Reservoir simulation

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. 

The number and shape of the grid blocks in the model depend upon the objectives of the simulation. A 100 grid block model may be sufficient to confirm rate dependent processes described in the previous section, but a full field simulation to be used to optimise well locations and perforation intervals for a large field may contain up to 100,000 grid blocks. The larger the model, the more time consuming to build, and slower to run on the computer. 

The amount of detail input, and the type of simulation model depend upon the issues to be investigated, and the amount of data available. At the exploration and appraisal stage it would be unusual to create a simulation model, since the lack of data make simpler methods cheaper and as reliable. Simulation models are typically constructed at the field development planning stage of a field life, and are continually updated and increased in detail as more information becomes available. 

At the field development planning stage, reservoir simulation may be used to look at questions such as  

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). 

---

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... 

Keywords compressibility, primary-, secondary- and enhanced oil-recovery, drive mechanisms (solution gas-, gas cap-, water-drive), secondary gas cap, first production date, build-up period, plateau period, production decline, water cut, Darcy s law, recovery factor, sweep efficiency, by-passing of oil, residual oil, relative permeability, production forecasts, offtake rate, coning, cusping, horizontal wells, reservoir simulation, material balance, rate dependent processes, pre-drilling. 

Figure 8.18 Typical grid block configurations for reservoir simulation...

Analytical models using classical reservoir engineering techniques such as material balance, aquifer modelling and displacement calculations can be used in combination with field and laboratory data to estimate recovery factors for specific situations. These methods are most applicable when there is limited data, time and resources, and would be sufficient for most exploration and early appraisal decisions. However, when the development planning stage is reached, it is becoming common practice to build a reservoir simulation model, which allows more sensitivities to be considered in a shorter time frame. The typical sorts of questions addressed by reservoir simulations are listed in Section 8.5. 

The most reliable way of generating production profiles, and investigating the sensitivity to well location, perforation interval, surface facilities constraints, etc., is through reservoir simulation. 

The type of development, type and number of development wells, recovery factor and production profile are all inter-linked. Their dependency may be estimated using the above approach, but lends itself to the techniques of reservoir simulation introduced in Section 8.4. There is never an obvious single development plan for a field, and the optimum plan also involves the cost of the surface facilities required. The decision as to which development plan is the best is usually based on the economic criterion of profitability. Figure 9.1 represents a series of calculations, aimed at determining the optimum development plan (the one with the highest net present value, as defined in Section 13). 

At the stage of field development planning, reservoir simulation would normally be used to generate production profiles and well requirements for a number of subsurface development options, for each of which different surface development options would be evaluated and costs estimated. 

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). 

Reservoir pressure is measured in selected wells using either permanent or nonpermanent bottom hole pressure gauges or wireline tools in new wells (RFT, MDT, see Section 5.3.5) to determine the profile of the pressure depletion in the reservoir. The pressures indicate the continuity of the reservoir, and the connectivity of sand layers and are used in material balance calculations and in the reservoir simulation model to confirm the volume of the fluids in the reservoir and the natural influx of water from the aquifer. The following example shows an RFT pressure plot from a development well in a field which has been producing for some time. 

During the design phase, facilities (the hardware items of equipment) are designed for operating conditions which are anticipated based upon the information gathered during field appraisal, and upon the outcome of studies such as the reservoir simulation. The design parameters will typically be based upon assessments of... 

The above example is a simple one, and it can be seen that the individual items form part of the chain in the production system, in which the items are dependent on each other. For example, the operating pressure and temperature of the separators will determine the inlet conditions for the export pump. System modelling may be performed to determine the impact of a change of conditions in one part of the process to the overall system performance. This involves linking together the mathematical simulation of the components, e.g. the reservoir simulation, tubing performance, process simulation, and pipeline behaviour programmes. In this way the dependencies can be modelled, and sensitivities can be performed as calculations prior to implementation. 

Peaceman, D. W. Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam 977). 

Standard programs must be broken into smaller pieces to run on a hypercube. Each processor is assigned the responsibility for calculations for a specific piece of a problem. For example, in petroleum reservoir simulation, each processor might be assigned a different section of the reservoir to model. In modeling a complex chemical plant, each processor might be assigned a different piece of equipment. As each processor proceeds, it informs the other processors of its results, so that all the other processors can incorporate the information into their respective portions of the overall calculation. 

There are several other applications where significant gains could be made through the use of supercomputer simulations of detailed physical models. Reservoir simulations was one of the first areas where the value of supercomputing was recognized by Industrial companies. It Is only possible to measure a few properties of Interest to enhanced oil recovery. Furthermore, field tests are extremely expensive, and the monetary... 

Alkaline/surfactant/polymer compositional reservoir simulator, 3-dimensional compositional reservoir simulator, for high-pH chemical flooding processes [178]... 

D. Bhuyan. Development of an alkaline/sutfactant/polymer compositional reservoir simulator. PhD thesis, Texas Univ, Austin, 1989. 

M. Rame and M. Delshad. A compositional reservoir simulator on distributed memory parallel computers. In Proceedings Volume, pages 89-100. 13th SPE Reservoir Simulation Symp (San Antonio, TX, 2/12-2/15), 1995. 

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. 

A numerical example for the estimation of unknown parameters in PDE models is provided in Chapter 18 where we discuss automatic history matching of reservoir simulation models. 

History matching in reservoir engineering refers to the process of estimating hydrocarbon reservoir parameters (like porosity and permeability distributions) so that the reservoir simulator matches the observed field data in some optimal fashion. The intention is to use the history matched-model to forecast future behavior of the reservoir under different depletion plans and thus optimize production. 

Furthermore, the implementation of the Gauss-Newton method also incorporated the use of the pseudo-inverse method to avoid instabilities caused by the ill-conditioning of matrix A as discussed in Chapter 8. In reservoir simulation this may occur for example when a parameter zone is outside the drainage radius of a well and is therefore not observable from the well data. Most importantly, in order to realize substantial savings in computation time, the sequential computation of the sensitivity coefficients discussed in detail in Section 10.3.1 was implemented. Finally, the numerical integration procedure that was used was a fully implicit one to ensure stability and convergence over a wide range of parameter estimates. 

This indicates that after an initial overhead of 0.319 model runs to set up the algorithm, an additional 0.07 of a model-run was required for the computation of the sensitivity coefficients for each additional parameter. This is about 14 times less compared to the one additional model-run required by the standard implementation of the Gauss-Newton method. Obviously these numbers serve only as a guideline however, the computational savings realized through the efficient integration of the sensitivity ODEs are expected to be very significant whenever an implicit or semi-implicit reservoir simulator is involved. 

It is of interest in a reservoir simulation study to compute future production levels of the history matched reservoir under alternative depletion plans. In addition, the sensitivity of the anticipated performance to different reservoir descriptions is also evaluated. Such studies contribute towards assessing the risk associated with a particular depletion plan. 

Free-flowing stream reaches and reservoirs, simulated by the RCHRES module. 

Oldenburg C. and Pmess K. EOS7C Gas reservoir simulation for THOUGH2. 2000 Lawrence Berkeley National Laboratory Report, LBNL. 

Kumar A., Noh M., et al. Reservoir simulation of C02 storage in deep saline aquifers. 2004 SPE/DOE Fourteenth Symposium on Improved Oil Recovery, Tulsa, USA(89343). 

Zhang K., W.Y.S., et al. Parallel computing techniques for large-scale reservoir simulation of multi-component and multi-phase fluid flow. In Proceeding of the 2001 SPE reservoir simulation synposium, Texas.2001 SPE. 

---