diff --git a/storage_v2/v1adapter/ptrace_model.go b/storage_v2/v1adapter/ptrace2model.go
similarity index 57%
rename from storage_v2/v1adapter/ptrace_model.go
rename to storage_v2/v1adapter/ptrace2model.go
index 01db4f4816b..dd177a71dab 100644
--- a/storage_v2/v1adapter/ptrace_model.go
+++ b/storage_v2/v1adapter/ptrace2model.go
@@ -4,23 +4,24 @@
 package v1adapter
 
 import (
-	"go.opentelemetry.io/collector/pdata/pcommon"
 	"go.opentelemetry.io/collector/pdata/ptrace"
 
 	"github.com/jaegertracing/jaeger/model"
 	"github.com/jaegertracing/jaeger/pkg/iter"
+	"github.com/jaegertracing/jaeger/storage/spanstore"
 	otel2model "github.com/open-telemetry/opentelemetry-collector-contrib/pkg/translator/jaeger"
 )
 
-// PTracesSeq2ToModel consumes an otel trace iterator and returns a jaeger model trace.
+// PTracesSeq2ToModel consumes an otel trace iterator and returns a model trace.
 //
-// When necessary, it groups chunks of traces into one single trace
+// When necessary, it groups chunks of a trace into a single model trace
 func PTracesSeq2ToModel(seqTrace iter.Seq2[[]ptrace.Traces, error]) ([]*model.Trace, error) {
 	var (
-		jaegerTraces []*model.Trace
-		err error
-		tracesByID map[pcommon.TraceID]*model.Trace
+		err         error
+		lastTraceID *model.TraceID
+		lastTrace   *model.Trace
 	)
+	jaegerTraces := []*model.Trace{}
 
 	seqTrace(func(otelTraces []ptrace.Traces, e error) bool {
 		if e != nil {
@@ -30,14 +31,17 @@ func PTracesSeq2ToModel(seqTrace iter.Seq2[[]ptrace.Traces, error]) ([]*model.Tr
 
 		for _, otelTrace := range otelTraces {
 			spans := modelSpansFromOtelTrace(otelTrace)
-			for _, span := range spans {
-				traceId := span.TraceID.ToOTELTraceID()
-				if _, exists := tracesByID[traceId]; !exists {
-					tracesByID[traceId] = &model.Trace{}
-				}
-				trace := tracesByID[traceId]
-				trace.Spans = append(trace.Spans, span)
-				tracesByID[traceId] = trace
+			if len(spans) == 0 {
+				continue
+			}
+			currentTraceID := spans[0].TraceID
+			if lastTraceID != nil && *lastTraceID == currentTraceID {
+				lastTrace.Spans = append(lastTrace.Spans, spans...)
+			} else {
+				newTrace := &model.Trace{Spans: spans}
+				lastTraceID = &currentTraceID
+				lastTrace = newTrace
+				jaegerTraces = append(jaegerTraces, lastTrace)
 			}
 		}
 		return true
@@ -47,8 +51,8 @@ func PTracesSeq2ToModel(seqTrace iter.Seq2[[]ptrace.Traces, error]) ([]*model.Tr
 		return nil, err
 	}
 
-	for _, trace := range tracesByID {
-		jaegerTraces = append(jaegerTraces, trace)
+	if len(jaegerTraces) == 0 {
+		return nil, spanstore.ErrTraceNotFound
 	}
 	return jaegerTraces, nil
 }
@@ -58,7 +62,10 @@ func modelSpansFromOtelTrace(otelTrace ptrace.Traces) []*model.Span {
 	spans := []*model.Span{}
 	batches := otel2model.ProtoFromTraces(otelTrace)
 	for _, batch := range batches {
-		spans = append(spans, batch.Spans...)
+		for _, span := range batch.Spans {
+			span.Process = batch.Process
+			spans = append(spans, span)
+		}
 	}
 	return spans
 }