Building a simulation model: input data and results

We build a model for a question: which decision it must support, which process it must reproduce, and what accuracy is enough for that (the stages of working with a model, Types of reservoir simulation model). The question decides what goes into the input data. The lesson on the reservoir simulation model lists the data and their sources. Here another point matters: the form in which the data reach the simulator.

Other programs, called preprocessors, prepare most of the data. They build the grid and the cell properties from the geological model and transfer them to the simulation grid (Permeability upscaling for single-phase flow). They make the PVT tables from laboratory analyses of samples (Laboratory PVT tests, How to read a PVT report), and the tables of relative permeability and capillary pressure from special core analysis (Petrophysical input for simulation: relative permeability and capillary pressure). They take the well completions from the trajectories and the perforation data. They take the history schedule from the field production database (the data for history matching). They calculate the tubing pressure-loss tables from multiphase flow in pipes (Multiphase flow in tubing). Arrays for hundreds of thousands or millions of cells are stored in separate files, and one line attaches each of them to the main deck.

We write an array in a fixed order of cells. The $x$ index ($i$) changes fastest, then the $y$ index ($j$), and the layer number ($k$) changes most slowly. Cell $(i, j, k)$ of an $N_x \times N_y \times N_z$ grid stands at position $i + (j - 1)N_x + (k - 1)N_xN_y$ in the array. In the $10\times8\times3$ grid of the lesson, cell $(10, 4, 2)$ is number 120 ($10 + 3\cdot10 + 1\cdot80$). A mistake in the order, for example listing the layers from the bottom up, gives no error message but shuffles the properties.

The input formats of simulators differ, but they are built in the same way: the file is divided into sections that come in a strict order. Below, each section has a name that says what it holds, and in brackets the name used in the common keyword format. Over the decades this format has become the standard of the industry in practice (a de facto standard). Many commercial and open-source simulators read it, so it is useful to know even if you work in another program.

The order of the sections follows what depends on what. We cannot specify the porosity until the dimensions of the grid are known. We cannot calculate the initial equilibrium until the capillary pressure and density tables have been read. We cannot run wells until the initial pressure is known. Inside the schedule, the events follow by date: everything written before the next date or step takes effect from that moment.

For a simple Cartesian grid (a grid of rectangular boxes), we give the cell sizes and the depth of the top of the upper layer. The simulator finds the depths of the other layers by adding the thicknesses. For a grid of complex structure, we transfer the geometry from the geological model in corner-point form: the coordinates of the pillars (the lines along which the cell corners lie) and the depths of the corners of each cell (types of grid). We exclude cells outside the reservoir and cells with a negligible pore volume, either with an activity array (a list that marks each cell active or inactive) or with a threshold on the minimum pore volume. The threshold is convenient but dangerous: it can discard thin oil-bearing streaks, and you see this only when you check the pore volume.

We give the permeability in three directions. In the common format, the net-to-gross ratio reduces not only the pore volume but also the transmissibility between cells in the horizontal direction. It does not reduce it in the vertical direction. So we give the vertical permeability already averaged over the whole thickness of the cell, together with the shale interbeds. We use the harmonic average if the interbeds are continuous (averaging over layers). We represent impermeable interbeds and faults by transmissibility multipliers (history-matching parameters). For faults that shift the layers, the simulator finds the connections across the fault itself, from the corner-point geometry.

There are two ways to specify aquifer water, the water that flows in from the water-bearing rock around the reservoir (Aquifer models: water influx). An analytical aquifer is an influx model (Fetkovich, Carter–Tracy; Simplified water influx models: Fetkovich and Carter–Tracy) attached to the faces of the boundary cells. The data give the size and properties of the aquifer and the cells it is connected to. A numerical aquifer is a set of extra grid cells beyond the oil outline, with a large pore volume. We usually refine the aquifer parameters from the pressure history (History matching of aquifer parameters).

In a black oil model (Black oil model: solution gas–oil ratio and formation volume factors) we give the fluid properties as tables against pressure. For oil with dissolved gas, the table runs against the solution gas–oil ratio: for each $R_s$ it gives the bubble point pressure (the pressure at which gas starts to come out of the oil), the formation volume factor and the viscosity. For undersaturated oil (oil above its bubble point) it adds a few more rows at pressures above the bubble point pressure. If the reservoir pressure will never fall below the bubble point pressure, the solution gas–oil ratio stays constant, and we can describe the oil more simply: a table of the formation volume factor and viscosity against pressure, as “dead” oil (oil without dissolved gas). We describe water by a single record: the formation volume factor and viscosity at the reference pressure, and the compressibility. The tables must cover the whole range of pressures of the run. Outside the table the simulator extrapolates (extends the last trend), and the result loses its meaning.

