# Theis Confined Aquifer Multi-Well Pumping & Recovery Superposition

> Theis Confined Aquifer Multi-Well Pumping & Recovery Superposition is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Computes explicit drawdown and recovery at arbitrary observation points in a confined aquifer by superposing Theis solutions across multiple pumping wells with piecewise-constant pumping rate histories.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/theis-confined-aquifer-multiwell-pumping-recovery-superposition?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/theis-confined-aquifer-multi-well-pumping-recovery-superposition-572abb4e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_t2iDnWz_Lr27IJuEBOIMM

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability theis-confined-aquifer-multi-well-pumping-recovery-superposition-572abb4e -d '<json body>'
```

Example prompt: Calculate the drawdown superposition in a confined aquifer with transmissivity 500 m²/day and storativity 0.0001, with two pumping wells at positions (0,0) and (200,0) — the first pumping at a rate change of 1000 m³/day starting at t=0, the second at 500 m³/day starting at t=1000 — and give me the drawdown at observation point (100,50) at time t=5000 days.

## When to prefer this

Use this endpoint when you need analytically exact drawdown or recovery calculations in a homogeneous, isotropic confined aquifer under the Theis assumptions, especially for multi-well interference or stepped pumping histories. Prefer this over numerical groundwater models when the aquifer is confined, laterally infinite, and you need fast, deterministic answers without discretizing a grid. Best suited for pumping test analysis, wellfield design screening, and regulatory drawdown estimation.

## Known failure modes

- Transmissivity or storativity out of allowed range returns validation error
- Well or query positions outside ±10000 coordinate bounds rejected
- More than 16 wells or 32 pumping steps per well exceeds schema limits
- More than 32 query points per request returns error
- Zero or negative transmissivity causes numerical instability
- Query time of zero with active pumping may produce undefined Theis function value
- Malformed artifact/claim structure causes request rejection

## How this service works

Compute explicit pumping and recovery drawdown superposition in an ideal aquifer.

## Output

Returns superposed drawdown values (in meters or consistent units) at each queried observation position and time, computed by applying the Theis well function to each pumping step of each well and summing contributions via the principle of superposition, including both pumping-induced drawdown and recovery phases.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "theis"
   ],
   "properties": {
    "theis": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "transmissivity",
        "storativity",
        "wells",
        "queries"
       ],
       "properties": {
        "wells": {
         "type": "array",
         "items": {
          "type": "object",
          "required": [
           "position",
           "pumping_steps"
          ],
          "properties": {
           "position": {
            "type": "array",
            "items": {
             "type": "number",
             "maximum": 10000,
             "minimum": -10000
            },
            "maxItems": 2,
            "minItems": 2
           },
           "pumping_steps": {
            "type": "array",
            "items": {
             "type": "object",
             "required": [
              "time",
              "rate_change"
             ],
             "properties": {
              "time": {
               "type": "number",
               "maximum": 100000000,
               "minimum": 0
              },
              "rate_change": {
               "type": "number",
               "maximum": 10000,
               "minimum": -10000
              }
             },
             "additionalProperties": false
            },
            "maxItems": 32,
            "minItems": 1
           }
          },
          "additionalProperties": false
         },
         "maxItems": 16,
         "minItems": 1
        },
        "queries": {
         "type": "array",
         "items": {
          "type": "object",
          "required": [
           "position",
           "time"
          ],
          "properties": {
           "time": {
            "type": "number",
            "maximum": 100000000,
            "minimum": 0
           },
           "position": {
            "type": "array",
            "items": {
             "type": "number",
             "maximum": 10000,
             "minimum": -10000
            },
            "maxItems": 2,
            "minItems": 2
           }
          },
          "additionalProperties": false
         },
         "maxItems": 32,
         "minItems": 1
        },
        "storativity": {
         "type": "number",
         "maximum": 1,
         "minimum": 1e-8
        },
        "transmissivity": 
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/theis-confined-aquifer-multi-well-pumping-recovery-superposition-572abb4e/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)