Material Balance by Joo

The reservoir is treated as a tank at uniform pressure. The tool finds the in-place volume and drive parameters that best reproduce the observed pressure history: it marches the material balance equation forward month by month, solving for pressure at each step, and regresses the parameters to minimise the difference between modelled and measured pressure (RMSE).

Five regions, from top to bottom.

The tool opens with example data already loaded and solved. Replacing it with your own case goes like this.

Listed in sidebar order. The names in these tables match the labels on screen exactly.

4.1 Model Identification global

A single field: the model name. It appears in the title-bar chip, as the printed report heading, and in the exported CSV filename. When used as a filename, anything other than letters, digits, . and - becomes _.

4.2 Tanks per tank

+ Tank adds a tank by splitting the largest existing share in half and copying Pi from the current tank. The × on a chip removes a tank, returns its share to the first tank, and deletes any connections that referenced it. At least one tank must remain.

4.3 Tank Connections shown only with 2+ tanks

Flow between two tanks is proportional to their pressure difference.

+ Add connection adds a row; pick the two tanks and enter T. Selecting the same tank on both sides is corrected automatically. T = 0 is equivalent to no connection. If you create no connections at all, the tanks are solved as fully independent compartments and the tool warns you.

4.4 Fluid & PVT shared by all tanks

Derived Bgi and Derived Bob are not inputs — they are read-outs computed from the values above. If Bgi looks wrong, suspect the temperature or z.

4.5 Drive Mechanism per tank

Swc, cf and cw together form the rock and connate-water expansion term.

With all three at zero the term disappears. They default to zero so that the built-in examples reproduce exactly. In real data this term matters more the more undersaturated the reservoir is.

4.6 Aquifer per tank

Each tank can carry a different aquifer model. Changing the model shows only the inputs that model needs, and rebuilds the regression parameter list to match.

Inputs by model

θ is the fraction of the reservoir's circumference in contact with the aquifer: 360° for a fully surrounded reservoir, 60° for contact along one flank. Carter–Tracy influx scales directly with θ, so this single value is a strong lever on aquifer strength.

4.7 History Match Regression

Tick the parameters you want fitted. The list rebuilds itself according to the number of tanks, the fluid mode and each tank's aquifer model. Section 6 covers it in full.

4.8 Forecast Assumptions

5.1 Typing into the table

The columns of the Production History tab:

What makes a row count

• The date is filled in.
• At least one tank pressure is a number greater than zero.

You need three or more such rows before the tool will solve. The number beside the tab title and history rows in the status bar both show how many rows are actually being recognised.

Buttons under the table: + Add row appends a blank row, Load sample reloads the example data, Clear all empties the table. The × at the end of each row deletes it.

5.2 Importing CSV

Use File → Import History from CSV…. No header row is needed — only lines that begin with a YYYY-MM-DD date are read and everything else is skipped, so you can feed it an existing report and it will pick out just the history rows.

6.1 Two ways to run

N is always regressed, in both cases. Unticking it does not fix it — in a material balance, N is a quantity determined by the observed pressures, not one you specify.

6.2 What can be regressed

With several tanks the list is grouped per tank, each group headed by that tank's colour dot. When the regression finishes, the fitted values are written back into the sidebar, so what is on screen always describes the model that is plotted.

6.3 Judging the match

The KPI History match RMSE is the sole objective function: the root-mean-square residual over every (date × tank) pair that has an observed pressure, in psi.

6.4 How the solver works

• Nelder–Mead simplex. Every parameter is handled in log space, which keeps it positive.
• Iteration cap is min(600, 150 + 120 × number of parameters); convergence tolerance 1e-6.
• During regression only the history interval is simulated — the forecast adds run time without contributing to the objective.
• Elapsed time and the number of fitted parameters are reported in the panel afterwards.

7.1 The five KPIs

7.2 The two charts

Pressure History Match overlays observed pressure (dashed with markers), modelled pressure, and the forecast. Wherever the two visibly separate is where the model fails to explain the data.

Cumulative Production joins history and forecast into one curve — cumulative oil in oil mode, cumulative gas in dry-gas mode.

Both charts show a crosshair and a value tooltip on hover.

7.3 The five tabs

The View menu jumps to Production History, Match Diagnostics, Forecast and Diagnostic Plot. Open the Tanks tab by clicking it in the tab bar.

7.4 Forecast status values

7.5 Drive indices

The fraction of voidage supplied by each energy source at a given time. The five values sum to 1.

The Dominant drive column in Match Diagnostics names the largest contributor at that date, or — when nothing exceeds 2%.

Chosen from the Plot selector in the Diagnostic Plot tab. With several tanks a tank selector appears beside it. Every plot carries a paragraph underneath explaining how to read it.

8.1 Havlena–Odeh straight line oil mode

Total expansion Eₜ (rb/stb) on the x-axis; withdrawal with water influx and tank transfer removed, F − Wₑ − X (MMrb), on the y-axis.

