This paper proposes a distributed continuous aperture array (D CAPA) to support simultaneous wireless information and power transfer (SWIPT) to multiple information users (IUs) and energy users (EUs). Each metasurface supports continuous surface currents that radiate electromagnetic (EM) waves for information and energy transmission to the users. These waves propagate through continuous EM channels characterized by the dyadic Green function. We formulate a system power consumption (PC) minimization problem subject to spectral efficiency and energy harvesting quality of service (QoS) requirements, where the QoS requirements are derived under the equal power allocation (EPA) scheme. An efficient two layer optimization algorithm is developed to solve this problem by optimizing the power allocation subject to the QoS violation penalties using augmented Lagrangian transformation. Our numerical results show that well optimized current distributions over each metasurface in the proposed D CAPA achieve up to 65% and 61% reductions in overall system PC compared to the EPA and colocated CAPA (C CAPA) cases, while maintaining the same total aperture size and transmission power.