Closed-Loop Deposition Coupling

neqsim.process.chemistry.scale.ClosedLoopDepositionSolver couples PipeBeggsAndBrills pipe hydraulics with ScaleDepositionAccumulator so the deposition rate, velocity and effective inside diameter stay mutually consistent. Without coupling, deposition is computed at the clean velocity and over-predicts thinning; with coupling, the velocity rises as the ID shrinks and the system finds a quasi-steady deposition rate.

Why couple?

Scale deposition rate scales roughly as

\[\dot{m}_{dep} \;\propto\; SI \cdot v^{\alpha} \cdot t,\qquad \alpha \in [0.5, 1.5]\]

while velocity in a pipe of effective diameter $d_{eff}$ goes as $v \propto 1/d_{eff}^2$. A naive sequential calculation ignores that the shrinking diameter feeds back into the velocity term — producing an unphysical exponential collapse. The closed-loop solver iterates the two models until $|d_{eff}^{(k+1)} - d_{eff}^{(k)}| < \mathrm{tol}$.

API

PipeBeggsAndBrills pipe = new PipeBeggsAndBrills("Tieback", inletStream);
pipe.setLength(1000.0);
pipe.setDiameter(0.20);
pipe.setElevation(0.0);

ScaleDepositionAccumulator deposition = new ScaleDepositionAccumulator()
    .setBrineChemistry(1500.0, 400.0, 100.0, 5.0, 12000.0, 35000.0)
    .setExposureTimeS(30.0 * 24 * 3600.0);   // 30 days

ClosedLoopDepositionSolver solver = new ClosedLoopDepositionSolver(pipe, deposition)
    .setToleranceM(1.0e-4)
    .setMaxIterations(15)
    .solve();

int    its       = solver.getIterationsTaken();
double dEffFinal = solver.getFinalEffectiveDiameterM();
List<Double> velocityHistory = solver.getVelocityHistoryMs();
List<Double> diameterHistory = solver.getDiameterHistoryM();

Inputs

The solver consumes a configured PipeBeggsAndBrills and a ScaleDepositionAccumulator. The accumulator owns the brine chemistry:

Setter Units Notes
setBrineChemistry(Ca, HCO3, SO4, Ba, Mg, TDS) mg/L (× 6) Six-argument signature — order matters
setExposureTimeS(t) s Cumulative time over which the steady-state rate is integrated

The solver itself only owns numerical controls:

Setter Default Meaning
setToleranceM(tol) 1.0e-4 Convergence criterion on $d_{eff}$
setMaxIterations(n) 10 Iteration cap before bailout

Algorithm

Each iteration $k$:

  1. Run pipe.run() with the current effectiveDiameter to obtain $v^{(k)}$ and $\tau_w^{(k)}$.
  2. Pass these into deposition.evaluate() and read the deposition mass per segment.
  3. Convert mass to a uniform thickness using $\rho_{scale} = 2700$ kg/m³ (calcite default), update $d_{eff}$.
  4. Check convergence; if not converged, repeat.

The diameter and velocity at every iteration are stored in getDiameterHistoryM() / getVelocityHistoryMs() for diagnostics.

Worked example — 30-day scaling forecast on a subsea tieback

A 1 km × 0.20 m subsea tieback carries produced water with 1500 mg/L Ca, 400 mg/L HCO3, 100 mg/L SO4 at 35 °C. Forecast ID and velocity drift over 30 days:

SystemInterface fluid = new SystemSrkEos(308.15, 80.0);
fluid.addComponent("methane", 0.05);
fluid.addComponent("CO2", 0.05);
fluid.addComponent("water", 0.90);
fluid.setMixingRule("classic");
Stream feed = new Stream("feed", fluid);
feed.setFlowRate(50000.0, "kg/hr");
feed.run();

PipeBeggsAndBrills pipe = new PipeBeggsAndBrills("Tieback", feed);
pipe.setLength(1000.0);
pipe.setDiameter(0.20);

ScaleDepositionAccumulator dep = new ScaleDepositionAccumulator()
    .setBrineChemistry(1500.0, 400.0, 100.0, 5.0, 12000.0, 35000.0)
    .setExposureTimeS(30.0 * 24 * 3600.0);

ClosedLoopDepositionSolver solver =
    new ClosedLoopDepositionSolver(pipe, dep).solve();

System.out.printf("Iterations: %d%n", solver.getIterationsTaken());
System.out.printf("Effective ID after 30 days: %.4f m%n",
    solver.getFinalEffectiveDiameterM());

Typical output:

Iterations: 5
Effective ID after 30 days: 0.1872 m  (6.4 % reduction)

A 6 % ID reduction in 30 days corresponds to a roughly 27 % rise in pressure drop ($\Delta P \propto 1/d^4$ in the turbulent friction-dominated limit). Compare this with allowable backpressure and decide on inhibition strategy.

Failure modes and diagnostics

Symptom Likely cause Remedy
getIterationsTaken() == maxIterations Tolerance too tight or runaway deposition Loosen tol, shorten setExposureTimeS, or check brine chemistry
Final ID equals initial ID Brine undersaturated (SI ≤ 0) Verify setBrineChemistry arguments; check pH and CO2 partial pressure inside the accumulator
Final ID collapses to zero Exposure time longer than time-to-blockage Use a shorter integration window and march forward in steps

Standards traceability

Aspect Standard
Pipeline hydraulics API RP 14E (erosional velocity)
Scale formation potential NACE TM0374
Wall-loss / wall-gain integrity tracking NACE SP0775
Inspection planning intervals API 570

Validation

Regression-tested in ChemistryCoupledModelsTest. The test suite covers under- and oversaturated brines, low- and high-velocity pipes, and verifies monotone diameter contraction and convergence within ≤ 10 iterations for typical NACE TM0374 reference brines.