In shale reservoirs, efficient hydrocarbon extraction relies on the Stimulated Reservoir Volume (SRV) created by hydraulic fracturing. This study develops and applies direct analytical equations to determine the degree of fracture interconnection in a three-horizontal-well system using transient pressure and flow rate analysis with the TDS technique. The equations estimate permeability, area, and the epsilon (ε) parameter, representing the fracture interconnection fraction. They are applied to both pressure drawdown and buildup tests, as well as transient rate analysis in oil and gas wells. These equations were successfully verified using synthetic data, demonstrating their accuracy and usefulness. The methodology effectively identifies fracture interconnections and their impact on well productivity. This approach enables practical mitigation strategies to prevent rapid depletion of new wells.

Nomenclature: A: Drainage area, ft² ; B: Oil volume factor, rb/STB; c_t : Total compressibility, 1/psi; f_corr: Correction factor; h: Formation thickness, ft; k: SRV Permeability of the Observation Well, md; L_w: Horizontal well length, ft; m(P): Pseudopressure function, psi² /cp; P: Pressure, psi; P_D: Dimensionless pressure; Pi : Initial pressure, psi; P_wf: Well-flowing pressure, psi; q: Oil flow rate, BPD; q_g : Gas flow rate, MSCF/D; 1/q: Reciprocal rate, 1/BPD (oil) or Day/Mscf (gas); r_w: Wellbore radius, ft; t: Time, hrs; t*?P’: Pressure derivative, psi; t*?m(P)’: Pseudopressure derivative, psi2 /cp; t*(1/q’): Reciprocal rate derivative, 1/BPD (oil) or Day/Mscf (gas); tD: Dimensionless time referred to half-fracture length; t_D*P_D’: Dimensionless pressure derivative; t_D*m(P_D’): Dimensionless pseudopressure derivative; t_D*(1/q_D’): Dimensionless reciprocal rate derivative; T: Reservoir temperature, o R; X_D: Dimensionless distance in the x-direction; X_eA: Reservoir half-length at well A, md; X_f : Half-fracture length, md

Subscripts: 1l: first linear flow regime; 1lpssi: Intercept of the straight lines between the first linear flow regime and the pseudosteady-state period; A,B,C: Wells; corr: Correction; D: Dimensionless quantity; g: Gas; i: Initial conditions, intercept; maxd1l: Maximum point of the dimensionless pressure derivative in the downward concavity after the first linear flow regime; mind1l: Minimum point of the dimensionless pressure derivative in the upward concavity after the first linear flow regime; o: Oil; p1qq’: Late time of interception of the reciprocal rate and reciprocal rate derivative; pss: Pseudosteady-state; pss-int: Intercept of the dimensionless pressure derivative line; wf: At well-flowing pressure

Greek: ?: Change, drop; ε: Parameter indicating the degree of connectivity between the neighboring wells B and C with the observation well, well A. (Positive epsilon indicates there is an influx into well A); ?: Porosity, fraction; µ: Viscosity, cp