Points curving upward mean there is energy the model has not accounted for; curving downward means the aquifer has been overestimated.

8.2 p/z plot dry-gas mode

In dry-gas mode the first option becomes this plot: cumulative gas Gp (Bscf) against p/z (psia).

A purely volumetric gas tank plots as a straight line whose x-intercept is GIIP. Points above that line indicate aquifer support.

8.3 Campbell / Cole — aquifer diagnostic

The most practical test for whether an aquifer exists at all. Cumulative production on the x-axis; F/Eₜ, evaluated at observed pressures assuming no aquifer, on the y-axis.

• Horizontal → purely volumetric. Set the aquifer model to None.
• Rising → energy entering that depletion alone cannot explain: there is aquifer support.
• Falling → re-check the in-place volume and the PVT inputs.

The dashed horizontal line marks the fitted N (G for gas), giving you a reference to compare against.

8.4 Drive index history

The five drive indices from 7.5, stacked as cumulative areas over time. The thickness of each band is its contribution at that moment. Bands that contribute essentially nothing are omitted entirely.

Depletion dominating early and water influx taking over later is the classic signature of an aquifer-supported reservoir.

8.5 Water influx vs. time

Cumulative water influx Wₑ (solid) against cumulative produced water converted to reservoir conditions, Wp·Bw (dashed).

The crossing point matters: once water production catches up with influx, the aquifer stops adding net support and the pressure decline steepens.

8.6 Inter-tank transfer multi-tank only

Cumulative net volume received per tank (MMrb). Positive means the tank is being supported by its neighbours, negative that it is feeding them. The curves always sum to zero — transfer moves volume around, it never creates it.

8.7 Production share history multi-tank only

Each tank's share of field production, stacked as areas. Fixed through the history at the values you entered, then stepping up during the forecast as tanks reach abandonment and come off line. With reallocation switched off, the bands stay flat throughout.

Use separate tanks for compartmentalised reservoirs, fault-separated blocks, or regions whose pressure behaviour is clearly different. All tank pressures are solved as one coupled system by Newton iteration at every time step.

9.1 Building one

1. Add tanks with + Tank (⌥K) in the Tanks panel.
2. Click a tank chip to select it, then set its name, Pi and production share. Make sure Allocation total reads 100%.
3. Set Drive Mechanism and Aquifer separately for each tank — the badge beside the panel title shows which tank you are editing.
4. Add connections in Tank Connections and enter T for each.
5. The history table now has one pressure column per tank; enter the observed pressures for each.

9.2 Things to watch

• A tank with no pressure data has no resolvable in-place volume. Every tank needs at least a few observed pressures.
• With no connections the tanks are independent compartments. That still solves, but if that is really the case, separate models would be clearer.
• More tanks means more free parameters, and non-uniqueness gets much worse very quickly. Go beyond two or three compartments only with good reason.
• PVT is shared across all tanks. If fluid properties differ substantially between compartments, the case is outside this tool's scope.

10.1 CSV ⌥S

Available once the analysis has been run at least once. One file, several blocks in order:

The file is named 〈model name〉-report.csv.

10.2 PDF report ⌘P

The Report button, or File → Print Report / PDF. If the model has not been solved yet it runs once first, then opens the print dialog. The print layout hides the sidebar and menus and adds a heading carrying the model name. Choose “Save as PDF” as the destination in your browser's print dialog.

11.1 Shortcuts

On Windows and Linux, use Alt in place of ⌥ and Ctrl+P in place of ⌘P.

11.2 Every menu item

These appear in the Data quality checks box at the top of the stage. The calculation still runs when a warning is shown — except for the row-count check — but every one of them bears on how much you should trust the answer.

13.1 Governing equations

Both fluid modes use the same generalised material balance.

13.2 PVT correlations

z is constant across the whole history. In high-pressure gas reservoirs, where z varies significantly with pressure, this approximation introduces error.

13.3 Time marching

For every aquifer model except Pot, water influx is path dependent: how the pressure got here determines the influx now. That rules out inverting each row in closed form, so the solution is marched forward in time instead.

• The grid is monthly (one month = 30.4375 days). History dates off the grid are inserted as extra steps.
• Cumulative production between grid points is linearly interpolated from the history data.
• A single tank is solved by bisection on the pressure residual; multiple tanks are solved simultaneously by Newton iteration.
• Pressure is floored at 20 psia for physical reasons.

13.4 Aquifer equations

The dimensionless pressure P_D and its derivative use the Edwardson polynomial approximations. For screening purposes Fetkovich does not allow counter-flow — water never flows back into the aquifer.

13.5 Assumptions worth knowing

• Pressure inside a tank is always uniform. No gradients, no flow lag.
• PVT is shared by all tanks and z is constant.
• The producing gas–oil ratio Rp is derived from the cumulative oil and gas you enter.
• Forecast rates are constant. There is no decline curve and no well-level control.
• Relative permeability, coning and gravity segregation are not modelled at all.