We give the curves of relative permeability and capillary pressure as tables against saturation, one for each rock type. The lesson on petrophysical data for the model covers how to build and check them. The end points of the curves are the irreducible water and the residual oil (the water and oil that cannot be moved). If they vary from cell to cell, we give them as arrays, and the simulator scales the table of the rock type for each cell (end-point scaling).

We can specify the initial pressures and saturations in three ways. In equilibration, the simulator calculates them itself from the reference pressure, the densities and the contacts. This is the main method. In enumeration, we give the pressure and the saturation as arrays by cell, for example from the saturation derived from logs. Such a state is usually not in capillary equilibrium, so the fluids begin to flow at the very first step. In a restart, we continue the run from the saved state of another run. This is how forecasts begin from the end of the history run (forecast after history matching).

In equilibrium, the simulator finds the oil pressure at any depth from the reference point, using the density of the oil. It finds the water pressure from the contact depth, using the density of the water. The difference between them is the capillary pressure, and from it the simulator reads the saturation in the table of the region. The contact depth in the input data is the depth where the capillary pressure equals the specified value, usually zero. This is the free water level (FWL), the level where the oil and water pressures are equal. The OWC from logs is the first mark where water fills the pores completely. It lies above the FWL by a height that matches the entry pressure of the rock, the pressure the oil needs to enter the largest pores (FWL and OWC, transition zone).

The simplest method is to take the saturation at the centre of the cell, as in the example. Near a contact, a thick cell then loses or gains oil. Layer 3 lost all the transition-zone oil, while layer 2 gained a little: the saturation at its centre is lower than the average over the thickness, because the curve $S_w(h)$ is convex. Thin layers at the contact help, and so does averaging the saturation over several sublayers of each cell. The initialisation data say which method applies. We must know it, because different simulators have different defaults. An averaged saturation does not match the capillary pressure at the centre of the cell, so a check of equilibrium is especially important after it.

For each well the deck gives the name and group, the position in the grid, the depth to which the bottomhole pressure is referred and the main phase. Then it gives the completed cells: an interval of layers or the cells along the trajectory, the state (open, shut), the wellbore diameter and the skin factor. The simulator calculates the connection factor between a cell and the well itself (the number that links the well rate to the pressure difference between the cell and the well). It uses the permeability and net thickness of the cell and the Peaceman equivalent radius, the radius at which the pressure of the flow towards the well matches the pressure of the cell (well index). We set the factor by hand only for special reasons, for example for a hydraulic fracture.

The control of a well is a target and limits (well controls in the model). For example: a liquid rate with a lower limit on the bottomhole pressure, or an injection rate with an upper limit. In a history run, we give the wells the actual oil, water and gas rates, and we choose which quantity the model must honour (keep exactly), usually the liquid rate or the withdrawal at reservoir conditions (what the model is compared with). In a forecast, we set the targets and limits of wells and groups, together with voidage replacement (injecting as much as is withdrawn, measured at reservoir conditions) and economic limits. When the oil rate falls below a given value, or the water cut rises above a given one, the well is shut in or the watered-out intervals are closed off.

We divide the time in the schedule into report steps, given as dates or step lengths. At these moments the controls change and the results are written. The simulator chooses the calculation steps itself. It starts with a small step, makes it longer while the iterations converge quickly, and cuts it when they do not (step selection). So we set the report steps by the needs of the analysis, and not finer “for accuracy”.

The results of a run are of three kinds. The message file records the course of the calculation: errors in reading the data, warnings, switches of well controls, cuts in the time step, material balance errors, and reports of volumes in place by region at the start and at given dates. Time series (summary vectors, often called simply vectors) give rates, cumulative volumes, pressures, water cut and producing gas–oil ratio for the field, groups, wells, individual completions and regions. We plot them as graphs and use them to compare the model with the facts. Arrays by cell give the pressures and saturations at chosen dates, and the properties of the cells at the start (pore volumes, transmissibilities, depths). We use them for maps and cross-sections, and a restart begins from them.

Arrays by cell are large: each write date adds several numbers for each cell, and for large models the results files are measured in gigabytes. So we write arrays only for the dates we need for maps, for comparison with measurements and for restarts. Time series are cheap, so we ask for more than we need. A series that we did not write cannot be recovered after the run, and we would have to repeat the run.