# Multi-well Numerical Model

This module closely mirrors the single-well numerical model module, essentially adhering to the same fundamental principles. The primary distinction lies in its capacity to enable users to incorporate either a single well or multiple well within a single numerical model.

Fig. 1: Multi-well Model

## 1. Assumptions

### 1.1 Model Design

#### 1.1.1 Symmetry element

Fig. 2: Birds Eye View

Fig. 3: Gun Barrel View

In accordance with the *symmetry element* approach, it is assumed that all wells within the model have ** the same number of fractures**. This assumption makes it possible to model a half-fracture for all wells as illustrated in

**Fig. 2**and

**Fig. 3**. The scaling factor will subsequently be employed to adjust the production performances as defined below

#### 1.1.2 Fracture half-length

Each individual well can have different fracture half-lengths \(\left(x_f\right)\) and heights \(\left(h_f\right)\). The software allows user to have overlapping fractures in the same or different layer between adjacent wells as shown in **Fig.4**.

Fig. 4: Overlapping Fractures

#### 1.1.3 Enhanced Fracture Region (EFR) Option

This option is **not** supported by the current version of multi-well numerical model.

#### 1.1.4 Gridding

The numerical model utilizes logarithmic gridding for the matrix area between hydraulic fractures within the same well, i.e. along y-axis, while maintaining a uniform grid pattern along the x-axis, as visually depicted in **Fig.5**.

Fig. 5: Gridding of Numerical Model

The number of grid blocks is determined the same manner to that of the single-well numerical model. Here, users are provided with five levels of grid refinement: very low, low, medium, high and very high. *Very High* option is best capturing the details but compromised by expensive simulation run time. Conversely, selecting *Very Low* option yields the shortest simulation run time but may potentially lose some detail in the simulation outcomes.

## 2. Input

Fig. 6: Multi-well Numerical Model in whitson+

### 2.1 Reservoir Data

Reservoir height \(\left(h_f\right)\), matrix permeability \(\left(k_m\right)\), matrix porosity \(\left(\phi_m\right)\), rock compressibility \(\left(c_r\right)\), fracture \(\left(\gamma_f\right)\) and matrix gamma \(\left(\gamma_m\right)\) are entered through this data card. The model can be configured as a single- or multi-layer system as depicted in **Fig. 7**.

Fig. 7: Reservoir Data Input

### 2.2 Well & Fracture Data

This data card allows user to input all properties related to well and fractures. Well lateral length \(\left(L_w\right)\), number of fractures \(\left(N_f\right)\), and dimensionless fracture conductivity \(\left(F_{cd}\right)\) are properties applicable to all wells. Properties for each well includes:

**Linked Well**: to honor historical data associated with a specific well within the project.**Synthetic Well**: to create a synthetic well. This designated well name serves a role for plotting and visualization purposes.**Distance to Next Well (ft)**: well spacing between two individual wells.**Fracture Half Length (ft)**: presumed to be uniform for both left and right \(x_f\).**Perforated Layer**: landed layer.**Fractured Layers**: may span across multiple layers.**\(A\sqrt{k}\)**: automatically calculated by the software.

Fig. 8: Well & Fracture Data Input

### 2.3 Fluid Initialization

This feature offers both single and multi-layer fluid initialization options, seamlessly integrated with PVT characteristics of a designated well. The requirement is to input initial GOR \(\left(R_{ti}\right)\), initial water saturation \(\left(S_{wi}\right)\) and initial reservoir pressure \(\left(p_i\right)\). While for initial solution GOR \(\left(R_s\right)\), initial solution CGR \(\left(r_s\right)\), oil \(\left(S_o\right)\) and gas saturation \(\left(S_g\right)\), and saturation pressure \(\left(p_{sat}\right)\) are calculated by incorporating black oil table and initial GOR, ensuring accuracy and reliability in the modelling process.

Fig. 9: Fluid Initialization Input

### 2.4 Relative Permeability

The numerical model incorporates a single set of matrix and fracture permeability.

Fig. 10: Relative Permeability Input

### 2.5 Well Schedule

There are six well control options:

- Oil
- Gas
- Water
- Liquid
- BHP
- BHP (synthetic)

Fig. 11: Well Schedule Input

### 2.6 Case Examples

Below are three case examples that demonstrate how to configure and run the model in whitson+:

**Case 1 - Linked Wells**: Model three SPE Data Repository wells and use production data as well schedule control.**Case 2 - Synthetic Wells**: Model two synthetic wells.**Case 3 - Combination**: Model two SPE Data Repository wells and a synthetic well.

#### 2.6.1 Case 1 - Linked Wells

Fig. 12: Example Case 1

#### 2.6.2 Case 2 - Synthetic Wells

Fig. 13: Example Case 2

#### 2.6.3 Case 3 - Combination

Fig. 14: Example Case 3