one fluid which is always associated with a petroleum reservoir, an understanding of what controls formation water density is required. Additionally, reservoir engineers need to know the fluid properties of the formation water to predict its expansion and movement, which can contribute significantly to the drive mechanism in a reservoir, especially if the volume of water surrounding the hydrocarbon accumulation is large. 

The gradients may be caloulated from surface fluid densities, or may be directly measured by downhole pressure measurements using the repeat formation testing tool (RFT). The interfaces predicted can be used to confirm wireline measurements of fluid contact. 

This section will look at formation and fluid data gathering before significant amounts of fluid have been produced hence describing how the static reservoir is sampled. Data gathered prior to production provides vital information, used to predict reservoir behaviour under dynamic conditions. Without this baseline data no meaningful reservoir simulation can be carried out. The other major benefit of data gathered at initial reservoir conditions is that pressure and fluid distribution are in equilibrium this is usuaily not the case once production commences. Data gathered at initial conditions is therefore not complicated... 

In the pre-development stage, core samples can be used to test the compatibility of injection fluids with the formation, to predict borehole stability under various drilling conditions and to establish the probability of formation failure and sand production. 

Introduction and Commercial Application The reservoir and well behaviour under dynamic conditions are key parameters in determining what fraction of the hydrocarbons initially in place will be produced to surface over the lifetime of the field, at what rates they will be produced, and which unwanted fluids such as water are also produced. This behaviour will therefore dictate the revenue stream which the development will generate through sales of the hydrocarbons. The reservoir and well performance are linked to the surface development plan, and cannot be considered in isolation different subsurface development plans will demand different surface facilities. The prediction of reservoir and well behaviour are therefore crucial components of field development planning, as well as playing a major role in reservoir management during 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. 

The prediction of the size and permeability of the aquifer is usually difficult, since there is typically little data collected in the water column exploration and appraisal wells are usually targeted at locating oil. Hence the prediction of aquifer response often remains a major uncertainty during reservoir development planning. In order to see the reaction of an aquifer, it is necessary to produce from the oil column, and measure the response in terms of reservoir pressure and fluid contact movement use is made of the material balance technique to determine the contribution to pressure support made by the aquifer. Typically 5% of the STOMP must be produced to measure the response this may take a number of years. 

Reservoir simulation is a technique in which a computer-based mathematical representation of the reservoir is constructed and then used to predict its dynamic behaviour. The reservoir is gridded up into a number of grid blocks. The reservoir rock properties (porosity, saturation, and permeability), and the fluid properties (viscosity and the PVT properties) are specified for each grid block. 

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). 

It Is important to know how much each well produces or injects in order to identify productivity or injectivity changes in the wells, the cause of which may then be investigated. Also, for reservoir management purposes (Section 14.0) it is necessary to understand the distribution of volumes of fluids produced from and injected into the field. This data is input to the reservoir simulation model, and is used to check whether the actual performance agrees with the prediction, and to update the historical data in the model. Where actual and predicted results do not agree, an explanation is sought, and may lead to an adjustment of the model (e.g. re-defining pressure boundaries, or volumes of fluid in place). 

This is Widom s scaling assumption. It predicts a scaled equation of state, like the law of corresponding states, that has been verified for fluids and magnets [102]. 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Syimnetrical tricritical points are predicted for fluid mixtures of sulfur or living polymers m certain solvents. Scott (1965) in a mean-field treatment [38] of sulfiir solutions found that a second-order transition Ime (the critical... 

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