Matching Reservoir Pressure

The various simulation runs revealed that the Gauss-Newton implementation by Tan and Kalogerakis (1991) was extremely efficient compared to other reservoir history matching methods reported earlier in the literature. 

The fifteen layers of constant permeability and porosity were taken as the reservoir zones for which these parameters would be estimated. The reservoir pressure is a state variable and hence in this case the relationship between the output vector (observed variables) and the state variables is of the form y(t,)=Cx(t,). 

in the 2nd run the horizontal permeabilities of all 15 layers were estimated by using the value of 200 md as initial guess. It required 12 iterations to converge to the optimal permeability values. 

In the 3rd run the porosity of the ten zones was estimated by using an initial guess of 0.1. Finally, in the 4,h run the porosity of all fifteen zones was estimated by using the same initial guess (0.1) as above. In this case, matrix A was found to be extremely ill-conditioned and the pseudo-inverse option had to be used. 

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). 

---

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). 

Figure 18.25 Observed data and model calculations for initial and converged parameter values for the 2"d SPE problem, (a) Match ofgas-oil ratio and water-oil ratio, (b) Match of bottom-hole pressure and reservoir pressures at layers 7 and 8 [reprinted with permission from the Society of Petroleum Engineers].

Based on the reservoir simulation the overall conclusion is that the Ninotsminda oil field can technically be used as an underground gas storage facility. The developed reservoir simulation model is able to match reasonably well with the historically observed oil and gas production, and with average reservoir pressure for the Ninotsminda oil field. 

Figure 2-7 Match of observed oil gas production and reservoir pressure...

For mechanistic studies, ambient pressure experiments on emulsions and foams often offer significant experimental advantages over high-pressure experiments. However, high-pressure measurements are also needed since the phase behavior, physical properties of the fluids, and dispersion flow may all depend on pressure. Experiments under laboratory conditions that closely match reservoir conditions are particularly important in the design of projects for specific fields. Chapter 19, by Lee and Heller, describes steady-state flow experiments on CO2 systems at pressures typical of those used in miscible flooding. The following chapter, by Patton and Holbrook,... 

For applications that demand an exceptional installed reproducibility of better than 0.05 pH, the best technical choice is a spherical glass measurement electrode and a flowing junction reference electrode. The glass must be selected to match the pH and temperature range of the process. The reference electrode aperture area and reservoir pressure must be chosen to maintain a small constant flow of electrolyte into the process. However, this choice of electrode has special installation and maintenance requirements that make them an extremely unpopular choice compared to throwaway solid state combination electrodes. Spherical bulbs are more... 

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula is... 

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. 

Figure 1. Diagram of apparatus (M) monomer reservoir (F) flow meter (VG) vacuum gage (mercury manometer) (E) electrode (T) liquid nitrogen trap (P) mechanical pump (V,) needle valve (Vt) stop valve (Vs) pressure control valve (OSC) discharge frequency oscillator (AMP) amplifier (1MC) impedance matching circuit...

SimSim performs a pressure match of measured and calculated reservoir or compartment pressures with an automatic, non-linear optimization technique, called the Nelder-Mead simplex algorithm3. During pressure matching SimSim s parameters (e.g. hydrocarbons in place, aquifer size and eigentime, etc.) are varied in a systematic manner according to the simplex algorithm to achieve pressure match. In mathematical terms the residuals sum of squares (least squares) between measured and calculated pressures is minimized. The parameters to be optimized can be freely selected by the user. 

Figurel depicts the pressure matches and a prediction case with 600 million m3 yearly storage. The Zsana underground gas storage reservoir currently operates well, and contributes to the safe energy supply of the country...

Differential gas adsorption manometry. In the earliest form of this technique (Schlosser, 1959), represented in Figure 3.4, two carefully matched capillaries feed two bulbs (adsorption and reference) from a common reservoir of adsorptive. The pressure difference between the two sides provides a direct measurement of the amount adsorbed on the sample side, provided the gas flow rate through the two capillaries is the same this is no longer true when the difference between the two downstream pressures (on sample side and reference side) is too great For this reason, this technique is limited to downstream pressures lower than, say, 50 mbar. This allows one to determine surface areas by adsorbing Ar at 77 K, but not N2. 

The last differential viscometer design is the Waters Corporation detector [9], which is in the Alliance GPCV2000 high-temperature instrument. It is composed of three capillaries, two differential pressure transducers, and two holdup reservoirs it is represented in Fig. Id. The pressure transducers are connected flow-through this eliminates the need for frequent purges. This detector provides, at the same time, relative viscosity information and relative flow information. This design does not require a perfect matching of the capillaries. 

The first process equipment the incoming reservoir fluid enters after the initial pressure reduction is the primary separator. This unit removes most of the water from the oil, which continues to a secondary and possibly ternary separator (which is often equipped with electrodes to enhance coalescence). Often the primary separator removes all the water, and the other stages are used for pressure reduction and gas removal only. The final goal is to match the specifications of the refineries and/or transport companies. 

A set of hypothetical data shown in Table I was assumed true for an undercompacted, stress-sensitive reservoir whose pressures were to be matched. The match period in all runs was 200 days, at which time a pseudo-steady state condition in the reservoir would have been attained. A single producing well was located at the center of the reservoir and was allowed to produce for 200 days. The drawdown data for the 200 days were then matched. Two sets of simulated drawdown data were used. One set was obtained assuming there was no measurement error in the data and another set was obtained with 0.20 percent measurement error. Reservoir permeability and porosity were separately and jointly estimated, and pressure prediction for an additional 60 days was obtained. The confidence limits of the point estimates and the predicted performance (pressure) data at 95 percent confidence level were then calculated. The results are presented as follows ... 

---